Solving (nonlinear) eigenvalue problems by contour integration, requires an e↵ective discretization for the corresponding contour integrals. In this paper it is shown that good rational filter functions can be computed using (nonlinear least squares) optimization techniques as opposed to designing those functions based on a thorough understanding of complex analysis. The conditions that such an...

The design and analysis of a dielectric guided-mode resonance filter (GMRF) utilizing a nonlinear material for the waveguide is presented. Small changes to the parameters of a GMRF have a large impact on its resonance. A nonlinear material can provide a small change in the refractive index of the waveguide, altering the resonance of the device and resulting in modulation of the transmitted and ...

In this paper, the design of a fault detection filter for nonlinear systems is presented. The nonlinear system is represented as a sequence of linear timevarying approximations and at each linear approximation the design of an optimal stochastic fault detection filter for linear time-varying systems is applied. The final residual is primarily affected by a target fault and minimally by nuisance...

Particle filters and Rao Blackwellised particle filter have been widely used in solving nonlinear filtering problems. The particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One solution to this problem is to marginalize out the states appearing linearly in ...

We introduce a new model – the Filter-Combiner model – for memoryless synchronous stream ciphers. The new model combines the best features of the classical models for memoryless synchronous stream ciphers – the Nonlinear-Combiner model and the Nonlinear-Filter model. In particular, we show that the Filter-Combiner model provides key length optimal resistance to correlation attacks and eliminate...

A new filter-trust-region algorithm for solving unconstrained nonlinear optimization problems is introduced. Based on the filter technique introduced by Fletcher and Leyffer, it extends an existing technique of Gould, Leyffer, and Toint [SIAM J. Optim., 15 (2004), pp. 17–38] for nonlinear equations and nonlinear least-squares to the fully general unconstrained optimization problem. The new algo...

We have developed a new nonlinear filter that is superior to particle filters in five ways: (1) it exploits smoothness; (2) it uses an exact solution of the Fokker-Planck equation in continuous time; (3) it uses a convolution to compute the effect of process noise at discrete times; (4) it uses the adjoint method to compute the optimal density of points in state space to represent the smooth co...

The Kalman filter has been widely used for estimation and tracking of linear systems since its formulation in 1960 due to its simplicity and robustness. In many chemical engineering applications the extended Kalman filter (EKF) is often used to deal with certain classes of nonlinear systems. In spite of that, designing an EKF for highly nonlinear processes is not a trivial task, particularly th...

A new class of nonlinear filters called Vector Median Rational Hybrid Filters (VMRHF) for multispectral image processing is introduced and applied to color image filtering problems. These filters are based on Rational Functions (RF). The VMRHF filter is a two-stage filter, which exploits the features of the vector median filter and those of the rational operator. The filter output is a result o...

Robot localization using odometry and feature measurements is a nonlinear estimation problem. An efficient solution is found using the extended Kalman filter, EKF. The EKF however suffers from divergence and inconsistency when the nonlinearities are significant. We recently developed a new type of filter based on an auxiliary variable Gaussian distribution which we call the antiparticle filter ...