Self-Calibration direct position determination using a single moving array with sensor gain and phase errors

Abstract The problem of direct position determination (DPD) using a single moving array in the presence of deterministic sensor gain and phase errors is considered. To eliminate the localization bias caused by these errors, an eigenstructure based self-calibrating DPD method is first introduced, in which the sensor gain and phase errors and the emitter positions are jointly estimated by an iterative process. Considering the performance deterioration of eigenstructure methods when the signal to noise ratio or the number of samples is not sufficiently large, a maximum likelihood (ML) based two-step self-calibration approach for DPD is subsequently proposed. The sensor gain errors are provided using the diagonal of the covariance matrix of the array output by a closed form solution at the first step. Then, the phase errors and the emitter positions are jointly estimated by an iterative scheme based on ML, in which the phase errors are also determined by a closed form solution in each iteration. Besides, detailed analyses and discussions about the differences between the introduced eigenstructure based and the proposed ML based self-calibration DPD methods are also provided. At last, numerical simulations are involved to examine their performance.