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

In some estimation or identification techniques, a forgetting factor has been used to improve the tracking performance for time-varying systems. However, the value of 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 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.