Kalman filter based estimation of multiple signal waveforms from acoustic array data

This work presents a real-time signal processing algorithm that estimates time-domain waveforms of multiple plane wave signals on a sample-by-sample basis from data measured by an acoustic array. The algorithm is a modification of one presented at the ASA meeting in Ottawa, Canada, in May 2024 in which estimation is driven explicitly by performing nonlinear least-squares on sliding windows of data. In this new variation a state-variable approach is taken that enables the use of a Kalman filter for estimation, thus avoiding the sliding window approach. The algorithm essentially tracks estimates of the direction-of-arrival (DOA) of the waveforms from which the waveform estimates then can be obtained easily from the measured data. Other features of the approach include no restrictions on signal waveform shape and automatic estimation of the number of signals present. As before B-splines have been chosen for the waveform basis functions because of their partition-of-unity property.