时变系统遗忘因子最小二乘法的有界收敛性

利用随机过程理论研究了遗忘因子最小二乘法 (FFLS)的有界收敛性, 给出了参数估计误差的上界. 分析表明: i)对于时不变确定性系统, FFLS算法产生的参数估计以指数速度收敛于真参数; ii)对于时不变随机系统, FFLS算法给出有界均方估计误差; iii)对于时变随机系统, FFLS算法可以跟踪时变参数, 且跟踪误差有界.

Bounded Convergence of Forgetting Factor Least Square Algorithm for Time-Varying Systems

Based on stochastic process theory, the bounded convergence of forgetting factor least square algorithm (FFLS for short) is studied and the upper bound of the parameter tracking error is given. The analyses indicate that: i) for time-invariant deterministic systems, the estimates given by the FFLS algorithm converge to their true values at exponential rate; ii) for time-invariant stochastic systems, the FFLS algorithm can give a bounded mean square parameter estimation error; iii) for time-varying stochastic systems, the FFLS algorithm may track the time-varying parameters and its parameter tracking error is bounded (that is, the parameter tracking error is small when the parameter change rate is small).