用差商代替导数的非线性最小二乘估计

针对不同类型观测值的非线性最小二乘平差，介绍一种不使用导的解析方法。在这种解算中，由于只使用函数值，避免了二阶和二阶偏导数的计算，使原本复杂的计算得以简化。实例验证了本方法的有效性和可靠性。

Nonlinear Least Squares Adjustment of Non-derivative

In classical adjustment,most of observation values are still expanded to carry out linear adjustment at their approximations in terms of Taylor's series of which the first order term as a linear function is taken out for the treatment of nonlinear functions of observation values existing broadly in the field of surveying and mapping science and technology.This treatment is based on undetermined quantities which are very close to their true values.In effect,a number of nonlinear models can not be tackled as usual.It is more and more highly requiring for the quality of observation accomplishments,treatment of observation datum and accuracy appraise,especially in the rocket_sky development of today's high technology.Apart from this,traditional and single geodetic surveying or non_geodetic surveying datum has been expanded into the combination of observation quantities on geodetic surveying or lots of types,different accuracy observation quantities on non_geodetic surveying with the unending advent of modern observation apparatus,the continuous enhancement and improvement of surveying means. This paper gives a computational method of nonlinear least squares adjustment without derivative for different types of observation value,in which a function value instead of its derivative is only used.As far as we know,finding the partial value of a function is a troublesome task,especially when the components f i(x)(i=1,2,...,m n) of a nonlinear function f(x) are very complicated.The essence of the method is to simplify its computations for a Jacobi's matrix,which determines the coefficient matrix with relation to a linear equation set by utilizing algebraic interpolation method with function values.In a geometrical sense,what is different from that in Guass_Newton's method is that a series of super_tangent planes can be converted into super_cut ones or that it can be seen as a discrete deformation of Guass_Newton's method.Especially while every difference step size is taken as a constant,the calculation is even more convenient.Examples show that the method is an effective algorithm and is of super_linear convergence velocity.