Time Series Analysis of Real Time GPS-data

The recent development in GPS systems has lead to expanded use for surveying tasks. Based on experience, the precision value from the equipment suppliers is thought to be too optimistic. The uncertainty of the real precision of the system makes it less applicable for high precision point positioning. The thesis takes use of time series analysis to investigate the trends in real time GPS measurements. In the numerical investigation two separate time series is investigated, the first series with a observation period of two hours and the second with a period of 39 and a half hour. The investigation showed that using a limit of four standard deviations for outliers, less than one percent of the observations are removed. The series was also not accepted as a normal distribution in the goodness of fit test. It was however discovered that if more observations were classified as outliers, the sample would get closer to the limit of acceptance. For the dataset of the largest observation period, a significant linear trend was detected. The trend was decreasing with the ratio of 1,4 cm per day. The trend could be a part of a wave expanding over a long period of time. The spectrum of the series showed several significant waves in the series. The maximum value for the large time series had the period of 23 hours and 36 minutes. This periodic fluctuation may have connection with the duration of a day. In the correlation analysis the autocorrelation function for both datasets was computed. A weight-matrix was then designed for the estimated variance of the series. The ratio between the weighted and un-weighted variance was near 1 for both datasets. The un-weighted estimated variance was therefore verified as a good determination for the series. The numerical investigation of the thesis is based on single measurement experiments. Further experiments have to be performed in order to verify the results. The discoveries can however be the basis of future investigation.