Time delay estimation in discrete-time state-space models
Signal Processing
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A model for an adaptive time-delay estimator is proposed to improve its performance in estimating the difference in arrival time of a bandlimited random signal received by two spatially separated sensors in an environment where the signal and noise power are time varying. The system comprises two adaptive units: a filter to compensate time shift between the two receiver channels and a gain control to provide Wiener filtering. Both the filter coefficients and the variable gain are adjusted simultaneously by using modifications from the stochastic mean-square-error gradient in the traditional adaptive least-mean-square time-delay estimation (LMSTDE) method. The convergence characteristics of the proposed system are analyzed in detail and compared with those obtained by the traditional technique. Theoretical results show that, unlike the LMSTDE configuration, this arrangement can decouple the adaptation of time shift from the changing signal and/or noise power, which in turn gives rise to better convergence behavior of the delay estimate. Simulation results are included to illustrate the effectiveness of the new model and corroborate the theoretical developments