2014/12/01 by Sean Anderson, Timothy D. Barfoot, Anderson, Sean +5
Computer Science · Engineering · #FOS: Computer and information sciences #Fault Detection and Control Systems #Gaussian Processes and Bayesian Inference #Robotics (cs.RO) #Target Tracking and Data Fusion in Sensor Networks #Vehicle emissions and performance
paper · pdf · doi:10.48550/arxiv.1412.0630
openalex publication_date 2014/12/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this paper, we revisit batch state estimation through the lens of Gaussian\nprocess (GP) regression. We consider continuous-discrete estimation problems\nwherein a trajectory is viewed as a one-dimensional GP, with time as the\nindependent variable. Our continuous-time prior can be defined by any\nnonlinear, time-varying stochastic differential equation driven by white noise;\nthis allows the possibility of smoothing our trajectory estimates using a\nvariety of vehicle dynamics models (e.g., `constant-velocity'). We show that\nthis class of prior results in an inverse kernel matrix (i.e., covariance\nmatrix between all pairs of measurement times) that is exactly sparse\n(block-tridiagonal) and that this can be exploited to carry out GP regression\n(and interpolation) very efficiently. When the prior is based on a linear,\ntime-varying stochastic differential equation and the measurement model is also\nlinear, this GP approach is equivalent to classical, discrete-time smoothing\n(at the measurement times); when a nonlinearity is present, we iterate over the\nwhole trajectory to maximize accuracy. We test the approach experimentally on a\nsimultaneous trajectory estimation and mapping problem using a mobile robot\ndataset.\n