Detection of transient motions with the Global Positioning System

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Abstract
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 at a constant velocity of 1 mm h−1for a period of somewhat more than 24 hours while GPS data were recorded simultaneously. Other stationary antennas at distances of 10 m 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−1for 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 ≲0.2 mm for baselines ≤1000 m. We found it convenient to define a quantity ξ, which we term the dynamic resolution, equal to the ratio of the rms velocity variation to the mean velocity. For a random walk process, ξrwcan be used to calculate the variance per unit time σ2rwrequired 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 να, where ν is the frequency and the spectral index α depends on the value of ξ. For strongly constrained (yet unbiased) estimates (obtained by choosing ξrw= 10 and σrw= 0.05 mm h−½), the resultant value for α is −4, indicating a strong filtering of high‐frequency noise.