Single-platform passive emitter localization with bearing and Doppler-shift measurements using pseudolinear estimation techniques

The maximum-likelihood (ML) estimator for single-platform Doppler-bearing emitter localization does not admit a closed-form solution and must be implemented using computationally demanding iterative numerical search algorithms. The iterative ML solution is vulnerable to convergence problems due to the nonconvex nature of the ML cost function and the threshold effect. To alleviate these problems, this paper presents new closed-form Doppler-bearing emitter localization algorithms in the 2D-plane based on pseudolinear estimation techniques; namely, the pseudolinear estimator (PLE), the bias-compensated PLE and the weighted instrumental variable (WIV) estimator. The bias-compensated PLE aims to remove the instantaneous estimation bias inherent in the PLE. The WIV estimator incorporates the bias-compensated PLE to achieve an asymptotically unbiased estimate of the emitter position. The proposed WIV estimator is proved to be asymptotically efficient for sufficiently small measurement noise. Through simulation examples its performance is shown to be almost identical to that of the ML estimator, exhibiting small bias and approaching the Cramér-Rao lower bound at moderate noise levels.