Optimum Estimation of a Delay Vector Caused by a Random Field Propagating Across an Array of Noisy Sensors
William R. Hahn · Defense Technical Information Center (DTIC) · 1972
The problem of optimally processing multiple sensor data to determine the set of time delays generated by the propagation across an array of the wave fronts from a distant wide-band Gaussian noise source is investigated. It is assumed that the amplitude gradient across the array of the noise field is negligible, that the array outputs are corrupted by additive wide-band Gaussian independent sensor noises, and that the observation time is long. The Fisher Information Matrix is determined, and then used to show that the maximum likelihood estimate is asymptotically efficient (as theory dictates it should be). It is also shown that filtered correlator systems can provide asymptotically efficient estimates. Finally, the effects of suboptimal filtering of the inputs to a correlator system are investigated for the case when the signal and additive noise spectra are all band limited and have constant slopes of 0, -3, or -6 dB/octave.