Cooperative Sensing for Target Estimation and Target Localization

Preliminary Exam May 09, 2011 Cooperative Sensing for Target Estimation and Target Localization Wenshu Zhang Advisor: Dr. Liuqing Yang Department of Electrical & Computer Engineering Colorado State University Fort Collins, CO 80523 1

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 sensing Allows communications and information exchanges among multiple sensing devices, e.g., radar transceivers, sensor nodes and mobile handsets Applications: 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 estimation Transmits 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 localization Incorporates target-target communications to enhance coverage and accuracy 3

Roadmap 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 4

MIMO Comm. Inspired MIMO Sensing 10 0 Communications channel VS sensing targets Rich scattering [Skolnik 01]: 5-20 db target RCS fluctuation Diversity: in terms of BER VS in terms of Prob. of False Alarm, Prob. of Miss Detection Degrees of freedom: increased data rates VS higher resolution 10-1 1 0.8 10-2 10-3 10-4 Pe, N=1 Pe, N=2 Pf, N=1 Pf, N=2 Pmd, N=1 Pmd, N=2 0 5 10 15 20 SNR (db) AF 0.6 0.4 0.2 0 10 0-10 y in λ -15 5 0-5 -10 Performance Indicator: Mutual Information VS? x in λ 10 15 5

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 equiprobable partitions 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 8

MIMO Comm. vs. MIMO Sensing MIMO Comm. MIMO Sensing M=1, N=2 To estimate: MI: MMSE: M=1, N=2 To estimate: MI: MMSE: Insufficient degrees of freedom to optimize the waveform for both g1 and g2. 9

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 10

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 mode Total power constraint: : Zero-mean uncorrelated Gaussian noise with covariance matrix Waveform design Power Allocation 11

Power Allocation in White Noise White noise: MMSE estimator: MI : MMSE: Result: The optimum power allocation scheme in the following waterfilling form [Yang-Blum 07] maximizes MI and minimizes MMSE simultaneously, where constant ensuring the total power constraint. is a 12

An Alternative Thought 1 Example: 5 modes, 0.03 λ (i) 0.5 MMSE 0.02 0.01 D(i) 0 1 2 3 i 4 5 60 40 20 0 1 2 3 4 5 i Emphasizes stronger modes normalized MSE 0.4 0.3 0.2 0.1 0 1 2 3 4 5 i 0 1 2 3 4 5 i Weaker modes also important [Bell 93, Fuhrmann 08] 13

NMSE-Based Power Allocation 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 total power constraint. is used to ensure the 14

Example: 5 modes, MMSE vs. NMSE 1 0.04 λ (i) 0.5 MMSE 0.02 0 1 2 3 4 5 i 0 1 2 3 4 5 i 80 D(i) 60 40 20 normalized MSE 0.4 0.3 0.2 0.1 0 1 2 3 4 5 i 0 1 2 3 4 5 i 15

Power Allocation in Colored Noise 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 16

Numerical Example 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 i MMSE-based NMSE-based MI-based 1 2 3 4 5 i NMSE 2.5 2 1.5 1 0.5 0 10 0 10-1 1 2 3 4 5 MMSE-based NMSE-based MI-based 10-2 0 5 10 15 P0 (db) i 20 17

Joint Robust Designs 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 acceptable One widely used measure: worst case performance Minimax Joint Tx (waveforms) and Rx (estimator) robust designs Existing 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 models Reasonable when PSD is estimated from data Various uncertainty models 18

Minimax Robust Designs Minimax robust scheme Bounds the worst case performance Procedure: looking for the Least-Favorable Sets (LFS) Saddle point conditions: jointly design MMSE estimator and power allocation such that MMSE-based: Robust Designs NMSE- based: MI-based: 19

Robust Design in White Noise Uncertainty only exists in target PSD MMSE-based: NMSE-based: MI-based: 20

Robust Design in Colored Noise Uncertainties for target modes and colored noise MMSE-based: NMSE-based: i.e. MI-based: i.e. 21

Robust Design in Colored Noise with Power Ratio Constraint LFS for uncertain noise PSD with power ratio constraint MI, NMSE criteria: MMSE criterion: : to guarantee the average power ratio constraint 22

Numerical Examples (1) 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 0 1 2 3 4 5 Lower Bound Upper Bound Nominal LFS i 1 1.5 2 2.5 3 3.5 4 4.5 5 i 2.5 2 1.5 1 0.5 10 9 8 7 6 5 4 3 2 1 0 i Lower Bound Upper Bound Nominal LFS 1 1.5 2 2.5 3 3.5 4 4.5 5 i 23

10 1 Numerical Examples (2) 10 1 10 0 10 0 MMSE 10-1 NMSE 10-1 10-2 0 5 10 15 20 P0 (db) Nominal PSD, Nominal design LFS PSD, Nominal design LFS PSD, Robust design Nominal PSD, Robust design 10-2 0 5 10 15 20 P0 (db) MMSE- and NMSE- based robust designs: o Large gap for LFS PSD: worst performance improved o Red dashed line: performance lower bound 24

35 Numerical Examples (3) MI(bits) 30 25 20 15 Nominal PSD, Nominal design LFS PSD, Nominal design LFS PSD, Robust design Nominal PSD, Robust design 10 5 0 0 5 10 15 20 P0 (db) MI-based robust designs: o Performance difference comes from PSDs, but not from designs o Still provide performance lower bound 25

Summary Links between MIMO communications and MIMO sensing Using MI, MMSE, NMSE criteria Optimum 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 26

Roadmap 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 27

Background Two phases of the localization process Distance measurement Time-of-arrival (TOA) based Anchor Target TOA speed of light Ultra-wideband (UWB) Fine timing resolution High obstacle penetration capability Coexistence with existing systems Trilateration Location update Cooperative localization Allows target-target communications Dramatically increase accuracy and coverage 28

Motivation Existing optimal ML TOA estimator [Win-Scholtz 02] Known time-hopping and DS codes assumption Estimates amplitude and delay for each and every channel path Too 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-lowresolution digital UWB receivers Optimality has not been explored 29

Signal Model (1) First arrival time TOA estimation: finding 30

Signal Model (2) Rx segment t Unknown parameters to estimate Aggregate pulse First arrival time and 31

ML TOA Estimator: Step 1 Log-likelihood function ML Algorithm Step 1: Step 1: get as a function of, based on a fixed guess Step 2: replace with to look for the best 32

ML TOA Estimator: Step 2 ML objective function Windows ML timing estimation t t noise free part: Correct timing: Implementation: average correlations 33

Simplified ML (SML) TOA Estimator Drawbacks of the ML estimator: Define computational complexity and redundancy : constant 34

Simulations Normalized MSE: normalized MSE 10 0 10-1 10-2 10-3 10-4 -15-10 -5 0 5 10 15 20 E/N 0 (db) TDT can approach SML closely SML TDT IEEE 802.15.3a CM1 Tp = 1ns Tf = 35ns Nf = 32 frames K=2 K=4 K=8 K=16 K=32 K=64 K=128 Performance is improved with increasing K 35

Simulations BER performance: 10 0 average BER 10-1 10-2 10-3 10-4 10-5 no timing SML TDT K=2 K=4 K=8 K=16 K=32 K=64 K=128 10-6 5 10 15 20 25 30 35 SNR(dB) TDT can approach SML closely Performance is improved with increasing K 36

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 Optimum waveform designs 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 Cooperative target estimation Sensitivity analysis of the optimum waveform designs to overestimation error Cooperative target localization 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 Thank you! 39