Second-order extended H∞ filter for nonlinear discrete-time systems using quadratic error matrix approximation

Jwu-Sheng Hu; Chia Hsing Yang

doi:10.1109/TSP.2011.2138700

Second-order extended H_∞ filter for nonlinear discrete-time systems using quadratic error matrix approximation

Jwu-Sheng Hu^*, Chia Hsing Yang

^*Corresponding author for this work

Department of Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

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.

Original language	English
Article number	5762390
Pages (from-to)	3110-3119
Number of pages	10
Journal	IEEE Transactions on Signal Processing
Volume	59
Issue number	7
DOIs	https://doi.org/10.1109/TSP.2011.2138700
State	Published - 1 Jul 2011

Keywords

Discrete-time nonlinear system
game theory H filter
Kalman filter

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title = "Second-order extended H∞ filter for nonlinear discrete-time systems using quadratic error matrix approximation",

abstract = "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.",

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AB - 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.

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