Robots such as autonomous underwater vehicles (AUVs) and autonomous surface vehicles (ASVs) have been used for sensing and monitoring aquatic environments such as oceans and lakes. Environmental sampling is a challenging task because the environmental attributes to be observed can vary both spatially and temporally, and the target environment is usually a large and continuous domain whereas the sampling data is typically sparse and limited. The challenges require that the sampling method must be informative and efficient enough to catch up with the environmental dynamics. In this paper we present a planning and learning method that enables a sampling robot to perform persistent monitoring tasks by learning and refining a spatiotemporal environmental model. Our environmental sampling framework consists of two components: to maximize the information collected, we propose an informative planning component that efficiently generates sampling waypoints that contain the maximal information; To alleviate the computational bottleneck caused by large-scale data accumulated, we develop a component based on a sparse Gaussian Process whose hyperparameters are learned online by taking advantage of only a subset of data that provides the greatest contribution. We validate our method with both simulations running on real ocean data and field trials with an ASV in a lake environment. Our experiments show that the proposed framework is both accurate and efficient in learning the spatiotemporal environmental model
We develop an approach for sparse representations of gaussian process (GP) models (which are Bayesian types of kernel machines) in order to overcome their limitations for large data sets. The method is based on a Combination of a Bayesian on-line algorithm, together with a sequential construction of a relevant subsample of the data that fully specifies the prediction of the GP model. By using an appealing parameterization and projection techniques in a reproducing kernel Hilbert space, recursions for the effective parameters and a sparse gaussian approximation of the posterior process are obtained. This allows for both a propagation of predictions and Bayesian error measures. The significance and robustness of our approach are demonstrated on a variety of experiments. We present a simple sparse greedy technique to approximate the maximum a posteriori estimate of Gaussian Processes with much improved scaling behaviour in the sample size m. In particular, computational requirements are O(n2m), storage is O(nm), the cost for prediction is O(n) and the cost to compute confidence bounds is O(nm), where n ≪ m. We show how to compute a stopping criterion, give bounds on the approximation error, and show applications to large scale problems. We present a new Gaussian process (GP) inference algorithm, called online sparse matrix Gaussian processes (OSMGP), and demonstrate its merits by applying it to the problems of head pose estimation and visual tracking. The OSMGP is based upon the observation that for kernels with local support, the Gram matrix is typically sparse. Maintaining and updating the sparse Cholesky factor of the Gram matrix can be done efficiently using Givens rotations. This leads to an exact, online algorithm whose update time scales linearly with the size of the Gram matrix. Further, we provide a method for constant time operation of the OSMGP using matrix downdates. The downdates maintain the Cholesky factor at a constant size by removing certain rows and columns corresponding to discarded training examples. We demonstrate that, using these matrix downdates, online hyperparameter estimation can be included at cost linear in the number of total training examples. We describe a robust appearance-based head pose estimation system based upon the OSMGP. Numerous experiments and comparisons with existing methods using a large dataset system demonstrate the efficiency and accuracy of our system. Further, to showcase the applicability of OSMGP to a wide variety of problems, we also describe a regression-based visual tracking method. Experiments show that our OSMGP algorithm generalizes well using online learning. In this paper, we consider the problem of learning a two dimensional spatial model of a gas distribution with a mobile robot. Building maps that can be used to accurately predict the gas concentration at query locations is a challenging task due to the chaotic nature of gas dispersal. We present an approach that formulates this task as a regression problem. To deal with the specific properties of typical gas distributions, we propose a sparse Gaussian process mixture model. This allows us to accurately represent the smooth background signal as well as areas of high concentration. We integrate the sparsification of the training data into an EM procedure used for learning the mixture components and the gating function. Our approach has been implemented and tested using datasets recorded with a real mobile robot equipped with an electronic nose. We demonstrate that our models are well suited for predicting gas concentrations at new query locations and that they outperform alternative methods used in robotics to carry out in this task. Learning in real-time applications, e.g., online approximation of the inverse dynamics model for model-based robot control, requires fast online regression techniques. Inspired by local learning, we propose a method to speed up standard Gaussian process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained. The prediction for a query point is performed by weighted estimation using nearby local models. Unlike other GP approximations, such as mixtures of experts, we use a distance based measure for partitioning of the data and weighted prediction. The proposed method achieves online learning and prediction in real-time. Comparisons with other non-parametric regression methods show that LGP has higher accuracy than LWPR and close to the performance of standard GPR and ν-SVR.