{"paper":{"title":"Closed-form Solution of Wahba's Problem for Pairwise Similar Quaternions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.RA","authors_text":"Christian Scheunert, Frank H. P. Fitzek, Hristina Radak","submitted_at":"2025-12-08T14:45:16Z","abstract_excerpt":"Wahba's problem is fundamental to spacecraft attitude estimation, seeking the optimal rotation that minimizes the weighted misalignment between sets of vector observations. Traditional solvers, including Davenport's $q$-method, QUEST, and ESOQ, reformulate the problem as an eigenvalue task for a $4 \\times 4$ symmetric matrix, a process that obscures the underlying algebraic structure of the solution. This paper presents a novel, entirely quaternion-based closed-form solution for the pairwise similar quaternions. By establishing a direct connection to the homogeneous singular Sylvester equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.07597","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.07597/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}