Optimal filtering of linear discrete dynamic systems based on least absolute value approximations

This paper offers a new formulation for optimal linear filtering of dynamic systems based on Weighted Least Absolute Value (WLAV) approximations. We start, in this paper, with a single stage process as an introduction to the multistage processes. Given the initial estimation x ̄ (0) prior to the measurement at the initial stage, we calculate the error in each measurement. We choose from the set of measurement a number of observations which having the smallest residuals equal to the rank of the matrix H, n, provided that the number of measurements, m, is greater than the number of unknowns ( m > n). This set of measurements is used to estimate the unknown n states. It has been shown that the best WLAV is superior to the best Weighted Least Squares (WLS), when estimating the true form of data that contain some very inaccurate observations.