Kathleen MacWilliam ^1* Thomas Dietzen ¹ Randall Ali ² Toon Van Waterschoot ¹

• ¹ Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics, Department of Electrical Engineering, Faculty of Engineering Sciences, KU Leuven, Leuven, Belgium
• ² Institute of Sound Recording, University of Surrey, Guildford, Surrey, United Kingdom

The estimation of room impulse responses (RIRs) between static loudspeaker and microphone locations can be done using a number of well-established measurement and inference procedures. While these procedures assume a time-invariant acoustic system, time variations need to be considered for the case of spatially dynamic scenarios where loudspeakers and microphones are subject to movement. If the RIR is modeled using image sources, then movement implies that the distance to each image source varies over time, making the estimation of the spatially dynamic RIR particularly challenging. In this paper, we propose a procedure to estimate the early part of the spatially dynamic RIR between a stationary source and a microphone moving on a linear trajectory at constant velocity. The procedure is built upon a state-space model, where the state to be estimated represents the early RIR, the observation corresponds to a microphone recording in a spatially dynamic scenario, and time-varying distances to the image sources are incorporated into the state transition matrix obtained from static RIRs at the start and end point of the trajectory. The performance of the proposed approach is evaluated against state-of-the-art RIR interpolation and state-space estimation methods using simulations, demonstrating the potential of the proposed state-space model.