A target localisation estimator based on time difference of arrival (TDOA) measurement is proposed. The localisation estimator is designed in the framework of the recently developed robust least-squares (RoLS) estimator, which provides an unbiased estimation result and can be implemented with a recursive filtering structure. However, when the RoLS estimator is applied to the localisation problem, its localisation performance depends on the knowledge of the stochastic information of the TDOA measurement. This dependency means that incorrectly given information causes localisation error. Therefore to complement the dependency of the given stochastic information of the TDOA measurement, we design a compensation procedure based on the constraints on the state variables of the estimator. The performance of the proposition under several cases of incorrectly given stochastic information is verified through computer simulation, and its filtering structure is compared with other existing localisation algorithms mathematically. In addition, the entire process of the proposed localisation estimator is derived as a recursive form for real-time applications.

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