Distance measurements demonstrate distinctive scalability when used for relative state estimation in large-scale multi-robot systems. Despite the attractiveness of distance measurements, multi-robot relative state estimation based on distance measurements raises a tricky optimization problem, especially in the context of large-scale systems. Motivated by this, we aim to develop specialized computational techniques that enable robust and efficient estimation when deploying distance measurements at scale. We first reveal the commonality between the estimation problem and the one that finds realization of a sensor network, from which we draw crucial lesson to inspire the proposed methods. However, solving the latter problem in large-scale (still) requires distributed optimization schemes with scalability natures, efficient computational procedures, and fast convergence rates. Towards this goal, we propose a complementary pair of distributed computational techniques with the classical block coordinate descent (BCD) algorithm as a unified backbone. In the first method, we treat Burer-Monteiro factorization as a rank-restricted heuristic for rank-constrained semidefinite programming (SDP), where a specialized BCD-type algorithm that analytically solve each block update subproblem is employed. Although this method enables robust and (extremely) fast recovery of estimates from initial guesses, it inevitably fails as the initialization becomes disorganized. We therefore propose the second method, derived from a convex formulation named anchored edge-based semidefinite programming} (ESDP), to complement it, at the expense of a certain loss of efficiency. This formulation is structurally decomposable so that BCD can be naturally employed, where each subproblem is convex and (again) solved exactly...

翻译：距离测量在大规模多机器人系统的相对状态估计中展现出独特的可扩展性。尽管距离测量具有吸引力，但基于距离测量的多机器人在大规模系统中提出了一个棘手的优化问题。受此启发，我们旨在开发专门的计算技术，使得在大规模部署距离测量时能够实现鲁棒且高效的估计。我们首先揭示了该估计问题与传感器网络实现问题之间的共性，从中汲取关键经验以启发所提出的方法。然而，大规模求解后者仍然需要具有可扩展性、高效计算过程和快速收敛速率的分布式优化方案。为此，我们提出了一组互补的分布式计算技术，以经典块坐标下降算法为统一框架。在第一种方法中，我们将Burer-Monteiro分解视为秩约束半定规划的秩限制启发式方法，其中采用了一种专用块坐标下降类型算法来解析求解每个块更新子问题。尽管该方法能够从初始猜测中实现鲁棒且（极其）快速的估计恢复，但当初始化变得混乱时，它不可避免地会失败。因此，我们提出了第二种方法，该方法源于一种名为锚定边基半定规划的凸形式，以弥补前者的不足，但牺牲了一定的效率。该形式在结构上可分解，使得块坐标下降能够自然应用，其中每个子问题是凸的且（同样）可精确求解……