Second-Order Extended H Filter for Nonlinear Discrete-Time Systems Using Quadratic Error Matrix Approximation

• Published in: IEEE transactions on signal processing Vol. 59; no. 7; pp. 3110 - 3119
• Main Authors: HU, Jwu-Sheng, YANG, Chia-Hsing
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2011; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Approximation methods; Detection, estimation, filtering, equalization, prediction; Discrete-time nonlinear system; Estimation error; Exact sciences and technology; Filtering theory; Game theory; game theory H_{\infty} filter; Information, signal and communications theory; Kalman filter; Kalman filters; Noise; Noise measurement; Signal and communications theory; Signal, noise; Telecommunications and information theory; Performance evaluation; Discrete-time nonlinear system; Second order; Target tracking; Kalman filter; Discrete time systems; Non linear filter; H infinite control; Non linear system; Game theory; filter; game theory H; Dynamic measurement; First order; Quadratic approximation; Signal processing; Tracking error
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2138700

In this paper, the second-order extended (SOE) H ∞ filter for nonlinear discrete-time systems is derived based on an approximation to the quadratic error matrix. The solution is obtained by the game theory approach. It is shown that the result bears a strong resemblance to the SOE Kalman filter when the performance bound goes to infinity. An example of vehicle state tracking is simulated to compare the performances of the SOE Kalman filter, the first order extended and the SOE H ∞ filter. Noises with unknown bias are injected into both process dynamics and measurements. The results show that the SOE H ∞ filter has the smallest state tracking error.