APPLICATIONS OF PARAMETER ESTIMATION AND HYPOTHESIS TESTING TO GPS NETWORK ADJUSTMENTS
Kyle Snow · OhioLink ETD Center (Ohio Library and Information Network) · 2002
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 GPSbuoy has been used extensively in recent years by NOAA, The Ohio State University