Cooperative Sensing for Target Estimation and Target Localization · 2011-05-12 · Cooperative Sensing for Target Estimation and Target Localization 1 Wenshu Zhang. Advisor: Dr

Cooperative Sensing for Target Estimation and Target Localization

1

Wenshu Zhang

Advisor: Dr. Liuqing Yang

Department of Electrical & Computer Engineering

Colorado State University

Fort Collins, CO 80523

Preliminary ExamMay 09, 2011

Outline

Introduction

Cooperative target estimation

Optimum waveform designs

Robust transceiver designs

Cooperative target localization

The ML time-of-arrival estimator

The simplified (SML) TOA estimator

Conclusions and future work

2

Introduction

Cooperative sensingAllows communications and information exchanges among multiple sensing devices, e.g., radar transceivers, sensor nodes and mobile handsetsApplications: Through-the-wall sensing [Zhang-Amin’08] Medical imaging [Samardzija-Lubecke et.al.’05, Bliss-Forsythe’06] Target parameter estimation [White-Ray ’05, Yang-Blum’07] Target localization and tracking [Wymeersch-Lien-Win’09]

From the perspective of target estimationTransmits orthogonal waveforms or noncoherent waveforms instead of transmitting coherent waveforms which form a focused beam in the traditional transmit beamforming

From the perspective of target localizationIncorporates target-target communications to enhance coverage and accuracy

3

Roadmap

4

Introduction








MIMO Comm. Inspired MIMO Sensing

5

Communications channel VSRich scattering [Skolnik’01]: 5-20 dB target RCS fluctuation

Diversity: in terms of BER VS

Degrees of freedom: increased data rates VS

sensing targets

in terms of Prob. of False Alarm, Prob. of Miss Detection

higher resolution

-15-10

-50

510

15

-10

0

10

0

0.2

0.4

0.6

0.8

1

x in λy in λ

AF

Performance Indicator: Mutual Information VS ?0 5 10 15 2010-4

10-3

10-2

10-1

100

SNR (dB)

Pe, N=1

Pf, N=1

Pmd, N=1

Pe, N=2

Pf, N=2

Pmd, N=2

MI in Sensing: Waveform Design

Estimation of single extended target [Bell’93]

A single waveform

1 transmitter, 1 receiver

Optimization criterion: Mutual Information (MI)

Water-filling strategy

Proposition: for any decision rule assigning into one of equiprobablepartitions based on observation of :

Estimation of multiple extended targets [Leshem-Naparstek-Nehorai’07]

Multiple waveforms

Large co-located phased array: each target is seen from 1 viewing aspect

Optimization criterion: weighted sum of individual MIs

Water-filling-like solution

Balances among multiple targets using priority factors

6

MI in Sensing: Waveform Design

Estimation of an extended target [Yang-Blum’07]

Multiple waveforms

M transmitters and N receivers, both widely separated: the target can be seen from MN viewing aspects

Optimization criterion: collective MI and MMSE

Water-filling strategy

Establishes the equivalence between MI and MMSE criteria

Robust design for estimation of an extended target [Yang-Blum’07]

Same system setup as above

Uncertainty exists in the target PSD

Optimization criterion: collective MI and MMSE

Water-filling strategies

Equivalence between MI and MMSE does NOT hold

7

MIMO Sensing Model

Received signal [Yang-Blum’07]:

M transmitters, N receivers, L time slots (observation window):

MNK x 1 vector target impulse response (TIR)

from all transmitter-receiver pairs

: L x MK matrix transmitted waveforms

: LN x 1 vector observations from all receivers

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MIMO Comm. vs. MIMO Sensing

9

MIMO Comm.

M=1, N=2 To estimate: MI: MMSE:

MIMO Sensing

M=1, N=2 To estimate: MI: MMSE:

Insufficient degrees of freedom to optimize the waveform for both g1 and g2.

Mixed Structure

Transmitter: M widely spaced sensors, M waveforms

⇒ M viewing aspects Receiver: N closely separated sensors N coherent returns for each aspect ⇒ coherent processing gain

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Signal Model for Mixed Structure

Covariance matrix of target response : Target modes , MK x 1 vector

Covariance matrix:

Signal model in “mode” space [Yang-Blum’07]:

: Power allocation corresponding to the i-th modeTotal power constraint:

: Zero-mean uncorrelated Gaussian noise with covariance matrix

Waveform design ⇒ Power Allocation

11

Power Allocation in White Noise

12

White noise:

MMSE estimator:

MI : MMSE:

Result: The optimum power allocation scheme in the following water-filling form [Yang-Blum’07]

maximizes MI and minimizes MMSE simultaneously, where is a constant ensuring the total power constraint.

An Alternative Thought

13

Example: 5 modes,

1 2 3 4 50

0.01

0.02

0.03

i

MM

SE

1 2 3 4 50

20

40

60

i

D(i)

1 2 3 4 50

0.5

1

λ(i)

1 2 3 4 50

0.1

0.2

0.3

0.4

i

norm

aliz

ed M

SE

Emphasizes stronger modes Weaker modes also important [Bell’93, Fuhrmann’08]

i

NMSE-Based Power Allocation

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MMSE criterion: weaker modes experience larger relative error than the stronger ones

Normalized MSE:

Result: The optimum power allocation scheme in the form

minimizes the normalized MSE, where is used to ensure the total power constraint.

MMSE vs. NMSE

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Example: 5 modes,

1 2 3 4 50

20

40

60

80

i

D(i)

1 2 3 4 50

0.02

0.04

i

MM

SE

1 2 3 4 50

0.1

0.2

0.3

0.4

i

norm

aliz

ed M

SE

i1 2 3 4 5

0

0.5

1

λ(i)

Power Allocation in Colored Noise

16

Colored noise

Criterion Expression Power loading

MI

MMSE

NMSE

MMSE-optimum power loading is not water-filling MI differs from both MMSE and NMSE max{MI} = min{det{NMSE}} even for colored noise

Numerical Example

17

1 2 3 4 500.5

11.5

22.5

33.5

44.5

5

i

MMSE-basedNMSE-basedMI-based

200 5 10 1510 -2

10 -1

10 0

P0 (dB)

MMSE-basedNMSE-basedMI-based

NM

SE

i1 2 3 4 50

0.20.40.60.81

1.21.41.61.82

1 2 3 4 50

0.5

1

1.5

2

2.5

i

Joint Robust Designs

18

Why robust designs?The performance of an estimator designed for some nominally assumed PSD would degrade rapidly as the nominal PSD deviates from the true one.Robust: “overall” performance is good or acceptableOne widely used measure: worst case performance

Joint Tx (waveforms) and Rx (estimator) robust designsExisting work assumes (adaptively) optimum estimator while designing robust waveforms

Incorporating uncertainties in noise PSD as well as in target PSD:Existing work only considers target PSD uncertainty while assuming known white noise

Uncertainty band modelsReasonable when PSD is estimated from dataVarious uncertainty models

⇒ Minimax

Minimax Robust Designs

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Minimax robust schemeBounds the worst case performanceProcedure: looking for the Least-Favorable Sets (LFS)

Saddle point conditions: jointly design MMSE estimator and power allocation such that

MMSE-based:

NMSE- based:

MI-based:

Robust Designs

Robust Design in White Noise

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Uncertainty only exists in target PSD

MMSE-based:

NMSE-based:

MI-based:

Robust Design in Colored Noise

21

Uncertainties for target modes and colored noiseMMSE-based:

NMSE-based:

MI-based:

i.e.

i.e.

Robust Design in Colored Noise with Power Ratio Constraint

22

LFS for uncertain noise PSD with power ratio

constraint

: to guarantee the average power ratio constraint

MI, NMSE criteria: MMSE criterion:

Numerical Examples (1)

23

1 1.5 2 2.5 3 3.5 4 4.5 50123456789

10

i

Lower BoundUpper BoundNominalLFS

1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

33.5

i

Lower BoundUpper BoundNominalLFS

i0

0.20.40.60.81

1.21.41.61.82

1 2 3 4 5 1 2 3 4 50

0.5

1

1.5

2

2.5

i


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Nominal PSD, Robust design

LFS PSD, Robust design

LFS PSD, Nominal design

0 5 10 15 2010

-2

10-1

100

101

P0 (dB)

MM

SE

0 5 10 15 2010

-2

10-1

100

101

P0 (dB)N

MSE

MMSE- and NMSE- based robust designs:o Large gap for LFS PSD: worst performance improvedo Red dashed line: performance lower bound

Nominal PSD, Nominal design


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0 5 10 15 200

5

10

15

20

25

30

35

P0 (dB)

MI(

bits

)

MI-based robust designs:o Performance difference comes from PSDs, but not from designso Still provide performance lower bound

Nominal PSD, Robust design

LFS PSD, Robust design

LFS PSD, Nominal designNominal PSD, Nominal design

Summary

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Links between MIMO communications and MIMO sensing

Using MI, MMSE, NMSE criteriaOptimum power allocation in a mixed MIMO sensing setup

Joint robust designs with bounded and/or power constrained uncertainties

Observations:All three criteria are different in general settings

The NMSE criterion shares more similarities with the MI: The MI and NMSE criteria lead to identical LFS in the robust designs

The MMSE criterion always suggests otherwise

Future work:Sensitivity analysis of the optimum waveform designs to overestimation error

Roadmap

27

Introduction








Background

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Two phases of the localization process Distance measurement

Time-of-arrival (TOA) based

Ultra-wideband (UWB) Fine timing resolution High obstacle penetration capability Coexistence with existing systems

Location updateCooperative localization Allows target-target communications Dramatically increase accuracy and coverage

TOA speed of light

Anchor

Target

Trilateration

Motivation

Existing optimal ML TOA estimator [Win-Scholtz’02]

Known time-hopping and DS codes assumptionEstimates amplitude and delay for each and every channel pathToo computationally intensive due to huge number of multipath components of the UWB channels

Timing with “Dirty” Template (TDT) [Yang-Giannakis’05]

Advantages Without impractical assumptions Low complexity Applicable to general settings (narrowband/wideband, single/multiple

users) as long as ISI is absent Digital counterpart [Xu-Yang’08]: effective even when using very-low-

resolution digital UWB receivers

Optimality has not been explored

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Signal Model (1)

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First arrival time

TOA estimation: finding

Signal Model (2)

31

Rx segment

Unknown parameters to estimate

Aggregate pulse

First arrival time

t

and⇔

ML TOA Estimator: Step 1

32

Log-likelihood function

ML AlgorithmStep 1: get as a function of , based on a fixed guessStep 2: replace with to look for the best

Step 1:

ML TOA Estimator: Step 2

33

t

Implementation: average correlations

ML objective function

ML timing estimation

Windows

t

noise free part: Correct timing:

Simplified ML (SML) TOA Estimator

34

Drawbacks of the ML estimator: computational complexity and redundancy

Define

: constant

Simulations

35

TDT can approach SML closely

Performance is improved with increasing K

E/N0 (dB)-15 -10 -5 0 5 10 15 20

10-4

10-3

10-2

10-1

100

norm

aliz

ed M

SENormalized MSE:

SML

TDT

K=2K=4K=8K=16K=32K=64K=128

IEEE 802.15.3a CM1

Tp = 1ns

Tf = 35ns

Nf = 32 frames

Simulations

36

5 10 15 20 25 30 3510

-6

10-5

10-4

10-3

10-2

10-1

100

SNR(dB)

aver

age

BER

SML

TDT

K=2K=4K=8K=16K=32K=64K=128

BER performance:

TDT can approach SML closely

Performance is improved with increasing K

no timing

Summary

Developed the practical data-aided ML TOA estimator

Simplified the original ML estimator without affecting its optimality

Simulation shows TDT’s optimality in ML sense

Future work

Rigorous performance analysis for both ML and SML estimators

Optimum training sequence

Demonstration of TDT’s optimality in ML sense

Phase II: cooperative location update

37

Conclusions

Cooperative target estimation:

Links between MIMO communications and MIMO sensing


Joint robust transceiver designs

Cooperative target localization:

Developed the practical data-aided ML TOA estimator

Simplified the original ML estimator without affecting its optimality

Simulation shows TDT’s optimality in ML sense

38

Future Work


Sensitivity analysis of the optimum waveform designs to

overestimation error


Rigorous performance analysis for both ML and SML estimator

Optimum training sequence

Demonstration of TDT’s optimality in ML sense

Phase II: cooperative localization update

39

Thank you!

Documents

Cooperative Sensing for Target Estimation and Target Localization · 2011-05-12 · Cooperative Sensing for Target Estimation and Target Localization 1 Wenshu Zhang. Advisor: Dr