时变参数遗忘梯度估计算法的收敛性

CONVERGENCE OF FORGETTING GRADIENT ESTIMATION ALGORITHM FOR TIME-VARYING PARAMETERS

提出了时变随机系统的遗忘梯度辨识算法 ,并运用随机过程理论研究了算法的收敛性 .分析表明 ,遗忘梯度算法的性能类似于遗忘因子最小二乘法 ,可以跟踪时变参数 ,但计算量要小得多 ,且数据的平稳性可以减小参数估计误差上界和提高辨识精度 .阐述了最佳遗忘因子的选择方法 ,以获得最小参数估计上界 .对于确定性时不变系统 ,遗忘梯度算法是指数速度收敛的 ;对于时变或时不变随机系统 ,遗忘梯度算法的参数估计误差一致有上界 .

Forgetting factor stochastic gradient algorithm (FG algorithm for short) is presented and its convergence is studied by using stochastic process theory. The analyses indicate that the FG algorithm can track the time-varying parameters and has the same properties as the forgetting factor least squares algorithms but takes less computational effort, and that the stationary data can improve the precision of the parameter estimates. The way of choosing the forgetting factor is stated so that the minimum upper bound of the parameter estimation error is obtained. For time invariant deterministic systems, the FG algorithm is exponentially convergent; for time-varying or time invariant stochastic systems, the estimation error given by the FG algorithm consistently has the upper bound.