Parameter Estimation And Hypothesis Testing In A Two Epoch Dam Deformation Measurement

Abstract

As a result of the processing of GPS measurements the estimate for the coordinates unknown is accompanied by a measure of the quality of the estimator. In as much as the model used in the estimation holds true, the quality is described by precision. In practice however, one is never sure that the model employed is adequate. In such cases a statistical testing procedure is used to determine the validity of the model so as to detect problem misspecification.
In this study the absolute standard ellipse was used for presenting the  precision of station coordinates. The standard ellipse represented the propagation of random errors through the mathematical model into the coordinates of the monitoring stations. The error ellipse consisting of semi major axis A, semi minor axis B and the angle Ø between the semi majoe axis and the y-North axis of the coordinate system were computed for the nineteen reference and rover monitoring stations in the network. Statistical tests were performed in each of the estimated parameters using the F, W and t- tests to determine their significance. In the tests, the validity of the null hypothesis Ho, the model used in the estimation was opposed against an alternative hypothesis H₁. If any parameters were found to be statistically insignificant, they were eliminated and a new solution recomputed. Also computed along with the least square solution and statistical testing were the minimum detectable Bias (MDB) and the Bias to Noise Ratio (BNR). All tests and adjustments were carried out using MOVE 3 software along with the LEICA SKI Pro 2.1
From the results of the tests, only observation to Rover station RF 8 failed both the W – tests and t – tests and was therefore regarded as an outlier and the results rejected. The test results showed that there were no model errors present in the observation after rejection of outliers; and no  systematic errors were present in the results.

Keywords: Minimum Detectable Bias, Outliers, Bias to Noise Ratio, Error Ellipse, Cycle Slip