A 1-sigma pseudorange ground monitor (sigma monitor) is described. The sigma monitor calculates a weighted sum of squared deviations referred to as the discriminator for one or several reference receiver for a specific time period. The sigma monitor also calculates an alert threshold based on the chi-square or near chi-square probability distributions for one or several reference receivers and for the specific time period. The sigma monitor then compares the discriminator with the alert or alarm threshold. If the discriminator is greater than the alert or alarm threshold, an alert or alarm is issued and logged.