In this paper, we develop efficient spatial prediction algorithms using Gaussian Markov random fields (GMRFs) under uncertain localization and sequential observations. We first review a GMRF as a discretized Gaussian process (GP) on a lattice, and justify the usage of maximum a posteriori (MAP) estimates of noisy sampling positions in making inferences. We show that the proposed approximation can be viewed as a discrete version of Laplace’s approximation for GP regression under localization uncertainty. We then formulate our problem of computing prediction and propose an approximate Bayesian solution, taking into account observations, measurement noise, uncertain hyper-parameters, and uncertain localization in a fully Bayesian point of view. In particular, we present an efficient scalable approximation using MAP estimates of noisy sampling positions with a controllable tradeoff between approximation error and complexity. The effectiveness of the proposed algorithms is illustrated using simulated and real-world data.
- Dynamic Systems and Control Division
Efficient Spatial Prediction Using Gaussian Markov Random Fields Under Uncertain Localization
- Views Icon Views
- Share Icon Share
- Search Site
Jadaliha, M, Xu, Y, & Choi, J. "Efficient Spatial Prediction Using Gaussian Markov Random Fields Under Uncertain Localization." Proceedings of the ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference. Volume 3: Renewable Energy Systems; Robotics; Robust Control; Single Track Vehicle Dynamics and Control; Stochastic Models, Control and Algorithms in Robotics; Structure Dynamics and Smart Structures; Surgical Robotics; Tire and Suspension Systems Modeling; Vehicle Dynamics and Control; Vibration and Energy; Vibration Control. Fort Lauderdale, Florida, USA. October 17–19, 2012. pp. 253-262. ASME. https://doi.org/10.1115/DSCC2012-MOVIC2012-8596
Download citation file: