非线性函数拟合算法在遥感泥沙定量模式中的应用

Application of Fitting Method of Nonlinear Equations to Quantitative Models of Remote Sensing Data and Suspended Solids

关于水体悬浮泥沙浓度与陆地卫星遥感数据的关系,国内外学者提出了很多非线性定量关系式,这些非线性关系式可以转化为X、Y中含有待定参数的线性多项式。拟合这些线性多项式通常的做法是手工输入不同的参数,取相关系数最大时的拟合多项式作为最终的结果。手工方法费时费力。作者提出一种迭代算法,只要给待定参数和相应的步长赋初值,就能根据一定规则自动迭代,直到找到相关系数最大的拟合多项式。算法在实际应用中取得了很好的效果,同时可以推广到其它应用领域。

Various equations about Landsat data and measures of aquatic suspended solids concentration have been mentioned in literature. Most of them are nonlinear and can be transformed to linear polynomials with unknown parameters in X and Y. In order to fit these linear polynomials, scientists input different parameters manually, and get fitting polynomial with maximal correlation coefficient. The method has low efficiency. The article presents a kind of iterative algorithm, which calculates automatically from initial values of unknown parameters and corresponding interval according some rules until get the fitting polynomial with maximal correlation coefficient. The algorithm has good effect in practice and is all\|purpose for other fields.