An efficient three-level weighted essentially non-oscillatory scheme for hyperbolic equations

Neelan, A. Arun Govind; Chandran, R. Jishnu; Diaz, Manuel A.; Bürger, Raimund

doi:10.1007/s40314-023-02214-z

Cited by 2 publications

(1 citation statement)

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“…Because the polynomial representation of a function only needs to carry out a finite number of addition, subtraction, and multiplication operations on the independent variable to find the value of the function, we often use polynomials to approximate functions. It is natural to think of using higher-order polynomials to approximate functions in order to improve accuracy [ 27 , 28 , 29 , 30 ].…”

Section: Methodsmentioning

confidence: 99%

A Kalman Filtering Algorithm for Measurement Interruption Based on Polynomial Interpolation and Taylor Expansion

Cheng,

Wang,

et al. 2024

Entropy

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Combined SINS/GPS navigation systems have been widely used. However, when the traditional combined SINS/GPS navigation system travels between tall buildings, in the shade of trees, or through tunnels, the GPS encounters frequent signal blocking, which leads to the interruption of GPS signals, and as a result, the combined SINS/GPS-based navigation method degenerates into a pure inertial guidance system, which will lead to the accumulation of navigation errors. In this paper, an adaptive Kalman filtering algorithm based on polynomial fitting and a Taylor expansion is proposed. Through the navigation information output from the inertial guidance system, the polynomial interpolation method is used to construct the velocity equation and position equation of the carrier, and then the Taylor expansion is used to construct the virtual measurement at the moment of the GPS signal interruption, which can make up for the impact of the lack of measurement information on the combined SINS/GPS navigation system when the GPS signal is interrupted. The results of computer simulation experiments and road measurement tests based on the loosely combined SINS/GPS navigation system show that when the carrier faces a GPS signal interruption situation, compared with a combined SINS/GPS navigation algorithm that does not take any rescue measures, our proposed combined SINS/GPS navigation algorithm possesses a higher accuracy in the attitude angle estimation, a higher accuracy in the velocity estimation, and a higher accuracy in the positional localization, and the system possesses higher stability.

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