Passive acoustic localisation using blind Gauss-Markov estimate with spectral estimation at each sensor

Time-delay estimation has essential applications in the field of radar, sonar and robotics. For a very distant source, time-delay vector estimation across an M-sensor array is realised using the generalised cross-correlation (GCC) function and the estimates combined with their covariance matrix, expressed in terms of a priori known signal and noise spectra, to yield a linear minimum variance unbiased estimator, known as the Gauss-Markov Estimate. In the absence of a priori information, spectral estimation has to be done at one of the sensors. For close range sources, the use of amplitude attenuation information across the array will improve this estimate further. This study presents a new amplitude information related Gauss-Markov estimate, which calculates the power spectral density (PSD) at all the sensors of the array and gives more accurate time delay estimates in terms of the mean-square error when compared to the earlier constant amplitude-based technique using the PSD at the closest sensor. The performance has been evaluated against signal-to-noise ratio for varying distance of a source from the receiving array. The results have been verified by simulations and experiments for a two-dimensional source localisation problem.