Locating a Moving Source With Unknown Constant Velocity During a Short Period of Asynchronous TOA Collection

We revisit the classic problem of asynchronous time-of-arrival (TOA) based source localization, concentrating now on an expanded, vehicle-related scenario where the source exhibits motion at an unknown constant velocity over a short period of TOA collection. The state-of-the-art (SOTA) study in this field devised a constrained weighted least squares (CWLS) formulation and its associated semidefinite programming (SDP) solution. After thorough examination, we pinpoint two avenues for enhancing this benchmark. Firstly, while the SOTA research relies solely on numerical confirmation, we conduct a theoretical mean square error analysis, demonstrating analytically that the CWLS framework indeed allows for estimation accuracy close to the Cramér–Rao bound under moderate noise conditions. Secondly, the CWLS-SDP estimator has two key shortcomings: the high complexity of implementing SDP, and the potential bias introduced due to its approximations and transformations. To tackle these drawbacks, which could be problematic in location-based vehicular applications, we develop a more computationally efficient block majorization–minimization algorithm to directly solve the maximum likelihood estimation problem. This represents our second contribution, and simulations validate its superiority over the SOTA method.