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A Robust Multiquadratic Method and Its Application to DEM Construction

In order to resist the effect of outliers on DEM construction, a robust multiquadric method(MQ-R)has been developed. MQ-R firstly takes the estimation of the classical MQ as the initial values to compute the residuals of all sampling points, and then a weighted function has been constructed to determine the weights of sampling points based on the above residuals. Finally, a iteratively re-weighted MQ is formed to decrease the effect of outliers on DEM construction. At the same time, the smoothing parameter of MQ and MQ-R is determined based on a k-fold cross-validation. A synthetic surface was employed to comparatively analyze the estimation accuracies of MQ-R and the classcial MQ, where the sampling points are contaminated by three groups of errors with different distributions. These include the standard normal distribution, contaminated normal distribution with the contaminating proportion of 10%, 20% and 30%, and Cauchy distribution. Numerical tests indicate that when sampling errors are from the standard normal distribution, the accuracy of MQ-R is comparative to that of MQ. As the contaminating proportion increases, the accuracy of MQ becomes lower, whereas MQ-R can resist oultiers very well. When sampling errors are from Cauchy distribution, the results of MQ are completely destroyed, but those of MQ-R are still satisfactory. In conclusions, MQ-R with a high efficiency and a high robustness can be used to resist outliers in DEM construction.