Continuous-time batch estimation using temporal basis functions
- 1 May 2012
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 2088-2095
- https://doi.org/10.1109/icra.2012.6225005
Abstract
Roboticists often formulate estimation problems in discrete time for the practical reason of keeping the state size tractable. However, the discrete-time approach does not scale well for use with high-rate sensors, such as inertial measurement units or sweeping laser imaging sensors. The difficulty lies in the fact that a pose variable is typically included for every time at which a measurement is acquired, rendering the dimension of the state impractically large for large numbers of measurements. This issue is exacerbated for the simultaneous localization and mapping (SLAM) problem, which further augments the state to include landmark variables. To address this tractability issue, we propose to move the full maximum likelihood estimation (MLE) problem into continuous time and use temporal basis functions to keep the state size manageable. We present a full probabilistic derivation of the continuous-time estimation problem, derive an estimator based on the assumption that the densities and processes involved are Gaussian, and show how coefficients of a relatively small number of basis functions can form the state to be estimated, making the solution efficient. Our derivation is presented in steps of increasingly specific assumptions, opening the door to the development of other novel continuous-time estimation algorithms through the application of different assumptions at any point. We use the SLAM problem as our motivation throughout the paper, although the approach is not specific to this application. Results from a self-calibration experiment involving a camera and a high-rate inertial measurement unit are provided to validate the approach.Keywords
This publication has 27 references indexed in Scilit:
- Efficient Video Rectification and Stabilisation for Cell-PhonesInternational Journal of Computer Vision, 2011
- Particle filter theory and practice with positioning applicationsIEEE Aerospace and Electronic Systems Magazine, 2010
- View-based MapsThe International Journal of Robotics Research, 2010
- Vast-scale Outdoor Navigation Using Adaptive Relative Bundle AdjustmentThe International Journal of Robotics Research, 2010
- Real-time monocular SLAM: Why filter?Published by Institute of Electrical and Electronics Engineers (IEEE) ,2010
- Modeling and Calibration of Inertial and Vision SensorsThe International Journal of Robotics Research, 2010
- Continuous 3D scan-matching with a spinning 2D laserPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2009
- Square Root SAM: Simultaneous Localization and Mapping via Square Root Information SmoothingThe International Journal of Robotics Research, 2006
- Determining the Epipolar Geometry and its Uncertainty: A ReviewInternational Journal of Computer Vision, 1998
- Closed-form solution of absolute orientation using unit quaternionsJournal of the Optical Society of America A, 1987