基于双二次插值多项式的DEM传递误差模型

The Surface Propagation Error Model of DEM Based on Biquadratic Interpolation Polynomial

基于函数插值方法,得出了基于不完全双二次插值多项式的规则格网数字高程模型(DEM)的表面表达模型,并推导了相应的传递误差公式。公式表明,不完全双二次多项式的DEM传递误差与双线性多项式的传递误差相同。但由于不完全双二次多项式的DEM表面建模误差低于线性多项式的DEM表面建模误差,因此基于不完全双二次多项式的DEM表面模型具有更高的精度。

Based on the interpolation method, a model to represent the surface of a grid DEM based on biquadratic interpolation polynomial is obtained, and a propagation error formula by the polynomial is derived. The formula shows that the propagation error from biquadratic polynomial is the same as the error from linear polynomial. But the model error by biquadratic polynomial is smaller than the error by linear polynomial, hence the accuracy based on biquadratic polynomial is better than the accuracy based on linear polynomial.