Research On Biased Estimation Theory And Its Application In Modern Surveying Data Processing

The traditional least square method has characteristics of unbiasedness, consistency and variance optimal etc. In surveying adjustment, when determinant of normal equation is not equal to zero, a single least-square solution can be obtained. But when normal equation is pathological, using traditional LS method, little change resulted from rounding error, etc. existing in coefficient and constant term in normal equation will lead to large difference of values of parameters. In modern measurement, especially in process of GPS fast positioning, in several or even2epochs time interval, as for space structure constituted by observation satellites and GPS receivers, there is little change. So it has very bad geometric structure, so it is ill-conditioned. In conventional measurement, ill-posed problems often exist in measurement, for example, when establishing dam deformation monitoring regression forecast model, there is unavoidable correlation among observation variables that lead to ill condition of observation equation, and when using conventional LS method, the parameter estimation result is not very good, while we can use biased estimation method to improve the results.The main work of this paper concludes some aspects as follows:1) Research and analyze the pathological mechanism of ill-conditioned equation ansd pathological diagnosis methods, and through analysis of morbid equation disturbance we realize the large error resulted from ill condition;2) According to the key problem of confirming ridge parameters, on the basis of mastering methods of Ridge Trace, Hoerl-Kennard, Principal Component, min mean square error(MSE),L-curve, etc. in this paper a method of ranked search is put forward to confirm the inflection point of L-curve. Compile program via matlab and greatly raise efficiency. Through large quantities of examples, a conclusion is got that the method of L-curve has good applicability and could lead to a high precision;3) Improve method of Generalized Ridge Estimator in the way of choosing the max value of ridge parameters array and add to the part that are close to zero in the Eigen values diagonal matrix and the larger eigen values added no ridge parameters. In this way the result is more stable than that of generalized ridge estimation, and calculation program is simplified; besides it has good applicability.4) Introduce biased estimation to fields of modern measurement applications, including GPS fast positioning, space measuring side nets, establishment of deformation monitoring regression forecast model, etc. Compared with least square method, each biased estimation method consistently has a more accurate result, especially the L-curve method and improved generalized ridge estimation. And compare characteristics of each biased estimation method, summarize their applicability and precision.