Authors: Sean Anderson Timothy D Barfoot Chi Hay Tong Simo Särkkä
Publish Date: 2015/07/26
Volume: 39, Issue: 3, Pages: 221-238
Abstract
In this paper we revisit batch state estimation through the lens of Gaussian process GP regression We consider continuousdiscrete estimation problems wherein a trajectory is viewed as a onedimensional GP with time as the independent variable Our continuoustime prior can be defined by any nonlinear timevarying stochastic differential equation driven by white noise this allows the possibility of smoothing our trajectory estimates using a variety of vehicle dynamics models eg ‘constantvelocity’ We show that this class of prior results in an inverse kernel matrix ie covariance matrix between all pairs of measurement times that is exactly sparse blocktridiagonal and that this can be exploited to carry out GP regression and interpolation very efficiently When the prior is based on a linear timevarying stochastic differential equation and the measurement model is also linear this GP approach is equivalent to classical discretetime 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 datasetThanks to Dr Alastair Harrison at Oxford who asked the allimportant question how can the GP estimation approach Tong et al 2013 be related to factor graphs This work was supported by the Canada Research Chair Program the Natural Sciences and Engineering Research Council of Canada and the Academy of Finland
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