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Many aerospace navigation systems rely on Kalman filters for sensor fusion and processing. In the case of the optimal filter, the innovation covariance is Gaussian, and sensor fault detection is classically achieved by statistical analysis of the normalized innovation sequence. This is less straight-forward in real-time testing especially in the case of a sub-optimal filter. This paper proposes a statistical approach for fault detection in sub-optimal Kalman filters, which is based on testing the expectation of a stochastic quadratic process suggested by Song and Speyer (1985). Upper- and lower bounds of this process can be obtained by some spectral property of filter characteristic matrices. For an exponentially convergent sub-optimal filter, the quadratic process is shown to be a supermartingale. Testing for violation of the martingale condition provides a means for fault detection. In real time, the approach requires statistics of the true error covariance, which can be estimated by the algorithm of Mehra (1972) using innovation statistics. The approach is illustrated in an example of barometer-aided INS vertical channel.