— We compare the performance of the extended Kalman filter, the unscented Kalman filter, and two extensions of the H∞ filter when applied to discrete-time nonlinear state estimation problems with nondifferentiable dynamics. We compare the performance of all the estimation techniques on simple nonlinear examples and finally consider state estimation of… (More)
— We compare several reduced-order Kalman filters for discrete-time LTI systems based on reduced-order error-covariance propagation. These filters use combinations of balanced model truncation and complementary steady-state covariance compensation. After describing each method, we compare their performance through numerical studies using a compartmental… (More)
Mathematical models of physical phenomena are of critical importance in virtually all applications of science and technology. This paper addresses the problem of how to use data to improve the fidelity of a given model. We approach this problem using retrospective cost optimization, which uses data to recursively update an unknown subsystem interconnected… (More)
We consider a data assimilation technique for coupled iono-spheric and thermospheric dynamics. The Global Ionosphere-Thermo-sphere Model (GITM) is used to simulate the ionospheric and thermo-spheric dynamics, and evaluate the performance of the data assimilation scheme that estimates the ion densities and flow speeds. This estimation technique is based on… (More)
Mathematical models of physical phenomena are of critical importance in virtually all applications of science and technology. This paper addresses the problem of how to use data to improve the fidelity of a given model. We approach this problem using retrospective cost optimization, a novel technique that uses data to recursively update an unknown subsystem… (More)
— We consider the problem of data-based model refinement, where we assume the availability of an initial model, which may incorporate both physical laws and empirical observations. With this initial model as a starting point, our goal is to use additional measurements to refine the model. In particular, components of the model that are poorly modeled can be… (More)
— In this paper, we discuss an extension of the unscented Kalman filter that propagates a surrogate reduced-order covariance and also uses a complementary static esti-mator gain based on the steady-state correlation between the error in the estimates of the state and measurements to obtain estimates of the entire state.