Abstract
This paper proposes one new design method for a higher order extended Kalman filter based on combining maximum correlation entropy with a Taylor network system to create a nonlinear random dynamic system with modeling errors and unknown statistical properties. Firstly, the transfer function and measurement function are transformed into a nonlinear random dynamic model with a polynomial form via system identification through the multidimensional Taylor network. Secondly, the higher order polynomials in the transformed state model and measurement model are defined as implicit variables of the system. At the same time, the state model and the measurement model are equivalent to the pseudolinear model based on the combination of the original variable and the hidden variable. Thirdly, higher order hidden variables are treated as additive parameters of the system; then, we establish an extended dimensional linear state model and a measurement model combining state and parameters via the previously used random dynamic model. Finally, as we only know the results of the limited sampling of the random modeling error, we use the combination of the maximum correlation estimator and the Kalman filter to establish a new higher order extended Kalman filter. The effectiveness of the new filter is verified by digital simulation.
Highlights
The application of filters occupies an important position in various fields at the national and international levels
For the linear system, Chen designed the corresponding Kalman filter under the maximum correlation entropy criterion based on the limited realization of random variables [7]; this is called the maximum correlation entropy Kalman filter (MCKF) [8]
Both will eventually face the problems of degraded filtering performance and divergence as their nonlinearity increases [12]. This project proposes a higher order extended Kalman filter method based on maximum correlation entropy, under the assumption that both state and measurement equations can be modeled and based on a strong nonlinear function
Summary
The application of filters occupies an important position in various fields at the national and international levels. A large number of experiments have shown that both EKFs and UKFs can be approximated by a second-order polynomial at most [11], which will produce a large rounding error Both will eventually face the problems of degraded filtering performance and divergence as their nonlinearity increases [12]. This project proposes a higher order extended Kalman filter method based on maximum correlation entropy, under the assumption that both state and measurement equations can be modeled and based on a strong nonlinear function. The remaining parts of this paper are organized as follows: the first chapter is the preface of our knowledge, which introduces the definition of “entropy”; the Section 2 presents a method for identifying nonlinear functions based on multidimensional Taylor networks; the Section 3 presents a higher order extended Kalman filter method; the Section 4 presents the detailed design process of the maximum correlation entropy higher order extended Kalman filter; the Section 5 concerns simulation verification; and the Sections 6 and 7 presents a summary and outlook
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