The Criterion And The Application Of Vondrak Filter

Vondrak filter was founded by J.Vondrak in1967and was developed in1976.The Criterion function consisted of two sections, one named observation which was in relation to the residuals and the other named none observation which had nothing to do with the residuals. Vondrak filter had the ability of smoothing the equidistance or non-equidistance data, needed none of the change regulality or the fitting function.Consequently, Vondrak filter were widely used in various areas.The main topic of this paper was to investigate the Criterion function of the Vondrak filter and it’s application.(1)This paper studied the smoothness of the Vondrak filter’s criterion function.The explanation is given from the graduation and the essence,which was why the square of the smooth value’s third order difference was named smoothness.(2) This paper also analyzed the existing evaluation for the Vondrak’s filter.The existing evaluation included observation error method,error curve method, frequencyresponse approach, cross-identification, helmert type variance component estimate. A new criteria for evaluation was proposed that square root(δ) of the linear combination, which was the square of root-mean-square error (RMSE) and the smoothness. The new criteria for evaluation was a quantitative index. The practicability and the advantage of the new criteria for evaluation has been demonstrated through simulated data.(3)2-D Vondrak filter combined with the multisurface function was used in the height anomaly fitting.The experimental result shows that it is a practicable method in the height anomaly fitting.