1. Energy Based Acoustic Source Localization
Xiaohong Sheng, Yu-Hen Hu
University of Wisconsin – Madison
Dept. Electrical and Computer Engineering
Madison, WI 53706

2. 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

3. 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
The UWCSP architecture and a Matlab implementation will be presented along a poster paper by Marco F. Duarte this afternoon.

4. 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.

5. 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, 2003:4, pp

6. 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.

7. 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:

8. 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!

9. 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

10. 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

11. Simulation: Performance Comparison
Histogram of absolute localization error with different number of sensors within a sensor field of size 100 by 100 meters square. A single target with energy measured at 1meter equal to 5000 unit. Sigma_n = 1, mu = 1, average of 2000 independent trials. In each trial, all sensor locations and target locations are randomly chosen within the sensor field.
The purpose of this simulation is to compare the accuracy of different algorithms assuming the same acoustic energy attenuation model.
The Figure show that Ml estimation has better performance in the sense that it has less maximum estimation error and the estimation error are mainly concentrated on the small value. Both mean estimation error and estimation variance are smaller then other methods.

12. Cramer-Rao Bounds Analysis
Fisher Information Matrix
CRB

13. 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

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

15. Application to Field Experiment Data
Figure shows the sensor deployment, road coordinate and region specification for our experiments conducted in Nov The sensor field is divided into two sensor field, for region 1, manager node is 1, node 41,42,51,54,55,58 and 59 are detection node. For region 2, node 58 is manager node, node 47,48,49,50, 52,and 53 are detection nodes.
Each detection node first performs CFAR detection to detect the target, and then send the detection results to the manager node, manager node will perform region based fusion decision to detect whether or not the target is in the region. If it is in the region, then it will perform ebl to localize the target.
Sensor deployment, road coordinate and region specification for experiments

16. Localization Results (Experiments)
AAV DW
This figure shows the localization results based on the ML estimation and energy ratio based NLS estimation. Again, results show that both algorithm get good performance for the real experiment data.
Both ML and NLS algorithms perform well estimations of target location.
ML algorithm with projection solution outperforms to NLS algorithm
Less estimation error,
smaller maximum error
NLS algorithm needs less bandwidth.
NLS doesn't use noise variance for its estimation while ML algorithm does need it.
NLS algorithm save about 1/4 bandwidth.
Localization estimation results look bias from the real ground-truth.
Inaccurate GPS measurement, sharp background noise or sensor faults
Ground truth also looks bias from the road
Ground truth and estimation results
Estimation error histogram

17. Simulation on Multi-target Localization
We did simulation on multi-target localization. This is the sensor deployment and road coordinate for the multi-target localization simulation. The two targets move in opposite direction.
(a) sensor deployment and road coordinate for simulations
(b) Ground truth for two targets moving in the opposite direction

18. Comparison of ML estimation
Target 1
Estimation Error Distance
Target 2
Estimation distance error comparison for projection solution using MR search and exhaustive search and EM solution
(a) target 1, (b) target 2
two targets moving in opposite direction
Noise is uniformly distributed from 0.01ymax to 0.04ymax,
s1=s, s2=1.2s
Projection solution has much better performance than EM solution
Estimation distance error comparison for projection solution using MR search and exhaustive search and Direct solution with EM algorithm
Estimation Variance of Projection Solution approaches to its CRB ( reach its performance bounds
ML estimation with projection solution
Advantage.
Accuracy, Robust, Variance → CRB.
Disadvantage
Heavy computation burden
EM Algorithm
Advantage:
Low computation Complexity
Easy to track into local minimum
Nonlinear Least Square
Advantage
No need to use the variance estimation
Less communication bandwidth requirement
Disadvantage of NLS
Single Target localization
Performance is not as good as Projection solution
Projection solution + MR search
Reduce the computer burden a lot
Performance is still outstanding
Using previous estimated location
Reduce the search region
Improves the efficiency
Conclusion
Projection Solution + MR search + previous estimation location
outstanding performance and reasonable computation burden
The above estimation is based on the assumptions:
Noise i.i.d., Gaussian Distributed
No sharp background noise
Sensor fault doesn’t happen
The number of targets in the region has been estimated ( need to use sequential analysis)
Target 1
Estimation Variance and CRB
Target 2
Projection Solution with ES and MRS and EM solution

19. 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

20. The End
Thanks