Accurate 3D localisation of mobile target using single station with AoA–TDoA measurements

An attractive and challenging problem in source localisation is to locate a target in three‐dimensional (3D) space using a single station. To satisfy the observability requirements and achieve higher accuracy, the authors draw on the idea of the inverse synthetic aperture radar for single‐station localisation, which leverages the mobility of target and a time serial measurements of angle of arrival (AoA) and time difference of arrival (TDoA). A closed‐form pseudo‐linear estimator (PLE) is developed to estimate both 3D position and velocity of mobile target through the linearisation of AoA–TDoA measurement equations. Furthermore, to suppress the large bias of PLE caused by the correlation of measurement noise, the authors propose a superior bias‐reduced estimator (BRE), which imposes a quadratic constraint to minimise the noise correlation term. They prove that BRE is asymptotically efficient, attaining the Cramér‐Rao lower bound (CRLB) over the moderate noise region. Extensive simulations show that both bias and mean square error of BRE are well predicted by theoretical analysis. Most importantly, in comparison with both PLE and two traditional bias reduction methods, namely weighted total least squares and weighted instrumental variables, BRE can approach the CRLB over a wider noise region and maintain a lower bias.