Unifying the Parity-Space and GLR Approach to Fault Detection with an IMU Application, Report no. LiTH-ISY-R-2862

Using the parity-space approach, a residual is formed by applying a projection to a batch of observed data and this is a well established approach to fault detection. Based on a stochastic state space model, the parity-space residual can be put into a stochastic framework where conventional hypothesis tests apply. In an on-line application, the batch of data corresponds to a sliding window and in this contribution we develop an improved on-line algorithm that extends the parity-space approach by taking prior information from previous observations into account. For detection of faults, the Generalized Likelihood Ratio (glr) test is used. This framework allows for including prior information about the initial state, yielding a test statistic with a signi cantly higher sensitivity to faults. Another key advantage with this approach is that it can be extended to nonlinear systems using an arbitrary nonlinear lter for state estimation, and a linearized model around a nominal state trajectory in the sliding window. We demonstrate the algorithm on data from an Inertial Measurement Unit (imu), where small and incipient magnetic disturbances are detected using a nonlinear system model.