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.