Angles-Only Initial Orbit Determination Using Mean Motion Grid Search
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Solution Overview
Problem
Current methods for initial orbit determination from angles-only observations, such as the Gooding IOD procedure, face challenges in converging to accurate solutions when the observed arc is small, often failing to converge or resulting in non-physical orbits, especially when the satellite traces a small arc of only a few degrees.
Innovation Solution
A methodology that searches a grid of possible boundary values on the range-to-object over the observation interval to find the grid point and corresponding initial orbit that best fits all observations using an error metric, solving a boundary-value problem like Lambert's Problem, and employing optimization techniques to efficiently select the best-fit grid point, while rejecting invalid orbits based on orbital element parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the Gooding IOD procedure is used for initial orbit determination from angles-only observations, then the method can handle a wide variety of orbits and multiple observation sites, but it fails to converge or produces non-physical orbits when the observed arc is small (only a few degrees)
Solution Approach 1:
The invention changes the fundamental parameter being iterated from range values (in Gooding's method) to mean motion values. This parameter transformation allows the method to maintain stability and convergence for small observed arcs while preserving the ability to handle diverse orbit types and multiple observation sites through the universal applicability of mean motion in orbital mechanics
2Adaptability or versatility
If range iteration techniques are used to improve universality and robustness, then the method can handle wider varieties of orbits and observation arcs, but the convergence fails for small arcs of only a few degrees
Solution Approach 1:
The invention transforms the iteration parameter from physical range measurements to mean motion (a temporal parameter). This change enables precise determination of orbits from small arcs because mean motion can be accurately derived even from limited angular observations over short time intervals, avoiding the geometric ambiguities that plague range-based methods
3Productivity
If the observed arc is limited to a few degrees, then more observations can be collected in a shorter time, but current methods fail to converge to accurate solutions
Solution Approach 1:
By iterating on mean motion rather than range, the invention makes the solution process robust to the number of observations available. Mean motion can be precisely estimated from even three angle-only observations taken over a short arc, allowing the method to reliably converge regardless of whether the observed arc spans a few degrees or multiple half-orbits
Data Source
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AI summary
A methodology for initial orbit determination of an object about an astronomical body searches a grid of possible boundary values on the range-to-object over the observation interval to find the grid point and corresponding initial orbit that best fits all of the three or more (N) angles-only observations according to an error metric. The search is conducted by solving a boundary-value problem (e.g. Lambert's Problem) for different grid points. The state vector is propagated to determine estimated observation directions for the remaining N-2 observations. The grid point (and initial orbit) that best fit all of the observations is selected. The grid may be searched by testing each and every point on the grid or by using other optimization techniques such as hill climbing algorithms to find the optimal grid point.