CA1226355A - Method and system for determining position using signals from satellites - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE

A method and a system are disclosed for measuring the baseline vector between a pair of survey marks on the ground by radio interferometry using radio signals broadcast from the earth orbiting satellites of the NAVSTAR Global Positioning System (GPS), the radio signals broadcast by the satellites being double-sideband modulated with their carriers suppressed. An antenna is positioned at each survey mark.
The signals received by one antenna during a predetermined time span are separated into upper and lower sideband components. These separate components are filtered, converted to digital form, and then multiplied together. their product is analyzed digitally by means of correlation with quadrature outputs of a local oscillator to determine the power, and the phase relative to that local oscillator, of the carrier wave that is implicit in the double-sideband signal being received from each satellite. Differences in Doppler shift are utilized to distinguish the carriers of different satellites, The signals received at the same time by the other antenna are processed in the same manner. Thus, the powers and carrier phases of the signals from a plurality of satellites are measured simultaneously and numerical data representing the measurement results are obtained at each survey mark. The measurements are performed in real time at each mark without reference to signals that are received at any other place and without knowledge of any of the coded signals that modulate the GPS carriers. The data from the measurements performed simultaneously but independently at the two survey marks, once per second for a predetermined time span, are then processed together to determine the baseline vector that extends from one mark to the other. Two methods of processing are disclosed. In either method, an "ambiguity function" is computed which is a function of the measurement data and of a trial value ? of the baseline vector. The vector space of ?
is systematically searched to find the unique value of that maximizes the computed function. This value of ? is taken to be the desired determination of ?. By using signals from a plurality of five satellites and a time span of about 5000 seconds, a baseline vector determination can be obtained by the method of the present invention with an accuracy of about 5 millimeters in each coordinate for a baseline length of about 100 meters.

Description

B~CKGROU~ID OF TIIE INVENTION
The present inverltion relates generally to a method and system for determining position by radio and more particularly to a method and system for measuring the baseline vector between a pair of pointsf such as survey marks, on Earth by radio interferometry using radio signals broadcast from earth orbiting satellites.
Some systems Eor determining position by radio make use of the directionality of the pattern of radiation of a trans-mitting or a receiving antenna. Other systems, including the present invention, do not rely upon directionality of any antenna. The present invention belongs to the general class of systems in which the position of a receiving antenna is determined by measuring the difference between the phases or the group delays, or both, of signals arriving from -two or more different transmitting antennas whose positions are already known. If two transmission sources are synchronized, or if the departure from synchronism of two transmitters is known independently, then a measurement at the receiving site of the difference between the group delays of the signals arriving from the two sources determ nes that the receiver is located, in three dimensions, on a particular hyperboloid of I sd/¦~

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revolution whose focl are the positions of the transmitter If similar measurements at the same receiving site of signals from several different, suitably positloned, transmitters are combined, then the recelving position can be determined uniquely from the point of intersection o the corresponding hyperboloids.
Techniques of determining relative positions of different sites, one with respect to another, from measurements of the phase or the group delay differences between radio signals received simultaneously at those sites are also known in the art and are collectively referred eO as techniques of geodesy by radio interfetometry. The antennas at the separate sites are considered to form an interferometer, and the relative position vector that extends from one antenna to the other is called the baseline vector of the interferometer. The baseline, or relative-posltion, vector between two antennas can be determined usually with less uncertainty than the position of either individual antenna can be, because many potential sources of error tend to affect the measurements ae both antennas nearly equally, and therefore tend to cancel when differences are taken between the two antennas. The technique of geodesy by microwave radio interferometry is known to provide an unmatched combination of accuracy, speed, and range for the determination of relative-positlon or

2~ interferometer "baseline" vectors. Such a determination may be based upon measurements of either the group-delay diference, or the phase difference, or of both differences .

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between the slgnals received at the two ends of the basellne vector. Phase measurements are inherently more accurate thin group delay measurements, but the interpretation of phase measurements is more complicated due to thelr Intrinsic lnteger-cycle, ambiguity. A general discussion of interfero-metric measurement techniques and the associated problemR of interpretation is given in an article entitled "~adlo Astrometry,~ appearing in Annual Reviews of Astronomy and Astrophysics, Vol. 14 ~1976), pp. 197-214, by Charles C.
Counselman III. A large collection of relevant technical papers appears in Conference Publication 2115 of the Nationa Aeronautics and Space administration, entitled "Radio Interferometry Techniques for Geodesy." Geodesy by radio interferometry has been practiced with radlo signals emitted by various sources including natural ones such as quasars and artificial ones such as satellites of the NAVSTAR Global Positioning System (GPS~.
As is known, there are presently about six GPS satellites orbiting Earth. The orbits of the satellites can be deter-mined with an accuracy of about 2 meters. These satellites emit radio signals with wavelengths near 19.0 centimeters and also 24.4 centimeters. Provided that the integer cycle ambiguities of interferometrlc phase observations of these signals can be correctly resolved, the baseline vector extending from one antenna to another can be determined interferometrically with uncertainty much smaller than the wavelengths of the GPS transmissions. Detetminations of three ! - .:', 63~

baselines, each baseline having a length of the order of lO0 meters, by means of interferometric phase measurements of GPS
signals were shown to have been accurate within about 1 centi- -meter, according to a report published in Eos (Transactions of the American Geophysical Union), Vol, 62, page 260, Aprll 28, 1981, by Charles C. Counselman III, S. A. Gou{evitch, R. W.
King, T. A. Herring, I. I. Shapiro, R. L. Greenspan, A. E. E.
Rogers, A. R. Whitney, and R. J. Cappallo. The method employed in these interferometric baseline determinations was based on the known technique of direct crosscorrelation at a central location of the signals received separately but simultaneously at the two ends of each baseline.
In U.S. Patent 4,170,776, there is described a system for measuring changes in a baseline vector between a pair of locations on earth using signals transmitted from the GPS
satellites, in which the radio signals received at each location are precisely time tagged and then transmitted over telephone lines to a central location where a near real time phase comparison is made by crosscorrelating the two sets of signals. The system illustrated in the patent includes adish~
reflector type receiving antennas. Because the radio flux density of a GPS signal is small relative to the background noise level and because the bandwidth of a GPS signal greatly exceeds the bandwidth of a telephone line, the signal to noise ratio of the power transmitted over the telephone line from each location is small. It is largely for the purpose of raising this signal to noise ratio to a useful level that .

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dish" type antennas with larqe coilecting areas are used on this system Another important reason for the use of such antennas is that they are directive, so that signals arrivl~g at the antenna otherwise than directly from the desired source are rejected.
Systems for measuring baseline vectors using other kinds of signals from Earth orbiting satellites are also known.
In an article entitled miniature Interferometer Terminals for Earth Surveying" (MITES), appearing in aulletin Geodesique, Volume 53 (1979), pp. 139-163, by Charles C.
Counselman III and Irwin I. Shapiro, there is described proposed system for measuring baseline vectors using multi- I-frequency radio signals which would be broadcast from earth orbiting satellites, in which system the phases of the signals received are determined separately at each end of the baseline. That is, the signal received at one location is not crosscorrelated with the signal received at the other in order to determine the phase difference between the two signals. To resolve the phase ambiguity, the MITES system relies upon the combination of measurements at a set of up to ten frequencies suitably spaced between l and 2 GHz~ Unfortunately, as far as is known, there are no satellites presently orbiting the earth which emit such signals.
Systems for measuring relative position using signals transmitted from sources other than artificial satellites are also known One example of such a system using a lunas based -transmission is also disclosed in U.S. Patent 4,1iO,776.

, ~L226355 o0 Systems fox m~asurlng either a slngle po5ition or relative position uslng signals from sources other thDn orbiting satel11tes are also known. Por example in an artlcle by W. O. Henry, entitled "Some Developments in Loran, appear-ing in the Journal of Geophysical Research, vol. 65, pp. 506-513, Feb. 1960, there is described a system for determining a positicn such as that of a ship at sea) using signals from ground based stationary) transmitters. The system, known as the Loran-C navigation system, employs several-thousand-kilometer-long chains of synchronized transmitters stationed on the surface of the earth, with all transmitters using the same carrier frequency, 100 kiloHertz, and with each trans-mitter being modulated in amplitude by a unique, periodic, pattern of pulses. This pattern, which includes sign rever-sals of the amplitude, enables the receiver to distinguish between signals from different transmitters. A suitable combination of observations of more than one pair of trans-mitters can yield a determination of the receiver's position on the surface of the earth.
Another example of a system of this type is the Omega system which is described in an article by Pierce, entitled omega," appearing in IEEE Transactions on Aerospace and Electronic Systems, vol. AES-l, no.3, pp. 206-215, Dec. 1965.
In the Omega system, the phase differences of the signals received are measured rather than principally the group delays as in the Loran-C system. Because the frequencies employed ln - both the Loran-C and the Omega systems are very low, ~22~355 .. ._ . . ......... . .

accuracles ln position measurements with these systems are quite poor in comparison with the satellite systems mentioned, the prior art also includes other methods of d,etermining position and relative position by means of the Global Positioning System. The standard method, described or example in an article in Navigation, Volume 25, no. 2, (197a~, pp. 121-146, by J. J. Spilker, Jr., and further described in several other articles appearing in the same issue of that journal, is based on measurements of the differences between the group delays, or the times," of reception of the coded modulation of the GPS signals. In principle this method is a hyperbolic positioning method and is essentially similar to that of LORAN. The approximately 10 MHz bandwidth of the GPS
modulation limits the accuracy of group-delay measurement and hence of position determination by the standard method to several tens of centimeters. Accuracy of the order of one centimeter is potential}y available through the use of carrier yhase measurements, as described for example in an article by J. Do Bossler, C. M. Goad, and P. L. Render, entitled using the Global Positioning System for Geodetic Positioning appearing in Bulletin Geodesique, vol. 54, no. 4, p. 553 (1980). However, every published method of using the GPS
carrier phase for position determination has the disadvantage of requiring knowledge and use of the code modulation, which may be encrypted, or of requiring crosscorrelation of signals received at different locations, or of requiring the use of large antennas to raise the received signal to noise ratio and - ~2~:~35~

to suppress interference from reflected Signals, or else thy method suffers from more than one of these disadvantages. the present invention has none of these disadvantages.
In particular, the present invention requires no knoll-edge of the codes which modulate the GPS carriers, does not require crosscorrelation of a signal received at one location with a signal received at any other location, and does not require the use of a large or highly direceional receiving antenna, .

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SUMMARY OF THE INVENTION

It is an object of this invention to provide a ~eehod end system for determining position by r~dloO
It is another object of this invention Jo provide 2~ ' method and system for measurlng the baseline vector between pair of points by radio interferometry.
It is still another object of this invention to provide a method and system for determining the baseline vector between a pair of points on the earth, such as survey marks, using radio signals of the double sideband, suppressed carrier, type broadcast from earth orbiting satellites of the global Positioning System.
It is a further object of this invention to provide a method and system for determining the baseline vector between a pair of survey marks using radio signals from earth orbiting satellites of the Global Positioning System which determina-tion involves measuring the phases of the carrier waves implicit in the signals received at each survey mark.
It is still a further object of this inYention to provide a technique for processing phase information derived at two locations on earth from radio signals received from diffPrent directions, to determine relative position.
It is still a further object of this invention to provide a method and system for measuring the powers and the carrier-wove phases of the radio signals recelved fro: satellites of ' . , -12~ 3 the Global Positioning System wlthout knowledge of the coded signals which, in the transmitters-of these satellites, modulate the carrier waves.
It is still a further object of this invention to provide a method and system for determining the baseline vector between two points by measuring the phases of radlo signals received at each point without crosscorrelating the signal received at one point with the signal received at the other point, without recording the signal received at either point, lG and without otherwise transponding a signal from one point to the other or from both points to a common location.
It is still a further object of this invention to provide a method and system for determining position by radio without requiring the use of a directional antenna.
The method of measuring a baseline vector between a pair of points on Earth by radio interferometry using radio signals broadcast by GPS satellites according to the principles oi` the present invention comprises measuring the implicit caerier phases of the signals received from the satellites at each end of the baseline and then processing the phase information from both locations together to determine the baseline vector. The system for measuring a baseline vector between a pair of points on earth by radio interferometry using radio signals broadcast by GPS satellites according to the principles of the . present invention comprises a pair of interferometer field terminals, one interferometer field terminal adapted to be , , 3~5i positioned at each point, each interferometer field terminal including an antenna, an upper and lower sideband separator, a plurality of correlators and numerieal oscillatorss and a field terminal computer.
In summary of the above, therefore, the present inventlon provides method and system for deriving position related data, useful for determining position, from spread spectrum signals transmitted by GPS satellites. A first composite of overlapping satellite signals is collected with an essentially omni-directional antenna. This first composite signal is reconstructed to form a second composite of reconstructed components, each of which is related to the phase of a signal implicit in the satellite signals.
Predictions of the frequency changes from Doppler shift to be encountered by each such component are used to derive phase data from the composite of reconstructed components in order to derive phase data therefrom.
; Furthermore, the present invention provides system and method for determining position related data from spread spectrum signals without regard to interference. The spread spectrum signals are collected and continuous wave interference is rejected at or near a selected frequency.
The spread spectrum signals are then reconstructed to provide a continuous wave component at that frequency form which the position data may be derived. The data is derived without interference because the potentially interferring signals, if present, have been rejected before the components were reconstructed.

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GRIEF DESCRIPTION OF THE DRAWINGS

In the drawings wherein like reference numefals represent like parts:
Fig. 1 $11ustrates a system for determining a baseline vector by radio interferometry with GPS satellites according to the principles of the present invention;
Fig. 2 is a block diagram of one of the interferometer field terminals shown in Fig. l;
Fig. 3 is a block diagram of the antenna assembly shown in Fig. 2;
10 Fig. 4 is a block diagram of the receiver unit shown in Fig. 2;
Fig. 5 is a block diagram of the digital electsonics unit shown in Flg. 2;
Fig. 6 is a block diagram of the signal conditioner shown 15in Pig. 5;
Pig. 7 is a block diagram of one of the correlator modules in the correlator assembly shown in Fig. 5;
Fig. 8 is a block diagram of one of the numerical oscillator modules in the numerical oscillator assembly shown 20in Fig. 5;
Fig. 9 is a block diagram of the field terminal computer shown in Fig 2.

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DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present lnvention is directed to a technique for measuring the baseline vector betwecn a pair of points, such as survey marks, on Earth by radio interferometry using the double-sideband, suppressed-carrier, radio signals transmitted by Earth orbiting satellites of the NAVSTA~ Global Positioning Systems (GPS). The technique involves measuring the phases of the carrler waves implicit in the signals received at each location, and then processing the phase information obtained at both locations to determine the basellne vector One advantage of the technique is that it measures the carrier phases without reference to knowledge of the coded signals that are used in the satellites to modulate the carriers.
Another advantage is that it does not require transmission o$
the received signals, either in real time or by transportation of recordings, from two locations to a common locationO
Another advantage is that it does not require the use of large or highly directional antennas. Still another advantage is that it is relatively immune to errors caused by scattering and reflections of radio waves occuring close to the receiving antennas.
Although the invention will hereinafter be described specifically for use with GPS satellites it is to be understood that certain aspects thereof are not limited solely to use with such satellites and may be useful with signals received from other sources.

-- , -16~ 5 As is known, satellltes of the NAVSTAR Global Positionins System ~GPS) orbit the earth at approxlmately 20,000 kilome-- hers altitude and transmit signals in a frequency bdnd eentered at 1575.42 MHz, known as the ~Ll~ band, and signals in secondary band centered at 1227.fiO MHz, known as the ~L2 band. The signals are modulated such that nearly symmetr~c~l ; upper and lower sidebands are generated with the cartier completely suppressed.
For either band, the signal from a qiven satellite received at a given location may be considered, as a function - of time, to have the form:
s(t) = met) cos (2~fot+0) nut) sin(2~fOtl~) in which m(t) and n(t) are modulating functions, each a real-valued function of time; fO is the nominal carrier frequency, equal to 1575.42 MHz for Ll and 1227.60 MHz for the L2 band;
and o is the received carrier phase, in radians, which 1s unknown and to be determined. Each of the modulating functions, m(t) and n(t), is a pseudo-random function of time, with zero mean. The two functions are mutually orthogonal.
Each of the functions used for the modulation of the Ll carrier for any one satellite is also orthogonal to the corresponding function used for every other satellite, although for a given satellite the same met) or n(t) function, or both, may be used to modulate both the Ll and the L2 carriers. The bandwidths of the two functions, m(t) and n(t), differ by a factor of exactly 10, with met) having the narrower, and n~t~ tb~ wider, bandwidth. Usually at Ll both ',' . . .

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m~t~ and n(t~ slgnal component ore present, and ae L2 only the n(t) component is present, the m5t) function belng 5et to zero, or turned off The power spectral denslty of I J
which corresponds to the modulating s$gnal that is known in the GPS llter3ture as the ~clear/acquisition~ code, it proportional to the unction sln2(~F/1.023 MHz) . z_ (~F/1.023 MHz) wherein F represents modulation frequency. This function has a half width at half maximum of approximately 450 kHz. That is, the function value is approximately 0.5 for F = +450 kHz, whereas the value is unity for = 0. The power specttal density of nut), which corresponds to the modulating signal that is known in the GPS literature as the "precise code or np code," is proportional to sin2 (~F/10. 23 MHz) (lIE'/10~23 MHZ)2 Thus, the half width at half maximum of the power spectral density of n(t) is approximately 4.5 MHz.
For the Ll, 1575.42 MHz, signal, the mean-squared value of n(t) is ordinarily equal to one-half that of m(t); that Is ~n2(~)> = 0.5 <m2(t)>.
(It is possible for a GPS satellite to be operated in extra-ordinary modes in which the ratio of mean-square values, or power ratio, is differer.t from 0.5; in particular, a value of zero is possible.) Thus the ratio of the power spectral density of n(t) to that of m(t1 is ordinarily equal to around 2~355 0.5 - 10 = 0.~5 for a value of near zero, so that if a bond-pass filter matched to the spectrum of m(e) is centered on tho Ll carrier frequency, about 90 percent of the power con~n~d $n the output of this filter will stem from the met) signal component, and less than 10% will stem from the n(t1 componr ent. Por simplicity in the remainder of this d~scriptio~, therefore, it will be assumed that the GPS Ll signal has no ntt) component and has the simpler form:
s(t) = mtt~ cos~2~fOt~0).
In general, the received carrier phaser I, is a slowly varying function of time, so the actual received carrier frequency is given by the algebraic sum:
f = fO + (2~) 1 (d~/dt), where fO is the nominal carrier frequency and d~dt is the time-derivative of o. By slowly v~rying,~ it is meant that (2~) 1 (d$/dt) is very small in comp~risnn with ~0 and with the bandwidth of m(t). The main reason for the time-variation of is Doppler shift, which may cause to differ from fO by plus or minus up to about 4.5 kHz.
The received signal s(t) contains no discrete spectral component of power at the carrier frequency because the mean value of m(t) is zero. Thus, the carrier is completely suppressed and the power spectral density function of the Ll signal s(t) is equal to the power spectral density function of the modulation m(t), translated from baseband to the received carrier frequency f. Because mtt) is a real-valued function of time, its power spectral density is an even-symmetric 19~ 63~

function of frequency. Thus the power spectral density ox sot) has even symmetry with respect to the carrier frequency f, and is said to be a double sideband spectrum. The portion of this power spectrum corresponding to frequeneies greater than is called the upper sideband; the portion correspondinq to lower frequencies is the lower sideband. IThe slight asymmetry, at most about 3 parts in 106, between the upper and the lower sidebands due to Doppler ~stretchingV of the signal is not signlficant here.]
According to the present invention an antenna is positioned at each end of a baseline vector. The signals received by each antenna are separated into upper and lower sideband components. These separate components are filtered, converted to one-bit digital form, and then multiplied together. Their product is analy2ed digitally by means of correlation with quadrature outputs of a loca} oscillator to determine the power, and the phase relative to that local oscillator, of the carrier wave that is implicit in the double-sideband signal being received from each satellite.
Differences in Doppler shift are utili2ed to distinguish the carriers of different satellites. Thus, the powers and carrier phases of the slgnals from a plurality of satellites are measured simultaneously and numerical data representing the measurement results are obtained at each survey mark. The measurements are performed in real time at each mark without reference to signals that are received at any other place and without knowledge of any of the coded signals that modulate .' i" '.
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the GPS carrlers. The data from the measurements performed slmultaneously but independently at two survey marks, once per second for a time span of sufficient duration, such as abut 5,000 seconds, are then processed together to determine tho baseline vector that extends from one mark to the other. two methods of processing are disclosed. In either method, an "ambiguity function" is computed which is a functfon of the measurement data and of a trial value b of the basellne vector. The vector space of b is systematically searched to find the unique value of b that maximizes the computed function. This value of b is taken to be the desired determination of the unknown baseline vector by Referring now to Figure 1, there is illustrated a system 11 for determining a baseline vector b according to the present invention. The baseline vector I, whiz us also referred to hereinafter sometimes by the name nbascline," is the relative positlon vector of one survey matk SM-~ with respect to another mark SM-~. The baseline extends from survey mark SM-l which is at the origin or one end of the baseline, to survey mark SM-2 which ls at the terminus or other end of the baseline The system 11 comprises two intelligent inter~erometer field tesminals 13-1 and 13-2, one placed at each end of the baseline, and a computer which may be structurally and functionally incorporated into and be part of one of the terminals 13 or may be a separate unit 15 as shown.

, , s The system requires for its usual operation certaln numerical data from external sources. It also requires some means of transferring numerlcal data betw2en the computer 15 and eaeh terminal 13 before and after, or optionally) during performance of baseline measurements.
Before measurements to determine the baseline are begun, data from a first data store 17 representative of the orblts of a plurality of GPS satellites of which two, identified GPS-l and GPS-2, are shown for illustrative purposes is entered into the computer 15, together with approximate data representative of the locations of the survey marks SM-l and SM-2 which is obtained from a second data store 19. The latter data might, for example, represent the survey mark locations within a few kilometets accuracy. no these satellite orbital and survey location data computer 15 generates, in tabular form as a function of time, a prediction of the Doppler frequency shift that the 1575.42 MHz signal transmitted by each GPS satellite will have as it is received at each survey mark. Computer 15 also generates a tabular prediction of the power level of the signal to be received from each satellite at each mark. The predicted power is zero if the satellite will be below the horizon; and it is a function of the predicted angle o elevation of the satellite above the horizon, due to the angular dependence of the gain of a receiving antenna (at the mark) and, usually to a lesser extent, of the transmitting antenna (on the satellite). The tables of predicted frequenoy shifts and powers, for a span of ... .

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time encompasslng that of the anticipated measurements, for all GPS satellites expected to be vislble at each survey mark, are now communicated by any known means, such as for example by telephone or radiotelephone link to, and entered unto the the memory of a smaller computer contained within the particular interferometer field terminal 13 that will be, or may already have been, placed at that survey mark.
Alternately the frequency and power prediction tables may be generated by the computer inside the ~nterferomete~ field terminal.
The Doppler frequency predictions are computed according to formulas that are well known it the art The magnitudes of the errors in such predictions are f the order of 1 Hertz per kilometer of error in the assumed location ox the suruey Mark.
The additional error in the frequency prediction dye to error in the extrapolation o the satellite arbit i5 n~rma}ly of the order of 1 Hertz or less for predictions made ae least a day in advance. Frequency prediction errors of up to several Hertz are tolerable ln the context of the present invention.
The predictions of received power do not need to be very accurate; errors of several decibels would be tolerable, because these predictions are not used for any very critical purpose. They serve mainly to enable the field terminal computer to check whether the desired signal, not some spurious signal, is being received. At perhaps some sacrifice in reliabillty, the power prediction tables could be eliminated.

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", _ An interferometer field terminal 13, havlng been placed at a survey mark, now receives the 1575.42 MHz signals from plurality of satellites, up to seven but in no case fewer than two satellites, simultaneously For an accurate determination of the baseline to be obtained! it is essential for the terminals at both ends of the baseline to observe the satellites concurrently.
Electronic circuits (hereinafter to be described) within each terminal separate the received signals into upper and lower sideband components and, using the predictions o Doppler frequency shift, analyze these sideband components to determine the power and the phase of the carrl~r wave implicit in the signal received from each satellite. D~a from these power and phase determinations is stored within the field terminal and eventually returned to the central computer 15 by any conventional means.
The data from the two interferometer fleld terminals 13-1 and 13-2 must be processed together to obtain an accurate determination of the baseline vector.
It should be noted that means o long-distance communi-cation or transfer of data are not necessary for the operation of this system. The terminals 13-l and 13-2 may be physically transported to the same location as computer 15, and there the prediction tables may be transferred from computer 15 to the terminals 13. Then the terminals 13, containing the tables in their memories, may be carried to the survey marks SM-l and SM-2 where the satellites are observed. Following the , ,^ ;-, , .
, completion oE these observa-tlons the terminals 13 may be carried back to the location of the computer 15 where the carrier phase data may be transferred from both terminals to -the computer for processing.
Referring now to Figure 2, there is illustrated the major components of an interferometer terminal 13, also called the "field terminal". Each field terminal 13 has an antenna assembly 21 connected to an electronics assembly 23 by means of a coaxial cable Z5 n la Each antenna assembly 21 includes an antenna 27 and a preamplifier assembly 29. The antenna is positioned on the survey mark SM, and the location of -the phase center of the antenna 27 with respect to the survey mark SM must be accurately known. The antenna described in said pa-tent application is satisfactory in this respect; the uncertainty in the positioning of its phase center being a few millimeters at most.
Antenna 27 receives the 1575.42 MHz radio signals that are transmitted by the GPS satellites. The received signals are amplified by the preamplifier 29 and fed through the coaxial cable 25 to a receiver unit 31 contained in the electronics assembly 23, the receiver unit 31 including a sideband separate 33, a receiver power circuit 34, and an oscillator circuit 35.

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In the sideband separator 33 the per sideband portlon of the signals, comprlsing that portion of the signDlr received from all satellites combined which occupies D rall9e of radlo frequeneies extending upward from 1575.42 MHz, is separated from the lower sideband portion which coFresponds to radio frequencies below 1575.42 MHz. To effect this separation, the sideband separator 33 uses a ~575.42 MH~
reference signal which is supplied by the oscillator cl~cuit 35.
The receiver unit 31 furnishes three signals, in analog form, to a digital electronics unit 37. One analog signal, designated u(t), represents the upper sidebaad component of the received radio frequency signals, ttans~ated to baseband.
The second analog signal, designated e~t~, represents thy lower sideband component, also tranalated to base~and, Mach of these two signals contains contributions from all visible sa,ellites. ?he third signal furnished to the digital electronics unit 37 is a sinusoidal signal with a frequency of 5.115 MHz which is the output of a free-runniD~, stably, quartz crystal oscillator in the oscillator circuit 35~ Toe output of this same osclllator is multiplied in frequency by a fixed integer factor of 308 within the oscillator assembly to obtain the reference frequency of 1575.42 MHz used by the sideband separator. The accuracy of the frequencies generated by oscillator assembly 35 is typically around one part in 109, although accuracy of one part in 108 would be tolerable.

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In the digital electronics unlt 37 each of the three analog inputs is converted to a digltal logical signal. Thy digital slgnals are processed under the control of a field terminal computer 39 to generate the carrier power and phase data. The digital electronics assembly 37 is connected to the field terminal computer 3~ my means of a bidirectional data bus 41. Field terminal computer 39 may be a digital Equipmene Corporation (DEC) model LSI~ 2 microcomputer; the data bus 41 in this case may be the DEC ~Q~ bus.
e The carrier phase data ~5 sto}ed in the memory of the field terminal computer 39 until it is desired to communicate these data to the central computer 15 for processi.ng.. As noted, the central computer lS may be eliminated and the processing performed in one of the field ter~i;na~` computers 39. The phase data may also be writt.en out by the field compueer 39 onto a data storage medi.um such as a magnetlc tape cassette or a disk tnot shown).. rho data may also be communicated via direct electrical connectian ! Qr via a modem and telephone connectionr or by many other standard means.
Now referring to Pigure 3, there it shown in further detail the components of the antenna assembly 21~ Assembly 21 includes an antenna 27 which, as mentioned, is constructed so . that its phase center can be accurately positioned with respect to the survey mark. The 1575.42 MHz radio signals received by antenna 27 are fed to the preampllfier circuit 29 whose function is to raise their power level sufficiently to overcome the attenuation of thy coaxial cable 25 that connects ..

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the antenna assembly 21 to the recelver unit 31, Dnd to overcome the background noise that is generated with1n the input amplifier in the recelver unit 31.
In the preamplifier circult 29 the signals received from antenna 27 are first filtered by a bandpass filter 43 ox approximately 50 MHz bandwidth centered on 1575.42 MH~. The function of filter 43 is to prevent overloading of recelver assembly 31 by strong spurious signals that may be preset outside the GPS signal bandO The output of bandpass filter 43 is fed into a passive diode limiter 45 which serves to protect a low-noise amplifier 47 from being burned out by any very strong signals such as those that might be radiated by nearby high power radars. The low-noise amplifier 47 is a standard Gallium-Arsenide field-effect-transistor (FET) amplifier with a noise figure of about 2 db.
D.c. power for the low noise amplifier is supplied via the coaxial cable 25 connected to the preamplifiet assembly 29 from the receiver comb 31, through a radio-frequency choke 49 and a voltage regulator 51. A capacitor S3 couples the radio-frequency output of the low noise amplifier 47 ta the cable 25 whiie blocking the d.c. from the amplifler.
Referring to figure 4, there is shown in more detail the I, components of the receiver unit 31. The receiver unit 31 - includes a receiver power circuit 34, a sideband 3 and an oscillator circuit 35. The receiver power circuit 34 provides,d.c. power for the operation of the oscillator I" <'~
asse~b~ 35, the sideband separator 33, and, through the ., , - ", coaxial cable Z5, the low noise amplifier 47 in the antenna assembly 21. The osci}lator circuit provides a reference frequency of 1575.42 MHz to the sideband separator 33 and reference frequency of 5.115 MHz to the digital electronics 7 as~@~b~ 37. The sideband separator 33 separates the signals that are received in a radio frequency band ceneered on 1575.42 MHz and extending upwatd and downward from this frequency, into separate upper and lower sideband components at baseband.
The receiver power circuit 3~ contains reguIated d.c.
power supplies 61 and, in addition, a storage battery 63. The battery 63 enables power to be supplied without interruptlon to the crystal oscillator 65 in the oscillator circuit 35, to of the real-time clock in the digital e1ectronics a~se~*y 37, and to the data memory of the field terminal computer 39, despite interruptions of the main, external, soufce vf electrical power that may occur. Thus, the freguency stability of the oscillator will be maintained, the clock epoch setting will not be lost, and data stored in the computer memory will not be lost.
The oscillator 65 in the oscillator circuit 35 is a quartz crystal oscillator, such as a Frequency and Time Systems (FTS) model 1001, which provides an output frequency .
of 5.115 MHz within one part in 108 or less. The FTS model lO01 has stability of about one part ln 101 per day and one part in 1012 over time intervals of from 1 to 100 seconds, and is therefore more than adequate in this application.
.

,~-- . I:
,. I, ..

-29 3~S

Oscillator'65 provides two identical outputs, one whlch 9O~9 to the digital electronics unlt 37, and the other which goes to a 1575.4~ ~9Hz synthesizer 67 in 'the osclllator circuit 35.
The 1575.42 M~z synthesizer 67 contains a voltage-controlled transistor oscillator ~VCO~ 69 which oscillates at a frequency of 393.B55 MHz, equal to 77 times 5~II5 MHz. This oscillator's phase is stabilized with respect to the phase of the S.llS MHz reference through the actlon of a phase-locking loop comprised of the VCO 69, a coupler 71, a divider 73g a phase-frequency error detector 75, and a loop i:Lter 77. Part of the VCO 69 output power is coupled by the coupler 71 to the input of the frequency dividar 73 which is comprised of standard emitter-coupled-~c~ic (ECL] iRtegrated circuits that divide by 11 and then my 7. The output of divider 73 is the "variabler input and the 5.115 MH~ ~tput of oscillator 65 is the reference" input to the standard ECL integrated-circuit phase-frequency detector 7S such as Motorola type number MC12040. The output oi' the detector 75 is low-pass filtered in loop filter 77 to obtain the control voltage-which is input to the VCO 69. The output of VCo 6g it quadrupled in frequency by a succession of two standard, balanced, dlode doublers 79 and amplified by an amplifier 81 to obtain the 1575.42 MHz output frequency which drives the sideband separator 33~
The signals in a band centered on 1575.42 MHz, received from antenna assembly 21 through the coaxlal cable 25 at the 'I input 83 of the sideband'separator So are coupled by a d.c.

';_..!;'' 30~ 5 blocklng capacitor 85 through a bandpass fllter 87 and amplified by an lnput amplifier 89. D.c. power for the preamplifler 29 lin the antenna assembly) is coupled to the coaxial cable 25 throu h a adio-frequency choke 91 from the 5~ receiver power by The r.f. power-splitter, or hybrid" 93r the 1575.42 MHz local-oscillator quadrature hybrid 95, the two doubly-balanced mixers 97 and 99, and the broadband video frequency quadrature hybrid lUl in the sideband separator So comprise a dual, single-sideband, radio-frequency-to-baseband converter or "demodulator" of the conventional, phasing" type. Such a demodulator has been described, for example, in an article in the Proceedings of the IEEE, vol. 59 11971), pp. 1617-1618, by Alan E. E. Rogers. Its operation here may be desctibed as follows.
Let fO denote the frequency of the reference slgnal furnished to the sideband separator 33 by the oscillator circuit 35. Nominallyr fO equals lS75~42 MHz, which equals the nominal carrier frequency of the GPS satellite "Lln transmissions, before IfirSt-order) Doppler shift. Then the outputs 102 and 103 ox the quadrature hybrid 9~ may be written as sin 2~fot and cos 2~fot, respectively. These outputs, which are in phase quadrature, are the local oscillator inputs to mixers 97 and 99, respectively. The r.f. inputs to the two mixers are identical. The baseband outputs of the mixers are accordingly identical except for a phase shift of ~/Z radians. lBy "baseband" we refer to the range of -; . ,, 5~

, frequencies, nearer to zero than to fO, that corresponds tc the difference between the input frequency and fox The sense of this phase shift, leading or lagging, depends on whether the input signal frequency is above or below l Thus it s possible to select either upper-sideband (input frequency higher or lower-sideband inputs and to reject the opposite sideband by shifting the phase of one mixer output by an additional ~/2 radians, and then either adding ar subtracting (depending on which sideband is desired) the two mixes 1 outputs .
The quadrature hybrid 101, whi.ch has two inputs 109 and 111 and two outputs 105 and 107, perf:orms this l phase shift and addition/subtraction. The upper output 1.05. of the hybrid 101 is given by the arithmetic sum o the uppe~o i.nput. 109, plus the lower input 111, both input;s having been delayed in phase by an amount that is dependent on frequency,. but with the phase shift of the lower input greater than that Gf the upper input by a constant ~/2 radians, independ¢ne.o frequency. The lower output 107 i5 riven by the a.~ithmetic difference of the same two different~.ally phase--shited inputs 109 and 111, with the difference befng taken the sense:
upper minus lower. the specified, ~/~ radian (o~e-quarter cycle), phase difference is accurately maintained far all frequencies between fHp and at least fLp, where fHp10 kHz is much smaller than fLp~450 kHz, and fLp is approximately equal to the one-sided bandwidth of the GPS ~C/Aa modulation m(t), ~263~

as previously discussed. the design of a quadrature ~y~rid having these properties is given in the clted article my Rogers.
Now the outputs of the quadrature hybrld 101 are separately amplifled by identical video amplifiers 113 and 115, and filtered by high-pass 117 and 11~ and low-pass 121 and 123 filters. Filters 117 a II9 are identical high-pass filters with low-frequency cutoff at fHp. The purpose of the high-pass filters 117 and 119 is Jo eliminate the direct-current components an any lo~-frequency spectral components of the mixer outputs with frequencies similar to, or lower than, the maximum possibIe magnitude of Doppler shift that a GPS satellite signal might hs~e.
It is desired to reiect any such components because otherwise they could interfere with the subsequent determina-tion, in the digital electtoniGs assembly and computer of the field terminal, of thy receivedr Doppler-shifted, carrier phase. Such potentiaIly interfering signaIs might include low-frequency "flicker" noise generated in the mixers them-selves, or might result from 2~ combination of mixer imbalance and (undesired low-fre~uency amplitude or phase fluctuations of the 1575.42 MHz reference signal or of the gain of any radio-frequency slgnal amplifiers preceding the mixers.
Another potential source of low-frequency interference is Uhum'' or ripple on power-supply output voltages or currents.
Another source could be an lnterfering continuous-wave signal close in frequency to JO.

, _ . _ ~2263~
33~

Low pays filters 121 and 123 are identical low-pasa filters with bandwidth equal to Lp, equal Jo thy one-sided bandwidth of m(t). The response of each filter, as a function of frequency, is tailored eO match the power spectral density of m(t). The purpose of these filters is to reject noise dnd intererence outside the bandwidth of m~t)O Note what the wide bandwidth GPS "P code" modulatlor, signal nil here would normally constitute a source of interf:erence. oft approximately ~0 percent, of the power- stemming prom nut) is rejected by these low-pass filters. This degree: rejection is suff icient to ensure ehat the rp code interfecence has a negligible effect. We note, however, that i the narrowband, m(t), modulation were turned off in the GPS satelliees, then the wideband n(t) modulation would no longer represent an undesired, interfering, signal; it would become! the desired signal. Such a switch in the GPS sigrlal strueture could be accommodated b increasing the bandwidths of t~e~low-pass filters by a faceor of 10, to mat¢h them to the new signal. n The output, u(t), from low past ilter 1~1 represents the down-converted and filtered, upper ~icleband co~tp3~ent of the original signal s(t); and the output l(t) from Pow pass filter 123 represents the lower sideband. It should be noted that the spectrum of u(t) will be shifted upward in i-requency, and the spectrum of l(t) will be shifted downward in frequency, relative to the spectrum of the original modulation met) by an amount equal eo (f-fO), the difference between the actual I.' , I .

~;~2~i3~
.
received carrier frequency E and the local oscillator frequency fO. [If the Doppler shift of the carrier, (f-f ), is negative, then the u(t) spectrum is shifted downward and Q(t), upward.] The magnitude of this shift is assumed to be smaller than fHp, and much smaller than fLp. This assumption will be satisfied if the frequency shift arises primarily from Doppler shift, which can never exceed 5 kiloHertz in mag-nitude, provided that fEp is set approximately equal to 10 kHz. Any offset of the frequency of the reference crystal oscillator 65 from the desired, 5.115 MHz, frequency will cause a (308 times greater) shift of the u(t) and Q(t) spectra, too. Normally, however, such a shift Jill be very much smaller than fHp.
In addition to the frequency shift of the upper and lower sideband outputs u(t) and Q(t), there is a frequency-dependent, ; dispersive, phase shift of each output due to the quadrature hybrid 101. However, for the particular quadrature hybrid design of Rogers (op. cit.), this phase shift is too small to be important. Similarly, the additional phase shifts intro-duced by the bandpass filter 87 and the high and low pass filters 117, 119, 121, and 123, will be trivial if standard filter designs are employed. Mach of these effects also tends to cancel when the difference between terminals is taken in the subsequent data processing. The cancellation is not exact because no two filters are ever exactly the same; also, the Doppler shifts at different sites are different at any given time. However, the residual effects are negligible, as has - 3~ -jrc:`~

:~Z~35~

been shown by direct calculation and confirmed by actual experiment.
Dow referring to Figure 5, there is shown a block diagram of the digital electronics unit ~7. The digit~:L electronics unit 37 includes a signal conditioner 125, a correlator assembly 127 comprising a set of seven identicæ~ correlators, a numerical oscillator assembly 129 comprising a corresponding set of seven identical numerical osci~tatorsr end a real-time clock 131, with the correlator assembly 127, the numerical oscillator assembly 129 and the rea1 time cloch:1.31 being connected by a data bus 133 to one a~.other and: to the field terminal computer 39. The first junction of t:he s;ignal condi-tioner 125 is to convert thy anal.og uppe~-sideban~ signal u~t), the analog lower-sideband si~na,l. I,. an t:he analog 5.115 MHz sinusoidal signal each to a! ~lnary-~alued "digital"
or logic" signal that ls suitabl.e or processing by conventional transistor-transistor logic (TTL.) ci.rcuits.
The signal conditioner 125 produces juSe t.w~ outputs.
One is a binary-valuedr TTL-logic-leYel, square periodic waveform with a frequency of 10.Z3 M~z~ prod~cea` by frequency-doubling the 5.115 MHz input. Tl~is 10.23 M~z output serves as a clock" signal to control the timing of all the subsequent, digital circuits. This clock signal is divided by 1023 (= 3 x 11 x 31) in the real-time clock 131 to obtain one tick .25 per 100 microseconds; further divisions by successive factors of 10 then yield a complete decimal representation of the time in seconds, with the least significant digit representing .~

r .
,. .

~L~2~3~

units of 10 4 seconds. The time is always readable in this form via the data bus 133. The operations of the correlator assembly 127, the numerical oscillator assembly 129, and the field terminal computer 3~ are all governed by the real-time clock 131 through the data bus 133.
The second "digital" output of the signal conditioner 125 is derived from the analog u(t) and Q(t) inputs and is a binary-valued, TTL-logic-level, nonperiodic waveform. This output is produced by a TTL exclusive-nor logic gate which has two inputs: one input represents the sign of the u(t) input and the other, the sign of Q(t). Thus the gate output is "True" (T, or binary 1) if and only if the analog u(t) and Q(t) signals have the same sign.
In Figure 6 is shown a block diagram of the signal conditioner 125. The analog signal u(t) is input to a comparator 135 whose output is a TTL logic level, True when u(t) is positive and False when u(t) is negative. This TTL
logic signal is applied as one input to an TTL exclusive-nor gate 137. The analog signal Q(t) is similarly fed to a comparator 139 whose output is applied as the other input of the exclusive-nor gate 137. The sinusoidal 5.115 MHz signal obtained from crystal oscillator 65 is input to a conventional analog frequency doubling circuit 141 whose outpu-t is fed to a third comparator 143 to produce a 10.23 MHz, square-wave, TTL-level output. The 10.23 MHz output is also used as the "clock" input to a flip-flop 145 which samples and holds the output from gate 137. Thus the output of flip-flop 145 is the jrc:

~L~.2~
exclusive-nor function of the signs of u(t) and Q(t), sampled at a uni.form rate of 10.23 x 10 times per second, and held between sampling times. It is well known in the art of radio interferometry, as discussed for example by J.M. Moran in an article appea.ing in Methods of Experimental Physics, vol. 12, part C, pp. 228-260, that the binary-valued function of time U~L has a Fourier transform, or "spectrum", that is a good approximation, both in phase and in relative amplitude, to the Fourier spectrum of the analog product u(t)Q(t). The accuracy of the approximation depends on the analog signals being random and Gaussian in character. Also, the correlation coefficient between the two inputs must be much smaller than 1 in magnitude. (In effect, the noise "dithers" out the nonlinearities of the comparators. The exclusive-nor gate 137 may be regarded as a multiplier, each of whose inputs has values of +l and -1.). These conditions are well satisfied in the present system. Thus, in the ollowing, the logic-level from flip-flop 145 is considered as representing simply the product u(t)Q(t).
The U~L "product" from the signal conditioner 125 is input in parallel to each of seven identical correlators in the correlator assembly 127.
Before describing the construction of the correlator assembly 127, its principles of operation will be briefly explained.
In each correlator, the u(t)Q(t) product is correlated with binary approximations to sine and cosine functions of arc:

-time that are generated by a corresponding one of the seven numerical oscillators. The frequency of the oscillator is controlled by the field terminal computer 39 according to the time indicated by the real-time clock 131. it any given time, the oscillator frequency is set equal to twice the predicted Doppler frequency shift of the 1575.42 MHz carrier wave transmitted by one of the satellites. One oscillator and one correlator are associated with each of the satellites in view, up to a maximum of seven satellites. (In principle, if more than seven satellites were ever in view, more numerical oscillators and correlators could be used in the system. In practice, seven is sufficient.) If the predicted Doppler shift is sufficiently close to the actual Doppler shift, then the outputs of the correlator will accurately measure the power and the phase of the signal from the one particular satellite for which the prediction was made, and will not be significantly affected by the presence of signais from other satellites which have different Doppler shifts.
In mathematical terms, the operation of one of the numerical oscillators and its associated correlator is described as follows: As a function of the time, t, indicated by the real time clock 131, the predicted Doppler frequency shift of the satellite's carrier is given by fp(t). The value of fp(t) is interpolated from the table of pre-computed values that was previously stored in the memory of the field terminal computer. The numerical oscillator generates two functions of time: cos ~2~p(t)] and sin [2~p(t)], in phase quadrature, jrc wherein up represents a predicted _hase which is a functlon of time. The function up is initially equal to zero at the time, to, when the numerical oscillator begins to oscillate;
and at any subsequent time up is given by the integral t p( ) 2~ t fp(tl)dt where fp(t') represents the instantaneous value of fp at a intervening time t'. The factor of 2~ is necessary if, as is customary, the frequency fp is measured in units of cycles per unit of time and the phase up is supposed to be measured in units of radians rather than cycles.
Now the correlator, operating between time to and tl, forms quan-tities a and b from its inputs [u(t)Q(t)], cos [2~p(t)], and sin [2~p(t)], according to the formulas a = llu(t)Q(t) cos [2~p(t)]dt and tl b = I u(t)Q(t) sin [2~p~t)]dt.
to The time interval of integration, tl-to, is equal to 1 second, and the indication integrations are performed each second. it each l-second tick from the real-time clock, the values of the integrals are "strobed" into storage registers, the integrations are reset to zero, the numerical oscillator is restarted, and a new integration period be-gins. Thus, at the end of each second of time, the cor-relator delivers outputs a and b which represent the time-averages, over the preceding one-second interval, of the product u(t)Q(t) cos [2~p(t)] and the l /

3~5 -, . .

product us sin [2~ (t)],respectively. These outputs represent the correlations of the product u(t)Q(t) with the cosine and sine functions.
During the l-seccnd interval, the oscillator frequency fp(t) is updated every 0.1 second by the computer, prompted by the O.l~second "tricks" from the real-time clock. This updating is necessary because the satellite Doppler shift changes, due to the motion of the satellite relative to the field terminal on the ground, and the changing projection of the relative velocity along the line of sight, at a rate which may be a substantial fraction of 1 Hertz per second.
Now the correlator outputs a and b may be combined to obtain estimates of the power and the carrier phase of the signal from the particular satellite for which the prediction, fp(t), was made.
Define a complex number c whose real part is equal to a and whose imaginary part is equal to b. That is, c = a + jb where j is the square root of minus one. Then c C <m2> <exp[2j(~-~p)]>

where C is a positive, real, constant scale factor; <m2> is the time average, over the integration interval from to to ;tl, of the square of the GPS modulating function m(t); and <exp~2j(~ up)]> is the time average, over the same interval, of the complex exponential function exp[2j(~-~ )]. Provided that the difference, (~-~p), between the received GPS carrier signal phase, = I, and the corresponding prediction, ....
jrc:

~L~2~
~ql up = up, does not vary by a substantial fraction of a a e during the integration time, then the magnltude of c is - approximately proportional to the average received power:
I cl ~a2 + b2)1~2 I, C ~m2>
and ha allgle of c is approximately equal to twice the average phase difference, (~-tp~:
/c - tan llbfa) 2 p)> .
Note that from b and I, the ankle of c is determined uniquely, modulo 2~ radians Thus, the difference ~-tp) is determined modulo radians.
In order for the received signal power and carrier phase (modulo I) to ye determined accurately from a and b according to these formulas, two conditions must be satlsfied: first, as mentioned, the actual phase, i must dlffer from the pre-dicted phase, opt), by an amount that changes by much less than a cycle during the one-second integration time; second, the correlator output slgnal. to noise ratio, given by SNRC = ~2~)t~/4~effTintl = (}~2~8effT~nt)l~2 F , must be much greater than one, where Beff is the effective bandwidth of the signals u(t) and lot), equal to about 5 x 105 Hz; Tint is the integration time, equal to 1 second, and is the fraction of the power present in u(t) and l(t) that stems from the GPS m(t~ signal, not from noise. The factor of (2/~) accounts for the loss of correlation between u~t) and it that is caused.by the analog-to-digital conversion of these ' , .
.,: '.

-42~ 3~

signals by the comparators in the signal conditioner. Toe factor of (~/4) accounts for the loss associated with these of square-wave approxlmat~Rns to the sine and cosine funotions . I,? - .ln the correlator. The square root of the e~ffTlnt ptoduct ls equal to about 700v Ther~ore there is the relation:

The fraction, I, of e~ther-sideband power stemming from ehe GPS satellite depends on.the recel.vIng anion gain and the receiving system noise figure. Foc khe "MITES antenna and the receiving system descri`.bed abover and for a satellite elevation angle above 20~, lt is known from e.~periment that F
exceeds about O.D3. ~hereo~e, SNRc l A
which is sufficient for acculate power: and pee measurements.
The ~t~ndar~ deviation of the naise. in each part, real and imaginary, of the complex g,uanti~.y c i.s given by ac Icy R~
The first-mentione~ condit.ion. if accuFacy in the measurements of the power and phaset tamely that (o-~p) not vary by a substantial fraction of a cycle during the l-second integration tire, is equivalent to the corldLtion that the difference between the actual received carrier frequency, , and the local reference frequency, fO, does not differ from the predicted (numerical oscillator) frequency, fp, by a substantial fraction of 1 Hertz. This condition is satisfied in the present system by applylng feedback control to the frequency of the numerical oscillatort to keep this frequency .
s

4~ 63~

close to the actual recelved carrler frequency. This ~ontr~I
is exercised by means of a simple program executed by thy fleld terminal computer 3~. A description of this program follows.
The complex number c formed from the a and b correlator outputs at the end of thy kth one-second integration interval is designated elk where tk represents the time at the mîddle of that interval To the nwnerical oscillator frequency for the (k+lJst interval is added a corrective bias of K /[c(tk) c ttk_l)] /2n Hertz, where K is a positive r-eal constant less than l, ~[] denotes the angle of the complex quantity enclosed by the brackets l];
and c ttk 1) i5 the co~p~ex conjugate of the complex number c from the neAt-preceding, tk-llst intet~al.
The principle of operation o thiis program may be understood from the following example: If the frequency prediction is, say, too lo by 0.1 Hertzi, then the angle of c will advance by 0.1 cycle ln l secondl and the complex quantity c~tk)c ~tk_l) will have an angle of t~O.l) x t2~) radians tplus some zero-mean noise). Addition of the bias, which is positive in this c3se, will reduce the magnitude of the negative error in the frequency prediction from (0.1 Hz) to (l-K) x tO.l Hz).
The value of K must be greater than zero or no reduction of a frequency prediction error will result from the feedback.
Sbe value must ùe less than l or the Eeedùa~k will result In ..
it , _ , unstable osclllatl~n of the error, due to the delay ln applying the correction. The exact value is not critical, a the optimum Yalue may be determined by experiment. A nomlnal - ? . ' ' ' value of 0.5 is used in the present system.
An important other effect of this frequency feedback is that the numerical osclllator frequency will be pulled towasd the actual received carrier frequency from an initial frequency which may be as much as several oft above or below. This puffin phenomenon us welI know in the art of phase or frequency-tracking feedback lops, as discussed for example in the book entitled Phaselock. Techni~ues.r by Floyd M.
Gardner, published by John Wiley & S0~5~ I~c~, Neh~ York, 1966.
The significance of the npull--in." phenomenon. for the present system is that the a print knowI.edge of the survey mark position does not ne~a to hav* Iess Han a. D:ew kilometers of uncertai n ty .
A potentially adverse side e~.ect.of the "pull-in" phe-nomenon ln the present system is that the numerical oscillator that is supposed to be ticking a particular sa~.ellite may instead be pulled to the frequency of a different satellite if the latter's frequency is near the i~r~er'sr an lf the latter's signal is strong ln comparisvn Wit the former's. To li,mit tile damage that might result from.such occurrences, the field terminal computer proqram contains a provision that limits the magnitude of the accumulated bias that may be added to the a priori frequency prediction, to about 10 ~z. Since the difference between two satellites' requencies changes, _~5~ 3~

typically, by about 1 Hz per second, lt iollows that ~nl~y about 10 seconds of measurement data, or less than aboue 1 - percent of the total data obtained ae a fleld site, may be invalidated by tracking of a wrong satellite. Experience indicates that this percentage is ins~gniflcant.
Now referring to Figure 7, we 5ee lock diagram of a correlator module 14~r one of the seven identical such modules in the correlator assembly 127. R}l seven modules have the same input U~L, which the U0L output. o the signal conditioner 125. Each module 14~ al.s~ recei,~es a "cosine"
input and a sine input. fEom a colrrecpondlng one of the seven numerical oscillator modu~es~ The! Us i.np~.t: and the cosine input go to an exclus}ve-nor ga,te l.Si. whose out:put is the input to a "clocked" ~i~ital counter 153. Thle AL input and the sine input go to another excl.usi.ve-nor gate 155 whose output is the input tQ another coun,t,eo 157'.. Once per second, the contents of the mounter regis.ters.~.53,. Y.57 are latched in respective output buffers 15~r 16h by a, pu.lse fFOm the real-time clock 131 in the dig~:tal e1ectron.~cs as,sembly 37, and the counters are then reset to zeroO At. rate of 10.23 MHz, governed by the "clock signal from the signal conditioner 125, each counter 153, 157 increments by one if and only if its input, from its associated exclusive-nor gate 151, 155, is "True". Thus at the end of each one-second interval, the output buffer 159, 161 contents indicate the number of times between zero and 10,230,000, that the U~L and the cosine/sine inputs matched during the preceding 1 second. The output ~.~2~35~
_4~_ /5~ ~'6 buffer contents of each counter ore connected to thy data bus 133, through which the field tetminal computer 39 roads the contents each second. Each counter/latch may be a single integsated circuit such as the 32-bit device, model no.
LS7060, made by LSI Systems, Inc.
The quantity a, defined previously by the crosscorrela-tion between ~u~t)l(t)~ and cos [2~p~t)~ is obtained in the field terminal computer 3~ by subtracting 5,115,000 from the output of the "cosine" cQunter and dividing the result by

5,11~,000. The quantity b is obtained similarly by subtracting 5,115,000 rom the sine" counter output and dividing the result by ~115,000. thus, uni.t magnitude of a or b represents perfect: correlation between Eu~t~t)~ and the cosine or the sine fu~OEi.on, respectively. Before these results are stored in toe Emory of the fleld terminal computer 39, each number may be trun~ate.d to as few as 4 bits in order to conserve memory space Now reerring to ~iqure 8, therm is illustrated a block diagram of one of the sever iden~ica}. ~u~eri.cal oscillator ~0 nodules 163 in the nunerical oscillator assembly 129, each of which 163 furnishes cosine" and a "sine" input to one correlator module 149. Each numerical oscillator 163 comprises a binary phase register 167 and a binary frequency register 169; a binary adder 171; an e~clusive-nor gate 173, an inverter 175; and a frequency divider 177.
The phase register 167 and the frequency register 169 each have 32 bits, and the adder 171 Is a 32~bit adder. 7he :: . . . .

_ binary number contained in phase register 167 at any time represents the phase of the oscillator output, with the most significant bit representing one-half cycle, the next-most significant bit representing one-quarter cycle, and so on.
The binary number cont,ained in frequency register 169 similarly represents the frequency of the oscillator, with the most significant bit in this case having a value of 155,000 Hz, equal to 1/66th cycle per period of the 10.23 ~Hz "clock"
signal from the signal conditioner 125. Adder 171 adds together the numbers con-tained in the frequency 169 and phase 167 registers. The sum is loaded into the phase register 167, replacing the previous contents, once per cycle of the output from divider 177, which divides the 10.23 MHz "clock" signal by a fixed factor of 33. Phase register 167 is thus updated at a rate of exactly 310,000 times per second. The amount by which the phase advances upon each update is given by the contents of the frequency register 169. The frequency register 169, as mentioned, is updated 10 times per second via the data bus 133 by the field terminal computer 39. negative as well as positive frequencies are represented by the contents of the frequency register, using the conventional twos comple-ment method. According to this convention, the negative of a binary number is formed by complementing each bit, then adding one. The largest positive number is accordingly represented by having the most significant bit zero, and all other bits ones.
The most significant bit being one implies that the number is negative.) jrc: Q

i3~
The sine output ox the numerical oscillator 163 is obtained fxom inverter 175 which inverts the most signif-icant bit of the phase register 167. The sine output has a value of one when the phase is between zero and plus one-half cycle, and a value of zero when the phase is between one-half and one cycle (which is the same as the phase being between minus one-half and zero cycles). The cosine output of the numerical oscillator 163 is taken from the exclusive-nor gate 173 whose inputs are the most and the next-most signif-icant bits of the phase register The cosine output has a value of one when and only when the phase is within plus or minus one-quarter cycle of zero.
Now referring to Figure 9, there is shown a block diagram of the field terminal computer 39. The computer comprises a central processing unit (CPU) 181, a program memory 183, a data memory 185, an external, bi-directional data port 187 which is connected to an operator terminal 189, and an external, bi-directional data port 191 which is connected to a modulator-demodulator (modem) 193 which is in turn connected to a telephone line, a radiotelephone, or some other telecommunications link 195. The parts of the computer 39 are interconnected by means of a data bus 133, which also serves to connect computer 39 to other parts of the field terminal (see Figure 5).
CPU 181 may be a Digital Equipment Corporation (DEC) model LSI-11/2 (part number KDll-GC); program memory 183 may be a 32 k byte programmable read-only memory such as DEC part ..~, - ~8 jrc~

O4g_ ~z~3~

number MRVll-C; data memory 185 my be a 32 byte, random- :
access, read-write memory such as DEC part number MXVll-AC;
the two external bi-directlonal data ports ~187 and 191) may be the RS-232 serial data ports which are included in the MXVll-AC; operator terminal 189 may be the DEC moclel VT-100 or any equivalent serial ASCII terminal which, like the VT-100, can be connected to the RS-232 serial data interfz~ce of the MXVll-AC, or through any other suitable external. data port device to the computer; modem 193 may be any standard, RS-232 compatible, device, and may be eliminated completely if, as mentioned, the field terminal comput*r ~9 i5 connected .~ directly to the base terminal computer 15. The data bus ~9 may be the LSI-ll Q-bus. The real.-t.im~ clock 13}., the numerical oscillator assembly 12g~ and the co~rrel.ator assembly 127 may be connected to the Q-bus by constructing them on standard circuit cards that plug directly into the card-edge connectors of the ~backplane~ of an LSI-ll comp~teF SySteM.
Such circuit cards are available f:ro~ DEC equipped with special integrated circuits that can handle ~11 data communication between the Q-bus and the specia}. ~terferometer terminal circuits which are constructed on the cards.
The measurement data stored in the memory l~S of the field tPrminal computer 39 comprise a time series of complex numbers for each of up to seven satellites observed, with one such number being obtained each second of time. These data are obtained for a time span of about 5,000 seconds, during which at least two satellites are always observed, with the t ., ~2~i3~5 average number of satellites observed being at least four.
For the 1th satellite at the time t, the complex datum is designated Ai(t), where the magnitude of this complex number is proportional to the measured power of the signal received from -that satellite at that time, the constant of proportion-ality being arbitrary but the same for all satellites f and where the angle of the complex number is equal to twice the carrier phase measured for the same satellite at the same time, with the phase for each satellite being referred to the same local reference oscillator signal, namely the 1575.42 MHz signal generated by the oscillator circuit 35 of the field terminal 13-1.
The complex data Ai(t), i = 1, ..., 7, are derived by the field terminal computer 39 from t.he a and b outputs oE the seven correlators 149 in the correlator assembly 127 as follows. For the ith correlator, Ai(t) = [a(t) + jb(t)] exp[2j~p(t)]~

where a(t) and b(t) represent, respectively, the normalized a and b outputs for the l-second "integration", or counting, interval centered at the time t; j is the square root of minus one; and 2~p(t) is twice the predicted carrier phase of the _th satellite at the time t. Note tha-t the complex number Ai(t) is equal to the complex number c derived from the 1th correlator output, multiplied by exp[2j~p(t)]. The angle of Ai represents (twice) the received carrier phase referred to (twice) the phase of the 1575.42 MHz local reference, whereas , . .. .

~5~ 63~iiSi the angle of c is referred to twice) the sum ox that ref~r~nce oscillator phase the numerical oscillator phase . ' ' ' '`
For the purpose of this explanation, it is considered that the data set lAi~t~ is the one generated by the field terminal 13-1 which is at the origin of the baseline vector.
The other field terminal 13-2J that is the field terminal at the terminus of the baseline vector, observing the same satellites at the same times as the first terminal, yields data corresponding to At designate Bi(t~r The same satellites are observed because both terminals were given prediction data from the same centraI computer 15, which numbered the satellites 1 through 7 Pi just orse way. The observations at the two terminal.s are: ef.ect.i~el.y simultaneous because the two terminaIs' clocks were synchr~l.zed immedlate-ly prior to the observat.ions, and the c}ock raltes differ by a trivial amol~nt. (The principal effect o.f the rate difference between the crystal oscillators that.govern the rates of the clocks is to vary the phase difference between the 1575.42 MHz referencesO) It will not matter if r at a particular time, a particular satellite is visible from one terminal but hidden from the other. The magnitude of either Ai(t) or Bit) in this case will simply be zero, or nearly so.
The operations performed by the central computer 15 in order to complete the determination of the baseline vector of the interferometer, given the power and phase measurement data t ., .

~52~ 3~

collected from two field terminals 13-1 and 13-2 located the ends of the baseline vector, will now be discussed.
the first step in the prooessing of the All and the Bilt) data in the central computer is to multiply the complex conjugate of Ai(t), denoted by Alit), by Bit The product, Si(t) 5 Ai(t) Bit r has an angle, /Silt), equal to twi.ce the dif~rence between the measured phases of the~carrie~ signals recked from the ith satellite at the two termina~s.~ Mach phase havi.ng been _ measured with respect to the local reference o!scl:ll.atQr in the respective terminal. Accordinglyr t:he axle o Six) is related to the difference betweeni the! phases ox the local oscillators and to the baseIine vector between the terminals by the theoretical relation Sit LO 14~j~c)~
wherein LO represents the local-o~sci.llato~ phase di.fference, fi is the received irequency fot ye ith see , near1y equal to 1575.42 MHz, c ls the speed of }ight, i.s the baseline vector, and si(t) is a un!it: Hector I the direction of the 1th satellite as viewed at toe tire t f.r.o~ the midpoint of the baseline vector. (This rev on yield lie angle Sit in radians rather than cycles. Since the frequency fi is specified in cycles, rather than radians, per second, a factor of 2~ must be included. The reason that 4~, rather than 2~, appears here is that each field terminal measures twice the received signal phase.) This re1ation is approximate inasmuch as it ignores second-order parallax, .

' ~53~ ~2~

effects of the propagation medlum, multlpath, relativistic effects, noise, etcO These small effects are neglected here for the sake of clarity. The error associated with the neglect of these effects is equivalent to a baseline error of less than about 1 cm for a baseline length o less than about 1 km lExcept for the effect of noise, which is completely random, it is possible ~.o model the effects which we have neglected above, in ord~!r to obtain a more accurate theoretical representati.on of Sill This modeling is described, for exampl~r in the article by I. I. Shapiro entitled VEstimatisn of astrometrIc and geodetic parameters from VLBI observations.v~ appearing i.n Methods of Experimental Physics, vol. 12, part. C:r pp. 261-276, 1976.J
Theoretically, the magnitude of S is given by ISil = C~G2(cos~
where C is a constant a~d'G ls the directive power gain of a receiving antenna, w~it~en~ as a unction of the cosine of the ,th satellite's zenith angl.~ ei. G îs assumed to be independent of azimuth. and is normalized such that the power received by an isotroplc antenna of matched circular polarization is equal Jo 1. For the MITES antenna design, coos 11.23) cos~)2 sin2~(3~4)cose), 0<o<9~;
coos 0, 90~<o The value of this function is approximately 2.46 at the zenith C it has one maximum, of about 3.63, at 40, has unit value at 72~, and approaches 0 as approaches 90.

..

-~4~
, The next step In the processing of the measurement dDt~
obtaIned from the two interferometer terminals is to sum the complex numbers Si(t) over I to obtain a sum S(t) for each measurement time to n S(t~ = Si(t), i=l wherein the sum ranges over all the satellites that were observed at the time t.
The next step in the processing of the meas~re~ent data is to choose a trial value, b, of the baseline vector b, and from this value b to compute a function of time S~t~ which represents theoretically the value that: Sot) would have had if the true value, b, of the baseline vector were equal. to the trial valve, b l 1 i t) I I Bi ( t) I - opt j4 by Si t) /~ it wherein I is the radio wavelength coresponding to the received carrier frequency. That isr I = elf The method of choosing a value of b is describe below. Note. that in the theoretical function 5(t~, as oppose to the m~asu.rement-derived function So no term is present to repL-~sent the local-oscillator phase difference. Also, the constant scale factor C is omitted.
Next, ehe magnîtude of S(t) is multiplied by the magni-tude of 5(t~ and the product of these magnitudes is summed over all of the measurement times to obtain a value, R(b), that depends on b as well, of course, as on the measurements:

;3~i~

R(b) = ¦S(tQ)¦-¦S(t~

wherein tQ represents the Qth of the set of about 5,000 measurement times. R(b) is called an "amblguit~ function."
The next step in the processing is to repeat the computation of R(b) for various values of b and to determine the particular value of b for which the function of R(b) hhs the greatest value. This value of b is the desired deter mination of the baseline vector b.
The trial value b of the baseline vector is chosen initially to equal the best a priority estimate of b that is available from independent information on the positions of the survey marks, such as the positions obtained by identifying landmarks on a map. The maximization of I with respect to b is conducted by searching a three-dimensional volume that is centered on this initial value of b and is larye enough to encompass the uncertainty of the initial estimate. on the search, every point of a uniformly spaced three-dimensional grid is examined to locate the one point at which R(b) is maximum. The grid spacing is initially 1 meter. Then the volume extending 2 meters from that one point of maximum R(b) is searched by examining a grid with 20 centimeter spacing.
The maximum of R(b) is found on this more finely spaced grid.
Then the grid spacing is halved and the linear extent of the grid is also halved, and the search is repeated. This process of halving is continued until the grid spacing is under 1 millimeter The value of b that finally maximizes R(b) is taken to be the desired determination of the baseline vector . . , 5~

b. By usinq a number of sa-tellites n equal to 5, a baseline vector determination can be obtained by the method of the present inventlon wi-th an accuracy of about 5 millimeters in each coordinate for a baseline length of about 100 meters.
The above-described method of processing measurement data from a pair of interferometer terminals in order to determine the baseline vector between the -terminals represents a specialization of the general method described in an article by Charles C. Counselman and Sergei A. Gourevitch, entitled "Miniature Interferometer Terminals for Earth Surveying:
Ambiguity and Multipath with Global Positioning System,"
published in IEEE Transactions on Goescience and Remote Sensing, vol. GE~19, no. 4, pp. 244-252, October, 1981.
In another embodiment of a method of processing measurement data according to this invention, an ambiguity - function R(b) is also formed from the measurement data and from a trial value, b, of the baseline; however, the method of forming the function is different. In this embodiment, as in the previous embodiment, the complex conjugate of Ai(t) is multiplied by Bit to obtain a complex product Si(t):
Sit) = Ai(t) Bi(t) wherein Ai(t) is a complex number representative of the measurements of the signal received from the 1th satellite at one interferometer terminal at the time t, the magnitude of sd/` -5~-. !. i;

3~i Ai(t) being proportional to the power received and the angle /Ai(t) being twice the phase of the carrier relative to the local oscillator of the terminal, and Bi(t) is like Ai(t) except that it is derived from the other terminal, at the other end of the baseline vector.
Next, Si(t) is multiplied by a certain complex exponen-tial function of a trial value, b, of the baseline vector, and the product is then summed over all satellites observed at the time t to obtain a sum S(t) which is a function of the time and of the trial value, b:

S(t) = Si(t) exp~-j4~b silt i=L
wherein si(t) is a unit vector in the direction of the 1th satellite at the time t and I is the wavelength of the signal received from the lth satellite. (Note that if b equals b, then the angle of each term in the sum over i is equal to LO' independent of i.) Next, the magnitude of S(t)is taken and is summed over all observing times to obtain the function R(b):

R(b) = ¦S(tQ)¦ , Q

wherein tQ is the Qth of the approximately 5,000 measurement times.
Finally, the value of b which maximizes R(b) is found, by the same search procedure that was described in connection with the original data-processing method. This value of b is the desired determination of the baseline vector I.
This latter embodiment is more efficient computationally than the first described embodiment.

Claims (75)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. The method of deriving position related data, related to signals modulated by mutually orthogonal codes, from overlapping spread spectrum signals transmitted concurrently with the same frequencies by each of a plurality of satellites, the data being derived independently of externally derived knowledge of the information content of the related modulating codes, comprising:
receiving from the satellites a first composite of the overlapping spread spectrum signals with an upward looking, omni-directional antenna positioned at a first mark;
reconstructing the first composite of spread spectrum signals to form a second composite simultaneously including a plurality of reconstructed components related to the code modulated signals implicit in the signals received from the satellites; and applying predictions of the frequency histories of the signals from the satellites to the second composite to derive data therefrom.

2. The method of claim 1 wherein the data derived are related to the signals transmitted by a selected satellite.

3. The method of claim 1 wherein the data derived are related to signals transmitted by a plurality of the satellites.

4. The method of claim 1, further comprising:
deriving at a second mark data related to signals concurrently transmitted by the plurality of satellites and processing the data from both marks to determine relative position.

5. The method of claim 1 wherein the reconstructed components have discrete frequencies and phases related to the frequencies and phases of the code modulated signals.

6. The method of claim 1 wherein the reconstruction step further comprises:
applying a phase and frequency doubling non-linearity to the composite of spread spectrum signals to form the composite of reconstructed components.

7. The method of claim 1 wherein the reconstruction step further comprises:
separating the received signals into first and second components representing substantially different spectral portions thereof; and correlating the spectral portions to generate the composite of reconstructed components.

8. The method of claim 7 wherein the spectral component separation step separates the received signals into upper and lower sidebands of a center frequency carrier implicit therein.

9. The method of claim 7 wherein the correlating step further comprises:
generating a first binary signal representing the time varying sign of the first spectral component;

generating a second binary signal representing the time varying sign of the second spectral component; and correlating the first and second binary signals to form the composite of reconstructed components.

10. The method of claim 1 wherein the predicted frequency history step further comprises:
generating a signal whose frequency is proportional to an estimate of the frequency of a satellite signal as received; and combining the estimate signal with the reconstructed components to separate the component related thereto.

11. The method of claim 10 wherein the predicted frequency history step further comprises:
varying the frequency of the estimate signal to track the frequency of the satellite signals as received.

12. The method of claim 6 wherein the predicted frequency history step further comprises:
generating a predicted signal based on a prediction, made before the first composite is collected, of the Doppler shift of the signals from a selected satellite as received at the first mark; and correlating the predicted signal with the reconstructed components to separate the reconstructed component whose frequency and phase are related to the frequency and phase of the selected code modulated signal.

13. The method of claim 12 wherein the phase data deriving step further comprises:
varying the frequency of the predicted signal during the correlation step to maximize the separation of the related component.

14. The method of claim 1 wherein the date deriving step further comprises:
generating a series of signals whose frequencies are related to estimates of the frequencies of selected code modulated signals implicit in the signals received from the satellites; and combining each of the series of estimate signals with the composite of reconstructed components to separate the components related to each code modulated signal.

15. The method of claim 14 wherein the estimate signal generating step further comprises:
varying the frequencies of the series of estimate signals to track the frequencies of the components.

16. The method of claim 1 further comprising the following step before the reconstructing step:
filtering the first composite signal to reject signals received in a narrow band at the frequency of the implicit code modulated signals.

17. The method of claim 16 wherein the rejected frequency band includes the possible range of Doppler shifted frequencies of the implicit code modulated signals.

18. The system for deriving position related data, related to signals modulated by mutually orthogonal codes, from overlapping spread spectrum signals transmitted concurrently with the same frequencies by each of a plurality of satellites, the data being derived independently of externally derived knowledge of the information content of the related modulating codes, comprising:
an upward looking, omni-directional antenna positioned at a first mark for receiving from the satellites a first composite of the overlapping spread spectrum signals;
means for reconstructing the first composite of spread spectrum signals to form a second composite simultaneously including a plurality of reconstructed components related to the code modulated signals implicit in the signals received from the satellites; and means for applying predictions of the frequency histories of the signals from the satellites to the second composite to derive data therefrom.

19. The system of claim 18 wherein the date derived are related to the signals transmitted by a selected satellite.

20. The system of claim 18 wherein the data derived are related to signals transmitted by a plurality of the satellites.

21. The system of claim 18, further comprising:
means for deriving data at a second mark related to signals concurrently transmitted by the plurality of satellites; and data processing means for determining relative position from the data from both marks.

22. The system of claim 18 wherein the reconstructed components have discrete frequencies and phases related to the frequencies and phases of the code modulated signals.

23. The system of claim 18 wherein the reconstruction means further comprises:
means for doubling the phase and frequency of the first composite signal to form the second composite signal.

24. The system of claim 18 wherein the reconstruction means further comprises:
means for separating the spread spectrum signals into the first and second components representing substantially different spectral portions thereof; and a correlator for correlating the spectral portions to generate the composite of reconstructed components.

25. The system of claim 24 wherein the separating means separates the spread spectrum signals into upper and lower sidebands of a center frequency carrier implicit therein.

26. The system of claim 24 wherein the correlating means further comprises:

means for generating a first binary signal representing the time varying sign of the first spectral component;
means for generating a second binary signal representing the time varying sign of the second spectral component; and a correlator for correlating the first and second binary signals to form the composite of reconstructed components.

27. The system of claim 18 wherein the means for applying the predicted frequency history further comprises:
means for generating a signal whose frequency is proportional to an estimate of the frequency of a satellite signal as received; and means for combining the estimate signal with the reconstructed components to separate the component related thereto.

28. The system of claim 27 wherein the means for applying the predicted frequency history further comprises:
means for varying the frequency of the estimate signal to track the frequency of the satellite signals as received.

29. The system of claim 23 wherein the means for applying the predicted frequency history further comprises:
means for generating a predicted signal based on a prediction, made before the first composite is collected, of the Doppler shift of the signals from a selected satellite as received at the first mark; and means for correlating the predicted signal with the reconstructed components to separate the reconstructed component whose frequency and phase are related to the frequency and phase of the selected code modulated signal.

30. The system of claim 29 wherein the means for applying the predicted frequency history further comprises:
means for varying the frequency of the predicted signal during the correlation step to maximize the separation of the correlated component.

31. The system of claim 18 wherein the means for applying the predicted frequency history further comprises:
means for generating a series of signals whose frequencies are related to estimates of the frequencies of selected code modulated signals implicit in the signals received from the satellites; and means for combining each of the series of estimate signals with the composite of reconstructed components to separate the components related to each code modulated signal.

32. The system of claim 31 wherein the estimate generating means further comprises:
means for varying the frequencies of the series of estimate signals to track the frequencies of the components.

33. The system of claim 18 further comprising:
means for filtering the first composite signal to reject signal received in a narrow band at the frequency of the implicit code modulated signals.

34. The system of claim 33 wherein the rejected frequency band includes the possible range of Doppler shifted frequencies of the implicit code modulated signals.

35. A system for deriving position related data from signals modulated by mutually orthogonal, spectrum spreading codes, comprising:
antenna means for receiving a composite ofsignals including spread spectrum signals and potentially interfering continuous wave components;
filter means for rejecting the continuous wave components related to a selected frequency from the composite;
means for reconstructing at least one continuous wave component related to the selected frequency from the filtered spread spectrum components; and means for deriving data from the reconstructed component.

36. The system of claim 36 wherein the spread spectrum signals are transmitted concurrently with the same frequencies by each of a plurality of satellites, and the filter means further comprises:
means for rejecting continuous wave interference in a narrow band of frequencies including the maximum Doppler shift of the selected frequency due to relative motion between the satellites and the antenna means.

37. The system of claim 35 wherein the filter means further comprises:
means for converting the received signals to baseband; and high pass filter means for rejecting a narrow band of frequencies at baseband.

38. The system of claim 36 wherein the filter means further comprises:
means for converting the received signals to baseband, and high pass filter means for rejecting a narrow band of frequencies at baseband.

39. The system of claim 37 or 38 wherein the filter means further comprises:
low pass filter means for rejecting frequencies outside a wide band of frequencies substantially including the signals whose spectrum was spread by a particular modulating code.

40. The system of claim 35 or 36 wherein the selected frequency is a suppressed center frequency carrier.

41. The system of claim 35 wherein the reconstructing means reconstructs a plurality of continuous wave components.

42. The system of claim 36 wherein the reconstructing means reconstructs a plurality of continuous wave components.

43. The system of claim 41 or 42 wherein the plurality of continuous wave components are related to the same selected frequency.

44. The system of claim 41 or 42 wherein the plurality of reconstructed components are related to the same spectrum spreading modulating code.

45. The system of claim 35 wherein the reconstructing means further comprises:
phase and frequency doubling means for reconstructing the signals whose spectrum was spread by a particular modulating code independently of externally derived knowledge of the information content of that modulating code.

46. The system of claim 36 wherein the reconstructing means further comprises:
phase and frequency doubling means for reconstructing the signals whose spectrum was spread by a particular modulating code independently of externally derived knowledge of the information content of that modulating code.

47. The system of claim 45 wherein the rejecting and reconstructing means further comprise:
means for separating the received signals into first and second spectral components representing substantially different portions of the spectrum thereof;

and means for cross-correlating the spectral components to reconstruct the spread spectrum signals.

48. The system of claim 46 wherein the rejecting and reconstructing means further comprise:
means for separating the received signals into first and second spectral components representing substantially different portions of the spectrum thereof;
and means for cross-correlating the spectral components to reconstruct the spread spectrum signals.

49. The system of claim 47 wherein the rejecting means further comprises:
means responsive to the first spectral component to reject continuous wave components therein related to the selected frequency; and means responsive to the second spectral component to reject continuous wave components therein related to the selected frequency.

50. The system of claim 48 wherein the rejecting means further comprises:
means responsive to the first spectral component to reject continuous wave components therein related to the selected frequency; and means responsive to the second spectral component to reject continuous wave component therein related to the selected frequency.

51. The system of claim 49 or 50 wherein each spectral component rejecting means further comprises:
high pass filter means for rejecting a narrow band of frequencies including the maximum Doppler shift of the selected frequency due to relative motion between the satellites and the antenna means; and low pass filter means for rejecting signals outside a wide band of frequencies substantially including the signals spread by the particular modulating code.

52. The system of claim 47 or 48 wherein the first and second spectral components are upper and lower sidebands of a suppressed center frequency carrier implicit in the spread spectrum signals.

53. The system of claim 45 or 46 wherein the reconstructing means reconstructs continuous wave components implicit in the signals received from each of the satellites and the data deriving means further comprises:
means for deriving data related to different satellites from the reconstructed signals based on the difference in frequencies thereof as received due to Doppler shift.

54. The system of claim 45 or 46 wherein the reconstructing means generates a second composite simultaneously including continuous wave components implicit in the signals received from each of the satellites and the data deriving means further comprises:
means for generating a series of predicted signals whose frequencies are related to the frequencies of the signals from each satellite as received;
means for correlating each of the series of predicted signals with the second composite signal to isolate the reconstructed components related to each satellite; and means for deriving data from each of the isolated components.

55. The method of deriving position related data from signals modulated by mutually orthogonal spectrum spreading codes, comprising the steps of:
receiving a composite of spread spectrum signals including potentially interfering continuous wave components with an antenna;
rejecting the continuous wave components related to a selected frequency from the composite of signals received, then;
reconstructing a continuous wave component related to the selected frequency from the remaining spread spectrum signals; and deriving data from the reconstructed component.

56. The method of claim 55 wherein the spread spectrum signals are transmitted concurrently with the same frequencies by each of a plurality of satellites and the interference rejecting step further comprises:
rejecting continuous wave interference in a narrow band of frequencies including the maximum Doppler shift of the selected frequency due to relative motion between the satellites and the antenna means.

57. The method of claim 55 wherein the interference rejecting step further comprises:
converting the received signals to baseband; and rejecting a narrow band of frequencies at baseband.

58. The method of claim 56 wherein the interference rejecting step further comprises:
converting the received signals to baseband; and rejecting a narrow band of frequencies at baseband.

59. The method of claim 57 or 58 wherein the interference rejecting step further comprises:
rejecting frequencies outside a wide band of frequencies substantially including the signals whose spectrum was spread by a particular modulating code.

60. The method of claim 55 wherein the selected frequency is a suppressed center frequency carrier.

61. The method of claim 56 wherein the selected frequency is a suppressed center frequency carrier.

62. The method of claim 60 wherein the reconstructing step reconstructs a plurality of continuous wave components.

63. The method of claim 61 wherein the reconstructing step reconstructs a plurality of continuous wave components.

64. The method of claim 62 or 63 wherein the plurality of continuous wave components are related to the same selected frequency.

65. The method of claim 62 or 63 wherein the plurality of reconstructed components are related to the same spectrum spreading modulating code.

66. The method of claim 55 wherein the reconstructing step further comprises:
doubling the phase and frequency of the signals whose spectrum was spread by a particular modulating code to reconstruct those signals independently of externally derived knowledge of the information content of that modulating code.

67. The method of claim 56 wherein the reconstructing step further comprises:
doubling the phase and frequency of the signals whose spectrum was spread by a particular modulating code to reconstruct those signals independently of externally derived knowledge of the information content of that modulating code.

68. The method of claim 66 wherein the rejecting and reconstructing steps further comprise:
separating the received signals into first and second spectral components representing substantially different portions of the spectrum thereof; and cross-correlating the spectral components to reconstruct the spread spectrum signals.

69. The method of claim 67 wherein the rejecting and reconstructing steps further comprise:
separating the received signals into first and second spectral components representing substantially different portions of the spectrum thereof; and cross-correlating the spectral components to reconstruct the spread spectrum signals.

70. The method of claim 68 wherein the rejecting step further comprises:
rejecting continuous wave components in the first spectral component related to the selected frequency; and rejecting continuous wave components in the second spectral component related to the selected frequency.

71. The method of claim 69 wherein the rejecting step further comprises:
rejecting continuous wave components in the first spectral component related to the selected frequency; and rejecting continuous wave components in the second spectral component related to the selected frequency.

72. The method of claim 70 or 71 wherein each spectral component rejecting step further comprises:
means for rejecting a narrow band of frequencies including the maximum Doppler shift of the selected frequency due to relative motion between the satellites and the antenna means; and rejecting signals outside a wide band of frequencies substantially including the signals spread by the particular modulating code.

73. The method of claim 68 or 69 wherein the first and second spectral components are upper and lower sidebands of a suppressed center frequency carrier implicit in the spread spectrum signals.

74. The method of claim 66 or 67 wherein the reconstructing step reconstructs continuous wave components implicit in the signals received from each of the satellites and the data deriving step further comprises:
deriving data related to different satellites from the reconstructed signals eased on the difference in frequencies thereof as received due to Doppler shift.

75. The method of claim 66 or 67 wherein the reconstructing step generates a second composite simultaneously including continuous wave components implicit in the signals received from each of the satellites and the data deriving step further comprises:
generating a series of predicted signals whose frequencies are related to the frequencies of the signals from each satellite as received;
correlating each of the series of predicted signals with the second composite signal to isolate the reconstructed components related to each satellite; and deriving data from each of the isolated components.