广义非线性动态最小二乘问题的一个直接解算方法

A direct solution method for generalized nonlinear dynamic least squares problem

构建“数字地球”、“数字国家”等数字化科学工程的基础是数据[1 ] ,其数据具有多源、多维、多种类型、多种时态、多种精度并具有非线性特征等特点[2 ] ,首先要进行数据处理并应采用全新的广义非线性动态最小二乘法[3] [4] ,数据处理方法的核心是广义非线性动态最小二乘问题参数估计的函数模型及其解算方法 ,迄今国内外对这方面的研究尚不多。本文在作者前期研究、提出的广义非线性动态最小二乘函数模型参数估计迭代法求解[5] 的基础上 ,进一步研究、提出了一种广义非线性动态最小二乘模型参数估计的直接解算方法 ,将问题分离 ,把待求参数减半 ,直接求解。从而大大降低求解问题的维数 ,大大减少计算难度和计算工作量 ,这是国内外首次研究提出的一种比迭代法更快速、更有效、更科学的解算方法。为多源、多类、多时态数据处理开辟了一新途径 。

Data are basic to build the digital earth,the digital nation and so on.These data come from many sources and have the characteristics of multi-dimensions,multi-types,multi-temporal states,different accuracies and nonlinear^().So a new generalized nonlinear dynamic least squares method should be used to process these data^().The function model and its solution method of generalized nonlinear dynamic least squares parametric estimation are the key to process these data.So far these studies are seldom made internally and externally.Based on the iterative solution of generalized nonlinear dynamic least squares parametric estimation^(),a direct solution method to the problem is put forward in the paper.The method separates the problem into two sub-problems,reduces the unknown parameters half and directly calculates the optimal results.Therefore the method can decrease the dimensions of the problem and reduce the computing difficulty and work load.It is more rapid effective and scientific than the iterative method so that it opens a new way to process these data which come from multi-sources and have multi-types and multi-temporal states.The direct method can widen the application of generalized nonlinear dynamic least squares method.