Abstract
Monitoring widespread environmental fields is undoubtedly a practically important area of research with many complex and challenging tasks. It involves the building of models of the fields or natural phenomena to be monitored, the estimation of the spatio-temporal distribution of a variety of environmental parameters of interest, such as moisture or salinity in a crop field, or the spatial distribution of vital natural resources such as oil and gas, etc. Sampling, a key operation of the monitoring process, is a broad methodology for gathering statistical information about the phenomenon, or environmental variable, being monitored. To efficiently monitor widespread fields and estimate the spatio-temporal distribution of some particular environmental variable, calls for the use of a sampling strategy can fuse information from different scales of sensors. Such an attractive strategy is well catered for by both the capabilities and distributed nature of wireless sensor networks and the mobility of robots performing the sampling (sensing) tasks. This sampling strategy could even be rendered “adaptive” in that the decision of “where to sample next” evolves temporally with past measurements and is optimally computed. In this article, we examine various single-robot and multi-robot adaptive sampling schemes based on different extended Kalman filter filtering structures such as centralized and decentralized filters as well as our own novel decentralized and distributed filters. Our investigation shows that, whereas the first two filters suffer from a heavy computational or communication load, our proposed method, through its key feature of distributing the filtering task amongst the robots used, manages to reduce both loads and the total reconstruction time. It also enjoys the added attractive feature of scalability that allows the structure of the proposed monitoring scheme to grow with the complexity of the field under study. Our results are corroborated by our simulation work and offer ample encouragement for a further theoretical investigation of some properties of the proposed scheme and its implementation on a physical system. Both of these activities are currently underway.
Highlights
Mobile robots are being increasingly used as sensorcarrying agents to perform sampling missions, such as searching for harmful biological and chemical agents, search and rescue in disaster areas, and environmental mapping and monitoring
The rest of the article is organized as follows: in Section 2, we present the general formulation of the adaptive sampling (AS) problem; Section 3 summarizes the existing centralized and decentralized filters, and their application to sensor network for field estimation; in Section 4, we present the novel federated distributed KF; Section 5 presents the simulation results for the proposed algorithm, and their discussion; Section 6 concludes the article
In this article, we studied the problem of estimating the field distribution of some particular environmental variable using both single-robot and multi-robot AS schemes and different filtering structures, such as the centralized and decentralized ones as well as our proposed federated distributed filtering structure
Summary
Mobile robots are being increasingly used as sensorcarrying agents to perform sampling missions, such as searching for harmful biological and chemical agents, search and rescue in disaster areas, and environmental mapping and monitoring. In [15], the authors represent the time-varying field with a random process with a covariance known up to a scaling parameter They proposed gradient descent algorithm which can run in a distributed fashion on multiple robots. The extended Kalman filter (EKF) is used to derive a quantitative information measure that is needed for the selection of sampling locations that are mostly likely to yield optimal information In this approach, the existing low-resolution information of the field is first used to acquire an initial parametric representation of the field whose parameters have a higher initial error covariance which gradually reduces as high-resolution samples are taken and processed. In this approach, FCM clusters samples based on the estimated centers of the approximating Gaussians used to map the field. EKF Post-Measurement update ða posterior estimateÞ ePqkuþa1ti1⁄4onÂ"sP:kÀ1 þ GkT RÀ1Gk ÃÀ1 X N
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