BIAS analysis of an algebraic solution for TDOA localization with sensor location errors

The nonlinearity inherent in the time difference of arrival (TDOA)-based source localization problem leads to biased source location estimates. The estimation bias of the closed-form TDOA-positioning technique, two-stage least squares(TSWLS) technology was established analytically in previous works. This paper extends the theoretical developments in the case where there exists no sensors location errors to investigate the bias of TDOA-positioning in the presence of sensor location errors. Specifically, the estimation bias of the algebraic two-stage TDOA localization algorithm proposed is derived. Simulations validate the obtained theoretical results. It is shown that different from the findings in previous works where the estimation bias of the two-stage solution mainly comes from its Stage-1 processing, both stages of the localization algorithm considered in this work can introduce significant estimation biases when sensor location errors are present.