Complex-step derivative-based extended Kalman filter for state estimation in twin rotor MIMO system

Abstract

This paper presents the design of a complex-step extended Kalman filter (CS-EKF) to estimate the states of the twin-rotor MIMO system (TRMS) which is a non-linear system. Since the model of TRMS is quite complex and contains discontinuous functions, it is very difficult to calculate the Jacobian matrix in the TRMS analytically by hand. This makes it difficult to implement control methods that require Jacobian matrix calculation for TRMS. Herein, to calculate the Jacobian matrix, the CS-EKF uses the complex-step derivative approach, which is a numerical technique and offers near-analytical accuracy in a single function evaluation. The effectiveness of the CS-EKF is demonstrated through simulation and real-time experiments. Also, The CS-EKF is compared to the finite-difference extended Kalman filter (FD-EKF) and the unscented Kalman filter (UKF) in terms of estimation accuracy, computational load, and ease of implementation.