Comparison of three methods to determine the spectral parameters (P and T) for GPS tracking error calculation

The tracking error at the output of the Phase Locked Loop (PLL) in the receiver causes by the ionospheric scintillation, limits the accuracy of the range measurements which the receiver uses to compute the position. Determination of tracking error variance is accomplished using Conker's model which requires the spectral parameters (spectral slope, p and spectral strength at frequency 1 Hz, T). Three methods to accurately determine the tracking error variance by making use of high sample rate scintillation data and/or scintillation indices are investigated. These all find the spectral parameters (p and T) required by the Conker model. The first method determines the spectral parameters p and T from the Power Spectrum Density (PSD) of phase, obtained from the detrended high sample rate phase data, through performing the Fast Fourier Transform (FFT). The second method, proposed by Hal J. Strangeways, finds these parameters from the scintillation indices using an approximation model of the phase and amplitude spectra together with an estimated Fresnel frequency, thus without the need to perform FFTs and useful when high sample rate data is not available. The third method, which is the new method that has been implemented, filters the detrended high sample rate phase scintillation data employing five band pass filters to allow an approximate phase spectrum to be obtained. The comparison is made between the three methods of determining spectral parameters in order to determine their relative accuracies and their respective appropriate areas of usefulness and validity.