A novel step-by-step linearization high-order Extended Kalman filter SH-EKF is designed for a class of nonlinear systems composed of linear functions and the product of several separable basic functions. The basic functions in the state and measurement models are defined as latent variables; the state and measurement models are equivalently formulated into pseudo-linear models based on the combination of the original variable and the latent variables; latent variables are regarded as new variables,and a dynamic linear model between each latent variable and other latent variables with original state is established;the measurement model is rewritten into the first-order linear product form between the current state and each latent variable; latent variables are solved by Kalman filter step by step, and a stepwise linearized high-order extended Kalman filter is designed. Illustration examples are presented to demonstrate the effectiveness of the new algorithm.
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