Kalman filtering with inequality constraints for turbofan engine health estimation

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. Thus, two analytical methods to incorporate state-variable inequality constraints into the Kalman filter are now derived. The first method is a general technique that uses hard constraints to enforce inequalities on the state-variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate those state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) 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 simulations are used to show that the proposed algorithms can provide an improved performance over unconstrained Kalman filtering.