M. Bachmaier and H. Auernhammer, “Yield Mapping Based on Robust Fitting Paraboloid Cones in Butterfly and Elliptic Neighborhoods,” In: J. V. Stafford and A. Werner, Ed., Precision Agriculture '05: Proceedings of the 5th European Conference on Precision Agriculture, Wageningen Academic Publishers, Wageningen, the Netherlands, 2005, pp. 741-750.

has been cited by the following article:

• TITLE: A Yield Mapping Procedure Based on Robust Fitting Paraboloid Cones on Moving Elliptical Neighborhoods and the Determination of Their Size Using a Robust Variogram

  AUTHORS: Martin Bachmaier

  KEYWORDS: Precision Agriculture, Yield Mapping, GPS, Elliptical Neighborhood, Paraboloid, Weighted Regression, Redescending M-estimate, Robust Variogram

  JOURNAL NAME: Positioning, Vol.1 No.1, November 26, 2010

  ABSTRACT: 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 an elliptical neighborhood that is wider across the harvest tracks than it is along them. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease quadratically from 1 in the middle to zero 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 shape, this yield mapping method is implemented by the Fortran program paraboloidmapping.exe, which can be downloaded from the web. The size of the selected neighborhood is considered appropriate if the variance of the yield map values equals 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.