Developing practical filters for non-linear systems using a new approach
Hosam E. Emara-Shabaik, Cornelius T. Leondes · International Journal of Systems Science · 1983
Practical filters for non-linear system, in the sense of having- finite dimensional equations, are treated through a new approach which combines the model simplification and filtering aspects of the problem. Three filters are derived, the first extended filter (E1F), the second extended filter (E2F), and the second extended non-linear filter (E2NF). The EIF enjoys the accuracy of the extended Kalman filter (EKF) and the computational simplicity of the Kalman filter (KF). The E2F and the E2NF have structures similar to the KF and the EKF respectively, with with new formulae for the filter gain. The gain formula for the E2F and the E2NF provide an explanation as to the effect of the system non-linearities. Numerical results comparing the performance of the developed filters to those of other known filters like KF, EKF, and the modified second order filter (M2F) using the van der Pol equations are given.