Wideband, Long-CPI GMTI Ali F. Yegulalp th Annual ASAP Workshop 6 March 004 This work was sponsored by the Defense Advanced Research Projects Agency and the Air Force under Air Force Contract F968-00-C-000. Opinions, interpretations, conclusions, and recommendations are those of the author, and not necessarily endorsed by the United States Government. WL GMTI-
Wideband, Long-CPI GMTI (WL-GMTI) Aperture (# Receiver Channels) Premise: Combine Combine physical physical aperture aperture of of GMTI GMTI with with bandwidth bandwidth and and integration integration time time of of high-resolution high-resolution SAR. SAR. Purpose: Supplement Supplement traditional traditional SAR SAR and and GMTI GMTI modes modes by by detecting detecting slow slow and/or and/or low low RCS RCS moving moving targets. targets. Bandwidth Potential Benefits: Lower Lower minimum minimum detectable detectable velocity velocity (MDV) (MDV) Detection Detection of of targets targets with with zero zero radial radial velocity velocity (but (but non-zero non-zero tangential tangential velocity) velocity) More More efficient efficient use use of of radar radar resources resources in in multimodmode SAR/GMTI SAR/GMTI platforms platforms multi- Reduced Reduced array array requirements requirements (sparser/shorter) (sparser/shorter) Greater Greater robustness robustness to to clutter clutter internal internal motion motion Coherent Processing Interval (CPI) WL GMTI-
Background and References J.K. Jao, J. Tsay, and S. Ayasli, Single-Aperture SAR Detection of Moving Targets, Proc. 00 MSS Tri-Service Radar Sym., John Hopkins Univ., Maryland, May 00 (SECRET). J. Franz, A. Yegulalp, J.K. Jao, and Serpil Ayasli, Adaptive Airborne Radar Detection of Moving Targets Under Foliage, Proc. 00 MSS Tri-Service Radar Sym., John Hopkins Univ., Maryland, May 00 (SECRET). J.K Jao, Theory of Synthetic Aperture Radar Imaging of a Moving Target, IEEE Trans. on Geoscience and Remote Sensing, vol. 39, no. 9, pp. 984-99, September 00. J.K. Jao, T.J. Murphy, Results of the Foliage Penetration Radar and Electronic Support Measures Synergy for Targeting (FOREST) Test Bed Point Design Study, Lincoln Laboratory Project Report FPR-9, October 00. A.F. Yegulalp, FOPEN GMTI Using Multi-Channel Adaptive SAR, 0 th Annual ASAP Workshop, Lincoln Laboratory, Lexington, Massachusetts, March 00. A.F. Yegulalp, Analysis of SAR Image Formation Equations for Stationary and Moving Targets, Lincoln Laboratory Project Report FPR-4, June 00 (Distribution Unlimited). J.K. Jao, A.F. Yegulalp, J.R. Franz, and S. Ayasli, New Results of Airborne Multi-Channel Radar Detection of Moving Targets Under Foliage, 48 th Tri- Service Radar Sym., Naval Post-Graduate School, Monterey, California, June 00 (SECRET). WL GMTI-3
Purpose of this Talk Develop a basic framework for discussing and analyzing WL-GMTI Show how some of the basic tools of adaptive processing translate to WL-GMTI Steering vectors SINR loss Detection Stimulate further interest and work! WL GMTI-4
Outline SAR as the WL-GMTI pre-processor WL-GMTI steering vectors SINR loss prediction for WL-GMTI Theory Examples Detection Summary WL GMTI-5
SAR Pre-processing Data Cube Vectorized Data Cube Linear transformation to SAR basis Multi-channel SAR image Space (phase centers) Fast time (range) z z z 3 z 4 s = M z s = M z s = M 3 3z3 s = M 4 4z4 Space (phase centers) Range Slow time (pulse) Stagger data in slow time to meet DPCA condition WL GMTI-6 SAR processor knows locations of phase centers Cross-range Each SAR resolution cell is automatically phased up for stationary clutter at that location
Properties SAR is the wideband, long-cpi generalization of the Doppler processor in ordinary post-doppler STAP Linear transform of input data cube Annihilates the exoclutter subspace Invertible transformation of the endoclutter subspace Freezes clutter into SAR resolution bins Clutter in one bin is well-decorrelated from other bins multiple resolution cells away. Stationary targets have trivial steering vectors Stationary clutter has trivial covariance Moving targets smear over multiple resolution cells WL GMTI-7
Benefits of High Resolution for GMTI Target-to-clutter and target-to-noise ratio improve with increasing resolution Improvement holds at least until target is resolved Improvement can continue further if target contains small dominant scatterers High spatial resolution provides more clutter per unit area for training adaptive processor Can train in both range and azimuth Abundance of training data facilitates more powerful adaptive processing methods Algorithms with more adaptive DOFs Automated data editing to eliminate potential movers from training data WL GMTI-8
Outline SAR as the WL-GMTI pre-processor WL-GMTI steering vectors SINR loss prediction for WL-GMTI Theory Examples Detection Summary WL GMTI-9
y Image Domain SAR Steering Vector * Constant Velocity Point Target k y Spatial Frequency Domain Slant range Cross-range ( x, y s s ) x Slant range spatial frequency Cross-range spatial frequency k x ( ε x x ) + y = s y s G( k x, k y ) = γ k k y y + εk x e ix s k x iy s k y + εk x WL GMTI-0 v v target platform γ = v platform ε = γ * Analysis of SAR Image Formation Equations for Stationary and Moving Targets, A.F. Yegulalp, Lincoln Laboratory Project Report FPR-4, 0 June 00 (Distribution Unlimited)
WL-GMTI Steering Vector Constant Velocity Point Target Other elements Transmit phase center Receive element of interest d x s d ( d) = x (0) + ψ γ cos s y s ( d) = y s d (0) sinψ v v target platform γ = cosψ = v platform ( v v platform vtarget) platform v target ε = γ v v platform platform G( k x, k y ; d) = γ k k y y + εk x e ix s ( d ) k x iy s ( d ) k y + εk x WL GMTI-
Outline SAR as the WL-GMTI pre-processor WL-GMTI steering vectors SINR loss prediction for WL-GMTI Theory Examples Detection Summary WL GMTI-
Simplifying Assumptions Large clutter-to-noise ratio Elements are mutually calibrated No internal clutter motion, crab, unmeasured aircraft motion and vibration No jammers and other interference Isotropic element patterns Optimal AMF processing with perfect knowledge of steering vectors and clutter covariance WL GMTI-3
WL GMTI-4 = = N n n n ) ( ) v( e u Clutter-Limited SINR Loss Calculation Target steering vector Vectorized target image from n-th channel Element space basis vector Clutter + noise covariance Inverse covariance Large clutter-tonoise limit SINR loss Noise power Clutter pixel-space covariance = = = N n n N N n n n ) ( ) ( H H v v u u u R u σ = = = 0 0 0 ) (, 0 0 0 (), 0 0 0 () M K M M N e e e = = N n n ) e( e H c ee R I I R + = n σ H c c 4 ee R I R I I R + = n n n N σ σ σ H 0 ee I I I R N σ n σ n
Outline SAR as the WL-GMTI pre-processor WL-GMTI steering vectors SINR loss prediction for WL-GMTI Theory Examples Detection Summary WL GMTI-5
SINR Loss Example Carrier = GHz Bandwidth = 0 MHz CPI = 50 ms Range = 0 km Airspeed = 80 m/s Phase center locations = [0,] m db WL GMTI-6
SINR Loss Example Carrier = GHz Bandwidth = 0 MHz CPI = 50 ms Range = 0 km Airspeed = 80 m/s Phase center locations = [0,30] m db WL GMTI-7
SINR Loss Example Carrier = GHz Bandwidth = 0 MHz CPI = 5 s Range = 0 km Airspeed = 80 m/s Phase center locations = [0,30] m Differential SAR zone: db Target moves > SAR resolution cells over time it takes platform to travel the length of the real aperture WL GMTI-8
SINR Loss Example Carrier = GHz Bandwidth = 300 MHz CPI = 5 s Range = 0 km Airspeed = 80 m/s Phase center locations = [0,30] m Differential SAR zone: db Target moves > SAR resolution cells over time it takes platform to travel the length of the real aperture WL GMTI-9
SINR Loss Example Carrier = GHz Bandwidth = 300 MHz CPI = 5 s Range = 0 km Airspeed = 80 m/s Phase center locations = [0,7,30] m Differential SAR zone: db Target moves > SAR resolution cells over time it takes platform to travel the length of the real aperture WL GMTI-0
Outline SAR as the WL-GMTI pre-processor WL-GMTI steering vectors SINR loss prediction for WL-GMTI Theory Examples Detection Summary WL GMTI-
SINR Loss vs. Detection Performance SINR loss is a useful diagnostic, but it does not always translate directly into what we care about: detection performance Case in point: SINR loss for stationary targets is infinite, but SAR detects stationary targets quite well! WL-GMTI straddles the regime between GMTI-type detection and SAR-type detection Need to consider detection theory to understand true capabilities of WL-GMTI WL GMTI-
Illustrative Toy Model Radar: single-phase center (pure SAR) Moving point target with Rayleigh fading 5 db mean target-to-clutter (for focused stationary target) Two clutter models: Rayleigh (unrealistic, weak tails) Log-normal (more realistic, heavier tails) WL GMTI-3
Stationary Target Detection Rayleigh clutter Log-normal clutter WL GMTI-4
Moving Target: Matched Filter Detector Rayleigh clutter Log-normal clutter, moving target smeared over N pixels N=0 N=5 N= N= More Gaussian WL GMTI-5
Moving Target: Bayes-Optimal Detector N=0 N=5 Rayleigh clutter N= Log-normal clutter, moving target smeared over N pixels N= WL GMTI-6
Moving Target: ALMF Sub-Optimal Detector N=0 N=5 Rayleigh clutter N=5 N= Optimal detector N= ALMF Detector (amplitude limiter + matched filter) WL GMTI-7
Summary Wideband, long-cpi methods offers the promise of detecting slow, low-rcs targets not detectable with traditional GMTI methods This talk has explored some basic building blocks for analysis Wideband, long-cpi data model and steering vectors SINR loss analysis It appears that the detection capability of WL-GMTI straddles the SAR and GMTI domains: SINR loss alone is not a reliable metric of performance Smearing of target over many pixels can enhance detection in strong-tailed clutter Sub-optimal detector can approach optimal bound Many other aspects of the problem are ripe to be explored WL GMTI-8