ガウス過程とマグヌス展開による連続時間軌道推定の再検討
Revisiting Continuous-Time Trajectory Estimation via Gaussian Processes and the Magnus Expansion
リー群上の連続時間軌道推定において、マグヌス展開を用いて大域的なガウス過程事前分布を導出し、従来の局所的な手法と比較した。
詳しい要約
1. どんなもの？
2. 先行研究と比べてどこがすごい？
3. 技術・手法の肝は？
4. どうやって有効だと検証した？
5. 議論はある？
6. 次に読むべき論文は？
※ AIが要旨から生成した要約です。正確性は原文をご確認ください。
著者: Timothy Barfoot, Cedric Le Gentil, Sven Lilge
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
Continuous-time state estimation has been shown to be an effective means of (i) handling asynchronous and high-rate measurements, (ii) introducing smoothness to the estimate, (iii) post hoc querying the estimate at times other than those of the measurements, and (iv) addressing certain observability issues related to scanning-while-moving sensors. A popular means of representing the trajectory in continuous time is via a Gaussian process (GP) prior, with the prior's mean and covariance functions generated by a linear time-varying (LTV) stochastic differential equation (SDE) driven by white noise. When the state comprises elements of Lie groups, previous works have resorted to a patchwork of local GPs each with a linear time-invariant SDE kernel, which while effective in practice, lacks theoretical elegance. Here we revisit the full LTV GP approach to continuous-time trajectory estimation, deriving a global GP prior on Lie groups via the Magnus expansion, which offers a more elegant and general solution. We provide a numerical comparison between the two approaches and discuss their relative merits.
