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.