Detection of transient motions with the global positioning system

To assess the capability of Global Positioning System (GPS) phase measurements for the determination of transient velocity, we have made measurements with a GPS antenna on a moving platform. The antenna was translated in the horizontal plane ai a constant velocity of 1 mm h(-1) for a period of somewhat more than 24 hours while GPS data were recorded simultaneously. Other stationary antennas at distances of 10 m to similar to 1000 km were also simultaneously recording GPS data. We calculated an average velocity of the moving antenna by modeling its time-dependent position as a random walk and fitting a straight line to the stochastic estimates. We have found that the accuracy of the resulting velocity estimates is dependent on the observing period and the baseline length. For 24-hour data time spans, rms horizontal velocity errors were less than 0.2 mm h(-1) for all baseline lengths; for similar time spans, rms vertical velocity errors were 0.3-0.9 mm for lengths between 100 and 1000 km, and less than or similar to 0.2 mm for baselines less than or equal to 1000 m. We found it convenient to define a quantity xi, which we term the dynamic resolution, equal to the ratio of the rms velocity variation to the mean velocity. For a random walk process, xi(rw) can be used to calculate the variance per unit time sigma(rw)(2) required by filter-based analysis software. We also investigated the power spectral density (PSD) of our estimates of time-dependent position and found that for the frequency range sampled (0.07-16 mHz), the PSD could be well modeled by nu(alpha), where nu is the frequency and the spectral index alpha depends on the value of xi. For strongly constrained (yet unbiased) estimates (obtained by choosing xi(rw) = 10 and sigma(rw) = 0.05 mm h(-1/2)), the resultant value for alpha is -4, indicating a strong filtering of high-frequency noise.