Assessing the error of polygonal area measurements: a general formulation with applications to agriculture

This paper proposes a simple and general theoretical framework for the error assessment of area measurements of planar polygonal surfaces. The general formulation is first developed, both for the case of correlated and for the case of independent measurements, where a compact formulation can be obtained for the latter. These results are then used in the context of agriculture, with the aim of assessing field area measurement errors when using a global positioning system (GPS) device, enhanced using a simulated EGNOS (European geostationary navigation overlay service) time series. They show that for GPS/EGNOS measurements made by an operator moving along the border of a field, area measurement error is linked both to the operator speed and to the acquisition rate of the GPS device. For typical field sizes found in the European Union, ranging from 0.5 ha to 5 ha, the coefficient of variation (CV) for area measurement errors is about 1% to 5%. These results depend on the field area, but they can be considered to be insensitive with respect to the field shape. They also show that field area measurement errors can be limited if an appropriate combination of operator speed and GPS acquisition rate is selected. Though the practical case study presented here is focused on polygonal agricultural fields, it is expected that various other fields (medical and remotely sensed imagery, geographical information system data, computer vision analysis....) should also benefit from the theoretical results hereby obtained