Bias Reduced Semidefinite Relaxation Method for 3-D Moving Object Localization Using AOA
Gang Wang, Peng Xiang, K. C. Ho
Abstract
This paper addresses the localization of a constant velocity moving object in 3-D using angle-of-arrival (AOA) measurements. Compared with the maximum-likelihood estimator, pseudo-linear approach for AOA localization has a large amount of bias resulting from the model transformation to simplify the solution finding. This work aims at reducing the bias and developing bias-reduced semidefinite relaxation (SDR) methods for estimating the initial position and velocity of the object, in a batch or sequential manner. This is accomplished by first formulating a bias reduced constrained weighted least squares (BR-CWLS) problem from the transformed measurements, through introducing an auxiliary variable and adding a quadratic constraint. Such an intractable non-convex problem is tackled next by applying the SDR technique and relaxing it into a convex semidefinite program (SDP), which is shown to be capable of reaching the solution of the original BR-CWLS problem. For sequential estimation, we formulate a different BR-CWLS problem and utilize SDR for obtaining a sequential estimation method that updates the initial position and velocity estimates at each time step. We conduct the mean square error (MSE) and bias analyses for both estimation methods to assess their expected performance. Simulation results verify the ability of bias reduction and the good performance of the proposed methods.