Angles-Only Orbit Determination With Grid Search and Covariance Clustering

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Existing angles-only initial orbit determination (IOD) algorithms are limited by requiring three measurements, lack robust initialization, fail to guarantee convergence, and do not provide state covariance estimates, leading to multiple candidate orbital solutions and computational inefficiencies.

Innovation Solution

A computer-implemented method that specifies input data, determines a bounded region in range-range space, implements a grid, computes Keplerian orbital properties, evaluates fit quality, polishes candidate solutions, and clusters them based on covariance, ensuring convergence and enumeration of all possible orbital solutions.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If a constrained nonlinear optimization procedure based on a Lambert solver is used, then the algorithm can process angle-angle measurements, but it cannot guarantee convergence and cannot identify multiple solutions

Engineering Contradiction:

Improveconvergence guaranteeVSAvoidalgorithm complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The algorithm segments the search space into multiple discrete grids, evaluating each grid point independently. This segmentation allows the algorithm to identify multiple local minima corresponding to different candidate orbital solutions, rather than converging to a single solution. Each grid point represents a potential orbital hypothesis that can be independently evaluated and polished.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The algorithm performs preliminary action by implementing a coarse grid search across the entire search space before refining specific candidate solutions. This preliminary evaluation of multiple grid points ensures that all potential solutions are identified before committing to a single optimized result, thereby guaranteeing convergence to all possible orbital solutions.

Inventive Principle:

Principle #10Preliminary action

2Measurement precision

If only three measurements are used, then the algorithm is simpler, but it cannot guarantee convergence and cannot provide state covariance estimate

Engineering Contradiction:

Improveorbit determination accuracyVSAvoidmeasurement requirements

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The algorithm transitions from requiring exactly three measurements to accepting any number of angle-angle measurements by adding a temporal dimension to the search space. The measurement index becomes an additional dimension, allowing the algorithm to evaluate candidates using varying numbers of measurements and select the optimal solution based on fit quality rather than being constrained to a fixed measurement count.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

3Reliability

If a nonlinear optimizer is used without robust initialization, then the algorithm is simpler, but it cannot guarantee convergence

Engineering Contradiction:

Improveconvergence guaranteeVSAvoidalgorithm implementation

Core Design Contradiction:

ReliabilityVSEase of manufacture

Solution Approach 1:

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The algorithm incorporates feedback mechanisms by evaluating fit quality at each grid point and using this information to guide the polishing phase. The feedback from coarse grid evaluation determines which candidates warrant refined optimization, creating a feedback loop that ensures convergence while maintaining computational efficiency.

Inventive Principle:

Principle #23Feedback

4Loss of information

If multiple candidate solutions are identified, then all possible orbits are found, but computational efficiency decreases

Engineering Contradiction:

Improvesolution completenessVSAvoidcomputational efficiency

Core Design Contradiction:

Loss of informationVSProductivity

Solution Approach 1:

The algorithm segments the computational process into two distinct phases: a coarse grid search phase that quickly identifies all potential solution regions, and a refined polishing phase that optimizes only the identified candidates. This segmentation prevents wasted computational effort on regions that do not contain solutions while ensuring all valid solutions are found.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The algorithm applies partial action by performing full optimization only on grid points that show promise of containing solutions, rather than optimizing every possible candidate. This selective refinement maintains solution completeness while significantly improving computational efficiency by avoiding excessive polishing of poor candidates.

Inventive Principle:

Principle #16Partial or excessive action

Data Source

PatentUS20260042554A1Angles-only initial orbit determination technique

Publication Date: 2026.02.12 AEROSPACE CORP

AI summary

A computer-implement method and apparatus for performing an angles-only initial orbit determination includes specifying input data to an algorithm, and determining a bounded region in a range-range space of candidate orbital solutions. The computer-implement method and apparatus also includes implementing a grid to a finite region of the range-range space, and computing Keplerian orbital properties on the grid. The computer-implement method and apparatus further includes evaluating quality of fit over angle-angle measurements to identify one or more candidate solutions, and polishing each of the one or more identified candidate solutions. The computer-implement method and apparatus also includes evaluating range-range covariance and state covariance for each of the one or more identified candidate solutions, and clustering the one or more identified candidate solutions into distinct groups based on the range-range covariance.