Wireless Localization in Modified Polar Representation by Rigid Body Receivers of Unknown Orientations Without Synchronizations and Transmitter Positions

A rigid body receiver (RBR) forms a sub-sensor network that can enhance the measurements and increase the fault tolerance for localization. We address the problem of locating an object using non-cooperative illuminators in the absence of their positions and time stamps, with the time measurements collected by several uncoordinated RBRs at noisy positions without their orientations and synchronizations. This work proposes the use of the modified polar coordinate representation to formulate the problem, which is found to achieve higher noise tolerance than the Cartesian counterpart. We first derive the Maximum Likelihood Estimator (MLE) based on such a formulation, and then investigate a distributed approach that determines the object position local to each RBR and combines the local positions to furnish the global position estimation. The analytical study shows that it yields identical performance to centralized processing when the observations are Gaussian and uncorrelated among the RBRs. Closed-form and generalized trust region subproblem solutions for distributed localization are developed, together with analysis and simulations to support the optimum performance.