引用本文: 陶本藻. 论最小二乘拟合[J]. 武汉大学学报 ( 信息科学版), 1980, 5(1): 27-34.
Tao Benzao. On the Least Squares Simulation[J]. Geomatics and Information Science of Wuhan University, 1980, 5(1): 27-34.
 Citation: Tao Benzao. On the Least Squares Simulation[J]. Geomatics and Information Science of Wuhan University, 1980, 5(1): 27-34.

## On the Least Squares Simulation

• 摘要: 在大地测量、地震及地球动力学数据处理中,常常需用一个函数去拟合已被测定的一组数据,这就是函数的拟合。函数的拟合通常采用最小二乘准则,即最小二乘拟合。在一般文献中,观测数据均假定具有独立性,但经常遇到的是处理相关数据。为了解决相关数据的拟合,本文按最小二乘相关估计的理论叙述了拟合的方法,监对这种方法的最优性作了全面的论证。考虑到处理数据时,经常要增添新的观测数据,为了解决数据的贮存便于电算和减少工作量,我们根据卡尔曼滤波的思想,推导了最小二乘拟合的递推公式。

Abstract: In geodetic,seismic and geodynamic data processing,a function is often required to simulate a group of measured data.That is the simulation of a function.The principle of the least squares being usually applied for this purpose,so it is called the least squares simulation,In the current literatures,the measured data are assumed to be independent with one another.In prance,however,we are frequently confronted with problems of handling correlated data.For solving such problems a method of simulation is suggested based upon the theory of least square correlation estimution.In addition,a comprehensive demonstration of the optimality of this method is made.In view of the fact that the new measured data are frequently to be supplemented to the data processing and also for economizing the data storage so as to reduce the workload in the computer,a recursion formula for the least squares simulation is derived according to the kalman filtering theory.

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