Robust Parameter Estimation for Geodetic Correlated Observations
YANG Yuan-xi 1, SONG Li-jie 2, XU Tian-he 2 (1. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China; 2. Institute of Surveying and Mapping, Information Engineering University,Zhengzhou 450052, China)
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.