Abstract
Our study aimed to improve the poor performance of existing filters, such as EKF, UKF and CKF, that results from their weak approximation ability to nonlinear systems. This paper proposes a new extended Kalman filter bank focusing on a class of product-type strong nonlinear systems composed by system state variables, time-varying parameters and non-linear basic functions. Firstly, the non-linear basic functions are defined as hidden variables corresponding to system state variables, and then the strong nonlinear systems are described simplistically. Secondly, we discuss building two dynamic models between their future values of parameters, as well as hidden variables and their current values based on the given prior information. Thirdly, we recount how an extended Kalman filter bank was designed by gradually linearizing the strong nonlinear systems about system state variables, time-varying parameters and hidden variables, respectively. The first extended Kalman filter about future hidden variables was designed by using these estimates of the state variables and parameters, as well as hidden variables at current. The second extended Kalman filter about future parameters variables was designed by using these estimates of the current state variables and parameters, as well as future hidden variables. The third extended Kalman filter about future state variables was designed by using these estimates of the current state variables, as well as future parameters and hidden variables. Fourthly, we used digital simulation experiments to verify the effectiveness of this method.
Highlights
With the development of the times, filtering theory has played an important role in various fields at the domestic and international level, especially in national defense, military and other fields, such as tracking navigation, signal processing, automatic control, target tracking, etc. [1–6]
The Kalman filter (KF) takes into account the statistical characteristics of the estimated and observed measures, and it designs an optimal filter based on the minimum mean square error to solve the problem of state estimation and target tracking in linear Gaussian systems [8,9]
The main contributions of this paper are as follows: (1) adopting the idea of splitting, the multiplicative basic function term is defined as the hidden variable of the system, and it is regarded as the time-varying parameter of the system to simplify the system model formally; and (2) adopting the idea of gradual linearization, respectively designing Kalman filters on hidden variables, time-varying parameters and state variables, improving the filtering effect of each weakly nonlinear factor
Summary
With the development of the times, filtering theory has played an important role in various fields at the domestic and international level, especially in national defense, military and other fields, such as tracking navigation, signal processing, automatic control, target tracking, etc. [1–6]. EKF is a function linear approximation method for nonlinear system models It retains the Taylor expansion of the nonlinear function to the first-order term, successfully solving the nonlinear Kalman filter problem [13]. Used the estimation result of the least square method as the initial value of the extended filtering algorithm and proposed a joint estimation method of the state and parameters of the polynomial system based on nonlinear filtering. The main contributions of this paper are as follows: (1) adopting the idea of splitting, the multiplicative basic function term is defined as the hidden variable of the system, and it is regarded as the time-varying parameter of the system to simplify the system model formally; and (2) adopting the idea of gradual linearization, respectively designing Kalman filters on hidden variables, time-varying parameters and state variables, improving the filtering effect of each weakly nonlinear factor. People usually use the method of expanding state variables to estimate the state and parameters jointly based on the standard extended Kalman filter
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