厳密にスパースなガウス過程回帰としてのバッチ非線形連続時間軌道推定
Batch Nonlinear Continuous-Time Trajectory Estimation as Exactly Sparse Gaussian Process Regression
連続時間の軌道推定をガウス過程回帰として定式化し、逆カーネル行列がブロック三重対角で厳密にスパースになることを示して効率的なバッチ推定を実現した論文。
著者: Sean Anderson, Timothy D. Barfoot, Chi Hay Tong, Simo Särkkä
分類: cs.RO
原文アブストラクト
In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any nonlinear, time-varying stochastic differential equation driven by white noise; this allows the possibility of smoothing our trajectory estimates using a variety of vehicle dynamics models (e.g., `constant-velocity'). We show that this class of prior results in an inverse kernel matrix (i.e., covariance matrix between all pairs of measurement times) that is exactly sparse (block-tridiagonal) and that this can be exploited to carry out GP regression (and interpolation) very efficiently. When the prior is based on a linear, time-varying stochastic differential equation and the measurement model is also linear, this GP approach is equivalent to classical, discrete-time smoothing (at the measurement times); when a nonlinearity is present, we iterate over the whole trajectory to maximize accuracy. We test the approach experimentally on a simultaneous trajectory estimation and mapping problem using a mobile robot dataset.
