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

An important method of locating acoustic or electromagnetic sources is based on the estimation of time of arrival (TOA) differences of the signal received at several physically separate locations. Most related research has emphasized methods for reducing the variance of TOA difference estimates for individual pairs of receivers, the estimate corresponding to each pair of receivers being treated as an independent variable. In reality, since the source can generally be considered as a single point, the TOA differences are subject to linear constraints resulting from the geometry of the system. For example, in a system consisting of three receivers, A, B, C in Fig. 1.1, simple inspection of the geometry shows that the TOA differences noted as T1, T2, 13, satisfy