Formal Linearization by Chebyshev Interpolation for Both State and Measurement Equations of Nonlinear Scalar-Measurement Systems and Its Application to Nonlinear Filter

• Published in: Journal of Signal Processing Vol. 16; no. 6; pp. 557 - 562
• Main Authors: Komatsu, Kazuo, Takata, Hitoshi
• Format: Journal Article
• Language: English
• Published: Tokyo Research Institute of Signal Processing, Japan 2012; Japan Science and Technology Agency
• Subjects: Chebyshev interpolation; formal linearization; linearizing function; nonlinear filter; nonlinear system
• ISSN: 1342-6230; 1880-1013
• DOI: 10.2299/jsp.16.557

This paper is concerned with a formal linearization based on Chebyshev interpolation for nonlinear dynamic and scalar-measurement systems with Gaussian white noise and its application to a filter design. A linearization function that consists of the Chebyshev polynomials up to the higher order is defined, and a given nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function by applying Chebyshev interpolation. Further more, an augmented measurement vector that consists of polynomials of measurement data is also defined and a measurement equation is transformed into an augmented linear one with respect to the linearization function in the same way. To these augmented linearized systems, a linear estimation theory is applied to design a new nonlinear filter. With this method, the formal linearization is easily incorporated into many practical systems by simple calculation using a computer, and a nonlinear filter with higher accuracy than those using conventional methods can be designed.