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(57) ABSTRACT A method for modelling integrity of a filtered global naviga tion satellite system, by calculating component navigation system error distributions for a set of fault conditions and a fault free condition, and determining overall navigation error distribution by forming a mixture distribution from these component navigation system error distributions. The mix ture distribution may be determined by weighted summation of navigation system error (NSE) distributions with weight ings determined according to prior probabilities for the fault conditions. Once the overall NSE mixture distribution is determined in this way, it can be used to derive one or more statistical quantities relevant to the integrity of the navigation system Such as the probability of exceeding given alert limits in a desired coordinate geometry.