New technique for linear static state estimation based on weighted least absolute value approximations (Q1102247)

This paper presents a new technique for solving the problem of linear static state estimation, based on weighted least absolute value (WLAV). A set of m optimality equations is obtained, where \(m=number\) of measurements, based on minimizing a WLAV performance index involving n 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. If k is the rank of the matrix H, \(k=n\), we choose among the optimality equations a number of equations equal to the rank k and having the smallest residuals. The solution of these n equations in n 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 best WLAV approximation is superior to best WLS approximation when estimation the true form of data containing some inaccurate observations.