Variational Inference of Kalman Filter and Its Application in Wireless Sensor Networks

An improved Kalman filter algorithm by using variational inference (VIKF) is proposed. With variational method, the joint posterior distribution of the states is approximately decomposed into several relatively independent posterior distributions. To avoid the difficulty of high-dimensional integrals, these independent posterior distributions are solved by using Kullback-Leibler divergence. The variational inference of Kalman filter includes two steps, the predict step and the update step, and an iterative process is included in the update step to get the optimized solutions of the posterior distribution. To verify the effectiveness of the proposed algorithm, VIKF is applied to the state estimation of discrete linear state space and the tracking problems in wireless sensor networks. Simulation results show that the variational approximation is effective and reliable for the linear state space, especially for the case with time-varying non-Gaussian noise