Stirling interpolation polynomial approximation based ellipsoid set-membership filtering method

Abstract

The invention discloses a Stirling interpolation polynomial approximation based ellipsoidal set-membership filtering method. The method includes: firstly utilizing Stirling interpolation polynomial to obtain linear approximation of a nonlinear state equation, constructing an uncertain interval of system state variable, using a second order difference operator to obtain a linear error bound, constructing a virtual noise outsourced ellipsoid, using the current state variable estimate value to predict a system state variable prediction error boundary of the next moment, carrying out system state variable update operation according to the observation vector, then utilizing linear ellipsoid set-membership filtering steps to carry out estimation calculation of system state variable and calculation of system state variable's estimation error ellipsoid, thus completing the estimation calculation task of system state variable. The method provided by the invention utilizes Stirling interpolation polynomial approximation calculation to realize ellipsoid set-membership filtering, effectively reduces the calculation amount, enhances the computational efficiency, and improves the calculation precision of extended set-membership filtering algorithm.

Description

technical field [0001] The invention belongs to the technical field of navigation guidance and control of aerospace system processing, and in particular relates to an extended ellipsoid filter method based on Stirling interpolation polynomial approximation, which can be applied to inertial navigation 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 i...

AI Technical Summary

Problems solved by technology

[0006] In order to solve the problem of the calculation of the extended ellipsoid filter algorithm based on Taylor series linear approximation in the calculation process of the initial alignment state parameters of the Strapdown Inertial Navigation System (SINS) in the prior art, the calculation is complex, the efficiency is low, and the actuarial accuracy cannot meet the requirements. Due to

Images