Energy Based Acoustic Source Localization

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Energy Based Acoustic Source Localization

• Xiaohong Sheng, Yu-Hen Hu
• University of Wisconsin Madison
• Dept. Electrical and Computer Engineering
• Madison, WI 53706
• sheng_at_cae.wisc.edu, hu_at_engr.wisc.edu
• http//www.ece.wisc.edu/sensit/

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Sensor Network Collaborative Signal Processing

• Sensor network is a novel signal processing
  platform
• Characteristics of sensor network
• Limited communication bandwidth
• Low power operation
• Collaborative signal processing is necessary
• Detection
• Classification
• Localization
• Tracking

Sitex 02 experiment sensir field
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UWCSP Univ. Wisconsin Collaborative Signal
Processing
Node Detection

• Distributed Signal Processing Paradigm
• (Local) Node signal processing
• Energy Detection
• Node target classification
• (Global) Region signal processing
• Region detection and classification fusion
• Energy based localization
• Kalman filter tracking
• Hand-off policy

Node Classi- fication
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General Localization Approach

• Physical Model
• Time Delay of Arrival (TDOA)
• Direction of Arrival (DOA)
• Received Signal Strength (Energy)
• Algorithm
• Linear Bayesian Estimation
• ML estimation
• Non-Linear Bayesian Estimation
• Particle Filter
• Least Square Estimation
• norm p, p2 ,

• Energy-based Approach
• Use signal strength (Model)
• Easier to measure
• no need to compute phase
• Less communication burden
• one energy measurement per thousands of time
  samples
• Less computation burden
• fast algorithm is available.

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Existing Energy-based Acoustic Source
Localization Methods

• 2d CPA Method (CPA)
• Compare sensor energy readings within the region.
  Use sensor locations that yields maximum reading
  as the target location (with a small
  perturbation)
• Energy-Ratio Nonlinear Least Square (ER-NLS)
  Method
• Take pair-wise ratio of acoustic energy readings.
  The potential target location then will be
  restricted to a hyper-circle in the sensor field.
  
• With all pair-wise energy ratios taken, a
  nonlinear least square solution to the target
  location can be sought.
• Energy-Ratio, Least Square (ER-LS) Method
• The nonlinear least square problem can be further
  simplified into a least square problem with
  non-iterative solution.

Dan Li, Yu Hen Hu, Energy-based collaborative
source localization using acoustic microsensor
array, EURASIP J. On Applied Signal Processing,
20034, pp. 321-337.
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Model of Acoustic Energy Measurements

• Source Energy attenuates at a rate that is
  inversely proportional to the Square of the
  distance to the source
• Energy Received by each Sensor is the Sum of the
  Decayed Source Energy
• gi gain factor of the microphone
• Sk(t) energy emitted by the kth source
• ?k(t) Source Ks location during time interval
  t.
• ri sensor location of the ith sensor
• ?i(t) perturbation term that summarizes the net
  effects of background additive noise and the
  parameter modeling error.

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Notations

• Let
• be the Euclidean distance between sensor i and
  target j, and

• Also define
• and
• Then, the energy attenuation model can be
  represented as

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Maximum Likelihood Parameter Estimation Problem
Formulation

• Likelihood function
• Log-Likelihood Function
• Parameters
• Need at least k(p1) sensors, p is the dimension
  of the location
• Non-linear optimization problem!

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Projection Solution

• Set

• Modified Likelihood Cost Function
• Insert the result to get the modified
  function

is the Reduced SVD of H
is the Projection Matrix of H
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EM-like Iterative Solution

• Set and substitute results into
  the modified likelihood function to solve for
• EM-like iterative solution
• Assume S, estimate
• Use updated re-estimate
• Challenge easily trapped in local minimum

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Simulation Performance Comparison
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Cramer-Rao Bounds Analysis

• Fisher Information Matrix
• CRB

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Ways to Reduce CRB

• Chebyshev's inequality
• Reduce CRB
• Decrease the overall distance between the sensor
  to the target
• Deploy sensor densely
• Good Deployment Structure
• when source is fixed,
• Deploy the sensors symmetrically around this
  source
• When source is moving
• Deploy the sensors uniformly distributed in the
  region
• When the source is along the road,
• deploy the sensors symmetrically along the two
  side of the road
• Avoid to deploy sensor on the same line

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CR Bounds Example different sensor deployment
results
Sensor Deployment
CRB for the Corresponding Sensor Deployment
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Application to Field Experiment Data

• Sensor deployment, road coordinate and region
  specification for experiments

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Localization Results (Experiments)
AAV
DW
Estimation error histogram

• Ground truth and estimation results

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Simulation on Multi-target Localization

• (a) sensor deployment and road coordinate for
  simulations

• (b) Ground truth for two targets moving in the
  opposite direction

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Comparison of ML estimation
Estimation Error Distance
Target 1
Target 2
Target 2
Estimation Variance and CRB
Target 1
Projection Solution with ES and MRS and EM
solution
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Conclusion

• We present a maximum likelihood based acoustic
  source localization method for wireless sensor
  network application.
• Bandwidth saving
• The feature used is acoustic energy averaged over
  a long period (say, 0.75 seconds). Hence, only
  small amount of information needs to be
  transmitted via wireless channel.
• Good performance
• ML estimation can be used for Multi-target
  localization
• Compared to CPA and ER-NLS, ER-LS method, the ML
  method yields best performance, variance ?its CRB
• ML Estimation with Projection Solution and MR
  Search provide good performance and good
  computation complexity

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Problems and Solutions

• Sensible to sharp background noise, sensor fault
  and gain estimation error.
• Ways to improve this method
• Sub-band Analysis
• Sub-band Detection, Sub-band Localization
• Sequential Analysis
• Using Tracking Results Kalman Filter
• Modeling the energy transition by Markov Modeling
• Fault sensor Identification
• Combine them together
• Robust Test
• Other Problems
• Number of the targets in the region ? HardBut
  can
• What if several different classes of the targets
  in the same region?
• Sub-band subtraction?

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The End
http//www.ece.wisc.edu/sensit/ Thanks
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Assumptions

• Sound propagates in the free air
• Target is pre-detected
• Propagation Delay can be omitted
• Sound source is omni-directional
• Size of engine is relative small compared with
  the distance between the sensor and the vehicle
• Propagation medium is roughly homogenous
• no gusty wind, no sound reverberation.
• Noise is uncorrelated to signal,
• Signal from different source is uncorrelated
• Time window (T) for averaging energy
• short enough so that acoustic waveform is
  stationary at this period,
• long enough ( more than 400 sampling point) so
  that the average noise energy in this period can
  be assumed as Gaussian distributed.