Scalable Distance-based Multi-Agent Relative State Estimation via Block Multiconvex Optimization

This paper explores the distance-based relative state estimation problem in large-scale systems, which is hard to solve effectively due to its high-dimensionality and non-convexity. In this paper, we alleviate this inherent hardness to simultaneously achieve scalability and robustness of inference on this problem. Our idea is launched from a universal geometric formulation, called \emph{generalized graph realization}, for the distance-based relative state estimation problem. Based on this formulation, we introduce two collaborative optimization models, one of which is convex and thus globally solvable, and the other enables fast searching on non-convex landscapes to refine the solution offered by the convex one. Importantly, both models enjoy \emph{multiconvex} and \emph{decomposable} structures, allowing efficient and safe solutions using \emph{block coordinate descent} that enjoys scalability and a distributed nature. The proposed algorithms collaborate to demonstrate superior or comparable solution precision to the current centralized convex relaxation-based methods, which are known for their high optimality. Distinctly, the proposed methods demonstrate scalability beyond the reach of previous convex relaxation-based methods. We also demonstrate that the combination of the two proposed algorithms achieves a more robust pipeline than deploying the local search method alone in a continuous-time scenario.