Sequential residual-based RAIM

This paper explores receiver autonomous integrity monitoring (RAIM) for sequences of filtered measurements. Optimal position estimation for navigation systems with known dynamics (such as carrier phase positioning or integrated GPS/INS navigation) is provided by filtering measurements over time. All measurements within the time-sequence are vulnerable to faults. There is currently no widely implemented algorithm for the detection of faults that last over multiple epochs. In this work, two sequential residual-based RAIM algorithms are investigated. The first algorithm is a batch-type procedure. The batch least-squares residual is computed at each epoch using a sliding-window mechanism. It is derived in a compact formulation using a forward-backward smoother (FBS). The iterative FBS residual generation process includes a residual norm weighting procedure accounting for measurement error correlation and prior knowledge of state variables. The second method, based on a Kalman filter (KF), is truly sequential. A KF detection test statistic is defined and its probability distribution is established (assuming time-uncorrelated normally distributed measurement noise). The KF RAIM residual is carefully derived to enable probability of missed-detection determination at each time step. In addition, in contrast to the KF implementation, the sampling interval within the batch may be treated as an extra navigation design parameter: increasing the batch sampling interval decreases the estimation performance but lowers the batch computation load. In this research, the fault-detection performance sensitivity to sampling interval is investigated. The analysis yields counter-intuitive results in the presence of time-correlated measurement errors. Finally, both batch and KF residual-based RAIM methods are evaluated for a benchmark application of aircraft precision approach, where differential GPS and Galileo code and carrier phase measurements are filtered for floating cycle ambiguity estimation.