Optimal estimation of time-varying delay

The authors report on time-varying delay estimation in a multisource single direct acoustic path environment. The signals are stochastic nonstationary processes. The time delays are deterministic time-varying functions described by a finite dimensional vector θ of unknown parameters. The observation noise is spatially correlated. The observation time interval is arbitrary. The estimation structure, based on maximum-likelihood (ML) techniques, performs the joint estimation of the signals along with the identification of the parameter vector θ. Under stationary, long observation time interval (SLOT), and time-invariant delay assumptions, two special problem categories are discussed. The first assumes signals with no overlapping frequency spectra. The second considers the mixing of strong and weak signals. For both classes of problem, nonoptimal simplified estimation structures are suggested. Monte Carlo simulation results illustrate how the optimal and nonoptimal processors´ mean square error performances compare to the Cramer-Rao bound