A Gibbs sampling approach to maximum a posteriori time delay and amplitude estimation

Arrival of a signal at a receiving sensor via multiple paths is a problem frequently encountered in many areas of signal processing, including sonar, radar, and communication problems. In this work, we present a novel method for estimation of time delays and amplitudes of multipath arrivals with a maximum a posteriori estimation approach. Maximum a posteriori estimation is optimal if appropriate statistical models are selected for the received data; its implementation, however, is computationally demanding. To reduce the computational requirements for the analytical calculation of the necessary probability distribution functions, we propose optimization using Gibbs sampling. Gibbs sampling allows the estimation of posterior probability distributions through an iterative process. Through a comparison to a simple matched filter and analytical maximum a posteriori estimation, the new method is shown to be accurate and efficient. The Gibbs sampling - maximum a posteriori estimation approach is also demonstrated to be more informative than other time delay and amplitude estimation methods, because it provides estimates of posterior probability distribution functions in addition to point estimates typically provided by other approaches.