Distributed Gaussian Process Regression Under Localization Uncertainty

Abstract

In this paper, we propose distributed Gaussian process regression (GPR) for resource-constrained distributed sensor networks under localization uncertainty. The proposed distributed algorithm, which combines Jacobi over-relaxation (JOR) and discrete-time average consensus (DAC), can effectively handle localization uncertainty as well as limited communication and computation capabilities of distributed sensor networks. We also extend the proposed method hierarchically using sparse GPR to improve its scalability. The performance of the proposed method is verified in numerical simulations against the centralized maximum a posteriori (MAP) solution and a quick-and-dirty solution. We show that the proposed method outperforms the quick-and-dirty solution and achieve an accuracy comparable to the centralized solution.

Feature selection for position estimation using an omnidirectional camera

“…Here S denotes the surveillance region, which is a compact set. Then, the accumulative image properties y is a random vector defined by y = (y 1 T , ⋯, y m T ) T ∈ ℝ nm , and y ρ = (y ρ [1] , ⋯, y ρ ) ∈ ℝ n contains n realizations of the ρ-th image property.…”

“…A random vector x, which has a multivariate normal distribution of mean vector μ and covariance matrix Σ, is denoted by x∼N μ; Σ ð Þ. The collection of n realized values of the ρ-th random field is denoted by z ρ := (z ρ [1] , ⋯, z ρ…”

“…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].…”

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:…”

“…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].…”