Parameter estimation in linear static systems based on weighted least absolute value estimation
We present a new method for estimating a parameter vector of which measurements are carried out; however, these measurements are subjected to noise. First, we briefly consider least square estimation of such vector to obtain some well-known results. Then, we proceed to formulate the problem in the least absolute value (LAV) sense and show that we can obtain a set of overdetermined equations for the components of the unknown vector. These equations are solved using the least square approach to ascertain which points give the least residuals. Having gained that information, we set to zero a number of residuals equal to the rank of the matrix H. Let this rank be k; then, the number of points which satisfy the LAV solution identically is k; this is a requirement that the LAV solution must satisfy [see, \textit{W. W. Kotiuga} and \textit{M. Vidyasagar}, IEEE Trans. Power Apparatus Syst. PAS-101, No.4, 844-853 (1982); and \textit{I. Barrodale} and \textit{F. D. K. Roberts}, SIAM J. Numer. Anal. 15, 603-611 (1978; Zbl 0387.65027)]. Several examples are presented in the paper.
scientific article; zbMATH DE number 4051480