DPD with IPF and GD method

Abstract

The localisation of a stationary emitter with several separated sensors is studied. At low signal-to-noise ratio, the direct position determination (DPD) approach is more precise than the two-step method which estimates the time difference of arrival (TDOA) first and locates the emitter by the TDOAs. However, the exhaustive search is usually employed to find the global maximum since the object function of DPD is non-convex. After analysing the characteristics of the object function, a DPD with improved particle filter and gradient descent method (GDIPF-DPD) is proposed. The initial and fine estimations are provided by the IPF and GD methods, successively, as the object function has single peak around the expected position and is differentiable. The IPF decreases the times of resampling through mapping the particle weights before normalisation into 0–1. The GD method improves the accuracy by seeking within the single peak. Furthermore, the position Cramér–Rao lower bound of DPD with attenuation coefficient is derived and proved to be consistent with the two-step method of TDOA. Simulation results indicate that the position accuracy of the proposed algorithm is equivalent with grad search method and its computation cost is less by two orders of magnitude.