A Yield Mapping Procedure Based on Robust Fitting Paraboloid Cones on Moving Elliptical Neighborhoods and the Determination of Their Size Using a Robust Variogram
Martin Bachmaier
Technische Universit?t München.
DOI: 10.4236/pos.2010.11004   PDF    HTML   XML   7,017 Downloads   12,591 Views   Citations

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.

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M. Bachmaier, "A Yield Mapping Procedure Based on Robust Fitting Paraboloid Cones on Moving Elliptical Neighborhoods and the Determination of Their Size Using a Robust Variogram," Positioning, Vol. 1 No. 1, 2010, pp. 27-41. doi: 10.4236/pos.2010.11004.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] M. Bachmaier, “Using a Robust Variogram to Find an Adequate Butterfly Neighborhood Size for One-Step Yield Mapping Using Robust Fitting Paraboloid Cones,” Precision Agriculture, Vol. 8, No. 1-2, 2007, pp. 75-93.
[2] G. C. Simbahan, A. Dobermann and J. L. Ping, “Site- Specific Management. Screening Yield Monitor Data Improves Grain Yield Maps,” Agronomy Journal, Vol. 96, No. 4, 2004, pp. 1091-1102.
[3] S. A. Shearer, S. G. Higgins, S. G. McNeil, G. A. Watkins, R. I. Barnhisel, J. C. Doyle, J. H. Leach and J. P. Fulton, “Data Filtering and Correction Techniques for Generating Yield Maps from Multiple Combine Harvesting Systems,” ASAE Paper No. 971034, Annual International Meeting, Minneapolis Minnesota, 10-14 August 1997.
[4] B. S. Blackmore and M. Moore, “Remedial Correction of Yield Map Data,” Precision Agriculture, Vol. 1, No. 1, 1999, pp. 53-66.
[5] S. Arslan and T. S. Colvin, “Grain Yield Mapping: Yield Sensing, Yield Reconstruction, and Errors,” Precision Agriculture, Vol. 3, No. 2, 2002, pp. 135-154.
[6] T. Steinmayr, “Fehleranalyse und Fehlerkorrektur bei der lokalen Ertragsermittlung im M?hdrescher zur Ableitung eines standardisierten Algorithmus für die Ertragskartierung,” Dissertation at the Technische Universit?t Mün- chen-Weihenstephan, 2003, pp. 24-27.
[7] L. Thylén, P. A. Algerbo and A. Giebel, “An Expert Filter Removing Erroneous Yield Data,” In: Robert et al., Ed., Precision Agriculture 2000: Proceedings of the 5th International Conference on Precision Agriculture, ASA, CSSA, and SSSA, Madison, WI, CD-ROM, 2001.
[8] L. Thylén, P. Jürschik and D. P. L. Murphy, “Improving the Quality of Yield Data,” In: J. V. Stafford, Ed., Precision Agriculture '97: Proceedings of the 1st European Conference on Precision Agriculture, BIOS Scientific Publishers Ltd, Oxford, UK, 1997, pp. 743-750.
[9] P. H .Noack, T. Muhr and M. Demmel, “An Algorithm for Automatic Detection and Elimination of Defective Yield Data,” In: J.V. Stafford and A. Werner, Ed., Precision Agriculture, Wageninen Academic Publishers, Wageningen, 2003, pp. 445-450.
[10] F. R. Hampel, P. J. Rousseeuw, E. M. Ronchetti and W. A. Stahel, “Robust Statistics,” John Wiley & Sons, Inc., New York, USA, 1986.
[11] 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.
[12] P. J. Huber, “Robust Statistics,” John Wiley & Sons, Inc., New York, USA, 1981.
[13] F. W. Satterthwaite, “An Approximate Distribution of Estimates of Variance Components,” Biometrics Bulletin, Vol. 2, No. 6, 1946, pp. 110-114.
[14] P. J. Huber, “Robust Statistical Procedures,” Regional Conference Series in Applied Mathematics 27, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1977.
[15] M. Bachmaier and H. Auernhammer, “A Method for Correcting Raw Yield Data by Fitting Paraboloid Cones,” In: Proceedings of the AgEng 2004 Conference — Engineering the Future, Session 10: Precision Agriculture, 8 pages on CD-ROM, 2004.
[16] N. A. C. Cressie, “Statistics for Spatial Data,” John Wiley & Sons, Inc., New York, USA, 1991.
[17] M. Bachmaier and M.Backes, “Variogram or Semivariogram? — Understanding the Variances in a Variogram,” Precision Agriculture, Vol. 9, No. 3, 2008, pp. 173-175.
[18] R. M. Lark, “A Comparison of Some Robust Estimators of the Variogram for Use in Soil Survey,” European Journal of Soil Science, Vol. 51, No. 1, 2000, pp. 137-157.
[19] N. A. C. Cressie and D. Hawkins, “Robust Estimation of the Variogram,” Mathematical Geology, Vol. 12, No. 2, 1980, pp. 115-125.
[20] P. A. Dowd, “The Variogram and Kriging: Robust and Resistant Estimators,” In: G. Verly et al., Ed., Geostatistics for Natural Resources Characterization, D. Reidel, Dordrecht, Part 1, 1984, pp. 91-106.
[21] M. G. Genton, “Highly Robust Variogram Estimation,” Mathematical Geology, Vol. 30, No. 2, 1998, pp. 213-221.
[22] M. Bachmaier, “Efficiency Comparison of M-Estimates for Scale at t-Distributions,” Statistical Papers, Vol. 41, No. 1, 2000, pp. 53-64.
[23] M. Bachmaier, “Finding Adequate Neighborhoods for Robust Yield Mapping,” 2006. http://www.tec.wzw.tum. de/ index.php?id=46
[24] M. Bachmaier, M. Rothmund and H.Auernhammer, An “Attempt to Optimize Yield Maps by Comparing Yield Data from a Plot Combine and from a Combine Harvester,” Agricultural Engineering International, Manuscript IT 07 009, Vol. 10, 12 pages, 2008. http://cigr- ejournal.tamu.edu
[25] M. Bachmaier, Fortran-Programme zum Herunterladen: Korrektur von Rohertragsdaten und Ertragskartierung: DOS/Windows-Programme paraboloidmapping.exe, and paraboloidcorrection.exe (in English), 2010http://www. tec.wzw.tum.de/index.php?id=46

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