A swarm intelligence-based search algorithm for ultra-high-dimensional insensitive subspace of asteroid physical parameters

Abstract The inversion of asteroid lightcurve data is formulated as a nonlinear optimization problem in a high-dimensional parameter space, which typically yields a large number of virtual solutions. These virtual solutions are characterized by small photometric chi-square values but large errors. To scientifically evaluate such virtual solutions, we introduce the concept of an insensitive subspace, defined as the subspace within which virtual solutions produce low chi-square values for lightcurve fits while still exhibiting large errors. To efficiently estimate the insensitive subspace, we propose an insensitive subspace search algorithm based on the Kepler optimization algorithm. First, the algorithm obtains an initial set of insensitive deviation vectors through singular value decomposition. Thereafter, vectors corresponding to large singular values are discarded, and those associated with smaller singular values are retained to construct a low-dimensional search space. Subsequently, the algorithm applies KOA to explore additional insensitive deviation vectors. Finally, these vectors are used to construct the insensitive subspace. In addition, we theoretically prove the chi-square constraint theorem for the insensitive subspace. Experimental results demonstrate that, compared to the dimension-ratio-based observability analysis method, our algorithm increases the dimensionality of the insensitive subspace from 4 to 8–9, and in some cases even up to 12, thereby significantly enhancing the ability to characterize observability, with stable performance across different parameter settings and optimization strategies. These findings provide a novel methodological approach for the observability analysis of asteroid physical parameters.