CN102288962A - Real-time motion compensation method for ultra-wide band synthetic aperture radar (UWB SAR) - Google Patents

Abstract

The invention provides a real-time motion compensation method for an ultra-wide band synthetic aperture radar (UWB SAR), which is characterized in that motion parameters output by a single-point global positioning system (GPS) are used for carrying out real-time motion compensation of the UWB SAR, the flight time is segmented according to Ta, when the current moment is a starting point of an imaging synthetic aperture, an imaging coordinate system is built, and if not, the next steps are carried out: step 1, eliminating the single-point GPS position jumping errors; step 2, calculating the transverse motion errors according to the single-point GPS positioning information; step 3, calculating the heading speed errors; and step 4, calculating the sight line direction motion errors and compensating the motion errors in the airborne UWB SAR sight line direction. In the method of the invention, the information processing is only carried out on the output data of a navigation system, the motion parameter evaluation does not need to be carried out, the storage space and the calculation quantity are saved, and the large-area imaging compensation precision is high. In addition, the cost is low, and the realization is easy.

Description

The compensation method of a kind of Research on UWB SAR real time kinematics

Technical field

The invention belongs to UWB (Ultra Wide Band, ultra broadband) SAR (Synthetic ApertureRadar, synthetic-aperture radar) signal processing technology field, relate to the compensation method of a kind of UWB SAR real time kinematics, particularly use GPS (Globe Positioning System, GPS) output movement parameter to carry out the method for UWB SAR real time kinematics compensation.

Background technology

UWB SAR is meant that radar system signal relative bandwidth is greater than 25% SAR, because relative bandwidth equals the ratio of transmitted signal bandwidth and radar system centre frequency, UWB SAR is usually located at the UHF/VHF wave band, belong to low-frequency range SAR, UWB SAR possesses the leafage of penetrating and shallow face of land imaging capability simultaneously, is one of the research focus in current SAR field.UWB SAR obtains the orientation high resolving power needs big accumulation angle, be installed on the UWB SAR on the airborne platform, the length of synthetic aperture of big accumulation angle correspondence can reach several kilometers, in an aperture time, airborne platform departs from the desirable at the uniform velocity relative motion error of straight line has very big influence to image quality, must carry out motion compensation.

The kinematic error of airborne platform is divided into attitude error and translation error.The compensation of attitude error can realize by the sensing (being referred to as direction of visual lines among the present invention) that the attitude information that receives navigational system output is adjusted the antenna beam center in real time, no longer discusses in the present invention.Translation error can cause UWB SAR echo data in the orientation to distance to envelope migration and phase error take place, cause defocusing and geometric distortion of image.Only can't eliminate translation error by adjusting direction of visual lines.Because Airborne UWB SAR requires to possess the real time imagery ability, therefore must in imaging process, carry out the real time kinematics compensation of translation error.

Traditionally, the real time kinematics compensation technique at translation error can be divided on the realization approach: based on the real time kinematics compensation of radar return data, based on the real time kinematics compensation of movement parameter measurement value.

Real time kinematics compensation method based on the radar return data can estimate that from original echo or coarse resolution image data obtaining kinematic parameter carries out error compensation by autofocus algorithm.Because UWB SAR single aperture data volume is very big, adopt this method to estimate that kinematic parameter required memory space and operand are all very big, and most of autofocus algorithm can only be estimated the kinematic error of low frequency; In addition, carry out based on the local strong point target in the scene because autofocus algorithm is many, estimate that the kinematic parameter that obtains is difficult to fit like a glove with the actual motion of SAR airborne platform, the motion compensation effect is not good during the large tracts of land imaging.

Real time kinematics compensation method based on the movement parameter measurement value is carried out error compensation by using the navigational system output movement parameter of installing on the airborne platform.The long-term bearing accuracy that conventional I NS (Inertial Navigation System, inertial navigation system) is provided is drifted about in time, and the bearing accuracy in short-term of GPS is not high, can not export attitude information.The integrated navigation technological synthesis these two kinds of independent sources of information with complementary characteristic, utilize INS to improve the precision in short-term of data, utilize GPS to guarantee the long-time stability of data, thereby be applied to SAR motion compensation field in recent years.It is reported, at present, the real time kinematics compensation methodes of adopting based on the movement parameter measurement value of the UWB SAR system of external development more, because compensation effect mainly depends on the precision of kinematic parameter, need on airborne platform, additionally install expensive high precision navigational system additional, as high precision INS/ differential GPS, bearing accuracy reaches 0.1 meter, rate accuracy is higher than 0.03 meter per second, and this method successful Application has obtained high-resolution UWB SAR image in U.S. Lynx SAR system.

High precision INS costs an arm and a leg, and same the existence located drift for a long time; Differential GPS operating distance is limited, is subject to disturb.In China, the INS/GPS integrated navigation system bearing accuracy that is equipped with on the airborne platform is generally on the low side, and the drift of INS output valve in 100 seconds reaches tens of rice, and the GPS output data rate mostly is 1-2Hz and location saltus step error.Concerning UWB SAR, reach several kilometers owing to realize the required aperture of high-resolution imaging, above-mentioned influence of measurement error is big, carries out the poor effect of UWB SAR real time kinematics compensation based on airborne INS/GPS integrated navigation system.

Just because of there are the problems referred to above, the method of UWB SAR real time kinematics compensation is carried out in utilization based on single-point GPS output movement parameter, in the real time kinematics compensation of using it for UWB SAR after the processing of single-point GPS kinematic parameter, can remedy the deficiency of original airborne INS/GPS integrated navigation system, improve the quality of UWBSAR imaging.This method does not see that at present document has concrete report.

Summary of the invention

Goal of the invention:, the invention provides a kind of UWB SAR real time kinematics compensation method based on single-point GPS in order to remedy the deficiency of existing UWB SAR real time kinematics compensation method.This method has remedied the low defective of the original integrated navigation system bearing accuracy of airborne platform, and has the little advantage of operand, is suitable for the real time kinematics compensation of Airborne UWB SAR.Compare with real time kinematics compensation method, only need the output data of navigational system is carried out information processing, need not to carry out kinematic parameter and estimate that saved storage space and operand greatly, large tracts of land imaging compensating precision is higher based on the radar return data.With compare based on the real time kinematics compensation method of high precision INS/ differential GPS, this method only need install a single-point GPS additional, improved the relative positioning precision of navigational system effectively by data processing method, and cost is lower, is easy to realize.

Technical scheme of the present invention is: the compensation method of a kind of Research on UWB SAR real time kinematics is characterized in that the kinematic parameter that uses single-point GPS to export carries out the real time kinematics compensation of UWB SAR imaging, comprising:

If the Data Update period T of single-point GPS _GPS, comprise at the kinematic parameter of moment t output: the longitude λ (t) of airborne platform, latitude

With height h (t); And the speed of airborne platform: the east orientation speed V in day coordinate system northeastward _e(t), north orientation speed V _n(t) with day to speed V _z(t).If airborne platform is the acceleration threshold value γ=[γ in day coordinate system northeastward _E, γ _N, γ _Z].If Polaroid aperture time of the T of UWB SAR _a

In UWB SAR imaging process, will the flight time press T _aSegmentation is equivalent to flight path according to Polaroid aperture length segmentation.

In any one period flight time, to any time t ∈ [n ₀T _a, (n ₀+ 1) T _a), n ₀＞1 and n ₀Be integer, carry out following treatment step:

During first kind of situation, if t=n ₀T _a, then set up imaging coordinate system, comprise the steps:

Utilize following formula to calculate the Desired Track angle β of current time t correspondence _RefWith desirable speed of a ship or plane V _Ref:

$\left\{\begin{array}{c}{\mathrm{\β}}_{\mathrm{ref}}=\frac{1}{T}{\∫}_{t-T}^t\mathrm{\β}\left(t^{\′}\right){\mathrm{dt}}^{\′}\\ V_{\mathrm{ref}}=\frac{1}{T}{\∫}_{t-T}^{t}V\left(t^{\′}\right){\mathrm{dt}}^{\′}\end{array}\right.$

Wherein, β (t ') and V (t ') are respectively the instantaneous flight-path angles of t ' airborne platform constantly and along the instantaneous speed of a ship or plane of flight-path angle direction, and β (t ')=arctg[V _n(t ')/V _e(t ')], T ∈ [T _a/ 3,2T _a], choose according to actual conditions, and airborne platform stability being good more, the value of T is more little.

With the initial moment of this imaging of UWB SAR, i.e. n constantly ₀T _aThe time, the position at airborne platform place is an initial point, with β _RefBe oriented to X-axis, on the surface level perpendicular to β _RefDirection be Y-axis, day to the imaging coordinate system of setting up Airborne UWB SAR for the Z axle.

During second kind of situation, if t ≠ n ₀T _a, establish t=n ₀T _a+ t ₀, t ₀∈ (0, T _a), then Airborne UWB SAR is carried out motion compensation based on above-mentioned imaging coordinate system, specifically comprise the steps:

The first step is eliminated single-point GPS position hopping error.

What most GPS in the market adopted is the localization method of carrier phase smoothing pseudo range, since in May, 2000 U.S. government stop at add in the satellite clock disturb after, the bearing accuracy of single-point GPS has had large increase.But, being subjected to all multifactor influences such as satellite geometry distribution, radio wave propagation sum of errors calculation method, the locating information in adjacent sometimes two moment phenomenon of can undergoing mutation is called the position hopping error.

Utilize following formula to calculate the current time t velocity equivalent of airborne platform in day coordinate system northeastward:

Wherein,

For at moment n ₀T _aThe latitude of airborne platform, a are average equatorial radius, and e is an eccentricity of the earth.

Utilize following formula to calculate the velocity equivalent difference:

ΔV(t)＝[V _E(t)-V _E(t-T _GPS)，V _N(t)-V _N(t-T _GPS)，V _Z(t)-V _z(t-T _GPS)]

Utilize following formula to judge and whether occur the position hopping error in the locating information:

Δ V (t)＞γ T _GPS(formula one)

If formula one is set up, the position hopping error then appears, according to the locating information of following formula correction current time t single-point GPS:

With the high value of revising of longitude and latitude

Replace t measured value constantly Promptly obtain removing the locating information after the position hopping error.

If formula one is false, the position hopping error does not then appear, need not to revise.

In second step, calculate the translation motion error according to single-point GPS locating information.

Utilize following formula, will go the single-point GPS locating information of current time t after the saltus step, be transformed into the solid rectangular coordinate system of ground heart from the WGS-84 coordinate system:

Then, utilize following formula that locating information is transformed into sky, northeast coordinate system from the solid rectangular coordinate system of ground heart:

Wherein, (x _E0, y _E0, z _E0) be moment n ₀T _aThe time UWB SAR the imaging coordinate system initial point coordinate in day coordinate system northeastward.

Utilize following formula that locating information is transformed into the imaging coordinate system from sky, northeast coordinate system again:

$\left[\begin{array}{c}{x}_i\left(t\right)\\ y_i\left(t\right)\\ z_i\left(t\right)\end{array}\right]=\left[\begin{array}{ccc}{\cos \mathrm{\&beta;}}_{\mathrm{ref}}& -\sin {\mathrm{\&beta;}}_{\mathrm{<figure-callout\; id="0"\; label="ref"\; filenames="HDA0000075407490000022.png,HDA0000075407490000031.png"\; state="\{\{state\}\}">ref</figure-callout>}}& 0\\ \sin {\mathrm{\&beta;}}_{\mathrm{ref}}& \cos {\mathrm{\&beta;}}_{\mathrm{<figure-callout\; id="0"\; label="ref"\; filenames="HDA0000075407490000022.png,HDA0000075407490000031.png"\; state="\{\{state\}\}">ref</figure-callout>}}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_g\left(t\right)\\ y_g\left(t\right)\\ z_g\left(t\right)\end{array}\right]$

The translation motion error of utilizing following formula to try to achieve three change in coordinate axis direction in the imaging coordinate system is respectively:

$\left\{\begin{array}{c}\mathrm{\&Delta;x}\left(t\right)=x_i\left(t\right)-V_{\mathrm{ref}}\&CenterDot;\left({t-n}_0{T}_a\right)\\ \mathrm{\&Delta;y}\left(t\right)=y_i\left(t\right)\\ \mathrm{\&Delta;z}\left(t\right)=z_i\left(t\right)\end{array}\right.$

In the 3rd step, calculate the course velocity error.

The purpose of this step is that the elimination airborne platform is inhomogeneous along the sampling interval that velocity perturbation caused of Desired Track direction.

Utilize following formula to calculate the speed of a ship or plane V of current time t airborne platform along the Desired Track direction _a(t):

V _a(t)＝V(t)·cos[β(t)-β _ref]

Then, calculate V _a(t) and V _RefBetween relative error V _Err(t):

V _err(t)＝V _a(t)-V _ref

Pulse recurrence interval (Pulse RepeatInterval is called for short PRI) according to relative error Verr (t) adjustment UWB SAR guarantees that UWB SAR can realize along the uniform sampling of Desired Track direction.

In the 4th step, calculate the direction of visual lines kinematic error.

The direction of visual lines kinematic error can be decomposed into distance empty constant sight line sum of errors and apart from space-variant sight line error, is located at that the nearest oblique distance of certain point and Desired Track is R in the imaging region of current time t _B, the direction of visual lines kinematic error of calculating this some correspondence according to following formula is:

Δr(R _B，t)＝Vx(t)cos[Ψ(R _B)]-Vz(t)sin[Ψ(R _B)]

In the following formula, Ψ (R _B) be R _BCorresponding depression angle.

Calculate the empty constant sight line error delta r (R of distance of UWB SAR according to following formula _S, t):

Δr(R _S，t)＝Vx(t)cos[Ψ(R _S)]-Vz(t)sin[Ψ(R _S)]

In the following formula, R _SBe the reference oblique distance of current time t mapping band center line to UWB SAR.

Is Δ r according to following formula calculating UWB SAR apart from space-variant sight line error _II(R _B, t):

Δr _II(R _B，t)＝Δr(R _B，t)-Δr(R _s，t)

Utilize the empty constant sight line error delta r (R of distance _S, t) with apart from space-variant sight line error delta r _II(R _B, t), the penalty function of generated error is realized the direction of visual lines kinematic error compensation of current time t to Airborne UWB SAR.

The invention has the beneficial effects as follows:

1, the technical scheme that adopts the present invention to propose need not high precision INS and differential GPS, only needs single-point GPS just can realize the real time kinematics compensation of Airborne UWB SAR, and its operating distance is not subjected to the restriction of fixed receiver position, ground, forms simply, and cost is lower.

2, adopt the method for the first step among the present invention can eliminate position hopping error in the output locating information of single-point GPS, and this method calculated amount is very little, is fit to very much handle in real time.

3, adopting the method that proposes among the present invention to set up imaging coordinate system and calculate the translation motion error, can reduce to resolve the fluctuation range of back single-point GPS translation motion error, mainly is to reduce side-play amount, reduces the difficulty of UWB SAR motion compensation.

Description of drawings

Fig. 1 is based on the process flow diagram of the UWB SAR real time kinematics compensation method of single-point GPS;

Fig. 2 is the imaging coordinate system synoptic diagram of setting up among the present invention;

Fig. 3 is the experiment effect figure that eliminates single-point GPS position hopping error;

Fig. 4 is the experiment effect comparison diagram that calculates the translation motion error;

Fig. 5 is the UWB SAR imaging results of not carrying out motion compensation;

Fig. 6 is that the method that adopts the present invention to propose is carried out the UWB SAR imaging results that real time kinematics compensates.

Embodiment

Below in conjunction with accompanying drawing the specific embodiment of the invention is done further detailed explanation.

Fig. 1 is based on the process flow diagram of the UWB SAR real time kinematics compensation method of single-point GPS.In the UWBSAR imaging process, will the flight time press T _aSegmentation if current time is the starting point of imaging synthetic aperture, is then set up imaging coordinate system, if not, then carry out the described step of Fig. 1: the first step, eliminate single-point GPS position hopping error; In second step, calculate the translation motion error according to single-point GPS locating information.The 3rd step, calculate the course velocity error, the concrete grammar that the real-time PRF that adopts among the present invention adjusts is seen document: Li Jianyang etc., " the real-time PRF of UWB SAR adjusts ", modern radar, 2009, the 31 the 4th phases of volume, p34-p37; In the 4th step, calculate the direction of visual lines kinematic error.But generate the concrete grammar list of references A.Moreira andY.H.Huang of penalty function apart from space-variant sight line error by the empty constant sight line sum of errors of distance, " Airborne SAR Processing of Highly Squinted Data Using a ChirpScaling Approach with Integrated Motion Compensation ", IEEE Trans.onG.R.S.Vol.32 No.5,1994, p1029-p1040 and document G.Fornaro, " Trajectory Deviationsin Airborne SAR:Analysis and Compensation ", IEEE Trans.on A.E.S.Vol.35No.3 July 1999, p997-p1007.

Fig. 2 is the imaging coordinate system synoptic diagram of setting up among the present invention.The initial point of sky, northeast coordinate system and imaging coordinate system all is the imaging aperture starting point of UWB SAR, is designated as O, and the north orientation axle clamp angle of the X-axis of imaging coordinate system and sky, northeast coordinate system is β _Ref, i.e. Desired Track angle, the Z axle of imaging coordinate system overlaps with the celestial axis of sky, northeast coordinate system, and the Y-axis of imaging coordinate system and XZ plane constitute right hand rectangular coordinate system.

Fig. 3 is the experiment effect figure that eliminates single-point GPS position hopping error.Adopt the position hopping error concealment step that proposes in the first step of the present invention result to single-point GPS test figure, the original displacement data that thin solid line records for single-point GPS among the measurement data figure of Fig. 3 top, there is the saltus step error, the precise displacement data of thick dotted lines for adopting the differential GPS testing equipment to record, thin dotted lines is eliminated the displacement data that obtains after the position hopping error for the 3rd step among employing the present invention; The error comparison diagram of front and back is handled in Fig. 3 below for the single-point gps measurement data, thin solid line is the displacement error of the relative differential GPS measured value of raw data, have tangible saltus step, thin dotted lines is the displacement error of relative differential GPS measured value after the elimination saltus step error, and saltus step is eliminated substantially.Illustrate and utilize the first step of the present invention can eliminate saltus step error in the single-point GPS displacement data.

Fig. 4 is the experiment effect comparison diagram that calculates the translation motion error.In flight experiment, after the method that adopts desired track angle to set up imaging coordinate system and employing the present invention proposition is set up imaging coordinate system, single-point GPS locating information is resolved the fluctuation range of observing the translation motion error in two kinds of imaging coordinate systems respectively.Solid line is depicted as and is 162.1938 ° according to desired track angle and sets up imaging coordinate system among the figure, and it is big to resolve the flight path curvilinear path fluctuating range that obtains, and the flight path average reaches-163.9m; Dotted line is depicted as and adopts 30 seconds average flight-path angles to resolve the flight path curve that obtains for 160.3983 ° as the Desired Track angle of imaging among the figure, and the track fluctuating range reduces, and the flight path average is reduced to-29.7m.The imaging coordinate system that adopts the present invention to set up is described, the fluctuation range of resolving back translation motion error reduces, and has reduced off-set value, can avoid introducing excessive space-variant error in the compensation of UWB SAR imaging moving.

Fig. 5 is the UWB SAR imaging results of not carrying out motion compensation, because the influence of kinematic error, image is very fuzzy, resolution that can't computed image; Fig. 6 is the UWB SAR imaging results after the method for employing the present invention proposition is carried out motion compensation, and the image focusing effect after the compensation is obviously improved, and image resolution ratio is 1.5m, proves that motion compensation process proposed by the invention is effective.

The above only is a preferred implementation of the present invention; should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the principle of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (1)

1. Research on UWB SAR real time kinematics compensation method, it is characterized in that, use single-point GPS (Globe Positioning System, GPS) Shu Chu kinematic parameter carries out UWB SARUWB (Ultra Wide Band, ultra broadband) SAR (Synthetic Aperture Radar, synthetic-aperture radar) real time kinematics of imaging compensation comprises:

If the Data Update period T of single-point GPS _GPS, comprise at the kinematic parameter of moment t output: the longitude λ (t) of airborne platform, latitude

With height h (t); And the speed of airborne platform: the east orientation speed V in day coordinate system northeastward _e(t), north orientation speed V _n(t) with day to speed V _z(t); If airborne platform is the acceleration threshold value γ=[γ in day coordinate system northeastward _E, γ _N, γ _Z]; If Polaroid aperture time of the T of UWB SAR _a

In UWB SAR imaging process, will the flight time press T _aSegmentation;

In any one period flight time, to any time t ∈ [n ₀T _a, (n ₀+ 1) T _a), n ₀＞1 and n ₀Be integer, carry out following treatment step:

If t=n ₀T _a, then set up imaging coordinate system, comprise the steps:

Utilize following formula to calculate the Desired Track angle β of current time t correspondence _RefWith desirable speed of a ship or plane V _Ref:

$\left\{\begin{array}{c}{\mathrm{\&beta;}}_{\mathrm{ref}}=\frac{1}{T}{\&Integral;}_{t-T}^t\mathrm{\&beta;}\left(t^{\&prime;}\right){\mathrm{dt}}^{\&prime;}\\ V_{\mathrm{ref}}=\frac{1}{T}{\&Integral;}_{t-T}^{t}V\left(t^{\&prime;}\right){\mathrm{dt}}^{\&prime;}\end{array}\right.$

Wherein, β (t ') and V (t ') are respectively the instantaneous flight-path angles of t ' airborne platform constantly and along the instantaneous speed of a ship or plane of flight-path angle direction, and β (t ')=arctg[V _n(t ')/V _e(t ')],

T ∈ [T _a/ 3,2T _a];

With moment n ₀T _aThe time, the position at airborne platform place is an initial point, with β _RefBe oriented to X-axis, on the surface level perpendicular to β _RefDirection be Y-axis, day to the imaging coordinate system of setting up Airborne UWB SAR for the Z axle;

If t ≠ n ₀T _a, establish t=n ₀T _a+ t ₀, t ₀∈ (0, T _a), then Airborne UWB SAR is carried out motion compensation based on above-mentioned imaging coordinate system, specifically comprise the steps:

The first step is eliminated single-point GPS position hopping error;

Utilize following formula to calculate the current time t velocity equivalent of airborne platform in day coordinate system northeastward:

Wherein,

For at moment n ₀T _aThe latitude of airborne platform, a are average equatorial radius, and e is an eccentricity of the earth;

Utilize following formula to calculate the velocity equivalent difference:

ΔV(t)＝[V _E(t)-V _E(t-T _GPS)，V _N(t)-V _N(t-T _GPS)，V _Z(t)-V _Z(t-T _GPS)]

Utilize following formula to judge and whether occur the position hopping error in the locating information:

Δ V (t)＞γ T _GPS(formula one)

If formula one is set up, the position hopping error then appears, according to the locating information of following formula correction current time t single-point GPS:

With the high value of revising of longitude and latitude

Replace t measured value constantly

Promptly obtain removing the locating information after the position hopping error;

If formula one is false, the position hopping error does not then appear, need not to revise;

In second step, calculate the translation motion error according to single-point GPS locating information

Utilize following formula, will go the single-point GPS locating information of current time t after the saltus step, be transformed into the solid rectangular coordinate system of ground heart from the WGS-84 coordinate system:

Then, utilize following formula that locating information is transformed into sky, northeast coordinate system from the solid rectangular coordinate system of ground heart:

Wherein, (x _E0, y _E0, z _E0) be moment n ₀T _aThe time UWB SAR the imaging coordinate system initial point coordinate in day coordinate system northeastward;

Utilize following formula that locating information is transformed into the imaging coordinate system from sky, northeast coordinate system again:

$\left[\begin{array}{c}{x}_i\left(t\right)\\ y_i\left(t\right)\\ z_i\left(t\right)\end{array}\right]=\left[\begin{array}{ccc}{\cos \mathrm{\&beta;}}_{\mathrm{ref}}& -\sin {\mathrm{\&beta;}}_{\mathrm{ref}}& 0\\ \sin {\mathrm{\&beta;}}_{\mathrm{ref}}& \cos {\mathrm{\&beta;}}_{\mathrm{ref}}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_g\left(t\right)\\ y_g\left(t\right)\\ z_g\left(t\right)\end{array}\right]$

The translation motion error of utilizing following formula to try to achieve three change in coordinate axis direction in the imaging coordinate system is respectively:

$\left\{\begin{array}{c}\mathrm{\&Delta;x}\left(t\right)=x_i\left(t\right)-V_{\mathrm{ref}}\&CenterDot;\left({t-n}_0{T}_a\right)\\ \mathrm{\&Delta;y}\left(t\right)=y_i\left(t\right)\\ \mathrm{\&Delta;z}\left(t\right)=z_i\left(t\right)\end{array}\right.$

In the 3rd step, calculate the course velocity error;

Utilize following formula to calculate the speed of a ship or plane V of current time t airborne platform along the Desired Track direction _a(t):

V _a(t)＝V(t)·cos[β(t)-β _ref]

Then, calculate V _a(t) and V _RefBetween relative error V _Err(t):

V _err(t)＝V _a(t)-V _ref

According to relative error V _Err(t) pulse recurrence interval of adjustment UWB SAR (Pulse Repeat Interval is called for short PRI) guarantees that UWB SAR can realize along the uniform sampling of Desired Track direction;

In the 4th step, calculate the direction of visual lines kinematic error;

Be located at that the nearest oblique distance of certain point and Desired Track is R in the imaging region of current time t _B, the direction of visual lines kinematic error of calculating this some correspondence according to following formula is:

Δr(R _B，t)＝Vx(t)cos[Ψ(R _B)]-Vz(t)sin[Ψ(R _B)]

In the following formula, Ψ (R _B) be R _BCorresponding depression angle;

Calculate the empty constant sight line error delta r (R of distance of UWB SAR according to following formula _S, t):

Δr(R _S，t)＝Vx(t)cos[Ψ(R _S)]-Vz(t)sin[Ψ(R _S)]

In the following formula, R _SBe the reference oblique distance of current time t mapping band center line to UWB SAR;

Is Δ r according to following formula calculating UWB SAR apart from space-variant sight line error _II(R _B, t):

Δr _II(R _B，t)＝Δr(R _B，t)-Δr(R _s，t)

Utilize the empty constant sight line error delta r (R of distance _S, t) with apart from space-variant sight line error delta r _II(R _B, t), the penalty function of generated error is realized the direction of visual lines kinematic error compensation of current time t to Airborne UWB SAR.

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