Zonotopic Extended Kalman Filter and Fault Detection of Discrete-time Nonlinear Systems applied to a Quadrotor Helicopter

This paper presents the extension of the zonotopic Kalman filter of linear systems to nonlinear systems subject to unknown-but-bounded system disturbances and Gaussian white noises known as zonotopic extended Kalman filter (ZEKF). Due to the computational simplicity of zonotopes, the uncertain system states are bounded into a zonotopic set. The system consistency test with the system measurements is completed without using the intersection between two sets but following the extended Kalman filtering procedure that requires to find the optimal observer gain. A fault detection method based on the ZEKF algorithm is also introduced. Finally, the proposed ZEKF algorithm is applied to the quadrotor helicopter under an on-line closed-loop simulation scheme and the simulation results illustrate the effectiveness of the proposed algorithm and fault detection method.