Curvature-guided probe-diffuse inversion approach for asteroid physical parameters with sparse samples

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 to locate a promising point in the parameter space, yielding a probed parameter vector. In the subsequent diffuse stage, guided by curvature analysis, the low-sensitivity subspace is constructed. The high-sensitivity components of the probed vector are maintained, while sparse samples generated by diffusing the probed vector within the low-sensitivity subspace serve as initial points. These sparse samples are then further refined by the LM algorithm to obtain the final asteroid physical parameter estimates. Simulation results demonstrate that the proposed CG-PDIA achieves a 60% higher estimation accuracy while requiring only 2.30% of the computation time compared to the traditional LM method alone.