基于阵列代数的测深数据拟合方法

Fitting Method of Hydrographic Data Based on Array Algebra

摘要: 传统水深测量涉及到大量离散的、分布不规则的水深数据，针对传统拟合方法计算复杂、速度慢的问题，该文将阵列代数思想应用于测深网格拟合。以双二次多项式拟合为例，建立了阵列代数最小二乘解模型，给出了基于正规方程的双二次矩阵方程的最小二乘解法；给出了改进拟合法实现的基本步骤，最后通过实验数据对反距离加权法、全局多项式法及阵列代数最小二乘拟合方法求得未知点水深的效率及精度进行比较。结果表明，在水深测量中引入阵列代数拟合结果效率要高于另外两种方法，可应用于水深测量数据网格化处理中。

Abstract: The traditional bathymetric survey involves a large number of discrete, irregularly distributed wa-ter depth data. In order to solve the problem of complex calculation and slow speed of traditional fitting method, the idea of array algebra is applied to the fitting of the sounding grid. The least squares solution of the array algebra is established by taking the biquadratic polynomial fitting as an example, and the least square solution of the quadratic matrix equation with the help of the normal equation is given. Moreover, the paper gives the basic steps to achieve the improved quasi legal, efficiency and accuracy of the experimental data to determine unknown point water depth on the inverse distance weighted method, global polynomial interpolation and least square fitting method of array algebra is compared. The results show that the efficiency of array algebra fitting is better than that of the other two methods, and can be applied to the data processing of hydrology survey.