Abstract
In this paper, we consider a formal linearization for multi-output nonlinear systems based on Chebyshev interpolation. Defining a linearization function that consists of Chebyshev polynomials, a given nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function by Chebyshev interpolation. Introducing a new augmented measurement vector that consists of polynomials of measurement data for a given multidimensional measurement equation, a measurement equation is transformed into an augmented linear one with respect to the linearization function in the same way. A linear estimation theory is applied to these augmented linearized systems and a nonlinear filter is synthesized. In order to show the performance of the method, a tentative estimation problem of a pendulum system is solved, with the results compared with those for the extended Kalman filter as a conventional method.
