Self-Tuning Unbiased Finite Impulse Response Filtering Algorithm for Processes with Unknown Measurement Noise Covariance

An unbiased finite impulse response (UFIR) filtering algorithm is designed in the discrete-time state-space for industrial processes with unknown measurement data covariance. By assuming an inverse-Wishart distribution, the data noise covariance is recursively estimated using the variational Bayesian (VB) approach. The optimal averaging horizon length Nopt is estimated in real time by incorporating the estimated data noise covariance into the full-horizon UFIR filter and specifying Nopt at a point, where the estimation error covariance reaches a minimum. The proposed VB-UFIR algorithm is applied to a quadrupled water tank system and moving target tracking. It is demonstrated that the VB-UFIR filter self-estimates Nopt more accurately than known solutions. Furthermore, the VB-UFIR filter is not prone to divergence and produces more stable and more reliable estimates than the VB-Kalman filter.