LAUSR

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 $N_{\mathrm {opt}}$ is estimated in real time by incorporating the estimated data noise covariance into the full-horizon UFIR filter and specifying $N_{\mathrm {opt}}$ 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 $N_{\mathrm {opt}}$ 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.