Iterative Robust H∞-FIR Filtering Algorithm for Disturbed Systems Under Harsh Conditions

State estimation of industrial processes is often carried out under harsh conditions in uncertain environments. Therefore, robust state estimators are required. To address this demand, in this article, a batch
$H_\infty$
finite impulse response (
$H_\infty$
-FIR) filter is developed for disturbed systems under measurement and initial errors. The gain for the batch
$H_\infty$
-FIR filter is numerically computed using linear matrix inequality (LMI). Since LMI contains a quadratic form with respect to the filter gain, a theorem is proved and an iterative computation algorithm is developed. Based on numerical simulations of harsh conditions and an experimental example, it is shown that the
$H_\infty$
-FIR filter significantly outperforms the Kalman filter and is almost as robust as the unbiased FIR filter.