Enhanced multiple model GPB2 filtering using variational inference

Multiple model filtering has been widely used to handle uncertainties in system dynamics and noise characteristics in state estimation problems. The generalized pseudo-Bayesian filter of order 2 (GPB2) is a suboptimal multiple model state estimator. It achieves computational tractability via approximating each model-matched state posterior, which is a Gaussian mixture, with a single Gaussian density. This paper illustrates from the viewpoint of variational inference that this approximation affects the performance of GPB2 through the model probability update stage. An enhanced GPB2 algorithm is proposed. It takes into account the above approximation by applying a correction factor that is dependent on the Kullback-Leibler divergence (KLD) of the Gaussian mixture and single Gaussian density. A control variate-based Monte Carlo method for evaluating the KLD is developed. The upper and lower bounds for the desired KLD are derived to correct the Monte Carlo KLD result if it falls out of bounds. Simulations show that the enhanced GPB2 algorithm outperforms the original GPB2 and interacting multiple model (IMM) methods in maneuvering target tracking tasks.