A new technique for linear static state estimation based on weighted least absolute value approximations

This paper presents a new technique for solving the problem of linear static state estimation, based on weighted least absolute value (WLAV). A set ofm optimality equations is obtained, wherem=number of measurements, based on minimizing a WLAV performance index involvingn unknown state variables,m>n. These equations are solved using the left pseudo-inverse transformation, least-square sense, to obtain approximately the residual of each measurement.Ifk is the rank of the matrixH,k=n, we choose among the optimality equations a number of equations equal to the rankk and having the smallest residuals. The solution of thesen equations inn unknowns yields the best WLAV estimation. A numerical example is reported; the results for this example are obtained by using both WLS and WLAV techniques. It is shown that the best WLAV approximation is superior to the best WLS approximation when estimating the true form of data containing some inaccurate observations.This work was supported by the Natural Science and Engineering Research Council of Canada, Grant No. A4146.