A Novel Robust Kalman Filter Based on Student’s t-inverse-Wishart Distribution

This paper investigates a linear system subject to the concurrent influence of process noise with an unknown mean vector and time-varying covariance matrix, along with heavy-tailed measurement noise, and proposes a state estimation approach for this type of system. To handle process noise with an unknown mean vector and a time-varying covariance matrix, we jointly model the unknown mean vector and the time-varying covariance matrix as a Normal-inverse-Wishart distribution. To capture heavy-tailed measurement noise, it is modeled as a Student’s t-inverse-Wishart distribution. Then, a new state-space model is introduced, which enables hierarchical modeling of the noise covariance matrix and the heavy-tailed adjustment factors separately. Since the joint probability density function of the state and noise parameters is non-Gaussian, a fixed-point variational Bayesian method is applied to obtain a set of approximate posterior distributions to jointly estimate the state vector and noise parameters. Real quadrotor Unmanned Aerial Vehicle experiments and numerical simulations have confirmed the effectiveness and superior performance of the proposed filter.