Satellite Orbit Parameterization Using Progressive Differentiable Functions
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Solution Overview
Problem
Current satellite navigation systems face discontinuities and inaccuracies in satellite position and clock corrections, leading to jumps in position and time calculations, which hinder navigation accuracy and increase acquisition time, especially in applications requiring rapid first fix.
Innovation Solution
A method using progressive systems of differentiable functions to parameterize satellite orbits and clock corrections, allowing for smooth transitions and reduced transmission requirements, enabling more precise and flexible navigation message updates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Duration of action of stationary object
If piecewise polynomial splines are used to parameterize satellite orbits and clock corrections, then the navigation message can be updated periodically, but discontinuities and jumps occur at transition points between time intervals
Solution Approach 1:
The patent changes the mathematical parameters used to describe satellite orbits and clock corrections from piecewise polynomials to progressive function systems with continuous derivatives. This parameter transformation eliminates discontinuities at transition points while maintaining the periodic update capability of navigation messages.
Solution Approach 2:
The invention introduces dynamic continuity by ensuring that the parameterization functions and their derivatives up to order p-1 are continuous across time interval boundaries. This dynamic approach allows smooth transitions between different navigation message periods without abrupt jumps in satellite position or clock correction values.
2Ease of manufacture
If Keplerian orbital elements are used in navigation messages, then the transmission format is standardized, but the flexibility to describe other types of trajectories is very low
Solution Approach 1:
The progressive function system serves multiple functions: it can describe Keplerian orbits, non-Keplerian trajectories, and intermediate cases within a unified mathematical framework. This universal parameterization maintains compatibility with standardized navigation message formats while providing the flexibility to represent diverse satellite motion types.
Solution Approach 2:
The patent segments the trajectory description into progressive intervals using continuous function systems, allowing each segment to be independently parameterized while maintaining continuity with adjacent segments. This segmentation approach enables flexible representation of complex trajectories while preserving standardized transmission protocols.
3Loss of energy
If navigation messages are transmitted at current frequency, then transmission bandwidth is conserved, but acquisition time for cold start increases
Solution Approach 1:
The continuous parameterization allows receivers to begin processing navigation data before the complete navigation message is received. By using the progressive function system, the receiver can interpolate satellite positions and clock corrections continuously, enabling earlier acquisition without requiring full message reception first.
Solution Approach 2:
The invention maintains continuous useful action by ensuring that satellite position and clock correction calculations can proceed uninterrupted throughout the navigation message reception process. The continuous derivatives enable smooth updates as data arrives, reducing the time to first fix without increasing transmission frequency.
4Duration of action of stationary object
If piecewise defined functions are used for satellite orbits and clock corrections, then updates can be performed periodically, but the quality of approximation decreases as time goes by
Solution Approach 1:
The patent transforms the parameterization from piecewise polynomials that degrade over time to progressive functions with continuous derivatives. This parameter change ensures that approximation quality remains consistent throughout the entire validity period of the navigation message, eliminating the time-dependent degradation observed with traditional methods.
Data Source
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AI summary
The invention relates to a method for generating a sufficiently smooth and highly flexible parameterization of satellite orbits and/or satellite clock corrections of a satellite. A first progressive system of differentiable functions (first function system) with high approximation accuracy and a long operating range is provided for describing the satellite orbits and/or satellite clock corrections. The satellite orbits and/or satellite clock corrections parameterized from the first function system are transmitted from a ground computing unit to one or more satellites and then to a user device, or the transmission can occur without using the space segment, solely via a ground infrastructure.Additionally, a second progressive system (second function system) consisting of at least continuous functions with moderate approximation quality and a very short operating range can be provided, which, particularly via the user terminal, allows conversion to the first function system. This significantly reduces the time until the first navigation information is available, i.e., the time to first fix.