A closed-form algorithm for covariance-constrained optimal estimation

The paper describes a new method which results in a closed-form solution for constrained optimal state estimation and system identification of discretely measured dynamic systems, and illustrates the method for a simple example. This post-experiment optimal state estimation method is especially appropriate in the presence of significant model error and/or significant measurement error. The new approach is robust in the presence of significant measurement noise and capable of estimating accurate states, by incorporating the known statistical characteristics of the noisy measurements as constraints. The determination of the optimal state estimates is derived from a minimization of a cost functional subject to differential equation constraints and statistical constraints of the noisy measurements. Estimation of the state and the dynamic model error are obtained as part of the solution of a jump discontinuous two-point boundary value problem associated with the algorithm. The resulting state estimates are continuous and optimal in a global sense. The dynamic model error terms to be identified are assumed unknown and may take any form (even nonlinear). This new constrained approach greatly improves computational speed and results in an exact analytical enforcement of the covariance constraint.