Kalman filtering with inequality constraints for turbofan engine health estimation

Kalman fllters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman fllters 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 flt easily into the structure of the Kalman fllter. This paper develops two an-alytic methods of incorporating state variable inequality constraints in the Kalman fllter. The flrst method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant fllter is a combination of a standard Kalman fllter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satis-fled rather than exactly satisfled.) The incorporation of state variable constraints increases the computational efiort of the fllter but signiflcantly improves its estima-tion accuracy. The improvement is proven theoretically and shown via simulatio