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This paper focuses on the bearing estimation problem of far-field signal source via time-difference-of-arrival (TDOA) with a synchronized array in 3-D space. It is usually assumed that the propagation speed (PS) is perfectly known in localization. In reality, only an imperfect knowledge of PS could be obtained. The traditional closed-form solutions without involving PS have the advantage of low complexity, but suffer from low estimation accuracy. A measurement-division model is proposed to offer an alternative solution without the need of the propagation speed. This speed-free model combines two original TDOA measurement equations into a division formula, whose Cramer-Rao lower bound (CRLB) is derived for the observed data. A typical optimization method, i.e. the Levenberg-Marquardt (LM) algorithm is adopted to resolve the nonlinear measurement-division model, resulting in an estimation accuracy improvement because of its iterative search behavior. The theoretical performance of this solution is evaluated in terms of bias and covariance. Simulations are conducted to demonstrate an accuracy advantage of the solution over the related methods.

A Measurement-Division Model for TDOA-Based Source Bearing Estimation With Unknown Propagation Speed