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 N-opt is estimated in real time by incorporating the estimated data noise covariance into the full-horizon UFIR filter and specifying N-opt 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 N-opt 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.

Automated summary

The UFIR filtering algorithm designed for industrial processes with unknown measurement data covariance estimates data noise covariance recursively using the VB approach, and optimizes the averaging horizon length in real time. Applied to specific systems, the VB-UFIR algorithm self-estimates N-opt more accurately than known solutions, producing stable and reliable estimates without divergence compared to the VB-Kalman filter.