Extended ellipsoidal set-member filtering method based on Fourier-Hermite orthogonal polynomial

An orthogonal polynomial and set membership filtering technology, which is applied in the field of navigation and positioning systems, can solve the problems of reducing the amount of filtering calculation, low efficiency, and complex calculation, and achieves the goal of improving calculation accuracy, reducing the amount of filtering calculation, and improving calculation efficiency. Effect

CN108508463AActive Publication Date: 2018-09-07ZHENGZHOU UNIVERSITY OF LIGHT INDUSTRY
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Publication Date
2018-09-07

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Abstract

The invention provides an extended ellipsoidal set-member filtering method based on a Fourier-Hermite orthogonal polynomial. The extended ellipsoidal set-member filtering method comprises the steps that a model equation of a GNSS / INS combined navigation system is established; uncertainty intervals of system state parameter components in the step k-1 are calculated; Fourier-Hermite series polynomial approximation is conducted on a state equation and an observation equation; an error boundary of the Fourier-Hermite series polynomial approximation is calculated, and an epibolic ellipsoid of Fourier-Hermite series polynomial approximation calculation errors of a nonlinear equation is obtained; a linear ellipsoidal set-member filtering algorithm is used for calculating the ellipsoid boundary ofpredicted state variables, updating a state ellipsoid boundary and calculating a state parameter variable estimation value and an estimation variance matrix. The extended ellipsoidal set-member filtering method utilizes the Fourier-Hermite series polynomial to obtain linear approximation of the nonlinear system model, the calculation accuracy is higher, the computational complexity is reduced, and the computational stability of the extended ellipsoid set-member filtering algorithm is effectively guaranteed.
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Description

technical field

[0001] The invention relates to the technical field of navigation guidance and control in the aspect of aerospace system information processing, in particular to a Fourier-Hermite orthogonal polynomial extended ellipsoid filter method, which can be applied to navigation and positioning systems. Background technique

[0002] The traditional stochastic probability filtering method generally requires the statistical characteristics of the process noise and observation noise to be known, or assumes that they meet certain distribution conditions, but the statistical characteristics of the system state or parameters in the actual nonlinear system are often unknown. Therefore, the conventional The application of stochastic probability filtering algorithm has great limitations. The membership filtering algorithm only requires the boundedness of the noise, and does not need to obtain the statistical characteristics of the noise accurately, which is usually guaranteed ...

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Embodiment Construction

[0096] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

[0097] The invention utilizes Hermite polynomials to construct nonlinear GNSS / INS combined navigation equation functions. First define the one-dimensional Hermite polynomial as:

[0098]

[0099] Hermite polynomials are a set of orthogonal polynomials that satisfy the orthogonality property,

[0100]

[0101] And the Hermite polynomials are complete, that is, all satisfies In the complete space formed by the function of , the Hermite polynomial sequen...