Extended Ellipsoid Membership Filtering Method Based on Fourier-hermite Orthogonal Polynomials

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.

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 ...

AI Technical Summary

Problems solved by technology

[0006] In view of the poor performance of the existing nonlinear filtering technology in the estimation of system state variables or parameters in the GNSS / INS compact integrated navigation system, the calculation of the extended ellipsoid filter algorithm based on the Taylor series linear approximation is complex, inefficient, and difficult to calculate. To meet the technical problems required by the system, the present invention proposes an extended ellipsoid filter method based on Fourier-Hermite orthogonal polynomials, and calculates nonlinear ellipsoid filter based on Fourier-Hermite series expansion approximation, making full use of Fourier-Hermite The orthogonality characteristics of extended polynomials effectively reduce the amount of filtering calculations, improve the calculation efficiency of system state parameter estimation, and effectively improve the calculation accuracy of the extended set membership filtering method

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