Applications of Parameter Estimation and Hypothesis Testing to GPS Network Adjustments
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Date
2002-12
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Ohio State University. Division of Geodetic Science
Abstract
It is common in geodetic and surveying network adjustments to treat the rank deficient normal equations in a way that produces zero variances for the so–called "control" points.
This is often done by placing constraints on a minimum number of the unknown parameters, typically by assigning a zero variance to the a priori values of these parameters (coordinates). This approach may require the geodetic engineer or analyst to make an arbitrary decision about which parameters to constrain, which may have undesirable effects, such as parameter error ellipses that grow with distance from the constrained point.
Constraining parameters to a priori values is only one way of overcoming the rank deficiency inherent in geodetic and surveying networks. There are more preferable ways, which this thesis presents, namely Minimum Norm Least–Squares Solution (MINOLESS) and Best Linear Minimum Partial Bias Estimation (BLIMPBE). MINOLESS not only minimizes the weighted norm of the observation error vector but also minimizes the norm of the parameter vector, while BLIMPBE minimizes the bias for a subset of the parameters. In this thesis, these techniques are applied to a geodetic network that serves as a datum access for GPS–buoy work in Lake Michigan. The GPS–buoy has been used extensively in recent years by NOAA, The Ohio State University (OSU), and other organizations to determine lake and ocean surface heights for marine navigation and scientific studies. The work presented in this paper includes 1) parameter estimation using (Weighted) MINOLESS and hypothesis testing for the purpose of determining if recent observations are consistent with published coordinates at an earlier epoch; 2) a discussion of the BLIMPBE estimation technique for three new points to be used as GPS–buoy fiducial stations and a comparison of this technique to the "Adjustment with Stochastic Constraints" method; 3) usage of standardized reliability numbers for correlated observations; 4) a proposal for outlier detection and minimum outlier computation at the GPS–baseline level. The work may also be used as an example to follow for establishing new fiducial points with respect to a geodetic reference frame using observed GPS baseline vectors.
The results of this work lead to the following conclusions: 1) MINOLESS is the parameter estimation techniques of choice when it is required that changes to all a priori coordinates be minimized while performing a minimally constrained adjustment; 2) BLIMPBE appears to be an attractive alternative for selecting subsets of the parameter vector to adjust. BLIMPBE solutions using various selection–matrix types are worthy of further investigation; 3) outlier detection at the GPS–baseline level permits the entire observed baseline to be evaluated at once, rather than making decisions regarding the ii
hypothesis at the baseline–component level. It is shown that the two approaches can yield different results.
Description
This report was prepared by Kyle Snow while a student in the Department of Civil and Environmental Engineering and Geodetic Science. It was submitted to the Graduate School of The Ohio State University in the Autumn of 2002 in partial fulfillment of the requirements of the Master of Science degree. Prof. Burkhard Schaffrin served as advisor and Prof. C.K. Shum as co–advisor, both in the program for Geodetic Science and Surveying.
The research was funded in part by the Office of Naval Research Naval Oceanographic Partnership Program (NOPP), under the Ohio State University component of the Gulf of Mexico Monitoring System, and the NASA Physical Oceanography program under the TOPEX/POSEIDON Extended Mission project.
The research was funded in part by the Office of Naval Research Naval Oceanographic Partnership Program (NOPP), under the Ohio State University component of the Gulf of Mexico Monitoring System, and the NASA Physical Oceanography program under the TOPEX/POSEIDON Extended Mission project.