This paper investigates the problem of elliptic localization in the absence of transmitter position. An efficient iterative method is developed to jointly evaluate the target and transmitter positions. Using the measurement information from the indirect paths reflected from the target and the direct paths between the transmitter and receivers, a non-convex maximum likelihood estimation (MLE) problem is formulated. Owing to the non-convex nature of the issue, we apply the majorization-minimization (MM) principle to address the MLE problem, which iteratively minimizes a convex surrogate function instead of the original objective function. Moreover, the proposed MM method is further extended to tackle a general scenario where both multiple unknown transmitters and receiver position errors are considered. Finally, numerical simulations demonstrate that the proposed MM method outperforms the state-of-the-art methods.
Keywords: elliptic localization; majorization–minimization (MM); maximum likelihood estimation (MLE).