如何完善非线性平差的精度评定理论是一个值得研究的问题。本项目从Sigma点的角度，通过偏差计算和方差或协方差计算，有望给出参数估值二阶精度及以上的精度评定信息，旨在突破现有精度评定理论依赖导数，没有顾及平差估值有偏性的局限性。本项目提出基于确定Sigma点的unscented transformation法和Sterling插值法及基于随机Sigma点的自适应Monte Carlo法处理一般的、附有约束和病态的非线性平差模型；提出基于重采样Sigma点的Jackknife法和Bootstrap法处理含有系统误差或粗差的非线性平差模型。在此基础上，本项目利用提出的方法进一步分析非线性平差参数估值对非线性模型的影响，进行非线性评价，把研究的精度评定理论应用于数据拟合、导航定位、大地测量反演等测量数据处理领域。本研究在理论与应用方面都具有重要的意义，是对非线性平差理论的进一步完善。

How to improve the theory on precision estimation of nonlinear adjustment is a very worthy of study. From the perspective of sigma point, the second and higher order information of precision estimation is expected to obtain based on processes of bias calculation and variance or covariance calculation. The aim of this project is a try to break through limitations existing in theory on precision estimation of depending on derivatives and ignoring biases of adjustment estimations. Methods of unscented transformation and Sterling interpolation based on determined sigma point, and adaptive Monte Carlo based on random sigma point are proposed for precision estimation related to general, constrained and ill-posed nonlinear adjustment models. And methods of Jackknife and Bootstrap based on resampling sigma point are applied and improved for nonlinear adjustment model with systematic error or gross error. On that basis, the effect of parameter estimation on nonlinear model and assessing nonlinearity are analyzed and conducted by proposed methods. The theory on precision estimation is applied for fields of surveying data processing, such as data fitting, navigation and position, and geodetic inversion. The research of this project is significant in aspects of theory and application, which also further improves and develops nonlinear adjustment theory.