Direct Target Tracking Using Laplace Approximation

The direct tracking of a moving radio transmitter using spatially distributed receivers is considered based on delay and Doppler-shift induced signal waveforms. One key step for direct tracking is to approximate the generalized likelihood function corresponding to the largest eigenvalue of a Hermitian matrix. Although stochastic approximations can be set arbitrarily close to the optimal solution, these methods generally have high computational cost and tend to be inefficient when applied to high dimensional problems. In this paper, we develop a Laplace approximation approach for direct tracking using Taylor series expansions. The proposed method belongs to the deterministic approximation domain and therefore it is computational efficient. The simulations validate the performance of the proposed method.