Bayesian active sound localisation: To what extent do humans perform like an ideal-observer?

Abstract

Self-motion is an essential but often overlooked component of sound localisation. As the directional information of a source is implicitly contained in head-centred acoustic cues, that acoustic input needs to be continuously combined with sensorimotor information about the head orientation in order to decode to a world-centred frame of reference. When utilised, head movements significantly reduce ambiguities in the directional information provided by the incoming sound. In this work, we model human active sound localisation (considering small head rotations) as an ideal observer. In the evaluation, we compared human performance obtained in a free-field active localisation experiment with the predictions of a Bayesian model. Model noise parameters were set a-priori based on behavioural results from other studies, i.e., without any post-hoc parameter fitting to behavioural results. The model predictions showed a general agreement with actual human performance. However, a spatial analysis revealed that the ideal observer was not able to predict localisation behaviour for each source direction. A more detailed investigation into the effects of various model parameters indicated that uncertainty on head orientation significantly contributed to the observed differences. Yet, the biases and spatial distribution of the human responses remained partially unexplained by the presented ideal observer model, suggesting that human sound localisation is sub-optimal.

Fig 1. Example posterior distribution of source direction at different time steps during yaw rotation.

Darker areas indicate higher probabilities. The blue ‘x’ is the true source direction.

Fig 2. Centroid and Kent distribution for condition BP and source direction (30°, 30°).

Black dots are the individual subject responses, from which the Kent distribution was calculated.

Fig 3. Centroids and Kent distributions of behavioural (B) and modelled (M) responses in the passive (P) and active (A) conditions, averaged over eight subjects.

The rows show the same data viewed towards the front, the right, and the back of the head. Quadrant errors were excluded.

Fig 4. Quadrant error rates [%] of behavioural (B) and modelled (M) responses in the passive (P) and active (A) conditions, averaged over eight subjects.

The rows show the same data viewed towards the front and the back of the head.

Fig 5. Lateral RMSE, polar RMSE and QE rate of the modelled data as a function of σ_itd (in units of the JND).

Blue markers are passive results, orange markers are active results. The markers and the error bars represent the mean and standard deviation over the eight modelled subjects. For reference, the dashed lines and the coloured areas show the behavioural means and standard deviations over the eight subjects, respectively.

Fig 6. Lateral RMSE, polar RMSE and QE rate of the modelled data as a function head orientation measurement noise σ_H, with head control noise σ_u = 0° (left column) and σ_u = 8°.

Blue markers are passive results, orange markers are active results. The markers and the error bars represent the mean and standard deviation over the eight modelled subjects. For reference, the dashed lines and the coloured areas show the behavioural means and standard deviations over the eight subjects, respectively.

Fig 7. Elevation gain [24] and QE rate of the modelled data as a function of σ_p (in degrees).

Blue markers are passive results, orange markers are dynamic results. The markers and the error bars represent the mean and standard deviation over the eight modelled subjects. For reference, the dashed lines and the coloured areas show the behavioural means and standard deviations over the eight subjects, respectively.

Fig 8. Lateral RMSE, polar RMSE, and QE rates of the modelled data as a function of time step size Δt.

The symbols show the averages and the error bars represent ±1 SDs over the (virtual) subjects. For reference, the horizontal dashed lines show the behavioural data.