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A Formal Linearization Method by the Cubic Hermite Interpolation and its Application to an Estimation Problem of Environmental Sounds

A computational method of the formal linearization by the cubic Hermite interpolation is proposed. A nonlinear system which described by a nonlinear difference equation is converted into an approximated linear system. The dimension of the converted linear system is automatically and finitely determined by the number of the state variables. Numerical computation is easily carried out with aid of computers because the linearization is done by the cubic Hermite interpolation and the inversion is obtained by simple matrix calculation. As an application of the linearization, a nonlinear filter is synthesized, and it is applied to state estimation problem of environmental sounds.