Towards Fast and Accurate 3D Direct Emitter Tracking via Laplace Approximation

In this article, the location and velocity of an emitter are estimated through spatially distributed receivers based on delay and Doppler-shift induced signal waveforms. In the context of Bayesian filtering, the main challenge in direct emitter tracking is to estimate the high-dimensional parameters based on the non-linear and non-Gaussian marginal posterior distribution. Although Monte Carlo approximations can be set as close to the optimal solution as expected, these methods usually incur a high computational cost and are inefficient in dealing with high-dimensional problems. Therefore, a novel Posterior Laplace Approximated Filter (PLAF) algorithm intended for direct emitter tracking is proposed in this article to achieve a comparable estimation performance close to the posterior Cramér-Rao lower bound but at a low level of computational complexity. The PLAF method relies on the Laplace approximation technique to approximate the marginal posterior as a Gaussian distribution, the mean and covariance matrix of which are explicitly calculated. Furthermore, an improved approach to unconstrained optimization is developed based on a feature space search technique. The proposed optimization method is capable to jump out of the neighborhood of the local optimum to find a better one. The PLAF algorithm performs well in computationally efficiency because it belongs to a deterministic approximation domain. Besides, it can maintain a superior performance, even in the context of a low signal-to-noise ratio. Simulation results are obtained to demonstrate the performance of the proposed algorithm.