Mahdi Jadaliha

Gaussian Process Regression for Sensor Networks Under Localization Uncertainty

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 Laplaces 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.

Environmental Monitoring Using Autonomous Aquatic Robots: Sampling Algorithms and Experiments

This brief presents a practical solution to the problem of monitoring an environmental process in a large region by a small number of robotic sensors. Optimal sampling strategies are developed, taking into account the quality of the estimated environmental field and the lifetime of the sensors. We also present experimental results for monitoring a temperature field of an outdoor swimming pool sampled by an autonomous aquatic surface robot. Simulation and experimental results are provided to validate the proposed scheme.

Adaptive Control of Multiagent Systems for Finding Peaks of Uncertain Static Fields

In this paper, we design and analyze a class of multiagent systems that locate peaks of uncertain static fields in a distributed and scalable manner. The scalar field of interest is assumed to be generated by a radial basis function network. Our distributed coordination algorithms for multiagent systems build on techniques from adaptive control. Each agent is driven by swarming and gradient ascent efforts based on its own recursively estimated field via locally collected measurements by itself and its neighboring agents. The convergence properties of the proposed multiagent systems are analyzed. We also propose a sampling scheme to facilitate the convergence. We provide simulation results by applying our proposed algorithms to nonholonomic differentially driven mobile robots. The extensive simulation results match well with the predicted behaviors from the convergence analysis and illustrate the usefulness of the proposed coordination and sampling algorithms. [DOI: 10.1115/1.4006369]

Feature selection for position estimation using an omnidirectional camera

Abstract This paper considers visual feature selection to implement position estimation using an omnidirectional camera. The localization is based on a maximum likelihood estimation (MLE) with a map from optimally selected visual features using Gaussian process (GP) regression. In particular, the collection of selected features over a surveillance region is modeled by a multivariate GP with unknown hyperparameters. The hyperparameters are identified through the learning process by an MLE, which are used for prediction in an empirical Bayes fashion. To select features, we apply a backward sequential elimination technique in order to improve the quality of the position estimation with compressed features for efficient localization. The excellent results of the proposed algorithm are illustrated by the experimental studies with different visual features under both indoor and outdoor real-world scenarios.

Distributed Gaussian Process Regression Under Localization Uncertainty

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.

Gaussian process regression using Laplace approximations under localization uncertainty

In this paper, we formulate Gaussian process regression with observations under the localization uncertainty. 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 Laplace approximations in different degrees of complexity. Such approximations have been carefully tailored to our problems and their approximation errors and complexity are analyzed. Simulation results demonstrate that the proposed approaches perform much better than approaches without considering the localization uncertainty correctly.

Efficient spatial prediction using gaussian markov random fields under uncertain localization

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.Copyright

Distributed Gaussian process regression for mobile sensor networks under localization uncertainty

In this paper, we propose distributed Gaussian process regression for resource-constrained mobile 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 ranges and computation capabilities of mobile sensor networks. The performance of the proposed method is verified in numerical simulations against the centralized maximum a posteriori solution and the quick-and-dirty solution. We show that the proposed method outperforms the quick-and-dirty solution and achieves an accuracy comparable to the centralized solution.

Fully Bayesian simultaneous localization and spatial prediction using Gaussian Markov random fields (GMRFs)

This paper investigates a fully Bayesian way to solve the simultaneous localization and spatial prediction (SLAP) problem using a Gaussian Markov random field (GMRF) model. The objective is to simultaneously localize robotic sensors and predict a spatial field of interest using sequentially obtained noisy observations collected by robotic sensors. The set of observations consists of the observed uncertain poses of robotic sensing vehicles and noisy measurements of a spatial field. To be flexible, the spatial field of interest is modeled by a GMRF with uncertain hyperparameters. We derive an approximate Bayesian solution to the problem of computing the predictive inferences of the GMRF and the localization, taking into account observations, uncertain hyperparameters, measurement noise, kinematics of robotic sensors, and uncertain localization. The effectiveness of the proposed algorithm is illustrated by simulation results.

Fully Bayesian Prediction Algorithms for Mobile Robotic Sensors under Uncertain Localization Using Gaussian Markov Random Fields

In this paper, we present algorithms for predicting a spatio-temporal random field measured by mobile robotic sensors under uncertainties in localization and measurements. The spatio-temporal field of interest is modeled by a sum of a time-varying mean function and a Gaussian Markov random field (GMRF) with unknown hyperparameters. We first derive the exact Bayesian solution to the problem of computing the predictive inference of the random field, taking into account observations, uncertain hyperparameters, measurement noise, and uncertain localization in a fully Bayesian point of view. We show that the exact solution for uncertain localization is not scalable as the number of observations increases. To cope with this exponentially increasing complexity and to be usable for mobile sensor networks with limited resources, we propose a scalable approximation with a controllable trade-off between approximation error and complexity to the exact solution. The effectiveness of the proposed algorithms is demonstrated by simulation and experimental results.