{"paper":{"title":"An intrinsic Cram\\'er-Rao bound on SO(3) for (dynamic) attitude filtering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"math.OC","authors_text":"Axel Barrau, Silv\\`ere Bonnabel","submitted_at":"2015-03-16T16:03:23Z","abstract_excerpt":"In this note an intrinsic version of the Cram\\'er-Rao bound on estimation accuracy is established on the Special Orthogonal group $SO(3)$. It is intrinsic in the sense that it does not rely on a specific choice of coordinates on $SO(3)$: the result is derived using rotation matrices, but remains valid when using other parameterizations, such as quaternions. For any estimator $\\hat R$ of $R\\in SO(3)$ we give indeed a lower bound on the quantity $E(\\log(R\\hat R^T))$, that is, the estimation error expressed in terms of group multiplication, whereas the usual estimation error $E(\\hat R-R)$ is mean"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04701","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":""},"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"}