[Paper Review] Initial Orbit Determination for the CR3BP using Particle Swarm Optimization

David Zuehlke, Taylor Yow+5 more|arXiv (Cornell University)|Jul 23, 2022

Spacecraft Dynamics and Control4 citations

TL;DR

This paper proposes a particle swarm optimization (PSO) approach for initial orbit determination (IOD) of a deputy spacecraft in cislunar space under the circular restricted three-body problem (CR3BP) dynamics. By leveraging PSO to minimize observation residuals using range and angular measurements, and combining it with a local nonlinear least squares optimizer, the method achieves sub-meter position and sub-meter-per-second velocity accuracy, demonstrating robust convergence across diverse cislunar orbit geometries with GPU-accelerated computation.

ABSTRACT

This work utilizes a particle swarm optimizer (PSO) for initial orbit determination for a chief and deputy scenario in the circular restricted three-body problem (CR3BP). The PSO is used to minimize the difference between actual and estimated observations and knowledge of the chief's position with known CR3BP dynamics to determine the deputy's initial state. Convergence is achieved through limiting particle starting positions to feasible positions based on the known chief position, and sensor constraints. Parallel and GPU processing methods are used to improve computation time and provide an accurate initial state estimate for a variety of cislunar orbit geometries.

Motivation & Objective

• To develop a robust initial orbit determination (IOD) method for cislunar space missions under CR3BP dynamics.
• To address the challenge of sparse and noisy optical observations in cislunar space-situational awareness (SSA).
• To improve initial state estimation accuracy for proximity operations and cataloging of cislunar objects.
• To reduce computation time using parallel and GPU-accelerated processing for PSO optimization.
• To validate the method across multiple cislunar orbit geometries, including NRHOs and L2 axial orbits.

Proposed method

• A particle swarm optimizer (PSO) is used to minimize the difference between actual and estimated observations (range and angles) and the predicted states under CR3BP dynamics.
• Particles are initialized within feasible bounds derived from the known chief satellite position and sensor constraints to improve convergence.
• A constriction factor and grid-based initialization strategy are applied to enhance PSO stability and convergence speed.
• The PSO solution is refined using a local nonlinear least squares optimizer (NLSQ) to achieve high-accuracy initial state estimates.
• Parallel and GPU-accelerated computation is implemented to significantly reduce processing time for large-scale PSO population evaluations.
• The method is tested across two scenarios: one with dense measurements in a halo orbit and another with sparse measurements in an L2 axial orbit.

Experimental results

Research questions

• RQ1 Can PSO effectively perform initial orbit determination for a deputy spacecraft in cislunar space under CR3BP dynamics using only optical range and angle measurements?
• RQ2 How does the PSO performance vary across different cislunar orbit geometries, such as near-rectilinear halo orbits and L2 axial orbits?
• RQ3 To what extent does constraining particle initialization improve PSO convergence and accuracy in IOD for cislunar missions?
• RQ4 How effective is the combination of global PSO and local NLSQ optimization in achieving high-accuracy initial state estimates?
• RQ5 What is the impact of GPU and parallel processing on the computational efficiency of PSO-based IOD in cislunar applications?

Key findings

• In Scenario 1, the PSO achieved a position error of less than 7 km and a velocity error of less than 0.05 m/s, which was further reduced to sub-meter and sub-meter-per-second levels by the NLSQ optimizer.
• In Scenario 2, with only 10 sparse measurements over 7 days, the PSO still achieved a position error below 7 km and a velocity error below 0.05 m/s, demonstrating robustness to sparse data.
• The PSO converged to a solution within 250 km in position and 0.1 km/s in velocity of the true initial state, showing strong global search capability.
• Velocity states converged faster than position states, indicating that angular rate and range measurements provide stronger constraints on velocity dynamics.
• GPU and parallel processing reduced computation time significantly, enabling real-time or near-real-time IOD for cislunar SSA applications.
• The method successfully generated accurate initial state estimates for both periodic halo orbits and L2 axial orbits, validating its applicability across diverse cislunar mission scenarios.