Source Velocity Beamforming via Inter-Frequency Coherence and Frequency-Domain Doppler Estimation

Kurzfassung

We present a proof-of-concept source velocity beamforming framework that estimate smoving-source kinematics from microphone-array cross-spectral statistics. The core operator is inter-frequency coherence, which compares spectral components across frequency after compensating deterministic phase drift induced by time scaling. Under a local-stationarity approximation, this yields an efficient frequency-domain surrogate for time-stretch alignment and enables estimation of pairwise relative Doppler factors without repeated time-domain resampling. Per short-time Fourier transform (STFT) frame, we estimate (i) relative delays (TDOA) using GCC-PHAT-style phasor alignment and (ii) pairwise relative Doppler factors with respect to a reference microphone via inter-frequency coherence maximization. These complementary measurements are fused in a nonlinear state-space model with an Unscented Kalman Filter (UKF) and constant-acceleration dynamics, yielding smooth position and velocity estimates, informative acceleration trends, and uncertainty envelopes. In the synthetic proof-of-concept scenario studied here, the approach provides velocity-sensitive tracking and short-horizon forecasting without exhaustive joint position--velocity grid scanning.