Binaural Sound Source Localisation and Tracking using a Dynamic Spherical Head Model Christopher Schymura, Fiete Winter, Dorothea Kolossa, Sascha Spors September 7, 2015 

Introduction Task: Tracking a moving sound source x y ψk φk T ˙ φk 1 / 9 

Introduction Some existing approaches for sound source tracking: [Portello et al. (2011), Traa & Smaragdis (2013)] using Kalman filters [Ward et al. (2003), Lu & Cooke (2011)] using particle filters 2 / 9 

Introduction Some existing approaches for sound source tracking: [Portello et al. (2011), Traa & Smaragdis (2013)] using Kalman filters [Ward et al. (2003), Lu & Cooke (2011)] using particle filters Head rotations can improve localisation by resolving front-back ambiguities (see [Wallach (1940), Blauert(1997)]). 2 / 9 

Introduction Some existing approaches for sound source tracking: [Portello et al. (2011), Traa & Smaragdis (2013)] using Kalman filters [Ward et al. (2003), Lu & Cooke (2011)] using particle filters Head rotations can improve localisation by resolving front-back ambiguities (see [Wallach (1940), Blauert(1997)]). Computational models investigating the effects of head movements: [Schymura et al. (2014), May et al. (2015), Ma et al. (2015)] 2 / 9 

System overview xk+1 = f(xk , uk ) + vk ˆ yk = h(xk ) + wk + ˆ yk yk − Process and measurement model equations ˆ xk = ˆ x− k + Kk ˆ ek ˆ ek ˆ x− k State estimation uk = g(ˆ xk ) ˆ xk Controller • uk 3 / 9 

System overview xk+1 = f(xk , uk ) + vk ˆ yk = h(xk ) + wk + ˆ yk yk − Process and measurement model equations ˆ xk = ˆ x− k + Kk ˆ ek ˆ ek ˆ x− k State estimation uk = fu (ˆ xk ) ˆ xk • Controller • uk 3 / 9 

Process model State space: xk = φk ˙ φk ψk T 4 / 9 

Process model State space: xk = φk ˙ φk ψk T Process model: xk+1 =   φk+1 ˙ φk+1 ψk+1   =   φk + T ˙ φk + vφ, k ˙ φk + v ˙ φ, k sat(ψk + T ˙ ψmax uk , ψmax ) + vψ, k   4 / 9 

Process model State space: xk = φk ˙ φk ψk T Process model: xk+1 =   φk+1 ˙ φk+1 ψk+1   =   φk + T ˙ φk + vφ, k ˙ φk + v ˙ φ, k sat(ψk + T ˙ ψmax uk , ψmax ) + vψ, k   vφ, k ∼ N(0, σ2 φ ), v ˙ φ, k ∼ N(0, σ2 ˙ φ ), vψ, k ∼ N(0, σ2 ψ ) sat(x, xmax ) = min(|x|, xmax ) · sgn(x), uk ∈ [−1, 1] 4 / 9 

Binaural front-end . . . g1 (n) gM (n) . . . g1 (n) gM (n) sL (n) • sR (n) • . . . . . . Binaural Processor τ1, k τM, k . . . δ1, k δM, k . . . yk = τ1, k , · · · , τM, k , δ1, k , · · · , δM, k T 5 / 9 

Measurement model Spherical head model [Brungart (1999), Algazi et al. (2001)]: Ri (xk , ω) = c 4πωa2 ∞ ν=0 hν ω c d hν ω c a (2ν + 1) Lν sin(ϑear ) cos (φk − ψk − φi ) i ∈ {R, L} a xL ϑear xR φR xps φps z x 6 / 9 

Measurement model Spherical head model [Brungart (1999), Algazi et al. (2001)]: Ri (xk , ω) = c 4πωa2 ∞ ν=0 hν ω c d hν ω c a (2ν + 1) Lν sin(ϑear ) cos (φk − ψk − φi ) i ∈ {R, L} a xL ϑear xR φR xps φps z x Spherical head parameters, taken from [Algazi et al. (2001)]: Head radius a: 8.5 cm Ear’s azimuth angle φi : 93.60◦ Ear’s polar angle ϑear : 110.67◦ 6 / 9 

Head rotation strategies Evaluation of three different approaches: No head rotation Periodic sweeping Smooth posterior mean fu 0 sin 2πk T Tp |φk−ψk| 1+|φk−ψk| sgn φk − ψk Type - feed-forward feedback 7 / 9 

Evaluation results Source position [deg] 30 60 90 120 150 Circular RMSE [deg] 0 20 40 60 80 100 120 140 Static head at 0° Periodic scanning around 0° Smooth posterior mean Static scenario Initial source position [deg] 30 60 90 120 150 Circular RMSE [deg] 0 20 40 60 80 100 120 140 Static head at 0° Periodic scanning around 0° Smooth posterior mean Dynamic scenario Evaluation metric: cRMSE = 1 K K k=1 min l∈Z ˆ φk − φk + 2πl 2 8 / 9 

Summary A binaural model for localisation and tracking of moving sound sources using continuous head rotations was proposed. 9 / 9 

Summary A binaural model for localisation and tracking of moving sound sources using continuous head rotations was proposed. The model allows for treating the localisation task as a closed-loop control problem. 9 / 9 

Summary A binaural model for localisation and tracking of moving sound sources using continuous head rotations was proposed. The model allows for treating the localisation task as a closed-loop control problem. Future extensions of the model may aim at investigating alternative control strategies, estimation of source distance and introducing additional degrees of freedom (e.g. translatory movements). 9 / 9 

Summary A binaural model for localisation and tracking of moving sound sources using continuous head rotations was proposed. The model allows for treating the localisation task as a closed-loop control problem. Future extensions of the model may aim at investigating alternative control strategies, estimation of source distance and introducing additional degrees of freedom (e.g. translatory movements). Thank you for your attention! 9 / 9