(yingwen)运动误差对机载双基SAR定位精度的影响1

Influence of the Motion Errors to Airborne BiSAR

Geolocation Accuracy

Ya Li

Yong Li

College of Electronic and Information Engineering, Nanjing University of Astronautics and Aeronautics

No.29 Yudao Street, Nanjing, 210016 China

limack@nuaa.edu.cn

Abstract—The image based geolocation accuracy is important in evaluating the performance of the bistatic synthetic aperture radar (BiSAR) system. Most of the errors are originated from the insufficient measurement accuracy of the motion parameters. In this paper, given the BiSAR geometric model, the influence on geolocation accuracy caused by the transmitter's motion errors from the viewpoints of imaging is mainly analyzed. The Newton iteration method is a method used to solve the nonlinear equations.Mathematic expressions can be derived using the Newton iteration method .Using the derived mathematic expressions in the text, the simulation results are provided to show the quantitative impact of motion errors on the image and target positioning.

Keywords-bistatic synthetic aperture radar (BiSAR); geolocation; parameter error

I. INTRODUCTION

Geolocation accuracy is one of the key terms applied to evaluate performance of synthetic aperture radar (SAR) systems, whose definition is the degree of closeness between the spatial entity's coordinate-dates and the real position of the entity. Those evaluated performance by the location-error is significant to SAR application: in the military reconnaissance, decision-makers have to strictly positioning targets on the ground; in the ocean surveillance, vessel monitoring and sea rescues have to accurate positioning the ships.

Bistatic synthetic aperture radar (BiSAR) has separated transmitter and receiver[1].Compared with the monostatic SAR, BiSAR has many advantages such as longer detection range, access to more abundant information, higher mobility and higher elu-sivness, better ECCM capability and anti-intercept capability, hence BiSAR has stronger living ability. These

advantages make BiSAR be promising in military application[6].

The factors that can influence positioning accuracy of the airborne SAR include motion errors of the transmitter and receiver, the height errors,etc. In this paper, the influence to the positioning accuracy because of the motion errors caused by the transmitter is mainly analyzed from geometrical model of the BiSAR [2][3].

II. GEOMETRICAL MODEL OF BISAR The Figure.1 is the geometric model of the bistatic SAR. Assume that the transmitter and receiver flying at velocities of Vtand Vrrespectively, and assume that the platforms are not parallel. Relative to the reference point on the ground, the squint angles respectively are?tand?rat the zero moment.Rstand Rsr are the ranges between the radar APC and the reference points.

Transmitting stationVtZ?tReceiving stationVrRst?rRsrXY

Figure 1. Geometric model of BiSAR

At t , the slope range is

R(t)?Rr(t)?Rt(t)

(1)

where

??Rt(t)?Rst2-2?Vt?t?Rst?sin(?t)?(Vt2??t)(2) ??Rr(t)?Rsr2-2?Vr?t?Rsr?sin(?r)?(Vr?t)2III.

FORMULA DEDUCTION

The imaging area will not be changed though there are errors, still in the effect of the wave. However, the position of the reference point will be changed because of the motion errors[2].

A. Influence caused by the motion errors to the imaging Linear Range-Doppler(LRD) algorithm will be applied in the imaging processing[7], the motion errors will change the ranges and the Doppler-frequency, so the position of the reference point will be changed, hence, the position of the targets on the ground also be changed. The variation of the ranges will cause distance-drift, and the variation of the Doppler-frequency will cause

azimuth-drift.

Distance variation caused by the motion errors can be expressed as follows:

?r?(Xt?Xo)2?(Yt?Yo)2?Ht2?(Xr?Xo)2?(Yr?Yo)2?Hr2 (3)

?(Xt?Xo')2?(Yt?Yo')2?Ht2?(Xr?Xo')2?(Yr?Yo')2?Hr2Where

（XO,YO,0）is the coordinate of the reference point before introducing errors, and

（XO',YO'，0）is the coordinates after introducing errors. We can obtain the

drift units at the range-direction:?Nr??r/pr,where pr is resolution in slant range . Doppler-frequency variations caused by the motion errors can be expressed as follows:

?f1Vtx(Xo?Xt)?Vty(Xo?Xt)?Vtz?Htd??(Xo?Xt)2?(yo?Yt)2?Ht2?1Vrx(Xo?Xr)?Vry(Yo?Yr)?Vrz?Hr?(Xo?Xr)2?(Yo?Yr)2?Hr2?1(Vtx?Vex)(Xo'?Xt)?(Vty?Vey)(Yo'?Yt)?（Vtz?Vez）?Ht?(Xo'?Xt)2?(Yo'?Yt)2?Ht2-1(Vrx?Vex')(Xo'?Xr)?(Vry?Vey')(Yo'?Yr)?（Vrz?Vez'）?Hr?(Xo'?Xr)2?(Yo'?Yr)2?Hr2 (4) Where （Vtx,Vty,Vtz）and（Vrx,Vry,Vrz）are the velocities of the transmitter and the receiver at X,Y,Z directions. （Vex,Vey,Vez）, （Vex‘,Vey’,Vez‘）are the velocity-error of

the

transmitter and the receiver.?Na??fdPRFNa, where PRF is the pulse

repeat frequency. PRF/Na is resolution in azimuth. B. Influence to the positioning

The motion errors cause the image drift, hence there must be positioning errors.

?fp?fdc?(m??N?a?Na/2)?PRF/Na?R?Rref?(n??N/2)?p (5) r?Nrrwhere,

Rref?（Xt?Xo）2?(Yt?Yo)2?(Zt?Zo)2 (6)

?(Xr?Xo)2?(Yr?Yo)2?(Zr?Zo)2 Where,mand nare coordinates of the corresponding

point in simulated imaging .Using the Newton iteration

method[8],new coordinate of the target

（Xp',Yp',Zp'） can be deduced.If there are no errors, the coordinate of the target is （XP,YP,ZP）. So the positioning error is :

??Xp?Xp'?Xp???Yp?Yp'?Yp(7)

?E??Xp??Yp22 (8)

IV SIMULATION RESULTS

According to the relative theory about imaging and targets positioning[4][7][9][10][11]. As is showed in figure 1 the reference point O is located at the origin of coordinate system, parameters are setted as table1. To deduce the influence caused by velocity errors of the transmitter at X-direction or Y-direction. The error-band is(-1.0m,1.0m) at regular interval, such as 0.1m.

TABLE 1

SIMULATION PARAMETERS

parameters Transmitter values Receiver values Figure 2. Positioning-error

Velocity in X direction 140.9m/sec 76.6m/sec Velocity in Y direction 51.3m/sec 65.0m/sec Velocity in Z direction 0m/sec Altitude 8000m 500m Center frequency Range bandwidth Doppler bandwidth X Band 80MHZ 2500HZ

Slope ranges 50000m 9000m Figure 3.Position-errors with different velocities

Squint angles 35.5° 40.0° Table 2 shows the geolocation-error caused by velocity error of transmitter at X-direction :

TABLE 2

POSITIONING-ERROR CAUSED BY MOTION-ERROR

IN X-DIRECTION

velocity 150m 100m

The influence caused by motion errors when the velocity of the transmitter is 150m/s is analyzed, the figure following is ?Ewhen the band of Vex and

Vey is (-1.0m,1.0m),at regular intervals, such as

Velocity-errors(m/s) -1.0 -0.5 0.5 1.0 0.1m.Figure 3 as following shows the different position-errors with different velocities in X-direction.

Positioning-errors(m) 113.247 56.445 56.093 111.837 Table 3 shows the influence caused by velocity error

of transmitter at Y-direction :

TABLE 3 POSITIONING-ERROR CAUSED BY MOTION-ERROR

IN Y-DIRECTION

Velocity-errors(m/s) -1.0 -0.5 0.5 1.0 Positioning-errors(m) 308.488 154.77 154.421 308.898 Next, the influence in positioning-errors caused by detection range will be considered. That the influence will be analyzed when the detection range is either 40km or 60km.Table 4 shows the different positioning-errors with different detection-ranges, positioning-errors(1) shows the errors when the detection-range is 40km and (2) shows the errors when the detection-range is 60km.

TABLE 4 DIFFERENT POSITIONING-ERROR WITH

DIFFERENT RANGES

Velocity-errors(m/s) -1.0 -0.5 0.5 1.0 Positioning-errors(1)(m) 89.925 44.821 44.541 88.806 Positioning-errors(2)(m) 136.441 68.006 67.581 134.742 According to table 2 and 4 ,we know that the positioning-error will increase with the increasement of the detection ranges .Also, that the positioning-error decrease as the velocity increase can be seen under the same parameters, as following table 5.Table 5 shows the different influence when the velocity at X-direction is either 140m/s or 160m/s.(1) shows the influence when the velocity is 140m/s, and (2) shows the influence when the velocity is 160m/s.

TABLE 5 DIFFERENT POSITIONING-ERROR WITH

DIFFERENT VELOCITIES

Velocity-errors(m/s) -1.0 -0.5 0.5 1.0 Positioning-errors(1)(m) 121.391 60.491 60.0865 119.772 Positioning-errors(2)(m) 106.127 52.907 52.597 104.888 V CONCLUSION

In this paper,the LRD algorithm and the Newton iteration method were used in research of the influences of the motion errors in airborne BiSAR geolocation accuracy .The relationship between velocity difference and position-error was deduced. Also, the relationship between the detection-range difference and the position-error was deduced. As the simulation results show that the relative theories introduced and analyzed in section III are reasonable .In later study, we'll consider the influence of other parameters.

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