The use of linear constraints to reduce the variance of time of arrival difference estimates for source location

Research on the estimation of time of arrival (TOA) differences has emphasized the reduction of variance for measurements corresponding to individual pairs of signals, each estimate being regarded as an independent variable. In reality, the geometry of a source location system results in linear constraints which must be satisfied by the TOA differences. These constraints, known from a priori information, can be formally incorporated into the estimation procedure to achieve lower variances than can be obtained with independent maximum likelihood estimation. An algorithm for constrained estimation has been developed in the frequency domain extending the algorithm proposed by Chan et al. [1] for independent estimation. The concept of constrained estimation is then shown applicable in the time domain provided that variance estimates of the independent TOA differences can be explicitly derived. Experimental results with stationary and nonstationary signals demonstrated reduction of the RMS location error in the order of 20 to 56 percent for signal-to-noise ratios ranging from 30 to 10 dB, respectively.