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Time difference of arrival (TDOA) positioning is one of the widely applied techniques for locating an emitting source. Unfortunately, synchronization clock bias and random sensor location perturbations are known to significantly degrade the TDOA localization accuracy. This paper studies the use of a set of calibration sources, whose locations are accurately known to an estimator, to reduce the loss in localization accuracy caused by synchronization offsets and sensor location errors. Under the Gaussian noise assumption, we first derive the Cramér–Rao bound (CRB) for parametric estimation with the use of calibration emitters. Some explicit CRB expressions are obtained, and the performance improvement due to the introduction of the calibration sources is also quantified through the CRB analysis. In order to achieve the optimum localization accuracy, we proceed to propose new localization methods using the TDOA measurements from both target source and calibration emitters. Specifically, two dimension-reduction Taylor-series iterative algorithms are developed, and both of them have two stages. The first stage estimates the clock bias and refines the sensor positions by using the calibration TDOA measurements and the prior knowledge of sensor locations. The second stage provides the estimates of source location by combining the TDOA measurements of target signal and the estimated values in the first phase. The mean square errors (MSEs) of the proposed methods are shown analytically to achieve the corresponding CRB by applying the first-order perturbation analysis. Simulations are used to corroborate and support the theoretical development in this paper.

On the use of calibration emitters for TDOA source localization in the presence of synchronization clock bias and sensor location errors