a self-calibrating system of distributed acoustic arrays

1. 1 A Self-Calibrating Systemof Distributed Acoustic Arrays Lewis Girod CENS Systems Lab girod@cs.ucla.edu

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3. 3 Problem Statement Target System: Input: Node placement: 3D, Outdoor, Foliage OK 20m Inter-node spacing Arrays are level Output: Estimates: XYZ Position ± 25cm Orientation ± 2° Results in James Reserve Accurate: Mean 3D Position Error: 20 cm Precise: Std. Dev. of Node Position: 18 cm

4. 4 Outline Overview of system Ranging and DOA DSP Algorithm Performance of Ranging and DOA Performance of overall system Conclusions and future work

5. 5 Acoustic Position Estimation System:A Vertical Distributed Sensing Application start by saying vertical application to compute position estiamtes using acoustic ranging etc and this needs all these start by saying vertical application to compute position estiamtes using acoustic ranging etc and this needs all these

6. 6 Position Estimation Application explain pn code ideaexplain pn code idea

7. 7 Acoustic Array Configuration 4 condenser microphones, arranged in a square with one raised 4 piezo “tweeter” emitters pointing outwards Array mounts on a tripod or stake, wired to CPU box Coordinate system defines angles relative to array

8. 8 Range and DOA Estimation Inputs: The input signals from the microphones The time the signal was emitted (used to select from input signal) The PN code index used Outputs Peak phase (i.e. range) The 3-D direction of arrival: ?, ?, and a scaling factor V Signal to Noise Ratio (SNR)

9. 9 Filtering and Correlation Stage Synchronized Sampling Layer completely abstracts application from synchronization details Correlation Generate reference signal from PN code index Correlate against the incoming signal

10. 10 Correlation Signal detection via “matched filter” constructed from PN code Observed signal S is convolved with the reference signal Peaks in resulting “correlation function” correspond to arrivals Earliest peak is most direct path

11. 11 Detection Stage Want to detect first peak above noise floor Need to capture approx. “peak region” – peak selection refined later Noise floor is time varying and must be estimated Use EWMA to compute continuous mean and variance estimate Selected a such that system adapts to 1% within 5ms Define threshold to be a multiple of the standard deviation First value over threshold considered “peak” How to select threshold?

12. 12 Selecting a Peak Detection Threshold Given a peak detection threshold, e.g. 12, we can determine for any given signal the “noise peak” and “detection peak”. To be certain not to detect noise, we want a wide gap between the distribution of rejected noise peaks and of detection peaks We selected a threshold of 12, and tested it with 100,000 trials collected at the James Reserve. picture of noise and detection peaks on this slide with arrows and draw in 12….picture of noise and detection peaks on this slide with arrows and draw in 12….

13. 13 Zooming in.. 8x Interpolation Sub-sample phase comparison is critical to DOA estimation Otherwise, large quantization errors: 1 sample offset = 5° Once a peak region is identified Zoom in by interpolating Use Fourier coefficients to expand the signal at higher resolution Equivalent to phase shift in FD But enables direct TD processing of correlation outputs

14. 14 DOA Estimation and Combining Stage 6-way cross-correlation of correlations ? DOA Estimator Filtered signals from each pair of microphones are correlated Offset of maximum correlation between pair (“lag”) recorded DOA Estimator uses least squares to fit “lags” to array geometry Key: Resilient to perturbations in microphone placement DOA estimate used to recombine signals to improve SNR Final peak detection yields range estimate

15. 15 An idea that didn’t work so well: “Angular Correlation” For each possible angle: Hypothesize incoming angle Shift correlation functions to match Multiply and accumulate Problem: Too Sensitive to microphone placement Slight shift misses peaks

16. 16 Position Estimation Problem: Given pair-wise range and DOA estimates Estimate X,Y,Z locations and orientation T for each node Solved using iterative non-linear least squares

17. 17 Experiments Component Testing Azimuth angle test Zenith angle test Range test

18. 18 Experimental Setup for Angular Tests

19. 19 Azimuth Errors as Function of Angle

20. 20 Overall Distribution of Azimuth Errors

21. 21 Zenith Errors as Function of Angle Negative angles are obstructed by the array itself, and have much worse variance. Zenith performance varies with the azimuth angle, perhaps a function of the array geometry. Our data only tested two azimuth angles.

22. 22 Overall distributions of Zenith Angle The zenith data does not fit well to a normal distribution (which is problematic because the position algorithms assume that). To improve things slightly, we computed statistics on subsets of the data. Both position algorithms can accept parameterized ? values.

23. 23 Experimental Setup for Range Tests

24. 24 Range Measurements with Mean Error

25. 25 Anomalous Behavior at 50m Might be due to bug in time synchronization service that has since been fixed, or to environmental variables.

26. 26 Overall Distribution of Range Errors Not a particularly good fit to normal distribution Might improve under more controlled experiment (e.g. lot 4) Doesn’t account for possible differences node to node

27. 27 System Tests Experimental Process Lay out 10 nodes, and run system to collect ranges and DOA Apply positioning algorithms to compute maps Compare to ground truth Metrics1 Average Range Residual Measures quality of fit, useful when GT unknown Simple average of range residual values Average Position Error Absolute measure of performance, useful when GT known Fit estimated map to ground truth Then compute average distance between corresponding points

28. 28 Fitting to Ground Truth to get “Fair” Position Error

29. 29 System Test: Court of Sciences 10 nodes placed at yellow dots Yellow lines denote tall hedges Ground truth measured as carefully as possible and arrays aligned to point west. Z axis was difficult to measure; used data from Google Earth, which is measured to the nearest foot.

30. 30 Repeatability: Per-node XY mean and std-dev these show the repeatability of positioning over multiplie experiments Are non-zero mean due to errors in ground truth or measurementsthese show the repeatability of positioning over multiplie experiments Are non-zero mean due to errors in ground truth or measurements

31. 31 Z and Orientation mean and std-dev Are non-zero means due to errors in ground truth or in measurements? X/Y estimates: unclear. Ground truth incorporated cumulative errors and obstructions often blocked efforts to measure both axes. Z estimates: likely inaccurate. The variation is larger than that expected from Google Earth data. Orientation estimates: likely accurate: They are generally low-variance and ground truth errors in alignment of 5 degrees are expected.

32. 32 James Reserve System Test Deployed 10 nodes in forested area. In many cases LOS was partially obstructed. Ground truth measured using professional surveying equipment. Nodes were aligned to point approximately west by compass.

33. 33 James Reserve per-node mean and std-dev

34. 34 James Reserve Z and Orientation mean/std-dev For many nodes, the variance in Z values for the hilly JR data is considerably lower than those in the courtyard data. The orientation repeatability is comparable to the courtyard data. All data taken from the 6 experiments that placed all 10 nodes. The location stakes are still in place.

35. 35 Conclusions Acoustic ENSbox platform supports distributed acoustic sensing Implemented ranging and position estimation application. Highly accurate positioning in a challenging environment XYZ Position ±20cm Orientation ±2° Nearly order of magnitude improvement upon prior work 9 cm XY error vs. 50 cm (UIUC) Supports XYZ+T estimation achieved with fewer nodes lower densities more difficult conditions.

36. 36 Future Work Array geometry calibration, tilt sensor New tests with better measurement of array orientation Forward/reverse range discrepancies Improvements to hardware, array geometry Development and testing of applications

37. 37 Review of Contributions start by saying vertical application to compute position estiamtes using acoustic ranging etc and this needs all these start by saying vertical application to compute position estiamtes using acoustic ranging etc and this needs all these

38. 38 Thank you!