1. Introduction

2. Problem Formulation

3. Candidate Selection

4. Extended Kalman Filter with PDA

5. Experimental Results

6. Conclusion

EXTENDED KALMAN FILTER WITH PROBABILISTIC DATA ASSOCIATION FOR MULTIPLE NON-CONCURRENT SPEAKER LOCALIZATION IN REVERBERANT ENVIRONMENTS

E-Mail: soumitro.chakrabarty@audiolabs-erlangen.de

1International Audio Laboratories, Erlangen, Germany 2Fraunhofer Institute for Integrated Circuits (IIS), Erlangen, Germany Soumitro Chakrabarty1, Konrad Kowlaczyk2, Maja Taseska1 and Emanuël A.P. Habets1,2

• Aim - Estimate the source position at each time step within an acoustic environment using signals acquired by distributed microphones• Conventional Method - Use broadband time-di�erence-of-arrival (TDOA) estimates as measurements within a state-space model based probabilistic framework

• Proposed Method - Use narrowband direction-of-arrival (DOA) estimates selected based on magnitude squared coherence between microphone signals as measurements within an extended kalman �lter (EKF) framework with probabilistic data association (PDA)

direct sound + early re�ections late reverberation noise signal array index

frequency indextime index re�ection order microphone index

Signal model in TF domain

state variable process noise

measurement noisemeasurements

State-space model

array center

Measurement function

• Given the model, compute the state estimate

Measurements• Multiple narrowband DOA estimates per array• Measurement for m-th array

- number of candidates

θ̄(m,2)nθ̄(m,3)

n θ̄(m,1)n θ̄(m,4)

n

θ̃(m,3)n

θ̃(m,2)n

θ̃(m,4)n

θ̃(m,1)n

Number

ofOccurrences

Direction of Arrival

• Candidates selected based on magnitude squared coherence (MSC)• Search for local maxima in the histogram of all narrowband DOA estimates:• Frequency indices of the candidates obtained by:

• Selected candidates:

Extended Kalman Filter• Kalman Gain:

• Measurement prediction covariance:

• Jacobian Matrix:

• Innovation vector:

Probabilistic Data Association Modi�cations• Innovation vector for multiple candidates: a posteriori probability

• Computed:

• State estimate:

• State covariance:

event: i-th measurement is from true source position

accounts for measurements not corresponding to true source position

each element

0 0.5 1 1.5 2 2.5 3 3.5 4

−0.02

−0.01

0

0.01

0.02

Actual Path PDA with ESPRIT ESPRIT SRP−PHAT

Am

plit

ud

e

0 0.5 1 1.5 2 2.5 3 3.5 4

3

4

5

6

7

8

X [

m]

0 0.5 1 1.5 2 2.5 3 3.5 4

3

4

5

6

7

8

Y[m

]

Time [s]

0 0.1 0.2 0.3 0.4 0.5 0.6

0.2

0.3

0.4

0.5

0.6

0.7

Reverberation Time[s]

RM

SE

[m]

0 10 20 30 40 50 600.2

0.4

0.6

0.8

1

SNR[dB]

RM

SE

[m]

PDA with ESPRIT ESPRIT SRP−PHATSimulation setup•

• STFT: 32 ms, 50% •

•

• DOA estimation method: ESPRIT

Figure: Microphone signal (top), and tracked position along X and Y dimensions (middle and bottom, respectively) for RT60 = 0.2s and SNR = 20dB.

Figure: Simulation setup

Figure: Position RMSE for varying reverberation times and constant SNR = 30dB (top) and varying SNR levels with a constant RT60 = 0.3s (bottom).

broadband speech presence probability

process noise covariance

measurement noise covariance

• A method for acoustic source tracking using EKF with PDA was proposed

• Multiple narrowband DOA estimates selected based on the MSC were used as measurement candidates• The proposed method yields an improved tracking performance over single-candidate based methods

estimated narrowband DOAs

Length 9.0 m

Width 9.0 m

[7.5m, 4m]

[5.2m, 5.4m]

Source 1 Trajectory

[3m, 3.5m]

[4.4m, 5.5m]Source 2 Trajectory

Mic.Array 1

Mic

.Arr

ay2

6cm

6cm

2m

2m

4.5m

4.5m