An H∞ optimization and its fast algorithm for time-variant system identification

In some estimation or identification techniques, a forgetting factor ρ has been used to improve the tracking performance for time-varying systems. However, the value of ρ has been typically determined empirically, without any evidence of optimality. In our previous work, this open problem is solved using the framework of H_∞ optimization. The resultant H_∞ filter enables the forgetting factor ρ to be optimized through a process noise that is determined by the filter Riccati equation. This paper seeks to further explain the previously derived H_∞ filter, giving an H_∞ interpretation of its tracking capability. Additionally, a fast algorithm of the H_∞ filter, called the fast H_∞ filter, is presented when the observation matrix has a shifting property. Finally, the effectiveness of the derived fast algorithm is illustrated for time-variant system identification using several computer simulations. Here, the fast H_∞ filter is shown to outperform the well known least-mean-square algorithm and the fast Kalman filter in convergence rate.