Gaussian Process Regression for Sensor Networks Under Localization Uncertainty

Abstract

In this paper, we formulate Gaussian process regression with observations under the localization uncertainty due to the resource-constrained sensor networks. In our formulation, effects of observations, measurement noise, localization uncertainty, and prior distributions are all correctly incorporated in the posterior predictive statistics. The analytically intractable posterior predictive statistics are proposed to be approximated by two techniques, viz., Monte Carlo sampling and Laplace's method. Such approximation techniques have been carefully tailored to our problems and their approximation error and complexity are analyzed. Simulation study demonstrates that the proposed approaches perform much better than approaches without considering the localization uncertainty properly. Finally, we have applied the proposed approaches on the experimentally collected real data from a dye concentration field over a section of a river and a temperature field of an outdoor swimming pool to provide proof of concept tests and evaluate the proposed schemes in real situations. In both simulation and experimental results, the proposed methods outperform the quick-and-dirty solutions often used in practice.

Optimization of Potable Water Distribution and Wastewater Collection Networks: A Systematic Review and Future Research Directions

“…In addition, this evaluation is inevitably required to be repeated many times for most advanced optimization methods. Simple numerical models have been emerging to simulate the hydraulic behaviors, however, from the system modeling perspective, more applications of advanced models, such as the fuzzy systems [151] with good model interpretabilities, Gaussian processes [152] with good probabilistic characteristics and support vector machines [153] with good generalization abilities, are expected to be integrated into the network optimization process to speed it up.…”

Appearance-based localization using Group LASSO regression with an indoor experiment

“…Define x i ∈ R 3 as the state vector that includes the position and the heading angle of the robot, e.g., x i = [q [1] i q [2] i ψ i ] T . Therefore, the state transition equation of the two wheeled robot is:…”

“…The group LASSO regression uses the training data to train the estimate matrix B and the validation data to compute the optimal matrixB, then appliesB to estimate the test dataŶ. • Group LASSO-based and EKF localization: We apply the EKF as a post-processing to the test result of the group LASSO-based localization as described in Section V. Figure 2 shows the evolutions of the first and second entries of the diagonal of matrix P i (P [1,1] and P [2,2] ) that represent the uncertainties in x and y axes. Notice that the variance of position coordinates drops whenever an observations is made.…”

“…Minimizing levels of location uncertainties in sensor networks or robotic sensors is important for regression problems, e.g., prediction of environmental fields [1], [2]. Localization of a robot relative to its environment using vision information (i.e., appearance-based localization) has received extensive attention over past few decades from the robotic and computer vision communities [3], [4].…”

Feature selection for position estimation using an omnidirectional camera

“…Minimizing levels of location uncertainties in sensor networks or robotic sensors is important for regression problems, e.g., prediction of environmental fields [1,2]. Localization of a robot relative to its environment using vision information (i.e., appearance-based localization) has received extensive attention over the past few decades from the robotic and computer vision communities [3][4][5].…”