Semi-coherent time of arrival estimation using regression

Time of arrival (ToA) estimation is essential for many types of remote sensing applications including radar, sonar, and underground exploration. The standard method for ToA estimation employs a matched filter for computing the maximum likelihood estimator (MLE) for ToA. The accuracy of the MLE decreases rapidly whenever the amount of noise in a received signal rises above a certain threshold. This well-known threshold effect is unavoidable in several important applications due to various limitations on the power and the spectrum of a narrowband source pulse. A measurement performed in the presence of the threshold effect employs a receiver which operates in the semi-coherent state. Therefore, the conventional methods assuming a coherent state receiver should be adapted to the semi-coherent case. In this paper, a biosonar-inspired method for the semi-coherent ToA estimation is described. The method abandons the exploration of an echo signal by a single matched filter in favor of the analysis by multiple phase-shifted unmatched filters. Each phase-shifted unmatched filter gives rise to a biased ToA estimator. The described method uses regression for combining these estimators into a single unbiased ToA estimator that outperform the MLE in the presence of the threshold effect.