A real-time model error filter and state estimator

In this paper, a new real-time filter and state estimator is developed which provides a method of determining optimal state estimates in the presence of significant error in the assumed (nominal) model. Also, the new algorithm is able to determine actual model-error time histories using sequential measurements. The real-time filteristate estimator is derived for continuous systems. The functional form for this case involves the determination of an algebraic Riccati equation, a Lyapunov equation, and a linear equation to determine the gain matrix used in the filter design. Three examples are shown which demonstrate the usefulness of this new algorithm. The lirst example involves the estimation of a single state using no assumed model. The second example involves the estimation of the nonlinear trajectory of Van der Pol’s equation using a linear state model matrix. The third example involves the estimation of the orientation of a highly maneuverable fighter aircraft using an inaccurate system model. Results indicate that this new algorithm is able to determine accurate state estimates in the presence of significant errors in the assumed model.