Variational Nonlinear Kalman Filtering With Unknown Process Noise Covariance

Abstract

Motivated by the maneuvering target tracking with sensors such as radar and sonar, this article considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state-space models. Due to the nonlinearity of the models and the nonconjugate prior, the state estimation problem is generally intractable as it involves integrals of general nonlinear functions and unknown process noise covariance, resulting in the posterior probability distribution functions lacking closed-form solutions. This article presents a recursive solution for joint nonlinear state estimation and model parameters identification based on the approximate Bayesian inference principle. The stochastic search variational inference is adopted to offer a flexible, accurate, and effective approximation of the posterior distributions. We make two contributions compared to existing variational inference-based noise adaptive filtering methods. First, we introduce an auxiliary latent variable to decouple the latent variables of dynamic state and process noise covariance, thereby improving the flexibility of the posterior inference. Second, we split the variational lower bound optimization into conjugate and nonconjugate parts, whereas the conjugate terms are directly optimized that admit a closed-form solution and the nonconjugate terms are optimized by stochastic gradient, achieving the tradeoff between inference speed and accuracy. The performance of the proposed method is verified on radar target tracking applications by both simulated and real-world data.