Robust direction of arrival estimation

Transcription

1 Tuomo Pirinen 26th February 2004 ICSI Speech Group Lunch Talk

2 Outline Motivation, background and applications Basics Robustness Misc. results 2

3 Motivation Page1 3

4 Motivation Recent (last 20 years or so) developments have made required hardware available at reasonable cost Jim Gray (1998 ACM Turing Award Winner): 3. Hear as well as a person 8. Remember what is seen and heard and quickly return it on request. 10. Build a system that, given sounds, can answer questions about the sounds and summarize them as quickly and precisely as a human expert. 12. Simulate being some other place as an observer and a participant. 4

5 Applications Seismic measurements, localization of earthquake epicenters Medical devices, especially ultrasonic imaging Telecommunications (e.g. localization of a mobile phone) Sonars, ships, boats, submarines Radars, airplanes, flight contol, ships Infrasonics, CTBT nuclear test ban surveillance 5

6 Acoustic applications Multimedia applications, multichannel spatial recordings Pre-processors: video conferences, automated cameras Advanced acoustic (noise) measurements and research Automatic surveillance (harbors, large storage areas, peace keeping) Illegal arms detection 6

7 Acoustic localization: Application examples Images c Museum Waalsdorp, Image from Blumrich, Altmann : Medium-range localisation of aircraft via triangulation, c JASA

8 Speech applications Speech and sound enhancement Hands-free systems Speech recognizers Hearing aids Meeting rooms 8

9 Spatial signals Signals: s(x,t), x =[x, y, z] T Planar wave solution Propagating waves: 2 s(x,t)= 1 c 2 2 s(x,t) t 2 Spherical wave solution 9

10 Spatial signals Observations at isolated points Resulting signals: s i (t) =s(x i,t+ τ i ) Relation between sensors (slightly ideal...) s i (t) =s j (t + τ ij ) Sensor and source locations, and shape of wavefront determine τ ij Time delays, array, and wavefront assumption give the source "location" 10

11 Localization prototype Sensors (mics) Pre-processing Time delay estimation Direction of arrival estimation Localization Sometimes the last two steps are difficult to separate 11

12 Time delay estimation Problem generally solved in the 70 s No "silver bullet", optimal practical Usually utilize some form of "alignment", or correlation: ^τ (i,j) = arg max τ N 1 t=0 With speech, reverberations are a problem s i (t)s j (t + τ) GCC-PHAT has been proposed to be robust Major improvements not very likely 12

13 DOA estimation - spherical waves Hyperbolic equations Practical situations include noise and errors No (accurate) closed form solution Iterative solutions time-consuming Distance of source affects the solution, initial guess needed If successful, solution gives DOA and location Requires propagation speed a priori 13

14 DOA estimation - planar waves Time delay Angle of arrival ϑ = cos 1 τ (i,j)c d (i,j) τ (i,j) = d (i,j) cos(ϑ) c Requires propagation speed 14

15 DOA estimation - planar waves τ (i,j) = 1 c d (i,j) cos(ϑ) is actually τ (i,j) = k x (1,2) cos(ϑ) = k x (1,2) linear! Group everything: τ (1,2) τ (1,3) τ (1,4). τ (M 1,M) = x T (1,2) x T (1,3) x T (1,4). x T (M 1,M) k τ = Xk 15

16 DOA estimation - planar waves To find out where the source is, invert: ^k = ( X T X) 1 XT ^τ Propagation speed not needed at all Solution gives an estimate ( k = 1 c ) A linear solution, no compensation for nonlinearities required Lower bound for error: c ^k 1 16

17 Problems Time delays may be erroneous Quantization Difficult signals (noise, reverb) Hardware problems Array configuration may be unknown Speech applications require accuracy and fast updates 17

18 Solutions Closed-form solutions Grid-based searches Least squares Averaging with subarrays Fast, but not very robust Work well with small errors MAD Count-distance More robust, but slow Can avoid a few large errors 18

19 Time delay selection Sum of time delays on a closed path should be zero: (i,j) P x (i,j) = 0 (i,j) P xt (i,j) k = 0 (i,j) P τ (i,j) = 0 Test all triangles ^τ (i,j) +^τ (j,m) +^τ (m,i) <THR? m i j Confidence of τ (i,j) is the number of tests passed by triangles including τ (i,j) DOA from a 3-D set of time delays with maximal minimum confidence 19

20 Failure detection Channel failure all time delays from channel have zero confidence Detect with a buffer Remove detected channels from processing Experiment: insert failures and attempt detection 20

21 Results Confusion matrix for number of failures Number of detected failures

22 Results Were correct sensors detected? correct correct correct correct order order set set % of all % of correct # % of all % of correct #

23 Results DOA estimation performance Number of failures Method LS LSD AVG AVGD TDS TDSD CNT CNTD

24 Results 1 0 failures ratio Reference LS 0.3 LSD AVG 0.2 AVGD TDS TDSD 0.1 CNT CNTD error / degrees 24

25 Results 1 1 failures ratio Reference LS 0.3 LSD AVG 0.2 AVGD TDS TDSD 0.1 CNT CNTD error / degrees 25

26 Results 1 2 failures ratio Reference LS 0.3 LSD AVG 0.2 AVGD TDS TDSD 0.1 CNT CNTD error / degrees 26

27 Results 1 3 failures ratio Reference LS 0.3 LSD AVG 0.2 AVGD TDS TDSD 0.1 CNT CNTD error / degrees 27

28 Results 1 4 failures ratio Reference LS 0.3 LSD AVG 0.2 AVGD TDS TDSD 0.1 CNT CNTD error / degrees 28

29 Results 150 1st failure 1st detection 2nd failure 2nd detection LS LSD 100 error / degrees time / seconds 29

30 Example: performance analysis Cumulative distribution of errors (simulated) ratio D array, 4 sensors (reference) 2D array, 4 sensors 0.2 2D array, 3 sensors 2D array, 4 sensors, random propagation speed 2D array, 4 sensors, random propagation speed error / degrees 3 and 4 sensors, 0.5 m tetrahedron/triangle array, sampling rate 48 khz 30

31 Example: effect of propagation speed Angular RMS error as a function of true propagation speed D array, 4 sensors (reference) 2D array, 4 sensors 2D array, 3 sensors RMS error / degrees propagation speed / m/s Same setup as in previous example, assumed propagation speed 343 m/s 31

32 Example: error detection with propagation speed true azimuth and elevation estimated azimuth estimated elevation AOA / degrees time / s error time / s 32

33 Conclusions Time delay based methods are quite robust Good accuracy, low complexity Confidence factors will increase robustness For good & fast results, use LSD Propagation speed not needed in estimation Can be used for error detection and minimization 33

34 Future directions Optimum array configurations Activity detection Faster grid-based methods Automatic selection of method Time delay errors vs. array errors, automatic correction Multiple sources Data needed 34

35 Acknowledgements Jari Yli-Hietanen Adam & Chuck Konsta Our group at TUT: Prof. Ari Visa Pasi Pertilä Jari Yli-Hietanen Mikko Parviainen Teemu Korhonen Atte Virtanen 35

36 Thanks for the cash Tampere University of Technology National Technology Agency of Finland (TEKES) The Nokia Foundation Finnish Foundation for Advancement of Technology (TES) The Emil Aaltonen Foundation 36

37 The Sapphire Challenge Find some published work about time delay based propagation vector estimation Must be prior to Yli-Hietanen et al. "Low-Complexity Angle of Arrival Estimation of Wideband Signals Using Small Arrays", Proceedings of the 8th IEEE SSAP Workshop, 1996 Win a bottle of Bombay Sapphire! Please drink responsibly 37