cooperative sensing for target estimation and target localization · 2011-05-12 · cooperative...
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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
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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
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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
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Roadmap
4
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
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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
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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
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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
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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
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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.
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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
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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.
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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
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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.
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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)
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Power Allocation in Colored Noise
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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
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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
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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
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Minimax Robust Designs
19
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
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Robust Design in White Noise
20
Uncertainty only exists in target PSD
MMSE-based:
NMSE-based:
MI-based:
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Robust Design in Colored Noise
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Uncertainties for target modes and colored noiseMMSE-based:
NMSE-based:
MI-based:
i.e.
i.e.
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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:
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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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Numerical Examples (2)
24
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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Numerical Examples (3)
25
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
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Summary
26
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
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Roadmap
27
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
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Background
28
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
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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)
30
First arrival time
TOA estimation: finding
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Signal Model (2)
31
Rx segment
Unknown parameters to estimate
Aggregate pulse
First arrival time
t
and⇔
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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:
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ML TOA Estimator: Step 2
33
t
Implementation: average correlations
ML objective function
ML timing estimation
Windows
t
noise free part: Correct timing:
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Simplified ML (SML) TOA Estimator
34
Drawbacks of the ML estimator: computational complexity and redundancy
Define
: constant
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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
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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
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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
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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
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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
39
Thank you!