Internal and External Double-Cycle High-Order Kalman Filter Design

Accurate state estimation depends on the design of a high-precision filter, while the design of a high-precision filter relies on the use of high-order nonlinear information of the model. For a class of nonlinear dynamic systems whose state and measurement model are composed of several nonlinear functions respectively, and each nonlinear function consists of the product of several weak nonlinear multipliers functions, a series of high-order Kalman filter bank constructed with the internal and external double-cycle is designed. In this proposed filter bank, each of the additive nonlinear functions is defined as the overall hidden variable, and the weak nonlinear multipliers in the additive nonlinear functions are defined as the basic hidden variables. Linear dynamic modeling of hidden variables is carried out, an internal cycle high-order Kalman filter bank is designed by implementing the step-by-step linearization for each basic hidden variable, an external cycle high-order Kalman filter bank is designed by making use of all the sequentially estimated overall hidden variables. Original state variables are estimated based on internal and external double-cycle Kalman filter bank. Compared with some existing methods, the effectiveness of the proposed method is verified by comparative experiments.