H2 inferential filtering, prediction, and smoothing with application to rolling mill gauge estimation

A new minimum mean square error optimal linear estimation problem is considered where no direct measurement of the output to be estimated is available. The optimal filter, predictor, and smoother are derived for this case where outputs must be inferred from available measurements. The results cover the usual Wiener or Kalman filtering problems and also optimal deconvolution estimation problems. However, they also apply to the situation, often found in industry, where estimates of signals are required that can only be determined from secondary measurements. A weighted H₂ cost-function is minimized where the weighting function can be chosen to improve the robustness of the solution. The optimal estimators are derived both for stable and for unstable signal source models. A signal-processing application is considered in detail to demonstrate the use of the optimal filter. The gauge control problem in metal rolling mills is discussed where only force measurements are available