Uncertainty Suppression Methods for the Exploration of Sparsely Sampled Fields

Sargis S. Yonan, Renwick E. Curry, Gabriel Hugh Elkaim

Abstract:	The exploration of unknown areas has been accelerated by the development of consumer grade UAVs. Sensors and sensing systems have also become commodity items that researchers and developers can use to gain an understanding of the composition and concentrations of nutrients, moisture, and pollutants in soil, water, and air. A large unknown field of interest (a target field) can be explored to a high degree of accuracy if the entire field could be scanned using any of the various autonomous exploration system. This may not be possible if the field is very large and the exploration vehicle has limited exploration time due to terrain restrictions, battery/fuel limitations, and/or sensing capabilities. If the quantity of interest being predicted in a target field exhibits a degree of spatial autocorrelation, then estimates can be made at all points in the field based on observations taken at a few selected points. This paper explores where an exploration vehicle should travel to collect samples that create minimum variance estimates of all points in the field. It does this by determining the spatial autocorrelation of the estimated quantity, and uses this information to determine the next portion of the path that minimizes the sum of the variances of every point in the field. The Kriging Method, a Best Linear Unbiased Predictor, generates a prediction, and variance of that prediction, of a single point in a target field given a set of observed points. Averaging the estimation variances across all points in the field provides an objective function to guide path planning. The goal of each of the planners introduced is to assist in the discovery of a field’s features with an adjustable trade-off between arc length of the total path traveled and confidence of field prediction. Each of the path planners introduced attempts to reduce Kriging prediction variance by steering an exploration vehicle through a target field in a fashion that is predicted to reduce overall field uncertainty.
Published in:	Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019) September 16 - 20, 2019 Hyatt Regency Miami Miami, Florida
Pages:	2480 - 2511
Cite this article:	Yonan, Sargis S., Curry, Renwick E., Elkaim, Gabriel Hugh, "Uncertainty Suppression Methods for the Exploration of Sparsely Sampled Fields," Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, Florida, September 2019, pp. 2480-2511. https://doi.org/10.33012/2019.17052
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