Variational adaptive Gaussian approximation filter for nonlinear systems with generalized unknown disturbances

This article investigates the joint estimation and identification problem of discrete-time nonlinear systems with generalized unknown disturbances (GUDs) and unknown noise covariance (UNC) in the measurement model. A variational adaptive Gaussian approximation filter (VAGAF) is proposed, in which the Gaussian approximation filter performs recursive state estimation, while the variational Bayesian inference identifies the UNC. Since the existence of GUDs makes it difficult to accurately derive the innovation covariance, it is approximated through matrix eigenvalue decomposition. The measurement noise covariance is estimated online by applying statistical linear regression (SLR) to the nonlinear measurement model, enabling the implementation of variational Bayesian inference. Based on the identified measurement noise covariance and the constructed innovation covariance, the Gaussian approximation filter recursively achieves high-precision state estimation. Target-tracking simulations demonstrate that the proposed filter attains superior estimation accuracy compared with the minimum upper-bound filter and interacting multiple model method without requiring a finely designed model set.