Direct Position Determination Sensitivity to NLOS Propagation Effects on Doppler-Shift

In this paper, we consider the Direct Position Determination (DPD) algorithm for Doppler-shift based localization of radio-emitters. The DPD emitter location estimate is the location candidate that maximizes the largest eigenvalue of a location-dependent matrix. The sensitivity to multipath is analyzed by Small Error Analysis, which requires expressions for the derivatives of the largest eigenvalue with respect to the multipath parameters. We consider multipath conditions in which the line-of-sight path is obstructed and the receivers intercept a non-line-of-sight (NLOS) component. We provide compact closed-form expressions for these derivatives. Our theoretical results are corroborated by numerical experiments.