Stochastic Analysis of Differential GPS Surveys for Earth Dam Deformation Monitoring

Abstract

In GPS measurement, we try to model not just the deterministic part of the measurement but also try to account for their stochastic behavior using the measurement variance-covariance matrix. The variance-covariance matrices are computed as part of a least squares adjustment. In this study, the results of GPS survey by differential GPS technique were analyzed using the variance – covariance matrix of the adjusted unknown (coordinates). The GPS derived data were processed using Double Differencing (DD) technique and this enabled the removal of most of the errors in the GPS measurement. The variance – covariance matrix for three GPS receivers observing the four satellites for single difference and double difference wereformulated. Using the model for 3-D differential observation, the variance-covariance of the 20baselines in the Dam deformation monitoring network at Ikpoba Dam were computed as part of a least square solution of the observation equation using the Leica Ski pro and Move 3 software. Standard derivation in Northings, Eastings and Elevation were computed for each observation station in the network. The computed standard deviations along with the baseline length were used to determine linear accuracy and accuracy of the baselines in parts per Million PPM. The results revealed that the maximum standard deviation in Northings Eastings and Elevation were 1.42mm, 0.86mm and 0.57mm respectively. All the adjusted baselines satisfied 1st order class I accuracy standard which is the standard required for high precision measurements such as in Dam deformation monitoring.

Keywords: Differential GPS, Pseudo range, Carrier phase, Doppler frequency, Stochastic model.