Learning-based Gaussian Mixture Reduction for Distributed Bayesian Filter

Based on the Wiener approximation theorem, any distribution can be expressed or approximated by the finite sum of the known Gaussian distribution, so it has been widely used in many scenes. When one applies Gaussian mixture distribution (GMD) to state estimation, an urgent problem to be solved is that the number of Gaussian components will increase exponentially over time, which brings difficulties to the practical application. Therefore, it is particularly important to design appropriate methods to reduce the number of Gaussian components in the application of state estimation and keep the computational complexity at a feasible level. This paper proposes a learning-based improved Expectation Maximization (EM) Gaussian Mixture Reduction (GMR) method. This method is a multi-step optimization method, which can reduce the number of Gaussian components at the expense of a small amount of computational complexity. Finally, the proposed improved EM GMR method is applied to the target tracking scene of the distributed Bayesian filter. Simulation results show that compared with traditional algorithms, the proposed learning-based method can obtain a high estimation accuracy with a low computational cost.