DoA-Based Microphone Array Position Self-Calibration Using Circular Statistics

Transcription

1 DoA-Based Microphone Array Position Self-Calibration Using Circular Statistics Florian Jacob, Joerg Schmalenstroeer, Reinhold Haeb-Umbach Department of Communications Engineering - University of Paderborn May 29, 2013 Computer Science, Electrical Engineering and Mathematics Communications Engineering Prof. Dr.-Ing. Reinhold Häb-Umbach

2 Table of contents 1 Introduction 2 Maximum-Likelihood Geometry Calibration 3 Absolute Geometry Calibration 4 Simulation Framework & Results 5 Conclusions F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 1 / 9

3 Motivation Problem statement Array 2 Application areas of spatially distributed microphone arrays: Speaker localization & tracking Signal enhancement (e.g. beamforming) Geometry calibration required: Position & orientation of microphone arrays Array 1 Speaker Array 3 Task Automatic calibration procedure Input: Reverberant speech signal Direction-of-arrival measurements per array (avoid inter array clock sync.) F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 2 / 9

4 Overview y System overview b t e t Unknown parameters: Speaker position e t = [a t,b t] Array position p i = [x i,y i] Array orientation θ i Measured data: y i p i ϕ i,t θ i Direction of arrival ϕ i,t Observation model of a microphone pair Measurement: ϕ i,t := µ i,t +Noise Observation modeled by von Mises-pdf: p(ϕ i,t ;µ i,t,κ i,t ) = exp( κ i,t cos(ϕ i,t µ i,t ) ) 2πI 0 (κ i,t ) x i a t von Mises-pdf π π 2 0 µ i,t x κ = 1 κ = 2 π 2 π F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 3 / 9

5 Maximum-Likelihood Geometry Calibration Loglikelihood function Moving speaker Multiple measurements to a speaker position unavailable Independent observations ϕ i,t from I microphone pairs and T speaker positions: T I l(µ) := κ i,t cos(ϕ i,t µ i,t ) t=1 i=1 } #Unknowns = 2 I T #Unknowns > #Observation #Observation = I T How to overcome these drawbacks? Incorporate geometric relation: ( bt y i µ i,t := µ(p i,θ i,e t) = atan a t x i Approximate κ i,t : #Unknown=3 I +2 T κ i,t d i,t = e t p i ) θ i b t y i p i x i µ i,t θ i F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 4 / 9 y a t e t x

6 Maximum-Likelihood Geometry Calibration Optimization problem Resulting equation: p 2:I,θ 2:I,e 1:T = argmin p 2:I,θ 2:I,e 1:T { T t=1 i=1 Iterative optimization using Newton root finding algorithm I [ ( d i,t 1 cos ϕi,t µ(p i,θ i,e )]} t) Recovers array positions, orientations and speaker positions Result has arbitrary scaling F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 5 / 9

7 Absolute calibration using circular arrays How to recover the scaling? Literature: Knowledge of distance between two sensor nodes Proposed: Obtain scaling information from radius of circular microphone arrays g j p i i β θ i γ j Calibration using circular arrays Express position of microphone pair relative to center of circular array: p i = g j + i and θ i = γ j +β i Determine position and orientation of circular arrays instead of microphone pairs T J I g 2:J,γ 2:J,e 1:T = argmin [ ( d g 2:J,γ 2:J,e 1:T i,t 1 cos ϕi,t µ(g j,γ j, i,e )] t) t=1 j=1 i=1 Apply same optimization as before F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 6 / 9

8 Simulation Framework Scenario 3 circular arrays with 5 microphones 5 array arrangements, approx. distance of 1 m 6 min long speaker trajectory Reverberation times form 0ms to 500ms DoA estimates obtained by adaptive beamforming, on blocklength of kHz sample sensor configuration 5m Trajectory 8m Random Sample Consenus Framework Outlier rejection Handle large data sets Observation database Sub database selection RANSAC embedded calibration Result fusion Geometry F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 7 / 9

9 Simulation Results Error measure Mean position error: Average distance between real and estimated sensor position Apply rigid body transformation to match real and estimated positions Distinguish between 2 error types: Geometric + Scaling errors (MPE abs): Rotation + Translation Geometric errors (MPE rel): Rotation + Translation + Scaling Mean position error / [m] MPE abs MPE rel Room reverberation time T 60 / [ms] 500 DoA RMSE / [ ] RMSE Room reverberation time T 60 / [ms] F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 8 / 9

10 Conclusions Summary Geometry calibration framework base on reverberated speech input Circular arrays enable absolute geometry calibration ML-Estimator in case of von Mises distributed observations RANSAC-Framework: Outlier rejection and handling of large data sets Calibration Error: Relative positioning error < 10cm Absolute positioning error < 25cm } Even in case of high reverberation F. Jacob, J. Schmalenstroeer, R. Haeb-Umbach 9 / 9

11 Thank you for your attention! Questions? This work has been supported by Deutsche Forschungsgemeinschaft (DFG) under contract no. Ha3455/7-1. Florian Jacob University of Paderborn Department of Communications Engineering nt.uni-paderborn.de Computer Science, Electrical Engineering and Mathematics Communications Engineering Prof. Dr.-Ing. Reinhold Häb-Umbach