Central suboptimal H∞ filtering for nonlinear polynomial systems with multiplicative noise

This paper presents the central finite-dimensional H_∞ filter for nonlinear polynomial systems with multiplicative noise, that is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H_∞ filtering problem to the corresponding optimal H₂ filtering problem, using the technique proposed in [1]. The paper presents the central suboptimal H_∞ filter for the general case of nonlinear polynomial systems with multiplicative noise, based on the optimal H₂ filter given in [31]. The central suboptimal H_∞ filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H_∞ filters available for polynomial systems with state-independent noise and the corresponding linearized system.     

Optimal filtering over linear observations with unknown parameters

This paper presents the optimal filtering and parameter identification problem for linear stochastic systems over linear observations with unknown parameters, where the unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The resulting filtering system is bilinear in state and linear in observations. The obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed optimal state filter and parameter identifier is verified for both, positive and negative, parameter values.     

Raising Standards In Natural History Dioramas: The Background Painting of James Perry Wilson

Abstract James Perry Wilson transformed the subjective methodology of diorama background painting into a more objective practice by replacing an emotional and interpretive model with one based on the science of optics and other supportable references. He also succeeded in creating an overall mood in each of his diorama paintings. This article documents the step by step process of Wilson's methods. Wilson's two methods for documenting the site chosen for the diorama were: a plein air field painting, and panoramic photographs. At the museum, he created a complete scale model of the diorama and its background, accurate in all aspects, though miniature. On the full‐scale diorama background, a charcoal underdrawing preceded the painting. The sky was painted first, next the horizon, then the mid‐range distances, and finally the foreground. Each stage increased in colorvalue contrast and in resolution of detail. Wilson's mastery is most evident in the “tie‐up,” where the painted background meets the three‐dimensional foreground.