Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering
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Simon, D, & Simon, DL. "Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering." Proceedings of the ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference. Volume 1: Turbo Expo 2003. Atlanta, Georgia, USA. June 16–19, 2003. pp. 485-492. ASME. https://doi.org/10.1115/GT2003-38584
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