递推加权最小二乘算法的研究

Research of Recursive Weighted Least Squares Algorithm

通常在使用递推加权最小二乘算法时,需要设计矩阵列满秩。从极限理论的角度出发,对设计矩阵列不满秩时加权最小二乘估计的递推算法进行了理论证明和分析,得出了在任意第n步,未知参数估计值收敛于由前n组数据所决定的极小范数加权最小二乘解,并且此解是唯一的,仿真结果同样验证了该结论的正确性。

It is usually required that the design matrix is column full rank in applying recursive weighted least squares algorithm. Applying the limit theory, theoretical proof and analysis for the algorithm were given in the case that the rank of column of design matrix is non-full, and that after the arbitrary n-th step, the estimator of unknown parameter converges to the solution of the minimum norm weighted least squares was obtained In addition, the solution is unique and decided by the preceding n groups of sample. Furthermore, the simulations prove the validity of this conclusion.