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. Moreover, the algorithm provides sample-by-sample estimates of the direction-of-arrival (DOA) of the waveforms. In this case sample-by-sample means that as each sample of data is measured by the array estimates of the waveforms and their directions-of-arrival are updated. While the basic idea can be based on almost any finite-dimensional approximation to a function space, this algorithm makes use of B-spline basis for the signal waveforms. Other features of the approach include no restrictions on signal waveform shape, automatic estimation of the number of signals present, automatic step-size adjustment for correction of signal waveform and direction-of-arrival parameters to achieve good performance while guaranteeing stability, and the use of circular (spherical) statistical models for 2-D (3-D) DOA estimates. The approach contrasts with blind source separation (BSS) methods that are based on non-Gaussian statistical assumptions and that do not assume a known array geometry nor a propagation model. This method is closely related to algorithms based on block-of-data by block-of-data processing but does not require stitching results from block processing to create time-domain waveform estimates.
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