大地测量相关观测抗差估计理论

相关观测异常诊断、质量控制是测量数据处理领域亟待解决的难题之一。分别从方差膨胀模型和相关权元素压缩模型入手研究了相关观测的质量控制理论和方法；给出了误差影响函数；构造了方差膨胀函数和权因子收缩函数；利用观测量的等价协方差阵和等价权矩阵讨论了相关观测质量控制的计算方法。该等价协方差矩阵和等价权矩阵不仅保持了原有协方差矩阵和权矩阵的对称性，而且保持了原有协方差矩阵的相关性不变。计算结果表明异常观测的方差膨胀法和等价权法能有效地控制异常观测对参数估值的影响。

Robust Parameter Estimation for Geodetic Correlated Observations

Outlier diagnosis and quality control for correlated observations are two difficult problems which are urgent to be solved in the fields of measurement data processing. This paper presents two ways to control the influence of outliers in correlated observations by inflating the variance-covariance and shrinking the weight elements. A variance inflation function and a weight shrinking function are constructed and the error influence functions are given. The algorithms of quality control for correlated observations are constructed by use of equivalent covariance matrix and equivalent weight matrix. It is shown that the new equivalent covariance matrix and weight matrix keep not only the symmetry but also the relevance of the original covariance matrix. It is demonstrated by numerical example that the new methods can effectively control the influence of outliers to the parameter estimates.