Estimation of Impulse Responses for a Moving Source Using Optimal Transport Regularization

The estimation of impulse responses (IRs) is fundamental to various audio applications, including active noise control, telecommunication, and sound zone control. Despite its long history, estimating impulse responses remains challenging when dealing with short signals and with signals having poor spectral excitation. However, in many applications the source is moving such that one has access to several input-output signal pairs corresponding to closely spaced source positions. Intuitively, exploiting this spatial proximity when jointly estimating the full set of IRs should allow for improved estimation performance. In this work, we propose to leverage the information shared between the closely spaced source positions by means of an optimal transport regularizer when estimating IRs from noisy input-output relations. In particular, the proposed transport formulation allows for modeling shifts in time-delays, corresponding to the IR filter taps, caused by the spatial displacement. The method is validated through numerical experiments using a real voice recording as input signal, demonstrating its superior performance in the challenging scenario.