A Novel Robust Variational Bayesian Filter for Unknown Time-Varying Input and Inaccurate Noise Statistics

Considering that, in many practical applications, the unknown time-varying input and heavy-tailed process and measurement noises induced by some unpredictable anomalous behaviors may degrade the performance of conventional filters seriously, this letter proposes a new robust variational Bayesian (VB) filter. First, the modified one-step prediction and measurement likelihood probability density function are constructed. Then, the VB method is utilized to jointly infer the system state, unknown time-varying input, and inaccurate noise covariance matrices. Finally, a new robust filter is derived, and its effectiveness is verified by the numerical simulations.