Predictive Tracking Under Persistent Disturbances and Data Errors Using $H_2$ FIR Approach

Industrial processes may incur a significant loss in information under unspecified impacts and data errors. Therefore, robust predictors are required to ensure the performance. In this article, we design an
$H_2$
optimal finite impulse response (
$H_2$
-OFIR) predictor under persistent disturbances, measurement errors, and initial errors. The
$H_2$
-OFIR predictor is derived by minimizing the squared weighted Frobenius norms for each error. A suboptimal
$H_2$
finite impulse response (FIR) prediction algorithm is obtained using a linear matrix inequality. The
$H_2$
-OFIR predictive tracker is tested by simulations assuming Markov disturbances and data errors driven by the Gaussian, uniform, and industrial Cauchy heavy-tailed noise. It is shown experimentally that in predictive tracking of a moving robot using the ultrawideband technology, the
$H_2$
-OFIR predictor operating with full error matrices is more robust than the Kalman and unbiased FIR predictors.