GPS/IRS AIME: Calculation of Thresholds and Protection Radius Using Chi-Square Methods.

A mathematical justification for AIME is developed, and it is compared with the mathematical justification for RAIM. It is seen that the mathematical bases for the two approaches is essentially the same. The test statistic for AIME is based on the residuals in the innovations process of the Kalman filter, rather than the residuals from the instantaneous “snapshot” least squares solution used in RAIM. This is logical since the Kalman filter residual is the difference between measured Pseudo Range to each satellite and the predicted Pseudo Range from the estimated solution, which is the least squares solution based on all past measurements. Rather than the parity transformation used in RAIM, AlME transforms the residuals to the principal axes (eigenvectors) of the ellipsoid for the n dimensional normal distribution of the residuals. It is shown that any deterministic failure of a satellite leads to a non-central chi square distribution. This makes it possible to determine the exact probabilities for failure detection and exclusion on a single covariance nm, which corresponds to an infinite number of Monte Carlo runs.