Energy Based Acoustic Source Localization Xiaohong Sheng YuHen

Energy Based Acoustic Source Localization Xiaohong Sheng, Yu-Hen Hu University of Wisconsin – Madison Dept. Electrical and Computer Engineering Madison, WI 53706 sheng@cae. wisc. edu, hu@engr. wisc. edu http: //www. ece. wisc. edu/~sensit/

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

UWCSP: Univ. Wisconsin Collaborative Signal Processing Node Detection Node Classification • • 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

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, p=2 , … • 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.

Existing Energy-based Acoustic Source Localization Methods • 2 d 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, 2003: 4, pp. 321 -337.

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 K’s 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.

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:

Maximum Likelihood Parameter Estimation Problem Formulation • Likelihood function • Log-Likelihood Function • Parameters – Need at least k(p+1) sensors, p is the dimension of the location • Non-linear optimization problem!

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

EM-like Iterative Solution Set and substitute results into the modified likelihood function to solve for EM-like iterative solution: 1. Assume S, estimate 2. Use updated re-estimate Challenge: easily trapped in local minimum

Simulation: Performance Comparison

Cramer-Rao Bounds Analysis • Fisher Information Matrix • CRB

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

CR Bounds Example: different sensor deployment results Sensor Deployment CRB for the Corresponding Sensor Deployment

Application to Field Experiment Data • Sensor deployment, road coordinate and region specification for experiments

Localization Results (Experiments) AAV DW Ground truth and estimation results Estimation error histogram

Simulation on Multi-target Localization • (a) sensor deployment and road coordinate for simulations • (b) Ground truth for two targets moving in the opposite direction

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

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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