A minimum variance FIR filter with an H∞H∞ error bound and its application to the current measuring circuitry

• The proposed minimum variance finite impulse response (FIR) filter is obtained with a guaranteed H∞H∞ error bound.
• The proposed filter is more robust against temporary uncertainties than an existing mixed H2/H∞H2/H∞ filter.
• The proposed filter is successfully applied to the current measuring circuitry in the magnetic system.

In this paper, we propose a minimum variance finite impulse response (FIR) filter with a guaranteed H∞H∞ error bound. The proposed FIR filter is required in advance to make use of only inputs and outputs on the recent finite time so that its impulse response has a finite duration, or it has finite memory with respect to past data. From such requirement, a transfer function from the external noises to the estimation error is first obtained, and then the corresponding estimation error variance is minimized with respect to the filter gains while keeping its H∞H∞ norm bounded. The constrained minimization problem is represented with linear matrix inequalities (LMI) that can be efficiently solved using convex programming techniques. It is shown through application to the current measuring circuitry in the magnetic levitation system that the proposed FIR filter is more robust against temporary uncertainties than an existing mixed H2/H∞H2/H∞ IIR filter with a guaranteed H∞H∞ error bound.