Expanded ellipsoid set-membership filtering method based on Chebyshev interpolation polynomial approximation

Abstract

The invention provides an expanded ellipsoid set-membership filtering method based on Chebyshev interpolation polynomial approximation. According to the expanded ellipsoid set-membership filtering method, the problems of complexness in computation and low efficiency and computational accuracy in a method based on Taylor-series linear approximation are solved. The expanded ellipsoid set-membership filtering method comprises the following steps: establishing a nonlinear strapdown inertial navigation system equation and an observation equation; computing an indeterminate interval of a system state parameter component of a (k-1) step; carrying out Chebyshev polynomial approximation computation on the nonlinear equation and the observation equation of the inertial navigation system; computing an error boundary of the Chebyshev polynomial approximation computation, so as to acquire outsourcing ellipsoids of the Chebyshev interpolation polynomial approximation computation errors of the nonlinear system equation and the observation equation; and by virtue of a linear ellipsoid set-membership filtering method, computing and predicting an ellipsoid boundary of a state variable, updating a computation state ellipsoid boundary, computing an estimation value of a state parameter variable of a k step, and estimating variance matrix. The expanded ellipsoid set-membership filtering method has the beneficial effects that a computational accuracy is relatively high, the computational complexness of an algorithm is reduced, and the computational stability of the expanded ellipsoid set-membership filtering method is effectively guaranteed.

Description

technical field [0001] The invention relates to the technical field of navigation guidance and control in aerospace system processing, in particular to an extended ellipsoid filter method based on Chebyshev polynomial interpolation approximation to realize the optimal filter calculation of the state parameters of the nonlinear system error model of the inertial navigation system , which can be applied to inertial navigation systems. Background technique [0002] The traditional stochastic Bayesian 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, so As a result, its probability distribution assumption is difficult to be satisfied, especially when the noise itself is non-Gaussian, non-white noise or biased noise. In addition, ...

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Problems solved by technology

[0006] In order to solve the problem of complex calculation, low efficiency, and low For the technical problem that the calculation accuracy cannot meet the system requirements, the present invention proposes an extended ellipsoid filter method based on Chebyshev polynomial interpolation approximation, which makes full use of the characteristics of Chebyshev orthogonal polynomials, effectively reduces the amount of calculation, and improves the system performance. The calculation efficiency of state parameter estimation can effectively improve the calculation accuracy of the extended set membership filtering method

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