Modified Taylor-series method for source and receiver localization using TDOA measurements with erroneous receiver positions

Receiver location uncertainty plays an important role in passive source localization since it can significantly deteriorate the accuracy of the source location. This paper presents an iterative algorithm for estimating the location of an emitter and the positions of receivers using time difference of arrival (TDOA) measurements, when the receivers have random position errors. The proposed method is based on the Taylor-series method and jointly estimates both source and receiver positions simultaneously. One deficiency of the method is that it requires a good initial solution guess close to the true solution to begin with, in order to ensure convergence. In any case, the divergence behavior can often be detected so that re-initialization can be made. Simulation results indicate that the proposed method achieves an accuracy close to the CRLB under Gaussian noise in both near field and far field sources.