Curvature-guided probe-diffuse inversion approach for asteroid physical parameters with sparse samples — E8 Intelligence Research

Asteroid physical parameter inversion is a challenging problem prone to local optima, but massive sampling used to improve accuracy is computationally expensive. To address these issues, we propose a curvature-guided probe-diffuse inversion approach (CG-PDIA) that operates with sparse samples. We identify that the core challenge lies in the existence of a solution subspace where the chi-square value remains nearly constant despite significant errors in the asteroid physical parameters. We define this as the low-sensitivity subspace and its orthogonal complement as the high-sensitivity subspace. To formalize this insight, we present and demonstrate two theorems: the curvature irreducibility theorem, which justifies the necessity of introducing curvature, and the chi-square constraint theorem, which validates the feasibility of exploiting the low-sensitivity subspace. The CG-PDIA operates in two sequential stages. In the probe stage, the Levenberg-Marquardt (LM) algorithm acts as a probe Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com