Decentralized Indoor Direct Localization with Multiple Wi-Fi Access Points

In this paper, a decentralized iterative maximum likelihood (ML) direct position determination (DIM-DPD) algorithm is proposed based on the expectation maximization (EM) concept for user equipment (UE) localization in Wi-Fi systems. By innovatively treating the non-line-of-sight (NLoS) angles-of-arrival (AoAs) and observed times-of-arrival (ToAs) as nuisance parameters in the received signal model and parameter estimation procedure, the proposed DIM-DPD demonstrates its adaptability and localization efficiency in dense multipath indoor environments. In the proposed method, the position of the UE is incorporated in the vectors denoting the location differences between the UE and the access point (APs), referred to as the UE-AP location difference vectors. The set of UE-AP location difference vectors allows constructing the related UE-AP variables, serving as the latent variables in the EM iterations. Then, by taking advantage of the alternating projection technique, the nuisance parameters and UE-AP variables in the DIM-DPD algorithm are alternatively updated on separated APs in parallel. Furthermore, instead of traditional grid search, the UE position is updated with an efficient closed-form solution by aggregating the distributed estimated low-dimensional UE-AP variables. Thus, overall, the proposed DIM-DPD approach facilitates decentralized direct localization with implementation feasible processing complexity. The provided numerical simulation results demonstrate that the proposed DIM-DPD algorithm achieves high positioning accuracy, fast convergence, and a good balance between computational complexity and performance.