Eigenspace Solution for AOA Localization in Modified Polar Representation

This paper focuses on the development and analysis of algebraic solution for source localization using angles of arrival (AOAs) in the modified polar representation (MPR), where sensor position errors are present. MPR uses the arrival angle(s) and inverse-range to represent the source location, thereby integrating the localization of the source to a single framework regardless it is in the near-field or far-field. Previous solution for AOA localization in MPR ignores sensor position errors and uses the iterative Maximum Likelihood method with a coarse semi-definite relaxation solution as the initialization, which is computationally demanding and does not ensure global convergence. We propose the constrained eigenspace technique to this localization problem that yields computationally attractive algebraic solution without having the local convergence issue. Depending on the constraints imposed, two solutions are developed. One is more computationally efficient and the other has smaller bias. The solutions are studied theoretically by mean-square analysis to characterize their statistical performance. Simulations validate the CRLB performance of the two proposed solutions under Gaussian noise.