Abstract
A recursive testing procedure for use in integrated navigation systems is introduced. It can be used in conjunction with the Kalman filter algorithm. Diagnostic tools for inferring the detectability of particular model errors are given. The testing procedure consists of three steps: detection, identification, and adaptation. It can accommodate model errors in both the measurement model and the dynamic model of the integrated navigation system. The tests proposed are optimal in the uniformly-most-powerful-invariant sense. The procedure can accommodate slippages in the mean of the predicted residuals caused by outliers in the data, sensor failures, or switches in the dynamic model. The method is therefore also applicable to the important problem of GPS (Global Positioning System) failure detection and integrity checking.

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