Efficient Conjunction Assessment using Modified Chebyshev Picard Iteration
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abstract
Conjunction Assessment is one of the most important and computationally expensive components of modern SSA efforts. Timely warnings of potential conjunctions are critical for the protection of valuable space assets. Upgrades to the US Space Surveillance Network (SSN) such as the Space Surveillance Telescope and the new Space Fence become operational, the influx of newly trackable objects will exacerbate the current issues of computational tractability. Modified Chebyshev Picard Iteration (MCPI) is a numerical method for solving ordinary differential equations that can be utilized to efficiently proximate orbits with high accuracy. Unlike, more traditional stepping based integrators; MCPI uses recursive approximation using Chebyshev polynomials to estimate segments of an orbit. The end result of the propagation is orthogonal Chebyshev polynomial approximation of the orbital trajectory; this approximation is analytically differentiable and potentially accurate to machine precision. Once computed, these approximations provide an efficient method for evaluating and comparing the positions of space objects. The reduced cost of catalog propagation and subsequent conjunction probability analysis when using MCPI, allows for significant reduction in the cost to perform high fidelity conjunction assessment. A method for catalog propagation and conjunction assessment using MCPI is presented, along with results from implementation running in a compute cluster environment are presented.
