Direction of Arrival Estimation Using Microphone Array Processing for Moving Humanoid Robots

TL;DR

This work tackles DoA estimation for moving microphone arrays on humanoid robots, where conventional stationary-array models fail due to ego-motion and relative motion to the sound field. It introduces a SH-domain signal model that represents motion as a sequence of linear transformations, decomposed into rotation and translation via Chasles’ theorem, and develops two processing strategies: motion compensation (aligning frames to a reference) and motion-based enhancement (fusion of multiple frames to boost effective aperture and SH order). Motion compensation recovers a PWD estimate comparable to a stationary setup, while motion-based enhancement leverages periodic signals to achieve superior DoA accuracy than any stationary-array configuration. Numerical simulations and experiments with a full-body humanoid validate that motion compensation nearly eliminates motion-induced DoA errors and that motion-based enhancement can surpass stationary-array performance, highlighting a generic framework for integrating robot motion into DoA estimation in arbitrary head geometries. The SH-domain formulation supports generic DoA methods and demonstrates practical feasibility for real-time robot audition.

Abstract

The auditory system of humanoid robots has gained increased attention in recent years. This system typically acquires the surrounding sound field by means of a microphone array. Signals acquired by the array are then processed using various methods. One of the widely applied methods is direction of arrival estimation. The conventional direction of arrival estimation methods assume that the array is fixed at a given position during the estimation. However, this is not necessarily true for an array installed on a moving humanoid robot. The array motion, if not accounted for appropriately, can introduce a significant error in the estimated direction of arrival. The current paper presents a signal model that takes the motion into account. Based on this model, two processing methods are proposed. The first one compensates for the motion of the robot. The second method is applicable to periodic signals and utilizes the motion in order to enhance the performance to a level beyond that of a stationary array. Numerical simulations and an experimental study are provided, demonstrating that the motion compensation method almost eliminates the motion-related error. It is also demonstrated that by using the motion-based enhancement method it is possible to improve the direction of arrival estimation performance, as compared to that obtained when using a stationary array.

Figures (12)

• Figure 1: An illustration of a rectangular $4$-microphone array moving from the original position in (a) to the final position in (c). The motion is divided into a rotation from (a) to (b) and a subsequent translation from (b) to (c).
• Figure 2: Effective rank of the combined model matrix $\mathbf{A}(\omega)$ at $2$ kHz (see \ref{['eq:c6']}) as a function of (a) rotation angle $\alpha$, (b) translation distance $r$.
• Figure 3: Effective rank of $\mathbf{A}(\omega)$ as a function of frequency for three different modes of motion. The rotation and translation curves almost overlap.
• Figure 4: A schematic illustration of the microphone array, the initial source position, and the rotation direction that were used for the investigation of DoA estimation performance using the motion compensation approach. Microphone positions are indicated by the black dots on the sphere surface.
• Figure 5: STD of the DoA estimation error $\Delta$ as a function of angular velocity $\alpha_z$.