SANDIA REPORT SAND2009-1797 Unlimited Release Printed April 2009
Clutter in the GMTI Range-Velocity Map Armin W. Doerry Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000. Approved for public release; further dissemination unlimited.
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Clutter in the GMTI Range-Velocity Map
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SAND2009-1797 Unlimited Release Printed April 2009
Clutter in the GMTI Range-Velocity Map Armin Doerry SAR Applications Department Sandia National Laboratories PO Box 5800 Albuquerque, NM 87185-1330
Abstract Ground Moving Target Indicator (GMTI) radar maps echo data to range and range-rate, which is a function of a moving target’s velocity and its position within the antenna beam footprint. Even stationary clutter will exhibit an apparent motion spectrum and can interfere with moving vehicle detections. Consequently it is very important for a radar to understand how stationary clutter maps into radar measurements of range and velocity. This mapping depends on a wide variety of factors, including details of the radar motion, orientation, and the 3-D topography of the clutter.
Approved for public release; further dissemination unlimited.
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Acknowledgements This report was funded by the Joint DoD/DOE Munitions Program Memorandum of Understanding project. Thanks to Jeff Hollowell for reviewing an earlier draft of this report and identifying several needed corrections and enhancements.
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Contents Foreword ............................................................................................................................. 6 1 Introduction................................................................................................................. 7 2 The Range-Velocity Map............................................................................................ 9 2.1 Moving Target Range ....................................................................................... 11 2.1.1 Range Difference Expansion .................................................................... 11 2.1.2 Range Resolution ...................................................................................... 13 2.2 Moving Target Velocity.................................................................................... 15 2.2.1 Line-of-Sight Velocity Expansion ............................................................ 15 2.2.2 Velocity Resolution .................................................................................. 20 2.3 Clutter in the Range-Doppler Map ................................................................... 21 2.3.1 Flat Terrain in Straight and Level Flight .................................................. 22 2.3.2 Elevated Terrain in Straight and Level Flight .......................................... 25 2.3.3 3-D Topography Effects – Range Dependent Topography ...................... 27 2.3.4 3-D Topography Effects – Azimuth Dependent Topography................... 27 2.3.5 Flat Terrain – Radar Vertical Velocity ..................................................... 31 2.4 Antenna Beam Alignment................................................................................. 32 2.4.1 The Antenna Beam Pattern Model............................................................ 32 2.4.2 The Target Scene Projection Model ......................................................... 35 2.4.3 Target Scene Projection Examples ........................................................... 36 2.5 Clutter Motion................................................................................................... 40 2.6 Summary Discussion ........................................................................................ 41 2.7 Clutter Mitigation ............................................................................................. 41 3 Conclusions............................................................................................................... 43 Appendix A – The Phase History Model.......................................................................... 45 Reference .......................................................................................................................... 59 Distribution ....................................................................................................................... 60
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Foreword Recently, questions have arisen over the precise interrelationships of various parameters and characteristics in GMTI radar mode. More recently, new questions have arisen over the impact of target scene topography on GMTI false alarms. The need to account for scene topography is reasonably well-known, and Sandia-designed GMTI systems routinely include provisions to do so. This was discussed to some extent in a section of an earlier limited-release report.1 This report details the analytical basis for the GMTI range and velocity measurements, and how clutter is perceived by the GMTI radar.
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1 Introduction Ground Moving Target Indicator (GMTI) radar is a technique whereby a radar measures delay and delay-rate from a sequence of pulses, and infers a moving target’s range and velocity from these measurements. However, the transmogrification of the radar measurements into useful range and velocity calculations contains subtleties that may result in errors unless these subtleties are accommodated and the otherwise resulting errors are mitigated. This requires an appreciation for the finer points of range and Doppler interaction for radar echoes from moving vehicles in various radar and vehicle geometries and motion. For this report, we will limit ourselves to an exo-clutter GMTI mode, that is, GMTI from a single antenna phase-center. In the subsequent sections we address a number of issues, including (but not limited to) •
the accuracy of a target velocity measurement,
•
the location and shape of clutter in the range-Doppler map,
•
the effects of antenna rotation on target scene illumination, and
•
the effects of target area topography on velocity measurements.
Examples are given to illustrate these issues. Clutter A reasonable question is “Why is the location/shape of the clutter band important?” First, the width of the clutter band in velocity-space defines the Minimum Detectable Velocity (MDV) for an exo-clutter GMTI radar. Things that cause the clutter band to widen or narrow, also cause the MDV to change. Second, the clutter band denotes a ‘stay-out’ region where otherwise clutter is expected to generate an unacceptable degree of false alarm detections. As the clutter-band moves, so too should the stay-out region. Third, the location of the center of the antenna beam footprint in velocity-space defines the reference velocity for any moving target, that is, the difference between this velocity and the raw measured velocity of a target detection represents the best estimate of the target’s own range-rate. As the center of the beam moves in velocity-space, so too does the reference velocity.
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"Nothing happens until something moves." — Albert Einstein
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2
The Range-Velocity Map
A model for the video phase history data for a stretch-processed2 GMTI Coherent Processing Interval (CPI) is derived in Appendix A. It is expressed as
⎧ ⎛ 2γ T ,0 ⎞⎫ ⎟⎪ (1 − ζ 0 ) rs,0,0 − rc,0,0 Tsi ⎪ ⎜− c ⎟⎪ ⎪ ⎜ ⎜ ⎟⎪ 2ωT ,0 ⎪ vlos, s,0,0 − vlos,c,0,0 T p n XV (i, n ) = Ar exp⎨ j ⎜ − ⎟⎬ . c ⎜ ⎟⎪ ⎪ ⎟⎪ ⎪ ⎜ 4γ T ,0 ⎪ ⎜ + 2 rs,0,0 − rc,0,0 vlos , s,0,0 − vlos,c,0,0 T p n ⎟⎪ c ⎠⎭ ⎩ ⎝
(1)
⎞ ⎛ (vlos,s,0,0 − vlos,c,0,0 ) = ⎜⎜ rs (t0 + tc,0,0 ) − rc (t0 + tc,0,0 ) ⎟⎟ • vc − vlos,t ,0,0 ⎝ rs (t0 + tc,0,0 ) rc (t0 + tc,0,0 ) ⎠
(2)
(
)
(
)
(
)(
)
where
and individual parameters are identified as
i = the index for ADC samples of a single pulse’s echo data, n = the pulse index within a CPI, Ar = the target’s echo strength. ωT ,0 = the transmitted reference radian frequency,
γ T ,0 = the transmitted reference radian chirp rate, ζ n = a factor that depends on line-of-sight velocity (see Appendix A),
rs (t ) = the vector difference between radar location and target location, rc (t ) = the vector location of the radar with respect to the SRP, rs , n,i = the nominal range between radar and target,
rc, n,i = the nominal range between radar and SRP, v c = the radar velocity vector, vlos , s , n,i = the nominal line-of-sight velocity between radar and target,
vlos ,c, n,i = the nominal line-of-sight velocity between radar and SRP, vlos ,t , n,i = the nominal line-of-sight velocity component of just the target, Ts = the ADC sampling period, T p = the pulse period, and c = the velocity of propagation.
(3)
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A more complete description of these parameters can be found in Appendix A. The Scene Reference Point (SRP) is the location at which the antenna is pointed, and to which any motion compensation is referenced. It defines zero range offset, and zero Doppler offset at that range. The third phase term is a consequence of the Residual Video Phase Error (RVPE) term resulting from stretch processing (deramping the chirp upon receive). It is typically ignored for GMTI applications, and we shall do so hereafter. In the first phase term, to simplify the following discussion, we define the range difference
(
)
rsc = rs,0,0 − rc,0,0 .
(4)
In the second phase term, to simplify the following discussion, we define the line-of-sight velocity difference
(
)
vlos, sc = vlos, s,0,0 − vlos,c,0,0 .
(5)
The model then becomes
⎧ ⎛ 2γ T ,0 ⎞⎫ (1 − ζ 0 )rscTs i ⎟⎪ ⎪ ⎜− ⎪ c ⎟⎪ . X V (i, n ) = Ar exp⎨ j ⎜ ⎜ ⎟⎬ ⎪ ⎪ ⎜ − 2ωT ,0 v los , scT p n ⎟⎪ ⎪⎩ ⎝ c ⎠⎭
(6)
An examination of the model for the video phase history data shows that the phase is a function of the two data indices n and i. A Discrete Fourier Transforms (DFT) across index n will then yield an Impulse Response (IPR) with peak at apparent velocity offset v peak = vlos , sc
(7)
A DFT across index i will yield an IPR with peak at apparent range offset rpeak = (1 − ζ 0 )rsc
(8)
We now examine these in turn.
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2.1 Moving Target Range 2.1.1
Range Difference Expansion
The entity of concern is (1 − ζ 0 )rsc . From Appendix A, we recall that the factor ζ 0 is given by
(
⎧2 ⎪ c vlos, s,0,0 − vlos ,c,0,0 ζ0 = ⎨ 2 ⎪ vlos , s ,0,0 c ⎩
)
if we modulate γ T , n
.
(9)
if we don' t
For all reasonable velocities of interest,
vlos, s,0,0
