Comparing performance bounds for chi-square monitors with parameter uncertainty

This paper compares methods for evaluating the performance of chi-square monitors while conservatively accounting for parameter uncertainty. Chi-square monitors, like the signal deformation monitors used in global positioning system augmentation, detect failures that threaten safety-critical navigation. A chi-square monitor creates a quadratic test statistic from a random vector (nominally zero mean and Gaussian distributed). Gaussian model parameters, which may be poorly characterized for a real system, strongly influence chi-square monitor performance. Through a combination of theory and simulation, it is established that tight yet conservative modeling of parameter uncertainty is possible with a generalized chi-square bound for false-alarm risk and with an ellipsoid bound for missed-detection risk.