Performance analysis and improvement of direct position determination based on Doppler frequency shifts in presence of model errors: case of known waveforms

摘要

The direct position determination (DPD) method based on Doppler frequency shifts for signals with known waveforms is first proposed by Amar and Weiss. Although this method exhibits excellent asymptotic performance, but does not account for the effects of uncertainties in the receiver positions and velocities. These uncertainties may result in a considerable reduction of localization accuracy. In this paper, the statistical performance of the DPD estimator is investigated under receiver position and velocity errors (also called model errors). We derive an analytical expression for the mean square error in the estimated source location in the case where the estimator assumes that the receiver positions and velocities are accurate, but they in fact contain errors. The main difficulty in the mathematical analysis is that the DPD cost function is not explicit with respect to the emitter position. Consequently, some algebraic manipulation is required to derive closed-form expressions for the first- and second-order partial derivatives of the cost function. The Cramer-Rao bounds (CRBs) for the target position estimation are also deduced in the presence and absence of model errors. These CRBs provide insights into the effects of model errors on the localization accuracy. Two improved DPD methods are developed based on our analysis results. The first has lower complexity than the common grid search, and the second exhibits increased robustness to model errors. Simulation results support and corroborate the theoretical developments in this paper.