Using a robust variogram to find an adequate butterfly neighborhood size for one-step yield mapping using robust fitting paraboloid cones
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The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on a neighborhood that looks like a huge butterfly flying along the harvest track. Wide wings of the butterfly guarantee that the map is sufficiently smoothed out across the tracks. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease with the distance from one to zero; the latter is at the border of the selected neighborhood. The robust way of estimating the model parameters supersedes a procedure for detecting outliers. For a given neighborhood size, this yield mapping method is implemented by the Fortran program butterflymap.exe , which can be downloaded from the web. To obtain the appropriate size of the selected neighborhood, the variance of the yield map values should equal the variance of the true yields, which is the difference between the variance of the raw yield data and the error variance of the yield monitor. It is estimated using a robust variogram on data that have not had the trend removed. Based on investigating butterfly neighborhoods the yield map was optimized if the search radius across the harvest tracks was eight times the swath width. One reason for this wide neighborhood is that the regression used for modeling the paraboloid cones is based on weights that decrease linearly from 1 in the middle to zero at the border of the neighborhood, so only data points close to the middle have a large weight.
KeywordsPrecision agriculture Raw data correction Yield map Paraboloid cone Weighted M-estimate Butterfly neighborhood Variance comparison
I thank Margaret A. Oliver, University of Reading, for her helpful and detailed remarks on this paper and Hermann Auernhammer, Technische Universität München-Weihenstephan, for supporting this work.
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