Source Localization and Beamforming

1
Source Localization and Beamforming

• Joe C. Chen, Kung Yao, and Ralph E. Hudson
• Presentation Tristan Boscardin
• 4/13/2005
• CS-791T Presentation

2
Outline

• Introduction
• Tracking Applications
• Microsensor Networks
• Physical Features
• System Features
• Self Organization and Ad Hoc Sensor Networks
• Layered Architecture for Energy Constrained
  Communications and Processing
• Source Localization, DOA Estimation and
  Beamforming
• Closed-Form Least Squares Source Localization
• Iterative Maximum-Likelihood Source Localization
  and DOA Estimation
• Cramér-Rao Bound Analysis
• Blind Beamforming
• Conclusion
• Acknowledgements

3
Introduction
s3
s4

• Sensor networks monitor and area and provide data
• Source is an motorized vehicle
• Emits low frequency vibration signals
• Data is analyzed to determine if a target is
  detected and what is its location
• Achieved using beamforming and source location
  methods

s1
s2
Source
Source
s1
s2
s3
s4
0
time
(Wang, Feb. 19, 2004)
4
Introduction

• Source localization
• Method for determining target location using DOA
  (direction of arrival) or distance of origin of a
  signal
• Beamforming
• Method of combining data in a system to eliminate
  noise and increase accuracy of results through
  shifting and summing multiple signals
• Two elements that can be used together for
• Detecting
• Identifying
• Localizing
• Tracking
• Capable of tracking multiple targets
• Limited by the number of sensors and saturation
  point of sensors

(Liu, Reich, and Zhao, 2003)
5
Tracking Applications

• Military
• Surveillance, Reconnaissance, Combat Scenarios
• Industry
• Intrusion Detection, Plant Monitoring
• Domestic
• Hearing Aids
• Camera Aiming
• Traffic Monitoring

(http//www.mvtec.com/halcon/applications/surveill
ance/xing-large.gif)
(http//www.gothamgazette.com/graphics/cameras-nyc
.jpg)
(http//www.missilesandfirecontrol.com/our_product
s/combatvision/SCOUT/images/main-420.jpg)
6
Physical Features of Signal

• Seismic and Acoustic Features Considered Only
• Acoustic versus seismic source
• Narrowband versus wideband signal
• Far-field versus near-field source
• Known versus unknown propagation speed
• Free-space versus reverberant space propagation
• Single versus multiple source
• Movement Generates Vibrational Wave Forms
• Personnel, car, truck, wheeled/tracked vehicles,
  vibrational machinery

7
Tracking Wheeled Vehicles

• Acoustic
• Range 20 Hz-2 KHz
• H-L Freq. Ratio 100
• Wideband
• Propagation Speed 345 m/s
• Wind velocity has second order effect
• Subject to reverb based upon environment.
• Indoors performance is inferior to outdoor
• Varies 10-90 when striking a surface
• Acoustic energy dissipates at a rate proportional
  to the inverse of the square of the distance
  traveled.

• Seismic
• Range 5 Hz-500 Hz
• H-L Freq. Ratio 100
• Wideband
• Propagation Speed Medium Dependent
• Generally much faster than sound through air
• Considerable reverb due to non-homogeneity of
  medium.
• Multiple Signals
• Difficult DOA estimation
• Confused with multiple sources
• Seismic energy dissipates more rapidly than
  acoustic

8
Microsensor Networks

• System Features
• Power-line versus battery power supply
• Wired versus wireless RF links
• Passive versus active sensor
• Collaborative versus non-collaborative sensing
• Coherent versus non-coherent processing
• Synchronous versus non-synch. sensing
• Known versus unknown sensor response
• Known versus unknown sensor location
• Wideband versus narrowband processing
• Distributed versus central processing

9
Microsensor Networks

• Self Organization and Ad Hoc Sensor Networks
• Traditional design rules are generally not
  applicable
• Localized decision making and distributed
  processing
• Detection
• Identification
• Localization
• Beamforming
• Low Power Transceivers ? Multi-hop Transmission

10
Microsensor Networks

• Layered Architecture for Energy Constrained
  Communications and Processing
• Different operational modes for different tasks
  to reduce power consumption
• Thresholds set about ambient background noise
• Different sensors used for processing
• Detection verification
• DOA estimation
• Alert adjacent nodes of detection
• Adjacent nodes can provide verification of
  detection
• Data reduced to dominant Frequency Bands
• Whole sets of raw data are unnecessary

11
Source Localization, DOA Estimation and
Beamforming

• Narrow-Band Model
• DOA information contained in the phase difference
  among sensors
• Conventional beamformer is a spatial extension of
  a matched filter in addition to time/frequency
  filtering
• Beamforming enhances signal from the desired
  spatial direction
• Reduces signals from other directions
• DOA estimation provided an early version of the
  Maximum-Likelihood (ML) solution
• High computational cost deterred use
• Sub-optimal techniques developed to reduce
  computational load
• Multiple Signal Classification (MUSIC)
• Utilizes orthogonality between signals
• Easily confused by highly correlated sources
• Variants

12
Source Localization, DOA Estimation and
Beamforming

• Wideband Model more appropriate for
  acoustic/seismic sensors
• Unmodulated
• Wider bandwidth
• As source approaches the array both the angle and
  range become subjects of interest
• Different from narrowband signal
• Not stochastic Most likely to be deterministic,
  but unknown.
• Near-field scenario
• Each sensor may have a different gain
• Gain difference due to variation in propagation
  paths

13
Closed Form Least Squares Source Localization

• Data (x) collected at sensor (p) at time (n)
• p ? R Sensor array
• n is a location in time
• ap is the signal gain level
• s0 is the source signal
• tp is the fractional time delay
• wp is zero mean white Gaussian noise
• Fractional time delay (tp)
• rsm is the source coordinates
• rp is the sensor coordinates
• v is the velocity of propagation
• Relative time delay, (tpq)
• Convert to linear equation
• A is the system matrix containing the sensor
  locations
• y is the matrix of unknown source locations
• b is a function of sensor locations

14
Iterative Maximum-Likelihood Source Localization
and DOA Estimation

• Array signal model in time domainFor a randomly
  Distributed array of P Sensors, the data
  collected by the pth sensor at time n is
• For n0,,N-1
• For p1,,P
• Where aP is the signal gain level of the source
  at the pth sensor
• s0 is the source signal,
• tp is the fractional time delay in samples
  (tprs-rp/v).
• Array signal model in frequency domain
• where the array data spectrum
• The steering vector
• S0(k) is the source spectrum
• ?(k) is zero mean complex white noise with a
  variance of Ns2

Chen, Hudson, and Yao, 2002
15
Iterative Maximum-Likelihood Source Localization
and DOA Estimation

• ML source localization is based upon parameter
  estimation
• Increased computational complexity, but greater
  accuracy
• Introduces optimization criterion
• Estimation of time delay
• Calculation of source location
• Parametric solution obtained by Fourier transform
• By combining data spectrum vector in the positive
  bins, ML solution is given by
• T is the unknown parameter vector
• P(k,T) is the orthogonal projection matrix
• X(k) is the signal spectrum vector

16
Cramér-Rao Bound (CRB) Analysis

• The CRB (Cramer 1946) defines the ultimate
  accuracy of any estimation procedure
• Intimately related to the ML estimator
• Seeks the bound on the mean squared error
• A matrix is lower bounded by another matrix if
  the difference is non-negative definite.
• The variance of an estimator is inverse to the
  Fisher information matrix (I(?))

(Johnson 2003)
17
Cramér-Rao Bound (CRB) Analysis

• Limitation of performance capabilities
• Evaluated with the CRB
• Allows the calculation of the estimation variance
  (S) of the lower bound of an unbiased
  estimator
• G is dependent on the array geometry
• S is the scale factor contingent on the signal
• Linearly Proportional to noise variance, speed of
  propagation, and inversely to spectrum and
  frequency

18
Blind Beamforming

• Alternative to using other calibration techniques
• Enhances array without much information without
  array
• Cross-correlation only may increase
  communication cost
• Tends to detect loudest event.. May not be
  noise immune
• Narrowband
• Cumulant (HOS) used to estimate the steering
  vector of the source up to the scale factor
• Cancellation of HOS
• 4th-order (kurtosis) is most common
• If y1, y2, y3, y4 can be separated into 2 groups
  that are mutually independent, 4th-order cumulant
  is zero
• Must check all 4th-order cumulants
• Statistical properties of cumulant estimators are
  poor
• Online calibration requires large amounts of
  data
• Tough for realtime calculation

19
Blind Beamforming

• Wideband
• Second-order Statistic (SOS) is proposed
• Maximum power (MP) beamformer uses dominant eigen
  vector or singular value to create an array of
  weights
• Collects the MP fro the dominant source
• Rejects noise and interference from inferior
  sources
• The correlation matrix is defined as
• H denotes the complex conjugate transpose
• Desired beamformer output
• wrl denotes the lth weight coefficients for the
  rth sensor
• w matrix used to maximize correlation matrix and
  minimize noise

20
Conclusion

• Signal processing and sensor network capabilities
  must both be considered to formulate an effective
  localization tool
• Must match computation and communication
  constraints
• Improvements in electronics allow for more
  complex algorithms
• however energy consumption concerns are ever
  present in a sensor network.
• Algorithms which are highly sensitive to
  geometric, resource, and task orientated factors
  will provide invaluable flexibility to sensor
  network behavior

21
Acknowledgments

• Chen, Hudson, and Yao, 2002
• Liu, Reich, and Zhao, 2003
• Wang, 2004
• Minero 2004
• Savvides 2004
• (http//www.mvtec.com)
• (http//www.gothamgazette.com)
• (http//www.missilesandfirecontrol.com)

22
Raleigh Surface Wave

• Propagation speed of a Raleigh Surface Wave is
  dependent upon the material the vibration is
  traveling through (i.e. dry sand to hard rock).
• Varies from Mach 0.7 to 15
• Dependent on Mechanical Properties of the Medium
• Young's Modulus
• Bulk Modulus
• Density
• Etc
• Can be approximated with a LS estimation based on
  sensor collected data.

23
Qualities of Distributed vs. Centralized Wireless
Sensing

• Strengths
• Improved robustness by sensor redundancy
• Improved SNR by sensors spatial distribution
• Weaknesses
• Limited battery energy
• Limited wireless bandwidth
• Energy consumption per bit
• Wireless communication cost gtgt Processing cost
• Calls for distributed, in-network processing

(Wang, Feb. 19, 2004)