系统参数估计的递推最小范数解及其用于递推最小二乘算法的启动

用直接法导出了线性系统参数的递推最小范数(RMN)估计算法,并证明其结果与递推最小二乘(RLS)算法在参数估计初值取为零、且方差阵初值取为无穷大单位阵的极限情况下的启动阶段中所得结果相同,数字仿真表明,RMN算法用于RLS算法的启动阶段,一般地可使参数估计的初始收敛速度达到最快,此法也可用于控制理论中递推求解线性方程组。

Recursive Minimum Norm Solution to the Parameter Estimation for Linear Systems and Its Application to the Starting of RLS Algorithm

A recursive minimum norm (RMN) algorithm is developed, and its equivalence to the recursive least squares (RLS) algorithm using the ideal setting of initial values(i.e. zero initial parameter estimation and finite in variance matrix) is also proved. Moreover, numerical simulations have shown that the application of RMN algorithm to the starting stage of RLS algorithm enables the parameter estimation to converge at the highest rate. The method proposed can also be applied to the recursive solution of linear equations used in the modern control theory.