Nonlinear filtering method based on polytope differential inclusion

Abstract

The invention relates to a nonlinear filtering method based on polytope differential inclusion, which belongs to the technical field of system filtering and control. The method comprises the steps of describing a nonlinear filtering error system with a PLDI (Programming Language Design And Implementation) model, converting a nonlinear filtering algorithm design problem to a linear uncertain system robust filtering algorithm design problem, designing a dynamic equation for estimated error correction solving by a hybrid robust H2 / H-to-infinity filtering method, then designing a discrete nonlinear filtering equation by combining an EKF (Extended Kalman Filter) one-step prediction equation, and applying the discrete nonlinear filtering equation to a nonlinear discrete system to obtain the state estimation of the nonlinear discrete system in real time. According to the method, the nonlinear filtering design is simplified, the filtering gain is not required to be updated in real time, and the jacobian matrix is not required to be computed in real time in the implementation process, so that the computation amount is reduced greatly, the real-time performance of the nonlinear filtering is improved effectively, and the method is applicable to the design of a nonlinear filter.

Description

technical field [0001] The invention relates to a nonlinear filtering method based on multicellular differential inclusion, which belongs to the technical field of system filtering and control. Background technique [0002] For nonlinear filtering problems, it is difficult to find a strict optimal solution in theory, and approximate methods are generally used to solve them. According to the different methods of dealing with the nonlinearity of the system, nonlinear filtering methods can be mainly divided into three categories. The first category is the method of function approximation, which uses Taylor series expansion or interpolation polynomial expansion to approximate nonlinear functions; the second category is the method of function approximation. The second category is a deterministic sampling method, that is, a method for approximating a nonlinear probability density function; the third category is a method based on Monte Carlo simulation. Among them, the typical rep...

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Problems solved by technology

[0006] The purpose of the present invention is to solve the problem of complex filtering algorithm and large amount of calculation in general nonlinear systems, and proposes a nonlinear filtering method based on multicellular differential inclusion technology, which adopts the PLDI model of the nonlinear filtering error system to describe, so that the nonlinear filtering algorithm design problem is transformed into the linear uncertain system robust filtering algorithm design problem

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