An iterative algorithm for the joint estimation of multiple targets and observation stations using direction of arrival and time difference of arrival measurements despite station position errors

Direction of arrival (DOA) and time difference of arrival (TDOA) hybrid localisation is an effective localisation technique. Station position errors affect localisation performance. Owing to the highly non-linear nature of the problem, there are few methods of DOA/TDOA hybrid localisation in the presence of station position errors. Hence, an iterative constrained weighted least squares (ICWLS) algorithm is proposed to estimate locations of multiple targets and stations for DOA/TDOA hybrid localisation with station position errors. To ensure convergence to the global optimal solution, non-convex equality constraints are approximated to linear constraints during each iteration. The weighted averaging strategy using the results of the previous iteration is used to reduce the number of iterations. Theoretical analysis and simulation results show that the ICWLS can reach the Cramér–Rao lower bound. Additionally, the performance of multiple targets is better than that of a single target. The simulation results show that the ICWLS algorithm has higher accuracy than other methods and higher localisation accuracy can be maintained when the observation stations are under an ill-conditioned geometry.