Stochastic model and experimental measurement of ocean-scattered GPS signal statistics

Information about the roughness of the ocean, and related geophysical parameters, including wind speed, is present in the shape of the code-correlation waveform of forward scattered GPS signals. A model is developed for the statistics of this waveform, to be used in the prediction of retrieval accuracy and the design of optimal estimators for the retrieval of meaningful geophysical data. Time and frequency domain models for complex "voltage" correlation waveform are developed and compared against experimental results. The analytical form of a model for the autocorrelation of the "power" (real) waveform is also presented. These two models can be applied to determine the upper limit for predetection integration time, and the time between independent waveform samples, respectively. C/A code waveforms were produced, with a 1 msec integration time, from measurements of reflected GPS signals recorded in 1999 near Puerto Rico. Time and frequency domain measurements of the correlation time of these waveforms were estimated through fitting a Gaussian function to the autocovariance and through measuring the width of the power spectral density, respectively. Typical experimental values obtained for voltage model, at aircraft altitude and speed, were 4.2 msec at the peak of the waveform, decaying to 1 msec at a code lag of 3.5 chips. For power model, they were 3.5 msec at the peak of the waveform, decaying to 1 msec at a code lag of 1.8 chips.