Using the mixed Gaussian distribution method to design of a threshold for CCD monitor

This Code-Carrier Divergence (CCD) monitor is a main part of Signal Quality Monitoring(SQM)in LAAS Ground Facility integrity monitoring. CCD monitor calculates test statistics and compares the values of test statistics to the corresponding thresholds, and then decides if a failure is happening. A proper threshold is the key for the monitor to achieve perfect performance. Usually we assume that the probability density function (PDF) of the monitoring values follows the zero-mean Gaussian distribution. Although the Gaussian distribution curve overbounds the PDF of divergence results in the core preferably, due to multipath effects, or the influence of noise, etc., two tails of the PDF are not overbounded by the Gaussian distribution well. In this paper, firstly, the Code-Carrier divergence statistics changing chronologically are collected from one channel(define that a channel is one satellite tracked on one receiver) in a satellite-visible period time (about 6 hours); then, in accordance with the change of the zenith angle, divide the statistics into several segments, calculate the mean and the standard deviation of the statistics in each segment; interpolate the standard deviations of the segments with a reasonable high-order polynomial curve using Lagrange interpolation algorithm, correspondingly the elevation angle is an independent variable, and thus, by counting the numbers of different standard deviation value in different elevation angle to get the PDF of divergence; thirdly, to achieve the goal that the curve overbounds both the core and the tails of the PDF of divergence, set up two different standard deviations and two inflation factors forming a zero-mean Gaussian distribution linear combination using the mixed Gaussian distribution method; finally, under the condition of the ensured constant false alarm probability, combine the standard deviations and inflation factors talked above, later calculate the monitoring threshold of the mixed Gaussian distribut- on.