moving targets velocity estimation using aliased sar raw ... - CiteSeerX

MOVING TARGETS VELOCITY ESTIMATION USING ALIASED SAR RAW-DATA FROM A SINGLE SENSOR1 Paulo A. C. Marques * , Jos´e M. B. Dias ** *

ISEL-DEEC, R. Conselheiro Em´ıdio Navarro 1,1949-014 Lisboa, Portugal Fax: +351.21.218317114, E-mail: [email protected] ** IST-IT, Torre Norte, Piso 10, Av. Rovisco Pais, 1049-001 Lisboa, Portugal Fax: +351.21.8418472, E-mail: [email protected]

ABSTRACT This paper presents a new methodology to retrieve slantrange velocity estimates for moving targets with speeds inducing Doppler-shifts beyond the Nyquist limit imposed by the Pulse Repetition Frequency (PRF ). The proposed approach exploits the linear dependency of the Dopplershift with the slant-range velocity for each fast-time frequency. Therefore, the echo from a moving target in the twodimensional spectral domain exhibits a skew depending on the target range-speed that is not subject to PRF limitations. By combining the developed scheme to retrieve the slantrange velocity with a methodology proposed elsewhere to estimate the velocity vector magnitude, the full velocity vector is unambiguously retrieved without the need to increase the mission PRF . The effectiveness of the method is illustrated with simulated and real data.

1

INTRODUCTION

It is well known that a moving target induces a Dopplershift and a Doppler-spread on the returned signal in the slow-time frequency domain [1]. Most techniques proposed in recent literature take advantage of this knowledge to image moving targets and estimate their velocity parameters [2], [3], [4], [5]. The cross-range velocity of a moving target is responsible for the spread in the slow-time frequency domain, whereas the range velocity is responsible for the Doppler-shift. Given a PRF , the Doppler-shift fD vx =, where vx is the target slant-range velocity and  denotes the signal wavelength, is confined to jfD j  PRF= . If the Doppler-shift exceeds PRF= , it has been generally accepted that the true moving target range velocity cannot be uniquely determined using a single antenna and a single pulse scheduling [6], [7]. Classical solutions to resolve such targets with a single antenna consist in increasing the PRF [6] or, alternatively, in using a non-uniform PRF as proposed in [7] and [8]. Increasing the PRF leads to a decrease of the unambiguous range swath, besides larger memory requirements to store the received signal. The use of a non-uniform PRF requires a non-conventional pulse scheduling. Moreover, non-uniform sampling introduces higher complexity in image reconstruction. Using typical SAR mission parameters, a single sensor, and uniform pulse scheduling, we readily conclude that the maximum unambiguous range velocity is usually very small [9]. The approach herein proposed to estimate the range velocity of moving targets with velocities above the maximum

=2

2

2

1 This work was supported by the Fundac ¸ a˜ o para a Ciˆencia e Tecnologia, under the project POSI/34071/CPS/2000.

imposed by the PRF is based on the linear dependency of the Doppler-shift with the slant-range velocity for each fasttime frequency. In the two dimensional frequency domain, a moving target echo exhibits a skew which is not subject to PRF limitations. In reference [10] this fact has already been exploited to retrieve the correct PRF band with application to low contrast static ground scenes in spaceborne SAR, where the ground behaves as a moving target due to the earth rotation relatively to the radar platform. The technique proposed therein works by applying a linear regression on the estimated Doppler centroids at each fast-time frequency. The problem that we are dealing with in this work cannot be solved by the same technique, because we are interested in the returns from near point-like moving targets (man-made objects), that move relatively to the static ground. Even after digitally spotlighting the moving target signatures [9], the static ground echoes exhibit sufficient power to corrupt the estimates given by a simple spectral centroid estimator. We will present a technique that is able to cope with this scenario. The estimation results are good, even in the situation where the static ground echoes are completely superimposed, in the frequency domain, on the echoes from the moving objects

2

PROPOSED APPROACH

(

)

In [2] we have shown that the returned echo A ku ; k from a moving target takes, in the slow-time frequency domain ku , and fast-time frequency domain k = ( is the wavelength), the shape of the two-way antenna radiation pattern g according to,

=2



 1 A(ku ; k) / g 2 (ku , 2k) :

(1)

Relatively to a static target, the shape g becomes shifted by k and expanded by  va =V , where  vx =V denotes the moving target relative slant-range velocity with respect to the sensor velocity V , va is the target cross-range speed. If the transmitted pulse has bandwidth B , then k is confined to

2

= (1 +

)

=

B kmin = , B c + k0  k  k0 + c = kmax ;

=2

(2)

where k0 =0 , 0 is the carrier wavelength and c is the propagation speed. For a moving target with relative slantrange velocity , one see from equation (1), that the returned signal S ku ; k will exhibit a slope of  along the k axis, as illustrated in Fig. 1. In this figure, kuend and kustart denote the Doppler-shifts at the fast-time frequencies kmax and kmin , respectively. In the absence of noise, kuend and kustart

(

)

2

(

kuend

RSS (
ku ; k; k +
k) =

2k k u= ku

k k0

kmax

Figure 1: Returned signal from a moving target with relative slant-range velocity . could be inferred using a simple spectral centroid estimator. In this situation the relative velocity would thus be estimated as b b b = 2(kukend ,,kukstart) ;

max

(3)

min

and would not be restricted to the maximum value imposed by the PRF . The use of a spectral centroid estimator as proposed in [10] will not work for moving targets because the returned signal co-exists with the clutter returns, in the 2D spectra. Even after digitally spotlighting the moving targets signatures as proposed in [9], the clutter returns are strong enough to corrupt the estimates given by a centroid estimator1 . We show in [11] that if the number of static scatterers is large, none is predominant, and they are uniformly distributed within a wavelength, then the correlation of the static ground returns, in the ku ; k domain decays very quickly. Concerning moving targets, the same is not true as will be seen in the next subsection. The signal echoed from the moving targets have statistical properties that are quite different from those of the clutter. In this work we will exploit those properties to derive a methodology to retrieve unaliased estimates of the moving targets slant-range velocities.

(

)

2.1 MOVING TARGET SIGNATURE PROPERTIES The received signal from a moving target in the 2D frequency domain ku ; k , after pulse compression, is given by [2]

(

)

q

,
,j 4k2 , ku X ,j , ku
2 Y Sm (ku; k) = jP (!)j2 A(ku; k)fm e e ;

()

where P ! is the Fourier transform of the transmitted signal, fm is the moving target complex reflectivity, X; p Y are the 2  2 is motion transformed coordinates [9], and  the relative speed of the target with respect to the radar. k between The correlation function RSS ku ; k; k Sm ku ; k and Sm ku ; k k with respect to ku is

)

2


)

(

Z

+
)

(


( ) = + +
)

RSS (
ku ; k; k +
k) = Sm (ku ; k)Sm (ku ,
ku ; k +
k)dku: ku

(4)

1 The digital spotlight operation has to be relaxed because, at this stage, the moving targets are defocused.



 

(5)


ku2 ,j
ku Y , 2
k, 4(k+
k)2 X 4 2 j P ( w ) j j f j e m Z  A(ku; k)A (ku , 2
k ,
ku ; k)ej dku ; ku

start

kmin

(

+
) = (

From (1) we can write A ku ; k k A ku , k; k . Using this fact and after some algebraic manipulation, we are lead to

ku

The last line of eq. (5) is a correlation between A(ku ; k ) and u
ku 2 X . If the phase A(ku , 2
k; k)e,j , where  = 4(2kk+
k)  has an excursion smaller than  in the ku interval equivalent to the antenna bandwidth, then RSS (
ku ; k; k +
k )

exhibits a maximum which is linearly dependent of the fasttime frequency by a factor equal to k. The phase  can be made negligible, for typical mission parameters, by compensating the dependency of X using the target area approximate slant-range coordinates.

2


2.2 PROPOSED METHODOLOGY Based on the the analysis made so far we propose the following methodology to estimate :

  

Estimate a rough location of the moving targets using one of the strategies proposed in recent bibliography (see eg. [4], [9], or [12]). Process the SAR raw-data as if there were only static targets. The moving targets will appear smeared and defocused. For each moving target: 1) Digitally spotlight the moving target image in the spatial domain and re-synthesize its signature back to the ku ; k domain as described in [9], obtaining the signal Sm ku ; k . This procedure reduces the contribution of the undesired static ground echoes. 2) Compute the correlation RSS between Sm ku ; k0 and Sm ku ; k for a set of discrete wavenumbers in the transmitted pulse bandwidth. As shown in (5), RSS shall display a maximum for each k at frequency ku k , k0 . 3) Perform a linear regression on the maximum values of RSS to estimate  and subsequently retrieve the target slant-range velocity.

(

) ^ (

)

^ (

)

= 2(

)

^ (

)

To retrieve the cross-range component of the object speed we can use a combination of methodologies, as already stated in the introduction. In the next section we will combine the scheme herein proposed to estimate , with the methodology p presented by Soumekh in [9] to estimate  2  2 . With the two quantities  and  at hand, the estimation of  is straightforward.

^

^

=

+

3 RESULTS The scheme proposed in the previous section will now be evaluated using synthetic and real data. The synthetic data set includes seven moving objects, six of them are point-like targets. The seventh target is an extended object with dimensions of 6 meters in range by 2 meters in cross-range. The signal-to-clutter ratio (SCR) is dB .

23

Table 1: Mission parameters used in simulation. Parameter Carrier frequency Chirp bandwidth Altitude Velocity Look angle Antenna radiation pattern Oversampling factor

Table 4: Mission parameters used with real data from MSTAR.

Value 9 GHz 250MHz 12Km 637Km/h

200

Raised Cosine 2

Parameter Carrier frequency Chirp bandwidth Altitude Velocity Look angle Antenna radiation pattern Oversampling factor

Value 9.6 GHz 250MHz 12Km 637Km/h

150

Raised Cosine 2

Table 2: Moving targets parameters. Target 1 2 3 4 5 6 7

x0

[m] -64 0 64 -64 0 64 0

y0

[m] -64 -64 -64 +64 +64 +64 0

vx

vy

[km/h] -13.2 -26.5 -52.9 13.2 26.5 52.9 52.9

[km/h] -36 -36 -36 36 36 36 0

jvxj

vmax 2.5 5 10 2.5 5 10 10

The mission parameters are presented in Table 1. The moving targets trajectory parameters are summarized in Table 2. The last column of this Table displays the ratio between the moving target slant-range velocity vx and vmax which denotes the maximum slant-range velocity allowed by the mission PRF . Notice that all the moving targets have range velocities several times higher than vmax . The proposed methodology was applied to all the moving targets in the scene. To retrieve the full velocity vector we combined the unaliased estimates of the range velocity herein obtained, with the  estimates obtained as proposed by Soumekh in [9]. The resulting full velocity vector estimates are very accurate as can be seen in Table 3. We will now apply the proposed strategy to real data from the MSTAR public collection. The clutter scene is taken from Huntsville, Alabama. The moving objects are two BTR-60 Transport vehicles. The optical and X-band images of this type of vehicle are presented in Fig. 2. The mission parameters for the generated data are presented in Table 4. The BTR-60 vector speed and coordinates are presented in Table 5. The SCR is roughly dB . Notice

23

Table 3: Complete velocity vector estimation by joining two methodologies (SCR=23dB). Target 1 2 3 4 5 6 7

(vx; vy )[km=h] (^vx ; v^y )[km=h] (-13.2,-36) (-26.5,-36) (-52.9,-36) (13.2,36) (26.5,36) (52.9,36) (52.9,0)

Table 5: BTR-60 Transport vehicle trajectory parameters.

(-13.25,-35.53) (-26.69,-35.78) (-53.21,-32.9) (13.24,32) (26.26,38.8) (52.5,37.33) (53.03,1.54)

Target 1 2

x0

[m] 75 180

y0

[m] 220 122

vx

vy

[km/h] 29.85 59.69

[km/h] 36 7.2

jvx j vmax 6 12

that the range velocities of both targets induce Doppler-shifts corresponding to 6 and 12 times the maximum unambiguous value imposed by the used PRF . The resulting data was focused using the wavefront reconstruction algorithm with static ground parameters. The obtained image is presented in Fig. 3, where the moving objects appear defocused and misplaced as expected. Each moving object signature was digitally spotlighted in the spatial domain and resynthesized back to the ku ; k frequency domain as proposed in [9]. The resulting resynthesized signature in the ku ; k domain is presented in Fig. 4 (magnitude) for illustration purposes only. The data resulting from the proposed correlation is presented in the same figure, on the bottom, where the maxima of the correlation changes linearly with the fast-time frequency as predicted. As we did in the previous subsection, we retrieved the full velocity vector using the estimates of  and the estimates of . In Table 6 we see that the obtained results have good accuracy.

(

(

)

)

4 CONCLUSIONS In this paper we have presented a novel methodology to retrieve unaliased estimates of the slant-range velocity of moving targets which induce Doppler-shifts beyond the Nyquist limit imposed by the mission PRF . We have shown that the method provides good results even when the returned echo is completely superimposed with those from the static ground, provided that the signature is digitally spotlighted. By combining the methodology proposed herein with an existing methodology to retrieve the velocity vector magnitude we have shown that it is possible to estimate the full velocity vector with good accuracy using aliased data from a single SAR sensor. The effectiveness of the proposed methodology was shown using a combination of real and simulated data with moving objects which have range speeds several times higher than the maximum imposed by the used Pulse Repetition Frequency.

Resynthesized signature (BTR-60+clutter) -3 -2

ku

-1

1

b)

a)

0

2

Figure 2: BTR-60 Transport vehicle a)optical b)X-band.

3 199

201 202 203 k Correlation result (BTR60+clutter)

50

-3

100

-2

150

-1

200

200

204

ku

Cross-range [m]

Huntsville Alabama, 2 BTR60 Superimposed

0

250

1 300

2 350

3 199 50

100

150

200

250

200

201 k

202

203

204

Range [m]

Figure 3: Scene from Hunstville - Alabama, where two moving BTR-60 transport vehicles are superimposed.

5 ACKNOWLEDGMENTS The authors would like to acknowledge the Air Force Research Laboraty (AFRL) and the Defense Advanced Research Projects Agency (DARPA) for MSTAR data they promptly made available to us.

6

REFERENCES

[1] R. Keith Raney, “Synthetic aperture imaging radar and moving targets”, IEEE Transactions on Aerospace and Electronic Systems, vol. AES-7, pp. 499–505, 1971. [2] P. Marques and J. Dias, “Optimal detection and imaging of moving objects with unknown velocity”, in Proc. of the 3rd European Conference on Synthetic Aperture Radar, EUSAR 2000, 2000. [3] S. Barbarossa and A. Farina, “Space-time-frequency processing of synthetic aperture radar signals”, IEEE Transactions on Aerospace and Electronic Systems, vol. 30, pp. 341–358, April 1994. [4] A. Freeeman and A. Currie, “Synthetic aperture radar (sar) images of moving targets”, GEC Journal of Research, vol. 5, pp. 106–115, 1987. [5] Genyuan Wang, Xiang-Gen Xia, Victor C. Chen, and Ralph L. Fiedler., “Detection, location and imaging of fast moving targets using multi-frequency antenna array sar (mf-sar)”, in Proc. of the EUSAR’2000, pp. 557–560, 2000. [6] S. Barbarossa, “Detection and imaging of moving objects with synthetic aperture radar”, IEE Proceedings-F, vol. 139, pp. 79–88, February 1992. [7] J. A. Legg, A. G. Bolton, and D. A. Gray, “Sar moving target detection using non-uniform pri”, in Proc. of the EUSAR’96, pp. 423–426, 1996.

Figure 4: Top: Re-synthesized signature of BTR-60. Bottom: Result of the proposed correlation for a moving target with slant-range velocity which is 12 times the maximum imposed by the mission PRF (Darker regions correspond to higher values). Table 6: Complete velocity vector estimation results using an association of methodologies (SCR=23dB). Target 1 2

(vx; vy )[km=h] (^vx; v^y )[km=h] (29.85,36) (59.69,7.2)

(29.05,38.91) (61.24,8.21)

[8] Xiang-Gen Xia, “On estimation of multiple frequencies in undersampled complex valued waveforms”, IEEE Transactions on Signal Processing, vol. 47, pp. 3417–3419, December 1999. [9] Mehrdad Soumekh, Synthetic Aperture Radar Signal Processing with MATLAB algorithms, WILEY-INTERSCIENCE, 1999. [10] R. Bamler and H. Runge, “Prf-ambiguity resolving by wavelength diversity”, IEEE Transactions on Geoscience and Remote Sensing, vol. 29, pp. 997–1003, November 1991. [11] P. Marques and J. Dias, “True doppler-shift estimation for moving targets with high range velocity using sar raw-data”, IEEE Tansactions on Aerospace and Electronic Systems, vol. (to be submitted). [12] D. Blacknell, “Target detection in correlated sar clutter”, IEEE Proceedings on Radar, Sonar and Navigation, vol. 147, pp. 9– 16, February 2000.