Optimal and Robust State Estimation

7FIR Prediction and Receding Horizon Filtering

When the number of factors coming into play in a phenomenological complex is too large, scientific method in most cases fails. One need only think of the weather, in which case the prediction even for a few days ahead is impossible.

Albert Einstein, Science, Philosophy and Religion (1879–1955)

7.1 Introduction

A one‐step state predictive FIR approach called RH FIR filtering was developed for MPC. As an excerpt from [106] says, the term receding horizon was introduced “since the horizon recedes as time proceeds.” Therefore, it can be applied to any FIR structure and is thus redundant. But, with due respect to this still‐used technical jargon, we will keep it for one‐step FIR predictive filtering. Note that the theory of bias‐constrained (not optimal) RH FIR filtering was developed by W. H. Kwon and his followers [106].

The idea behind RH FIR filtering is to use an FE‐based model and derive an FIR predictive filter to obtain an estimate at over the horizon of most recent past observations. Since the predicted state can be used at the current discrete point, the properties of such filters are highly valued in digital state feedback control. Although an FIR filter that gives an estimate at over can also be used with this purpose ...