On the use of a calibration emitter for direct position determination with single moving array in the presence of sensor gain and phase errors

Abstract The problem of direct position determination (DPD) with single moving array in the presence of deterministic sensor gain and phase errors is addressed. To reduce the loss in localization accuracy due to these errors, a calibration emitter with known position is introduced. The Cramer-Rao lower bound (CRLB) for estimating these errors using this calibration emitter are first derived in two situations that the calibration emitter signals are exactly known or unknown. An interesting property of the CRLB is concluded that its value is independent with the sensor phase errors. The paper then proceeds to propose a two step procedure where the considered errors are estimated in the first step and the positions of other emitters are determined by DPD given the estimated errors in the second step. In the first step, the two situations introduced above are respectively considered. For the former, the errors are jointly estimated based on Maximum Likelihood with analytical solution. For the latter, a method that estimating the sensor gain and phase errors in sequence is proposed, which performs independently with the phase errors as the CRLB does. Furthermore, analytical solutions of the errors without estimation accuracy degradation can be provided by this method. Besides, the theoretical localization bias caused by these errors is also provided. Numerical simulations are used to examine the performance of the proposed method and corroborate the theoretical results at last.