{"paper":{"title":"Uncertainty Propagation and Bayesian Fusion on Unimodular Lie Groups from a Parametric Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.ST","stat.TH"],"primary_cat":"eess.SY","authors_text":"Gregory S. Chirikjian, Jikai Ye","submitted_at":"2024-01-07T09:04:38Z","abstract_excerpt":"We address the problem of uncertainty propagation and Bayesian fusion on unimodular Lie groups. Starting from a stochastic differential equation (SDE) defined on Lie groups via Mckean-Gangolli injection, we first convert it to a parametric SDE in exponential coordinates. The coefficient transform method for the conversion is stated for both Ito's and Stratonovich's interpretation of the SDE. Then we derive a mean and covariance fitting formula for probability distributions on Lie groups defined by a concentrated distribution on the exponential coordinate. It is used to derive the mean and cova"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.03425","kind":"arxiv","version":2},"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/2401.03425/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"}