Volumetric Orbital Encounter Probability Calculation
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Solution Overview
Problem
Current satellite tracking systems cannot accurately determine long-term collision risks due to uncertainties in positional knowledge and in-track positions of satellites, and volumetric methods using Monte Carlo sampling become computationally burdensome for small encounter volumes.
Innovation Solution
A volumetric approach is introduced to calculate encounter probabilities by rotating a volumetric shape along a satellite's orbit to determine nodal crossings and incremental mean anomalies, allowing for rapid assessment of encounter probabilities even for small volumes, with a five-orders-of-magnitude runtime improvement over Monte Carlo methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte Carlo sampling methods are used to assess encounter probabilities, then measurement precision is improved, but productivity deteriorates due to computational burden
Solution Approach 1:
The patent replaces the Monte Carlo sampling method (a computational/numerical approach) with an analytical closed-form solution. The analytical method uses mathematical formulas to directly calculate encounter probabilities based on orbital elements and encounter geometry, eliminating the need for repeated random sampling simulations. This substitution provides exact results without computational iteration, achieving both high precision and computational efficiency.
2Measurement precision
If volumetric methods are applied to small encounter volumes, then measurement precision is improved, but device complexity increases due to computational burden
Solution Approach 1:
The patent replaces complex volumetric integration methods with a simplified analytical approach. By deriving closed-form expressions for encounter probability that directly incorporate volumetric considerations, the method achieves precise assessment for small encounter volumes without requiring complex numerical integration or iterative computational procedures.
3Reliability
If long-term collision risks are assessed using current tracking systems, then reliability is improved, but productivity deteriorates due to positional uncertainties
Solution Approach 1:
The patent performs preliminary calculations of encounter geometry and probability using current orbital elements before propagation. By establishing closed-form expressions that account for positional uncertainties in advance, the method enables rapid long-term risk assessment without requiring repeated detailed simulations at each time step, thus improving both reliability and productivity.
Data Source
AI summary
Systems, methods, devices, and non-transitory media of the various embodiments provide for a volumetric approach to determining orbital encounters that may determine the number of encounters over a specified length of time. Such information may be used to determine how often during an orbit or period of time an object might trigger a conjunction warning for a neighboring satellite. The various embodiments may be used as a planning and characterization tool to estimate satellite encounter rates for a prospective orbit regime and may provide an efficient, in-line approach to assess the number of encounters occurring within a user-specified span of time.