Source range and depth estimation from multipath range difference measurements

A prefilter is developed that converts range differences into position estimates for the case of multipath range differences or simple range differences measured to a collinear element array. Lower bounds are placed on the variance of position estimates. The sensor placement providing the minimum bound variance is discussed, and an estimator-achieving the variance lower bound in the limit of small estimation errors-is presented. The estimator is the minimizer of a weighted equation error norm, and is a closed-form function of the measured range differences; analytic expressions for its bias and variance are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>