Kalman filter constraint switching 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. Recently published work has shown a new method for 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 has been shown to generally improve the filters estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy. After all, the Kalman filter is theoretically optimal, so the incorporation of heuristic constraints may degrade the optimality of the filter. This paper proposes a way to switch the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. If some measurement residuals are low, and those residuals are highly sensitive to a given state, then we are confident that the unconstrained estimate of that state is correct. Otherwise, we incorporate our heuristic knowledge as state constraints. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.