Reduced-Order Modeling and Filtering

Reduced Order Kalman Filtering Without Model Reduction

“…This paper does not make any approximations in the order of the model and does not assume any special structure in the system dynamics. This is similar to the approaches proposed by Sims [17], Bernstein [18], Nagpal [19], and Keller [20,21]. Sims' approach involves the solution of a two point boundary value problem, which can be numerically difficult.…”

Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems

“…This equation is posed in L(X ). Note that this is not a complete set of equations, but the last equation in Algorithm 2.3 can be replaced by the second equation in (20). Compared to the RDE (7) for the full state Kalman filter, this equation contains the additional load term in the last line of (20).…”

“…A similar method is developed by Simon in [19] with a more restrictive assumption on the filter structure. For a more thorough introduction and review on the earliest results on reduced-order filtering techniques, we refer to [22] by Stubberud and Wismer and to [20] by Sims. Infinite dimensional Kalman filter has numerous applications. The practical application that motivated the paper [17] is the electrical impedance process tomography, studied by Seppänen et al in [18].…”

A new strategy for designing a reduced-order Kalman filter

“…Aoki and Huddle (1967) and Brammer (1968) were the ® rst to propose use of the Luenberger observer for the problem of stochastic system estimation. Di erent approaches which consist in minimizing a weighted quadratic error criterion over the interval of interest have been presented by Sims (1982) and Bernstein and Hyland (1985). Nagpal et al (1987), imposed on the ® lter a similar quadratic performance criterion, but at a same time an algebraic constraint requiring that the estimate be unbiased.…”