Bias-Constrained H₂ Optimal Finite Impulse Response Filtering for Object Tracking Under Disturbances and Data Errors

The
H
₂
finite impulse response (FIR) filtering approach allows for optimal object tracking under harsh industrial conditions. In this brief, we propose a bias-constrained
H
₂
optimal unbiased FIR (
H
₂
-OUFIR) filter for linear discrete time-invariant systems under bounded disturbances, data errors, and initial errors. The
H
₂
-OUFIR filter is derived using the backward Euler method by minimizing the squared Frobenius norm of the weighted transfer function. A bias-constrained suboptimal
H
₂
FIR filtering algorithm using a linear matrix inequality (LMI) is also designed. Based on experimental examples of global positioning system (GPS)-based vehicle tracking and video human tracking, it is shown that the batch
H
₂
-OUFIR filter operating on short horizons with full error matrices is able to outperform the Kalman, optimal finite impulse response (OFIR), and unbiased finite impulse response (UFIR) filters.