Bayesian Prediction and Adaptive Sampling Algorithms for Mobile Sensor Networks (original) (raw)
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Sequential Bayesian Prediction and Adaptive Sampling Algorithms for Mobile Sensor Networks
IEEE Transactions on Automatic Control, 2012
In this paper, we formulate a full Bayesian approach for spatio-temporal Gaussian process regression under practical conditions such as measurement noise and unknown hyperparmeters (particularly, the bandwidths). Thus, multifactorial effects of observations, measurement noise and prior distributions of hyperparameters are all correctly incorporated in the computed predictive distribution. Using discrete prior probabilities and compactly supported kernels, we provide a way to design sequential Bayesian prediction algorithms that can be computed (without using the Gibbs sampler) in constant time as the number of observations increases. Both centralized and distributed sequential Bayesian prediction algorithms have been proposed for mobile sensor networks. An adaptive sampling strategy for mobile sensors, using the maximum a posteriori (MAP) estimation, has been proposed to minimize the prediction error variances. Simulation results illustrate the effectiveness of the proposed algorithms.
Gaussian Process Regression for Sensor Networks Under Localization Uncertainty
IEEE Transactions on Signal Processing, 2000
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.
An extension of Bayesian algorithm into gaussian processes for predicting sensor network
Journal of Statistics & Management Systems, 2008
This paper makes a long-term prediction of the sensor nodes network over some information seeking research in some randomly localized environment with the application of the Bayesian and Gaussian processes models. These properties may include life span of the sensors and their distance measurements from a decision centre. The data generated in probabilities representations are fitted with the Exponential, Gaussian and Fourier functions to enable decision taking. Of the three functions, Fourier series was estimated to be the best function for the curve fitting both graphically and numerically as shown through the experiments. It has a far and wider predictive horizon beyond the data locations than the other distributive functions.
Adaptive Sampling for Learning Gaussian Processes Using Mobile Sensor Networks
Sensors, 2011
This paper presents a novel class of self-organizing sensing agents that adaptively learn an anisotropic, spatio-temporal Gaussian process using noisy measurements and move in order to improve the quality of the estimated covariance function. This approach is based on a class of anisotropic covariance functions of Gaussian processes introduced to model a broad range of spatio-temporal physical phenomena. The covariance function is assumed to be unknown a priori. Hence, it is estimated by the maximum a posteriori probability (MAP) estimator. The prediction of the field of interest is then obtained based on the MAP estimate of the covariance function. An optimal sampling strategy is proposed to minimize the information-theoretic cost function of the Fisher Information Matrix. Simulation results demonstrate the effectiveness and the adaptability of the proposed scheme.
Spatial Gaussian process regression with mobile sensor networks
IEEE transactions on neural networks and learning systems, 2012
This paper presents a method of using Gaussian process regression to model spatial functions for mobile wireless sensor networks. A distributed Gaussian process regression (DGPR) approach is developed by using a sparse Gaussian process regression method and a compactly supported covariance function. The resultant formulation of the DGPR approach only requires neighbor-to-neighbor communication, which enables each sensor node within a network to produce the regression result independently. The collective motion control is implemented by using a locational optimization algorithm, which utilizes the information entropy from the DGPR result. The collective mobility of sensor networks plus the online learning capability of the DGPR approach also enables the mobile sensor network to adapt to spatiotemporal functions. Simulation results are provided to show the performance of the proposed approach in modeling stationary spatial functions and spatiotemporal functions.
Mobile Sensor Network Navigation Using Gaussian Processes With Truncated Observations
IEEE Transactions on Robotics, 2000
In this paper, we consider mobile sensor networks that use spatiotemporal Gaussian processes to predict a wide range of spatiotemporal physical phenomena. Nonparametric Gaussian process regression that is based on truncated observations is proposed for mobile sensor networks with limited memory and computational power. We first provide a theoretical foundation of Gaussian process regression with truncated observations. In particular, we demonstrate that prediction using all observations can be well approximated by prediction using truncated observations under certain conditions. Inspired by the analysis, we then propose a centralized navigation strategy for mobile sensor networks to move in order to reduce prediction error variances at points of interest. For the case in which each agent has a limited communication range, we propose a distributed navigation strategy. Particularly, we demonstrate that mobile sensing agents with the distributed navigation strategy produce an emergent, swarming-like, collective behavior for communication connectivity and are coordinated to improve the quality of the collective prediction capability.
Distributed Gaussian process regression for mobile sensor networks under localization uncertainty
52nd IEEE Conference on Decision and Control, 2013
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.
Active Learning of Gaussian Processes for Spatial Functions in Mobile Sensor Networks
Proceedings of the 18th IFAC World Congress, 2011
This paper proposes a spatial function modeling approach using mobile sensor networks, which potentially can be used for environmental surveillance applications. The mobile sensor nodes are able to sample the point observations of an 2D spatial function. On the one hand, they will use the observations to generate a predictive model of the spatial function. On the other hand, they will make collective motion decisions to move into the regions where high uncertainties of the predictive model exist. In the end, an accurate predictive model is obtained in the sensor network and all the mobile sensor nodes are distributed in the environment with an optimized pattern. Gaussian process regression is selected as the modeling technique in the proposed approach. The hyperparameters of Gaussian process model are learned online to improve the accuracy of the predictive model. The collective motion control of mobile sensor nodes is based on a locational optimization algorithm, which utilizes an information entropy of the predicted Gaussian process to explore the environment and reduce the uncertainty of predictive model. Simulation results are provided to show the performance of the proposed approach.
2012 4th Computer Science and Electronic Engineering Conference (CEEC), 2012
This paper presents a sparse history data based method for modelling a latent function with mobile wireless sensor networks. It contains two main tasks, which are estimating the latent function and optimising the sensor deployment. Gaussian process (GP) is selected as the framework according to its excellent regression performance. History data can improve the modelling performance with small amount of sensors in static or slowly changed environment. However, the GP kernel size is expended. On the one hand, in other kernel based (or non-parametric) methods, computation cost increases fast with kernel size. To control the size of GP kernel, informative vector machine (IVM) is introduced for history data selection. On the other hand, centroidal Voronoi tessellation (CVT), a gradient based method, is adopted for optimising sensor deployment. Simulation results with different data selection methods and analyses are given. It's proved that the data selection is effective in reducing computation cost and keeping the precision of the estimated model.
Stochastic adaptive sampling for mobile sensor networks using kernel regression
Proceedings of the 2010 American Control Conference, 2010
In this paper, we provide a stochastic adaptive sampling strategy for mobile sensor networks to estimate scalar fields over a surveillance region using kernel regression. Our approach builds on a Markov Chain Monte Carlo (MCMC) algorithm particularly known as the Fastest Mixing Markov Chain (FMMC) under a quantized finite state space for generating the optimal sampling probability distribution asymptotically. An adaptive sampling algorithm for multiple mobile sensors is designed and numerically evaluated under a complicated scalar field. The comparison simulation study with a random walk benchmark strategy demonstrates the good performance of the proposed scheme.