Joint State Estimation and Noise Identification Based on Variational Optimization

This article addresses state estimation problems with unknown process and measurement noise covariances in both linear and nonlinear systems. By formulating the joint estimation of system state and noise parameters into an optimization problem, a novel adaptive Kalman filter method based on conjugate-computation variational inference, referred to as CVIAKF, is proposed to approximate the joint posterior probability density function of the latent variables. Unlike existing adaptive Kalman filter methods utilizing variational inference in natural parameter space, CVIAKF performs optimization in expectation parameter space, resulting in a faster and simpler solution, particularly for nonlinear state estimation. Meanwhile, CVIAKF divides optimization objectives into conjugate and nonconjugate parts of nonlinear dynamical models, whereas conjugate computations and stochastic mirror-descent are applied, respectively. Notably, the reparameterization trick is employed to minimize the variance of stochastic gradients for the nonconjugate parts. The effectiveness of CVIAKF is validated through synthetic and real-world datasets of maneuvering target tracking.