Statistical Signal and Array Processing Harry L. Van Trees - - PDF document

1

Statistical Signal and Array Processing

Harry L. Van Trees University Professor Emeritus Kristine L. Bell Applied & Engineering Statistics

May 19, 2006

Van Trees & Bell 2

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 3

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 4

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

• ur 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 5 Van Trees & Bell 6

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 NT jammers in the AOI – Each beam may allow jmax 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 7

Full Beam Set Generation

• Define Grid Points on AOI

– e.g. hexagonal grid with 121 points

• For each Grid Point

– Find maximum SINR beam with jmax un-nulled jammers – MVDR with parametric interference covariance matrix, pointing to Grid Point Start by excluding jmax closest jammers Adjust jammer selection iteratively to improve SINR

• 200
• 100

100 200

• 250
• 200
• 150
• 100
• 50

50 100 150 200 250 AOI x (km) y (km)

Van Trees & Bell 8

Scenario

• 1084-element cantor ring array configuration
• NT = 20 randomly distributed jammers
• jmax = 3 un-nulled jammers per beam
• Beam set quality given as percent coverage of AOI

at -3 dB SINR loss level

• 10
• 8
• 6
• 4
• 2

2 4 6 8 10

• 8
• 6
• 4
• 2

2 4 6 8

meters meters Phased Array, N=1084

Van Trees & Bell 9

Typical Beams (jmax = 3)

Beam 17, SINRL=-0.98078 dB x (km) y (km)

• 200
• 100

100 200

• 200
• 100

100 200

• 50
• 40
• 30
• 20
• 10

Beam 50, SINRL=-2.6664 dB x (km) y (km)

• 200
• 100

100 200

• 200
• 100

100 200

• 50
• 40
• 30
• 20
• 10

Beam 96, SINRL=-2.9547 dB x (km) y (km)

• 200
• 100

100 200

• 200
• 100

100 200

• 50
• 40
• 30
• 20
• 10

Beam 121, SINRL=-1.6157 dB x (km) y (km)

• 200
• 100

100 200

• 200
• 100

100 200

• 50
• 40
• 30
• 20
• 10

Pointing Direction Un-nulled jammers Nulled jammers Nulled jammers

Van Trees & Bell 10

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 11

Courtesy of Dr. R. David Dikeman

Van Trees & Bell 12

CSTAP Scenario Modeled

Velocity Elevation Velocity Azimuth

Geometry

Passive elements Active elements

Antenna Array

• 40
• 20

30

• 150

60

• 120

90

• 90

120

• 60

150

• 30

180

Element Pattern

18 # Pulses 300 Hz PRF 3.75 MHz

• Samp. Freq.

3.75 MHz Bandwidth 435 MHz Frequency

Radar Parameters

Van Trees & Bell 13

Candidate techniques

• PRI LCMV – MQPC
• Adaptive Subspace

– Elgenspace – Conjugate gradient / MSWF

Van Trees & Bell 14

PRI LCMV-MQPC

Azimuth Angle (deg.) Doppler Frequency (Hz) PRI LCMV-MQPC, Iteration 5, SINR = 21.1981 dB

• 180
• 90

90 180

• 150
• 120
• 90
• 60
• 30

30 60 90 120 150

• 50
• 40
• 30
• 20
• 10

Van Trees & Bell 15

Battlefield Aeroacoustic Sensor Network

6.8 7 7.2 7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.2 Site 3 Site 1 Site 4 Site 5 x-position (km) y-position (km)

• Targets move along track

between arrays

• Arrays collect broadband

aero-acoustic data

• Bearing and power levels

seen at arrays change rapidly as vehicle passes

Sponsored by Army Research Lab

Van Trees & Bell 16

Target Data as Seen at Arrays

Bearing Spectrogram

Site 3 Time (sec)

• Freq. (Hz)

100 200 400 350 300 250 200 150 100 50 Site 1

• Freq. (H

z) 100 200 400 350 300 250 200 150 100 50 Site 4

• Freq. (H

z) 100 200 400 350 300 250 200 150 100 50 Site 5

• Freq. (H

z) 100 200 400 350 300 250 200 150 100 50

• 180

180 50 100 150 200 250 300 350 400

T gt1 T gt2

Time (sec) Site 3 Bearing (deg)

• 180

180 50 100 150 200 250 300 350 400

T gt1 T gt2

Site 1 Bearing (deg)

• 180

180 50 100 150 200 250 300 350 400

T gt1 T gt2

Site 4 Bearing (deg)

• 180

180 50 100 150 200 250 300 350 400

T gt1 T gt2

Site 5 Bearing (deg)

Van Trees & Bell 17

MAP-PF Position Tracking Results

7.4 7.6 7.8 8 8.8 9 9.2 9.4 9.6 9.8 10 Site 3 Site 1 Site 4 Site 5 x-position y-position Target 1

True MAP-PF

7.4 7.6 7.8 8 8.8 9 9.2 9.4 9.6 9.8 10 Site 3 Site 1 Site 4 Site 5 x-position y-position Target 2

True MAP-PF

• 1

8 1 8 5 1 1 5 2 2 5 3 3 5 4 Time (sec) S ite 3 B e a r in g (d e g )

T ru e T g t 1 T g t 2

• 1

8 1 8 5 1 1 5 2 2 5 3 3 5 4 S ite 1 B e a r in g (d e g )

T ru e T g t 1 T g t 2

• 1

8 1 8 5 1 1 5 2 2 5 3 3 5 4 S ite 4 B e a r in g (d e g )

T ru e T g t 1 T g t 2

• 1

8 1 8 5 1 1 5 2 2 5 3 3 5 4 S ite 5 B e a r in g (d e g )

T ru e T g t 1 T g t 2

Guided Signal Processing Tracking

Van Trees & Bell 18

Theory

• Recursive Bayesian bounds (DARPA SPO)
• Tracking using sparse arrays (DARPA SPO)
• Multistatic radar (DARPA SPO)

Van Trees & Bell 19

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 20

Parameter Estimation Bounds (Covariance Inequality)

Recursive WW

[Rapoport & Oshman 04 (T)] [Reece & Nicholson 05 (T)] [Bell & Van Trees 06 (T/A)]

Weiss – Weinstein (WW)

[Weiss & Weinstein 85, 88]

Recursive mixed

[Bell & Van Trees 06]

Mixed Bayesian

[Renaux et al 06]

Mixed

[Abel 93] [McAulay & Hofstetter 71]

RBZB

[Reece & Nicholson 05 (T)]

Bobrovsky – Zakai (BZB)

[Bobrovsky et al 76, 87] [Reuven & Messer 97]

Barankin

[Barankin 4-9] [McAulay & Hofstetter 71]

RB Bhat.

[Reece & Nicholson 05 (T)]

B Bhat. (BB)

[Van Trees 66, 68]

Bhattacharyya

[Bhat. 48]

RBCRB

[Tichavsky et al 98]

BCRB

[Van Trees 68]

Cramér-Rao

[Fisher 22, Dugue 37, Cramér 46, Rao 45]

Recursive Bayesian Bayesian Deterministic

Van Trees & Bell 21

An SAT – type analogy

are to

−30 −25 −20 −15 −10 −5 −45 −40 −35 −30 −25 −20 −15 −10 −5 SNR (dB) Local MSE (dB) MLE Barankin Cramer−Rao

ESTIMATION THEORY BOUNDS as BASKETBALL REBOUNDS

• IN BOTH CASES -

GEORGE MASON IS IN THE FINAL FOUR! are to

Van Trees & Bell 22

Tracking using sparse arrays

d1 d2 … dN-2 dN-1 θ

Target Track Target

Van Trees & Bell 23

Tracking using sparse arrays

• 1
• 0.5

0.5 1

• 40
• 35
• 30
• 25
• 20
• 15
• 10
• 5

u = cos(θ) Beampattern (dB)

Van Trees & Bell 24

Tracking using sparse arrays

• 1
• 0.5

0.5 1 50 100 150 200 250 300 350 400 450 500

Bearing (u) Time

• 50
• 40
• 30
• 20
• 10

50 100 150 200 250 300 350 400 450 500

RMSE Time

True Tracks Sim BCRB

• 1
• 0.5

0.5 1 50 100 150 200 250 300 350 400 450 500

Bearing (u) Time

• 50
• 40
• 30
• 20
• 10

50 100 150 200 250 300 350 400 450 500

RMSE Time

True Tracks Sim BCRB

• 1
• 0.5

0.5 1 50 100 150 200 250 300 350 400 450 500

Bearing (u) Time

• 50
• 40
• 30
• 20
• 10

50 100 150 200 250 300 350 400 450 500

RMSE Time

True Tracks Sim BCRB

• 1
• 0.5

0.5 1 50 100 150 200 250 300 350 400 450 500

Bearing (u) Time

• 50
• 40
• 30
• 20
• 10

50 100 150 200 250 300 350 400 450 500

RMSE Time

True Tracks Sim BCRB

Van Trees & Bell 25

Issues

• Bound performance of trackers
• Utilize sidelobe / grating lobe structure

to improve performance

Van Trees & Bell 26

Multistatic Radar Geometry

y

Target Track (xT,yT) RR

x

RX TXi θa RTi (xT,yT)

· · (xTXi ,yTXi) (0,0)

Target TXj RTj

(xTXj ,yTXj)

Van Trees & Bell 27

Two Transmitter Example

(x0,y0) 300 m/sec 200 sec RX 400 sec –60 –40 –20 20 60 40

x (km) y (km)

60 50 40 30 20 10 TX2 TX1 0 sec

Van Trees & Bell 28

Multistatic Radar BCRB

Van Trees & Bell 29

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 30

Optimum Array Processing

• Published in 2002
• Widely-used in graduate

schools & industry

• In 4th printing
• Chinese edition in print

Van Trees & Bell 31

Bayesian Bounds

• An IEEE Press Reprint Book published in conjunction with

Wiley

• Contains 80 selected papers which include most of the

important results in the area

• Contains about 50 pages of new text to provide context

and integration of the material

Van Trees & Bell 32

Summary

• An active research and educational program that

combines theory and practical application