{
  "id": "2212.02324",
  "version": "v1",
  "published": "2022-12-05T14:48:42.000Z",
  "updated": "2022-12-05T14:48:42.000Z",
  "title": "An optimal control approach to particle filtering on Lie groups",
  "authors": [
    "Bo Yuan",
    "Qinsheng Zhang",
    "Yongxin Chen"
  ],
  "comment": "6 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "We study the filtering problem over a Lie group that plays an important role in robotics and aerospace applications. We present a new particle filtering algorithm based on stochastic control. In particular, our algorithm is based on a duality between smoothing and optimal control. Leveraging this duality, we reformulate the smoothing problem into an optimal control problem, and by approximately solving it (using, e.g., iLQR) we establish a superior proposal for particle smoothing. Combining it with a suitably designed sliding window mechanism, we obtain a particle filtering algorithm that suffers less from sample degeneracy compared with existing methods. The efficacy of our algorithm is illustrated by a filtering problem over SO(3) for satellite attitude estimation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-05T14:48:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control approach",
      "lie group",
      "particle filtering algorithm",
      "optimal control problem",
      "filtering problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}