Dynamically Configured Waveform-Agile Sensor Systemslcarin/Papandreou_DUKE_MURI_June27_2006.… · Waveform-Agile Sensor Systems Antonia Papandreou-Suppappola in collaboration with

Dynamically ConfiguredWaveform-Agile Sensor Systems

Antonia Papandreou-Suppappola

in collaboration with

D. Morrell, D. Cochran, S. Sira, A. Chhetri

Arizona State University

June 27, 2006

Supported by AFOSR MURI on Waveform Diversity for Full Spectral Dominance and DARPA ISP program

Sensing Activities at Arizona State University

SenSIP: Sensing, Signal and Information ProcessingCenter (http://enpub.fulton.asu.edu/sensip/)

Research Topics

Waveform-agile sensingSensor scheduling for tracking applicationsReal-time sensing using Berkeley mote sensors(perimeter security)Adaptive tracking imager systems

http://enpub.fulton.asu.edu/sensip/

Waveform-Agile Sensing

Objective

To dynamically select and configure time-varyingwaveforms in clutter environments for waveform-agilesensors

Performance criterion: minimum mean square trackingerror

Nonlinear observation models preclude exact or closedform solutions

Solution

We use the unscented transform and a particle filter thatemploys probabilistic data association to deal with theuncertainty in the measurement origin due to clutter

A greedy search is used to find the sensor configurationthat minimizes the predicted tracking error

Target kinematics and observations models

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Trajectory Target

B

A

θB

[rA rA]

[rB rB]

y x

y

θA

(xA, yA)x

(xB, yB)

Constant velocitykinematics model

Sensors measuredelay-Doppler

Narrowband receivedsignal model

Xk = FXk−1 + Wk, zk = h(Xk) + Vk

Clutter Modeling

Range

Ran

ge R

ate

Clutter

Observation

Predicted

Validation Gate

Target

Each sensor validatesmultiple observations

Zk = [z1k , z2

k , . . . , zmkk ]

Number of false alarmsassumed Poissondistributed due to clutter

µ(m) =exp(−ρVk)(ρVk)

m

m!

Clutter is assumed to be uniformly distributed in theobservation space

Waveform Structure

At every sampling instant, each sensor transmits a generalizedFM chirp

s(t) = a(t) exp(j2πbξ(t)), |t| < T/2 + tf

t0

Ttf tf

a(t)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10−4

2

4

6

8

10

12

14

x 106

Time (s)

Fre

quen

cy (

Hz)

PFM κ = 2.8

LFM

EFM

HFM

Trapezoidal envelopeallows evaluation of theCRLB

Each sensor isindependently configured

Waveform parametervector is

θk = [ξk(t) λk bk]T

Problem Statement

At each sampling instant k, we seek the sensorconfiguration

θk =

[

θAk

θBk

]

,

that minimizes the predicted mean square tracking error

Cost function for greedy optimization

J(θk) = EXk, Zk|Z1:k−1

{

(Xk − Xk)TΛ(Xk − Xk)

}

The cost of using a waveform represents an average overfuture states, observations, and clutter realizations

Block Diagram

MSEPrediction

Target trackingParticle filter

Minimization

Sensors

Estimates of

Grid Search

MSE

TransformUnscented

Candidatewaveform

Configuration that minimizes predicted MSE

p(Xk|Z1:k, θ1:k)

∆f

λ[r r]T

ξ(t/tr)

p(Xk|Z1:k−1, θ1:k−1)

Performance Criterion

Due to the nonlinear observations model, the cost functionJ(θk) cannot be evaluated in closed form

Stochastic optimization techniques may be used to find thebest configuration θk, but they are computationallyexpensive and difficult to control

The unscented transform provides a suitable means ofevaluating the cost function

We use the covariance update of the unscented Kalmanfilter to approximate the cost

Predicted Cost Approximation

Prediction of state covariance Pk|k−1 = FPk−1|k−1FT + Q.

Unscented transform is used to generate Pixz and Pi

zzcorresponding to sensor i

Covariance update if there were no clutter

Pck|k = Pi

xz

(

Pizz + N(θi

k))−1

Pixz

T

Since measurements are of uncertain origin

Pik|k(θ

ik) = Pk|k−1 − qi

2kPc

k|k

Sequential updates for Sensor A and B yield Pk|k(θk)

Cost function is approximated as J(θk) ≈ Trace{ΛPk|k(θk)}

Radar SimulationAveraged mean square error - LFM only

0 1 2 3 4 5 610

1

102

103

104

Time (s)

Ave

rage

d M

SE

(m

2 )

λ minλ maxConfigured

ρ = 1e−3

ρ = 1e−4

Configured

Radar SimulationAveraged mean square error - agile phase function

0 1 2 3 4 5 6

101

102

103

Time (s)

Ave

rage

d M

SE

(m

2 )

LFMPFM κ = 2.8PFM κ = 3.0EFMHFMConfigured

Configured

Radar SimulationTypical waveform selection

0 1 2 3 4 5 6LFM

PFM (2.8)

PFM (3.0)

EFM

HFMSensor A

0 1 2 3 4 5 6LFM

PFM (2.8)

PFM (3.0)

EFM

HFM

Time (s)

Sensor B

Waveform Characterization

LFM PFM (2.8) PFM (3.0) EFM HFM0

0.5

1C

orre

latio

nco

effic

ient

LFM PFM (2.8) PFM (3.0) EFM HFM10

4

106

108

VG

Vol

ume

LFM PFM (2.8) PFM (3.0) EFM HFM

100

105

Waveform type

Con

ditio

nal

Var

ianc

e

Heavy Clutter Maritime Scenarios

Returns from sea clutter are known to exhibit spatial andtemporal correlation

For detection of small-RCS targets using low grazing angleradars, clutter density is high and thus SCR low: if weassume similar clutter statistics in several range bins andhigh pulse repetition frequency (PRF), then estimation ofthe subspace occupied by the clutter returns is possible

In low SCR scenarios, we can improve detection andtracking performance by subspace-based cluttersuppression

Sea Clutter Modeling

Following the work of Watts, Ward and Tough (2005)

Sea surface presents the incident radar beam with a largenumber of scattering centers

Independent contributions from the speckle give rise tolocally Gaussian statistics, characterized by shortcorrelation time (10–20 ms) and length scales

Texture (large-scale swell structures) modulates the localmean power of this speckle-like return

This texture can be modeled by a gamma distributedprocess which de-correlates much less rapidly (50-60 s)than the local speckle process

Radar return is then represented as the product of thisgamma process and a unit power Gaussian/Rayleighprocess

Waveform Adaptive Detection and Tracking

Clutter mapping,

Tracker updateinterval. . . . . . . . .. . .

. . . . . . . . . . . . . .

0 1 2 N−1 0 1 2 N−1

Waveform adaptation

PRI

Tracker update

dwell #

suppression and detection

k k + 1

k k + 1 k + 2 k + 3

Two time frames - short PRI and long tracker update

Radar scene is unchanged over two successive dwells

Clutter Suppression

. . . . . . . .

. . . . . . . . . . . . . . . .

MF output in range bins

range bins

. . . . . . . .

Transmittedsignal

r1r0 rj

0

1

N − 1

Scatterers assumed stationary across N snapshots in adwell in jth range bin (due to high PRF)Due to high clutter, target contribution is minimal acrossrange bins; estimate clutter space by estimating covariancematrix of clutter returns across neighboring range binsMeasurements extract a waveform-independent estimateof clutter subspace; orthogonal projection of receivedsignal on subspace can yield a clutter-suppressed signal

Clutter Suppression

Form the estimate of the covariance matrix of clutterreturns in the jth bin as Rj = 1

L

∑Li=1 ri rH

i where L is thenumber of bins surrounding the jth bin (training data)

Qj is the subspace corresponding to the M largest eigenvalues of Rj

r⊥j = (I − Qj)rj is the clutter suppressed signal

SCR is defined as the ratio of target power over total clutterpower in the range bin containing the target; betterdetection is achieved with higher scatterer density

Simulation Example

Pulse length: 100 ns

PRF: 2 kHz

Bandwidth: 15 MHz

SCR: −20 dB

LFM chirp waveform

N = 20 snapshots

L = 40 range-bins for covariance estimation

about 750 scatterers in the observation space

020

4060

80

05

1015

2025

0

10

20

30

40

Range bin

SCR −20 dB, ρ = 0.001

Tracker update

Mag

nitu

de o

f MF

sig

nal

Original signal, |rj|2

020

4060

80

05

1015

2025

0

0.5

1

1.5

Range bin

SCR −20 dB, ρ = 0.001

Tracker update

Mag

nitu

de o

f clu

tter−

supp

ress

ed s

igna

l

Clutter suppressed signal, |r⊥j |2

Performance of Clutter-suppression Algorithm

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pfa

Pd −80

−75

−72

−71−70

−68

−67

−65

−55

Clutter map generated during the first dwell of each pairwill be used to design the waveform for the second dwell

Waveform design will aim at improving range estimation ofthe target, and eventually minimizing tracking error

Conclusions: Waveform Design

A greedy optimization algorithm for waveform scheduling tominimize the predicted mean square tracking error waspresented

Nonlinear observations models significantly complicate thewaveform selection problem

In more recent work, we incorporate the affect of thesidelobes of the ambiguity function on the estimation errors

We exploit the temporal correlation of clutter in asubspace-based approach to the suppression of clutterreturns (Asilomar 2006)

Binary Programming for Sensor Scheduling

Problem Statement

Track a moving target through a field of motes.

Measurements are acoustic energy from target; trackingdone at a base station

Motes are either active or in very low power standby mode.

Goal is to activate selected sensors to minimize energyconsumed while maintaining a desired track accuracy

Constrained discrete optimization problem: find set ofsensor configurations to satisfy constraint

Computational intractable as number of motes increases

Combined Tracking and Scheduling

Sensor Scheduling Approach

Pose constrained discrete optimization problem as aconstrained binary programmingApproximate computation of predicted tracker error

Linearize measurement model about predicted state(e.g. Extended Kalman Filter)Inverse of error covariance matrix (constraint function) islinear in binary control variables (1 if mote is used, 0 ismote is not used)Error is polynomial function of control variables

Binary programming for sensor schedulingNatural framework for on/off scheduling problemsLinear programming relaxation combined with Branch &Bound algorithm (existing software)Typically avoids significant enumeration of solution space

Sensor Costs: Energy Model

Packet Transmit Energy

Packet Receive Energy

Sensor Circuitry Energy

Processing Energy

Simulations and Results

Sensor field 100 m x 100 m

400 randomly placed acoustic sensors

Maximum sensors scheduled: 70

Energy use adopted from MICA2 datasheet

Target velocity: (3, -3) m/s

Target travels for 35 time steps of 1 s each

4,000 particles used in particle filter

Error threshold: 0.1 m2 to 0.6 m2

Tracking Performance

MC = true SE averaged over MC simulationsPred = SE predicted by schedulerPF = SE approximated by particle filterError threshold is 0.3 m2


Average number of sensors activated versus error threshold


Average energy consumption versus error threshold


Average run time versus error threshold

Conclusions: Sensor Scheduling

Sensor scheduling: Integral part of sensor signalprocessing:

Intelligent allocation of sensing resourcesReduce cost consumption of sensors

Sensor scheduling effective when:Scheduling formulation is amenable to optimizationNeed to exploit structure of the problem

Binary programming for sensor scheduling is a naturalframework for on/off scheduling problems that avoidssignificant enumeration of solution space

Documents

Dynamically Configured Waveform-Agile Sensor Systemslcarin/Papandreou_DUKE_MURI_June27_2006.… · Waveform-Agile Sensor Systems Antonia Papandreou-Suppappola in collaboration with