High-Eccentricity Orbit Ephemeris Calculation via Uneven Interpolation
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Solution Overview
Problem
Current methods for calculating dense ephemeris of high-eccentricity orbits in space object cataloging face inefficiencies due to high computational costs and inaccuracies, particularly when dealing with high-eccentricity orbits, which are common among space debris, and existing interpolation methods are not suitable for achieving both high accuracy and efficiency.
Innovation Solution
A method involving the construction of uneven interpolation nodes combined with a selected interpolation polynomial for high-eccentricity orbits, using a transformation parameter to optimize the distribution of interpolation nodes and employing the Hermite method for interpolation, allowing for efficient and accurate calculation of dense ephemeris.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerical methods are used for orbital calculation to achieve higher accuracy, then orbital calculation accuracy is improved, but calculation efficiency deteriorates due to complex integral right functions and increased computational time
Solution Approach 1:
The patent pre-calculates and stores ephemeris data at uniformly spaced time nodes before interpolation is needed. This preliminary computation allows the system to have ready-to-use data points that can be quickly interpolated, avoiding the need for complex real-time numerical integration during actual orbital calculations.
Solution Approach 2:
The patent introduces an intermediary polynomial interpolation function that bridges the gap between pre-calculated ephemeris data and real-time orbital position requirements. This polynomial acts as a mediator that translates discrete stored values into continuous orbital position information without requiring complex numerical integration.
2Productivity
If interpolation methods are used to improve calculation efficiency, then calculation time is reduced, but accuracy deteriorates because existing methods are not suitable for high-eccentricity orbits
Solution Approach 1:
The patent applies different interpolation strategies for different regions of the orbit based on local characteristics. For high-eccentricity orbits, the method uses non-uniform node distribution that provides higher interpolation density in regions where the satellite moves faster (perigee area) and lower density where it moves slower (apogee area), matching the local quality requirements of different orbital regions.
Solution Approach 2:
The patent changes the parameter of node distribution from uniform to non-uniform spacing. By modifying how interpolation nodes are distributed in time, the system adapts the interpolation method to better suit the varying speed characteristics of high-eccentricity orbits, improving both accuracy and efficiency simultaneously.
3Ease of manufacture
If uniformly spaced interpolation nodes are used, then the interpolation process is simple, but accuracy deteriorates for high-eccentricity orbits due to mismatched node distribution with orbital characteristics
Solution Approach 1:
The patent introduces asymmetry in the interpolation node distribution to match the asymmetric speed characteristics of high-eccentricity orbits. Instead of symmetric uniform spacing, the method uses non-uniform spacing that is denser in high-speed regions and sparser in low-speed regions, creating an asymmetric node pattern that accurately reflects orbital dynamics.
Solution Approach 2:
The patent makes the interpolation node distribution dynamic rather than static. The node spacing adapts to the orbital characteristics, providing finer resolution where the satellite moves quickly and coarser resolution where it moves slowly. This dynamic adjustment maintains interpolation simplicity while significantly improving accuracy for eccentric orbits.
Data Source
AI summary
A method for accurately and efficiently calculating a dense ephemeris of a high-eccentricity orbit is provided. With respect to the ephemeris calculation of the high-eccentricity orbit, the method constructs uneven interpolation nodes through time transformation and interpolates by an interpolation polynomial based on uneven interpolation nodes to obtain a dense ephemeris, which significantly improves the calculation efficiency and accuracy. Based on a large-scale numerical experiment, the method derives an optimal universal value (that is, 0.3) of a transformation parameter for all orbital eccentricities and various interpolation polynomials. In the case of using the optimal universal value of the transformation parameter δ, the method further verifies the Hermite interpolation polynomial as the preferable one among various interpolation polynomials.