Robust extended Kalman filter estimation with moving window through a quadratic programming formulation

Abstract

In this work, two new formulations for the extended (MW-EKF) and robust extended Kalman filter with moving window estimation (MW-REKF) are proposed. The MW-EKF and MW-REKF are formulated using an elegant quadratic programming problem that facilitates its implementation and decreases its computational cost. Besides that, the constrained extended Kalman filter (CEKF), constrained extended Kalman filter and smoother (CEKFS) and the moving horizon estimation (MHE) are compared in terms of computational cost and fit to the real data. The comparison is performed over a spherical-quadruple-tank model with different settings aiming to raise each approach's advantages and disadvantages. For both state and parameter estimation the MW-REKF has shown the smoothest and most robust behavior among all methodologies. This technique minimized the effect of the outliers, physical limitations, structural discrepancies, among others. The computational cost of the proposed techniques is only four times higher than CEKF and nine times smaller than the MHE.