An Iterative Approach for Moving Target Detection ...

Invited Paper

An Iterative Approach for Moving Target Detection and Geolocation in SAR Thomas L. Lewis*a, Atindra K. Mitra, Ph.D.a, Arnab K. Shaw, Ph.D**b a Air Force Research Laboratory; bWright State University ABSTRACT We propose a novel approach to focus and geolocate moving targets in synthetic aperture radar imagery. The initial step is to detect the position of the target using an automatic target detection algorithm. The next step is to estimate the target cross-range velocity using sequential sub-apertures; this is done by forming low resolution images and estimating position as a function of sub-aperture, thus yielding an estimate of the cross-range velocity. This cross-range estimate is then used to bound the search range for a bank of focusing filters. Determining the proper velocity that yields the best focused target defines an equation for the target velocity, however both components of the targets velocity can not be determined from a single equation. Therefore, a second image with a slightly different heading is needed to yield a second focusing velocity, and then having a system of two equations and two unknowns a solution can be obtained. Once the target velocity is known the proper position can be determined from the range velocity. Synthetic data will be used with a point source target and both background clutter and noise added. The results support the development of staring radar applications with much larger synthetic aperture integration times in comparison to existing SAR modes. The basic idea of this approach is to trade-off the development of expensive phased-array technology for GMTI applications with the potential development of advanced processing methods that show potential for processing data over very large aperture integration intervals, to obtain similar GMTI geolocation results that would be compatible with current radar technology. Keywords: SAR, Moving Target Detection, Geolocation

1. INTRODUCTION GMTI is the most common approach to exploit moving targets, while SAR is typically reserved for stationary targets or other stationary items of interest such as buildings. GMTI relies on the Doppler frequency shifts induced by the targets motion to separate it from the stationary background clutter [1]. This allow a GMTI algorithm to find, and track moving targets, however when the targets velocity falls below the minimum detectable velocity (MDV) the GMTI system loses the target and subsequence tracks. Therefore, it would be desirable to have a system that pushes the MDV to zero, such as a method that uses SAR, which is the design of our approach. A typical SAR sensor is deployed with the radar side-looking, 90 degrees from aircraft path, and when collecting SAR data the platform motion generates Doppler frequency shifts which are directly proportional to the aircraft velocity, VA, and the distance a particular source is from boresight. That is to say that the further an object is from boresight then the larger the induced Doppler velocity, VD, this is caused by the fact that relative to the aircraft the objects on the ground appear to be moving, as shown for various points below in figure 1. In SAR processing it is assumed that all the returns are from stationary sources, therefore any measured Doppler frequency shifts are interpreted as the result of platform motion only.

Algorithms for Synthetic Aperture Radar Imagery XIII, edited by Edmund G. Zelnio, Frederick D. Garber, Proc. of SPIE Vol. 6237, 62370W, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.666560

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Figure 1 Diagram Showing Induced Doppler Velocities for Various Points on the Ground. Therefore, when a moving target has Doppler velocity, VD, induced by its motion paired with the fact that the SAR processing assumes everything is stationary, will result in the shift of the targets position in the cross-range direction. An example of this phenomenon is shown in figure 2, where the moving targets on the right have the same Doppler velocity as the stationary targets on the left. This would result in the moving targets appearing at the same location of the stationary objects.

/ I I

I

Figure 2 Diagram Showing Induced Doppler Velocities for Various Points on the Ground. Another phenomenon is the fact that moving targets tend to smear in cross-range due to the along-track component of the velocity. It will be shown that the smearing can be focused using a series of focusing filters, and that the translation can be corrected using two SAR images with different aircraft headings

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Section 2 provides a description of the data set that is used for purposes of this investigation. Section 3 provides a discussion of the algorithms that were developed and implemented for purposes of generating simulation results. Section 4 provides a presentation of the simulation results. Conclusions and scope for future research are also discussed.

2. MOVING TARGET IMAGES The data for this investigation was synthesized using the Moving Target Signature Generator, a Matlab tool, acquired from ARFL/SNAS and developed by ATK Mission Research. This SAR generation tool calculates the video phase history for the moving target, and then uses a back-projection image formation algorithm to calculate the moving target response. The data generated consists of two SAR images of two moving point-source targets each with constant linear velocity. The images were taken in succession with a one second delay between the apertures, and with the aircraft at different headings, as shown in Figure 3.

5100 5000 4800 4800 4700 300 250 200 ISO IOU

50 U

-50 -300

-200

-lOU

U

—4——Aircraft

lOU

Targeti

2UU

3UU

4UU

500

Tarqet2

Figure 3: Aircraft and Moving Target Trajectories for the Given Dataset The magnitude of the aircraft velocity was 100 m/s and the first target (Target1) had a velocity of 5 m/s in the x direction while the second target (Target2) had a velocity of 5 m/s in both the x and y directions, for both images. The SAR parameters were chosen to model an X-band system, with a center frequency of 9.66 GHz, a bandwidth of 600 MHz and integration time of three seconds, as shown in Table 1. Table 1: SAR Parameters

SAR Parameters Center Frequency Bandwidth PRF Integration Time

9.66 GHz 600 MHz 1000 Hz 3s

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Image 1

Target 1 & 2

Image 2

Target 2

Target 1

Figure 4: Synthetic SAR Images The SAR images of the moving point-source targets that were generated and used for the following investigation are shown in figure 4. Notice the point-source targets have smeared so extensively that they no longer resemble pointsources. Also note that the point-source positions and velocities were chosen such that they coincide in the first image. Gaussian noise and background clutter of various levels were added to the images. The equations for the noise and background clutter are shown in Eq. (1).

σ T = σ A + MNR * σ o

(1)

Where σA is additive noise component and σo represents the average background clutter and MNR is the multiplicative noise ratio. [2] A couple of example image chips are illustrated in figure 5. Shown are the original image and images with signal-to-background ratios (SBR) of 7.3 dB and 5.5 dB.

No Noise

SBR = 7.3 dB

SBR = 5.5 dB

Figure 5: Synthetic SAR Images with Various Levels of Noise Added

3. TARGET VELOCITY ESTIMATION AND FOCUSING ALGORITHMS The block diagram shown below in figure 6, points out that the first step is to create the SAR images which was described in the previous section. The next step is to form sub-aperture images, which will be used to estimate the crossrange velocity; this process is outlined in section 3.1. Once the velocity is estimated, focusing filters are applied to obtain an equation for the target’s velocity; this step is discussed in section 3.2. A metric that will allow future

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automation of this focusing process is outlined. The next stage is to repeat the process for the second image, and obtain a second equation for the target’s velocity. From the two equations both components to the target’s velocity can be accurately calculated and then the true target location can be determined, this is shown in section 3.3. No Create SAR Images

Sub-aperture Processing/ Estimate Velocity

Apply Focusing Filter

Focused?

Yes

Repeat Process for Second Image

Figure 6: Algorithm Block Diagram 3.1 Sub-Aperture Processing for Estimation of Target Cross-range Velocity The first step in estimating the target velocity is to form sub-aperture images. This is accomplished by dividing up the aperture into equal slices. The width of the slices needs to be chosen in such a way that multiple sub-apertures can be taken to form multiple low resolution images, hence giving a good representation of how the target position varies with time (sub-aperture). Also, the slice needs to be large enough to form a suitable image. In this investigation, we chose a sub-aperture time of 1/3 second, which equates to 333 pulses, given the PRF equal 1000 Hz. Figure 7 shows the 333 pulse sub-aperture images; notice the progression of the target in cross-range vs. sub-aperture. It is precisely this progression that allows the approximation of the cross-range velocity.

Figure 7: Sub-aperture Images The cross-range velocity can be estimated by calculating the distance the target moves per time interval [3], this is shown in Eq. (2).

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∆ xδx 2∆t

v XR ≈

(2)

Where ∆x is the number of pixels the target moved in time interval ∆t, and δx is the cross-range pixel spacing. The number of pixels the target moved, ∆x, was determined by tracking the centriod of the five brightest target pixels in each sub-aperture image. Once each ∆x was calculated the average was taken to generate the estimated cross-range velocity, this is shown in Eq. (3, 4 & 5). 5

∑P

xi =

n ,i

n =1

(3)

5 N −1

∆xi = ∑ xi +1 − xi

(4)

i =1

N

∆x =

∑ ∆x

i

i =1

(5)

N

Here Pn,i is the cross-range position of the nth brightest pixel in the ith sub-aperture, and xi is the centroid of the five brightest pixels. ∆xi is the number of pixels between the successive N sub-aperture centroids, and ∆x is the average pixel distance the target moves throughout the whole sub-aperture. 3.2 Focusing Filter Jao [4] has shown that the target smearing that results from cross-range motion can be modeled by a single parameter, the relative velocity VRel. Therefore a bank of Jao filters tuned to specific cross-range velocities would yield a focused target at the correct target velocity. However, another way to implement a Jao type filter would be to subtract the targets velocity from the aircraft’s velocity and re-form the image assuming the aircraft’s velocity had the same magnitude of the resulting velocity, VRel , but in the same direction as before. This result is illustrated in figure 8. This would have the effect of the target appearing to be stationary in the cross-range direction, resulting in a focused target. One side effect of this process is that any stationary targets would then become defocused as if they where moving at the actual targets velocity but in the opposite direction.

VA -VT VRel VTr

VTxr Figure 8: Calculation of Focusing Filter Velocity

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Where VA is the true aircraft velocity, VT is the targets velocity, and VRel is the result of VA – VT. Once the image is formed with the magnitude of the aircraft’s velocity set to VRel and having the same direction as VA the moving target will be focused. A method to allow for automation of this process has been developed, the procedure calculates the 3db with of the defocused target smear. The VRel is adjusted in such a way to minimize the 3db width, the process will automatically settle on the best focusing velocity. 3.3 Translation Correction and Range Velocity Determination The range velocity of a moving target can not be estimated in the same manner as the cross-range velocity, this is due to the fact that the target does not appear to have range movement in the SAR image, which can be seen by taking another look at figure 7. However, the calculation of the focusing filter will lead to a relationship between the relative velocity, VRel, and the targets velocity. Once the second focusing velocity is determined, the range velocity can be calculated. The range velocity introduces a Doppler frequency shift which causes the target to be relocated. The distance the target is translated is a function of the range velocity VTr [5], as shown in Eq. (6).

∆ XR ≈

vTr R vA

(6)

Where ∆XR is the distance the target is translated in cross-range, VTr is the component of the targets velocity in the range direction, VA is the aircraft velocity, and R is the minimum distance between the aircraft and the target. Let’s take a closer look at the focusing velocity calculated in the prior section. The magnitude of this velocity is calculated as follows in Eq. (7).

vRel = (vax − vTx )2 + (vay − vTy )2

(7)

In the previous section the calculation of the VRel was shown, and even though we know the aircraft velocities Vax and Vay, we still have two unknowns, and a unique solution can not be determined. However we have two images, therefore we can write two equations using the corresponding focusing velocities, and with two equation and two unknowns we can calculate a unique solution.

4. SIMULATION RESULTS AND CONCLUSIONS The results are shown in two sections starting with section 4.1, which shows the results from the sub-aperture processing and estimation of cross-range velocity, also the results from the focusing filtering process which produces further refinement of the velocity are discussed here. Section 4.2 shows the results of the translation correction for both images and the determination of the proper range velocity as well as target location. Lastly, section 4.3 will state the conclusions and address future work. 4.1 Cross-range Velocity Determination For image one the sub-aperture processing method for calculating the cross-range velocity yielded velocities of 4.77 m/s, 4.83 m/s, and 0.62 m/s for the cases without noise, with SBR=7.3dB and SBR=5.4dB,respectively. Where the actual cross-range velocity was 5 m/s, see Table 2. Similarly, for target one in image two, the sub-aperture method yielded cross-range velocities of 0.28 m/s, 0.28 m/s and 0.51m/s, while the true velocity was 0 m/s. Also, for target two in image two, the sub-aperture method yielded cross-range velocities of 4.32 m/s, 4.27 m/s and 0.67m/s, while the true velocity

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was 3.56 m/s. Notice that the results for SBR=7.3 dB agree quite well with the no noise case, however the algorithm breaks down when the SBR approached 5.5 dB. Table 2: Cross-range Velocity Estimates Estimated Velocity

True Relative Velocity

Focusing Velocity

5 m/s 0 m/s 3.56 m/s

95.1 m/s 100.25 m/s 96.52 m/s

No Noise SBR=7.3dB SBR=5.5dB

Image 1 Image 2, Target 1 Image 2, Target 2

4.77 m/s

4.83 m/s

0.62 m/s

0.28 m/s

0.28 m/s

0.51 m/s

4.32 m/s

4.27 m/s

0.67 m/s

(0

2

II

(0 9)

-

(0

(0

K)

2

J,

f!%

II

(0 9) 0)

C

In Figure 9 below is a visualization of the width of the de-focused target smear as a function of the focusing velocity, as discussed in section 3.2. From this illustration it can easily be seen that a focusing velocity of 96.5 m/s results in a much more sharply focused target, and note from Table 2 the final focusing velocity was 96.52, which was gotten by iterating between 96.5 and 96.6 m/s.

Figure 9: Illustration of De-focused Target Smear Widths Figure 10 shows sample images after the relative velocity was used to in place of the true aircraft velocity in the image formation of the SAR images. The relative velocities, VRel, for this figure are as follows, from top to bottom, 95 m/s, 96 m/s, 97 m/s, 98 m/s, 99 m/s and 100 m/s. Notice that the smear on the left (target 2) appears most focused in the 96 and 97 m/s images while the smear on the right (target 1) appears most focused in the 100 m/s image. Again referring to Table 2, it can been seen that the final focusing velocity for target 1 was 100.25 m/s and the final focusing velocity for target 2 was 96.52 m/s.

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VReI = 95 mIs VReI = 96 mIs VReI = 97 mIs VReI = 98 mIs

VRel=99m/s VReI

100 mIs

Figure 10: Application of Relative Filter Velocity 4.2 Range Velocity Determination Now we have two equations and two unknowns. See Eq. (8 & 9) for target one in image one and two respectively, and Eq. (8 & 10) for target two in image one and two respectively. However the equations are quadratic and a numeric solution is not easily obtained. One simple method to solve the equations is to graph the equations and determine where the equations intersect.

95.04 = (100 − vTx ) 2 + (0 − vTy ) 2

(8)

100.25 = (100 cos θ − vTx ) 2 + (100 sin θ − vTy ) 2

(9)

96.52 = (100 cos θ − vTx ) 2 + (100 sin θ − vTy ) 2

(10)

The resulting graph is shown in figure 11. Notice that for target one the intersection occurs at (4.96, 0.05), and therefore the y-component of the targets velocity was determined to be 0.05 m/s and the x-component of the velocity was 4.96 m/s. Notice that the real target one had a velocity of 5 m/s in the x direction. Also the graph shows that for target two the intersection occurs at (5.09, 5.08), and therefore the y-component of the targets velocity was determined to be 5.08 m/s and the x-component of the velocity was 5.09 m/s, the actual target two had a velocity of 5 m/s in both the x and y directions.

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(5.09,5.08)

1

4.2

44

45

48

0.05)

6

5

x-component of velocity (mis) Figure 11: Determination of Range Velocity Now that the velocities have been calculated we can use Eq. 5 to determine the correct position of the targets. For target one the shifts were calculated to be 2.5 m and 17.7 m, for image one and image two respectively. Also for target two this calculation yields shifts of 254 m and 349.7 m, for image one and image two respectively. See Table 3 for a comparison to the true target positions. Table 3: Cross-Range Translation Amounts (Calculated/Actual) Image 1 Image 2

Target 1 2.5m / 0m 17.7m / 21m

Target 2 254m / 263m 349.7m / 352m

Figure 12 graphically compares the calculated position of the target with the true position, also the point at which the defocused target smear materialized is shown. The lines show constant range profiles, one for image one and two line for image two. One for each target smear. Recall that image two was taken with a one second delay and the integration time was three seconds, therefore a four second time differential exists, consequently the target positions vary from image one and two.

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Image 2

C

Figure 12: Target Position 4.3 Conclusion and Future Directions The velocity and correct position of a moving target was calculated using two successive SAR images. The calculation of both the x-component and y-component of the target velocity was fairly accurate for both targets. Also recall that the target overlapped in the first image, leaving the appearance of a single target. However this method using two SAR images from distinct headings separates the targets and correctly geolocates them within 10 m. Also it has been proposed that an automatic determination of when the best focus occurs, instead of the current method of aided visual inspection. Creation of a metric for this purpose has been discussed, however a truly automatic algorithm has not been implemented. This would allow for the automatic determination of the focusing velocity. Clutter or noise added were added to the SAR images, however since the modeling was done in the image domain the effects of varying the focusing velocity on the noise could not be examined, therefore it only clean images were used after the sub-aperture cross-range velocity estimation step. Hence, in the future it would be interesting to model the effects of both background clutter and noise in the video phase history (VPH) domain. This would allow for more accurate images and stationary clutter would become defocused as the focusing velocity is varied. Other future directions include trading off the amount of change in aircraft heading with the performance of the velocity estimation, thereby determining the amount of heading variation needed to accurately determine the moving target parameters. Another avenue of exploration might be to generate data with a more realistic curved path for the aircraft and more realistic target motion. This could support the development of staring radars which have much longer synthetic aperture integration times.

ACKNOWLEDGEMENTS The authors would like to acknowledge Dr. Michael Minardi and LeRoy Gorham, from AFRL/SNAS for the technical consultations and delivery of the Matlab moving target generation tools, and Edmund Zelnio, from AFRL/SNA, for initial guidance and problem formulation.

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REFERENCES 1. 2. 3. 4. 5.

Skolnik, M. I., Introduction to Radar Systems, 3rd ed., New York: McGraw-Hill, 2001 Walter G. Carrara, Ron S. Goodman, Ronald M. Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Artech House: Boston, 1995 K. Ouchi, “On the Multilook Images of Moving Targets by Synthetic Aperture Radars.,” IEEE Trans. Antennas and Propagation, Vol. AP-33, No. 8, pp. 823-827, 1985 J. Jao, “Theory of Synthetic Aperture Radar Imaging of a Moving Target,” IEEE Trans. Geosci. Remote Sensing, Vol. 39, No. 9, pp 1984-1992, Sept. 2001 M. Kirscht, “Detection, Velocity Estimation and Imaging of Moving Targets with Single-Channel SAR,” in Proc. EUSAR ’98, pp 587-590

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