Statistical Signal and Array Processing Harry L. Van Trees University Professor Emeritus Kristine L. Bell Applied & Engineering Statistics May 19, 2006 1 Objectives • Apply statistical signal processing techniques to important new systems • Advance the theory in the areas of: • Array processing • Bayesian estimation • Nonlinear tracking/filtering • Write / edit books Van Trees & Bell 2
Activities • Applications – Novel Satellite Communications (Argon ST / DARPA) – Space-time Adaptive Processing (STAP) for Navy E2C (Lockheed Orincon / ONR) – Aeroacoustic Sensor Networks (Army Research Office) • Theory – Recursive Bayesian bounds (DARPA SPO) – Tracking using sparse arrays (DARPA SPO) – Multistatic radar (DARPA SPO) • Books – Optimum Array Processing, Part IV of Detection, Estimation & Modulation Theory H. L. Van Trees, 2002 – Bayesian Bounds, H. L. Van Trees and K. Bell, IEEE Press, 2006 Van Trees & Bell 3 Novel Satellite Communications “ In the past, we successfully showed we can overcome the jamming of our satellite navigation systems. Can we also protect the uplinks of our satellite communications systems? The Novel Satellite Communications program (NSC) is using new phenomenologies to overcome this vulnerability, ensuring that our troops will always have robust satellite communications available. Last year, we performed field testing that confirmed the properties of the antijam phenomenologies we are exploiting. This year, three teams are developing the algorithms and techniques that exploit these phenomena to provide a robust antijam capability for our communications satellites.” Michael Zatman, DARPA Tech 2005, August 9-11, 2005 Van Trees & Bell 4
Van Trees & Bell 5 Overview • Full Beam Set Algorithm – Provides a set of beampatterns that collectively “cover” an Area of Interest (AOI) on the earth’s surface while suppressing up to N T jammers in the AOI – Each beam may allow j max jammers not to be nulled – Beams may be scanned to detect new users and jammers • Beam Subspaces – For a known user (or set of users), beam subspaces are collection of beams that span the user and un-nulled jammer subspaces – Subspace processing provides reduced rank data for subsequent processing Van Trees & Bell 6
Full Beam Set Generation AOI 250 • Define Grid Points on AOI 200 – e.g. hexagonal grid with 121 points 150 100 • For each Grid Point 50 y (km) 0 – Find maximum SINR beam with j max un-nulled jammers -50 – MVDR with parametric interference -100 covariance matrix, pointing to Grid -150 Point Start by excluding j max closest jammers -200 Adjust jammer selection iteratively to -250 -200 -100 0 100 200 improve SINR x (km) Van Trees & Bell 7 Scenario • 1084-element cantor ring array configuration • N T = 20 randomly distributed jammers • j max = 3 un-nulled jammers per beam • Beam set quality given as percent coverage of AOI at -3 dB SINR loss level Phased Array, N=1084 8 6 4 2 meters 0 -2 -4 -6 -8 -10 -8 -6 -4 -2 0 2 4 6 8 10 meters Van Trees & Bell 8
Typical Beams ( j max = 3) Beam 17, SINRL=-0.98078 dB Beam 50, SINRL=-2.6664 dB 0 0 Nulled 200 200 jammers -10 -10 100 100 -20 -20 y (km) y (km) 0 0 -30 -30 -100 -100 -40 -40 -200 -200 -50 -50 -200 -100 0 100 200 -200 -100 0 100 200 Pointing x (km) x (km) Direction Beam 96, SINRL=-2.9547 dB Beam 121, SINRL=-1.6157 dB 0 0 Un-nulled 200 200 jammers -10 -10 100 100 -20 -20 y (km) y (km) 0 0 -30 -30 -100 -100 Nulled -40 -40 jammers -200 -200 -50 -50 -200 -100 0 100 200 -200 -100 0 100 200 x (km) x (km) Van Trees & Bell 9 STAP for E2C • Program – Replace rotating linear array with circular phased array – Develop STAP algorithm • Our role – Full rank algorithms have too many DOF to be computationally feasible (e.g. 360) in real time – Develop clever reduced-rank algorithms that have acceptable performance Van Trees & Bell 10
Courtesy of Dr. R. David Dikeman Van Trees & Bell 11 CSTAP Scenario Modeled Geometry Antenna Array Element Pattern 90 120 60 Passive 150 30 elements 0 -20 -40 180 0 Velocity Active -150 -30 elements Azimuth -120 -60 -90 Radar Parameters Elevation Frequency 435 MHz Bandwidth 3.75 MHz Velocity Samp. Freq. 3.75 MHz PRF 300 Hz # Pulses 18 Van Trees & Bell 12
Candidate techniques • PRI LCMV – MQPC • Adaptive Subspace – Elgenspace – Conjugate gradient / MSWF Van Trees & Bell 13 PRI LCMV-MQPC PRI LCMV-MQPC, Iteration 5, SINR = 21.1981 dB 150 120 -10 90 Doppler Frequency (Hz) 60 -20 30 0 -30 -30 -40 -60 -90 -50 -120 -150 -180 -90 0 90 180 Azimuth Angle (deg.) Van Trees & Bell 14
Battlefield Aeroacoustic Sensor Network 10.2 • Targets move along track 10 between arrays Site 3 9.8 Site 1 9.6 • Arrays collect broadband y-position (km) Site 4 aero-acoustic data 9.4 9.2 Site 5 • Bearing and power levels 9 seen at arrays change 8.8 rapidly as vehicle passes 8.6 6.8 7 7.2 7.4 7.6 7.8 8 8.2 8.4 x-position (km) Sponsored by Army Research Lab Van Trees & Bell 15 Target Data as Seen at Arrays Bearing Spectrogram Site 3 Site 1 Site 4 Site 5 Site 3 Site 1 Site 4 Site 5 400 400 400 400 400 400 400 400 350 350 350 350 350 350 350 350 T gt2 300 300 300 300 300 300 300 300 T gt2 T gt1 250 250 250 250 250 250 250 250 Time (sec) Time (sec) 200 200 200 200 T gt1 200 200 200 200 T gt2 T gt2 150 150 150 150 150 150 150 150 T gt1 T gt1 100 100 100 100 100 100 100 100 50 50 50 50 50 50 50 50 0 0 0 0 0 0 0 0 -180 0 180 -180 0 180 -180 0 180 -180 0 180 0 100 200 0 100 200 0 100 200 0 100 200 Bearing (deg) Bearing (deg) Bearing (deg) Bearing (deg) Freq. (Hz) Freq. (H z) Freq. (H z) Freq. (H z) Van Trees & Bell 16
MAP-PF Position Tracking Results Guided Signal Processing Tracking S ite 3 S ite 1 S ite 4 S ite 5 4 0 0 4 0 0 4 0 0 4 0 0 Target 1 Target 2 10 10 Site 3 Site 3 3 5 0 3 5 0 3 5 0 3 5 0 9.8 9.8 3 0 0 3 0 0 3 0 0 3 0 0 Site 1 Site 1 9.6 9.6 2 5 0 2 5 0 2 5 0 2 5 0 y-position y-position Site 4 Site 4 Time (sec) 9.4 9.4 2 0 0 2 0 0 2 0 0 2 0 0 9.2 9.2 1 5 0 1 5 0 1 5 0 1 5 0 Site 5 Site 5 9 9 1 0 0 1 0 0 1 0 0 1 0 0 True True MAP-PF MAP-PF 8.8 8.8 5 0 5 0 5 0 5 0 7.4 7.6 7.8 8 7.4 7.6 7.8 8 T ru e T ru e T ru e T ru e x-position x-position T g t 1 T g t 1 T g t 1 g T t 1 T g t 2 T g t 2 T g t 2 g T t 2 0 0 0 0 -1 8 0 0 1 8 0 -1 8 0 0 1 8 0 -1 8 0 0 1 8 0 -1 8 0 0 1 8 0 B e a r in g (d e g ) B e a r in g (d e g ) B e a r in g (d e g ) B e a in r g (d e g ) Van Trees & Bell 17 Theory • Recursive Bayesian bounds (DARPA SPO) • Tracking using sparse arrays (DARPA SPO) • Multistatic radar (DARPA SPO) Van Trees & Bell 18
Recursive Bayesian Bounds • Observe a nonlinear function of a vector parameter θ on the presence of noise • Observe a nonlinear function of a discrete-time random process x(k) in the presence of noise • In general, an analytic expression for the performance of the estimator cannot be found • Lower bounds on performance are the primary approach Van Trees & Bell 19 Parameter Estimation Bounds (Covariance Inequality) Deterministic Bayesian Recursive Bayesian Cramér-Rao BCRB RBCRB [Fisher 22, Dugue 37, [Van Trees 68] [Tichavsky et al 98] Cramér 46, Rao 45] Bhattacharyya B Bhat. (BB) RB Bhat. [Bhat. 48] [Van Trees 66, 68] [Reece & Nicholson 05 (T)] Barankin Bobrovsky – Zakai (BZB) RBZB [Barankin 4-9] [Bobrovsky et al 76, 87] [Reece & Nicholson 05 (T)] [McAulay & Hofstetter 71] [Reuven & Messer 97] Mixed Mixed Bayesian Recursive mixed [Abel 93] [Renaux et al 06] [Bell & Van Trees 06] [McAulay & Hofstetter 71] Weiss – Weinstein (WW) Recursive WW [Weiss & Weinstein 85, 88] [Rapoport & Oshman 04 (T)] [Reece & Nicholson 05 (T)] [Bell & Van Trees 06 (T/A)] Van Trees & Bell 20
An SAT – type analogy 0 −5 −10 Local MSE (dB) −15 −20 −25 −30 −35 MLE Barankin −40 Cramer−Rao −45 −30 −25 −20 −15 −10 −5 SNR (dB) are to ESTIMATION THEORY BOUNDS as are to REBOUNDS BASKETBALL - IN BOTH CASES - GEORGE MASON IS IN THE FINAL FOUR! Van Trees & Bell 21 Tracking using sparse arrays Target Target Track θ d 1 d 2 … d N -2 d N -1 Van Trees & Bell 22
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