Unmanned Aerial Vehicles (UAVs) have been implemented for environmental monitoring by using their capabilities of mobile sensing, autonomous navigation, and remote operation. However, in real-world applications, the limitations of on-board resources (e.g., power supply) of UAVs will constrain the coverage of the monitored area and the number of the acquired samples, which will hinder the performance of field estimation and mapping. Therefore, the issue of constrained resources calls for an efficient sampling planner to schedule UAV-based sensing tasks in environmental monitoring. This paper presents a mission planner of coverage sampling and path planning for a UAV-enabled mobile sensor to effectively explore and map an unknown environment that is modeled as a random field. The proposed planner can generate a coverage path with an optimal coverage density for exploratory sampling, and the associated energy cost is subjected to a power supply constraint. The performance of the developed framework is evaluated and compared with the existing state-of-the-art algorithms, using a real-world dataset that is collected from an environmental monitoring program as well as physical field experiments. The experimental results illustrate the reliability and accuracy of the presented coverage sampling planner in a prior survey for environmental exploration and field mapping.
For an unknown environment, the underlying environmental model is learned by utilizing observations that are taken across the study area. Coverage sampling that is done to relax unrealistic assumptions is called an exploratory design, which provides sufficient flexibility to explore an unknown field @cite_18 . Such designs have been adopted in spatial mapping without rigid prior assumptions, for initial collection of prior knowledge, exploratory survey for long-term design improvement, or combination with optimum designs for improved estimation performance. In most existing monitoring programs, the exploratory sampling is required to learn the underlying field. Regular grid-based sampling approaches accomplish such objectives as exploratory designs @cite_19 @cite_7 . These approaches distribute sampling sites by decomposing the field into a grid of cells (e.g., squares, triangles, hexagons) where the samples are taken in the grid tessellation. In the absence of prior knowledge, a regular grid ensures overall coverage of the surveillance area. In particular, it provides a simple frame to distribute spatially balanced data samples across the study area for prior survey.
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When monitoring spatial phenomena, such as the ecological condition of a river, deciding where to make observations is a challenging task. In these settings, a fundamental question is when an active learning, or sequential design, strategy, where locations are selected based on previous measurements, will perform significantly better than sensing at an a priori specified set of locations. For Gaussian Processes (GPs), which often accurately model spatial phenomena, we present an analysis and efficient algorithms that address this question. Central to our analysis is a theoretical bound which quantifies the performance difference between active and a priori design strategies. We consider GPs with unknown kernel parameters and present a nonmyopic approach for trading off exploration, i.e., decreasing uncertainty about the model parameters, and exploitation, i.e., near-optimally selecting observations when the parameters are (approximately) known. We discuss several exploration strategies, and present logarithmic sample complexity bounds for the exploration phase. We then extend our algorithm to handle nonstationary GPs exploiting local structure in the model. We also present extensive empirical evaluation on several real-world problems. Received 28 May 2002; revised 18 September 2002; accepted 24 September 2002; published 14 February 2003. [1] When an inverse problem is solved to estimate an unknown function such as the hydraulic conductivity in an aquifer or the contamination history at a site, one constraint is that the unknown function is known to be everywhere nonnegative. In this work, we develop a statistically rigorous method for enforcing function nonnegativity in Bayesian inverse problems. The proposed method behaves similarly to a Gaussian process with a linear variogram (i.e., unrestricted Brownian motion) for parameter values significantly greater than zero. The method uses the method of images to define a prior probability density function based on reflected Brownian motion that implicitly enforces nonnegativity. This work focuses on problems where the unknown is a function of a single variable (e.g., time). A Markov chain Monte Carlo (MCMC) method, specifically, a highly efficient Gibbs sampler, is implemented to generate conditional realizations of the unknown function. The new method is applied to the estimation of the trichloroethylene (TCE) and perchloroethylene (PCE) contamination history in an aquifer at Dover Air Force Base, Delaware, based on concentration profiles obtained from an underlying aquitard. INDEX TERMS: 1831 Hydrology: Groundwater quality; 1869 Hydrology: Stochastic processes; 3260 Mathematical Geophysics: Inverse theory; KEYWORDS: stochastic inverse modeling, contaminant source identification, inference under constraints, Markov chain Monte Carlo (MCMC), Gibbs sampling, Bayesian inference This paper investigates data-adaptive path planning schemes for wireless networks of mobile sensor platforms. We focus on applications of environmental monitoring, in which the goal is to reconstruct a spatial map of environmental factors of interest. Traditional sampling theory deals with data collection processes that are completely independent of the target map to be estimated, aside from possible a priori specifications reflective of assumed properties of the target. We refer to such processes as passive learning methods. Alternatively, one can envision sequential, adaptive data collection procedures that use information gleaned from previous observations to guide the process. We refer to such feedback-driven processes as active learning methods. Active learning is naturally suited to mobile path planning, in which previous samples are used to guide the motion of the mobiles for further sampling. This paper presents some of the most encouraging theoretical results to date that support the effectiveness of active over passive learning, and focuses on new results regarding the capabilities of active learning methods for mobile sensing. Tradeoffs between latency, path lengths, and accuracy are carefully assessed using our theory. Adaptive path planning methods are developed to guide mobiles in order to focus attention in interesting regions of the sensing domain, thus conducting spatial surveys much more rapidly while maintaining the accuracy of the estimated map. The theory and methods are illustrated in the application of water current mapping in a freshwater lake. In this paper, we propose a non-local structured prior for volumetric multi-view 3D reconstruction. Towards this goal, we present a novel Markov random field model based on ray potentials in which assumptions about large 3D surface patches such as planarity or Manhattan world constraints can be efficiently encoded as probabilistic priors. We further derive an inference algorithm that reasons jointly about voxels, pixels and image segments, and estimates marginal distributions of appearance, occupancy, depth, normals and planarity. Key to tractable inference is a novel hybrid representation that spans both voxel and pixel space and that integrates non-local information from 2D image segmentations in a principled way. We compare our non-local prior to commonly employed local smoothness assumptions and a variety of state-of-the-art volumetric reconstruction baselines on challenging outdoor scenes with textureless and reflective surfaces. Our experiments indicate that regularizing over larger distances has the potential to resolve ambiguities where local regularizers fail.