Design of non-polarizing color splitting filters used for projection display system

Optical thin films used at oblique incidence exhibit inevitable polarization dependent properties. In reflective projection display systems, Philips prisms with color splitting filters are widely used. Generally, illuminating light at different polarization components passes the color splitting filters twice in such Philips prism. Color splitting filters operate as color separation for s-polarization and as color recombination for p-polarization, and thus performances of the color splitting filters for s- and p-polarization are equally important. In order to reduce stray light, it is necessary to design non-polarizing thin film edge filters for color separation and recombination system in projectors. The novel design method is based on a broad-band Fabry–Perot interference filter in which both sides of transmittance band can be used as initial designs for long-wave-pass filter or short-wave-pass filters, and through suitable refinement to reduce the transmittance ripples, it is possible to achieve zero separation between two polarization components.     

Constrained Kalman filtering via density function truncation for turbofan engine health estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This article develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the probability density function (PDF) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but also improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. It is also shown that the truncated Kalman filter may provide a more accurate way of incorporating inequality constraints than other constrained filters (e.g. the projection approach to constrained filtering).     

Approximate nonlinear filtering and its application in navigation

In this paper, we introduce for the first time particle filtering for an exponential family of densities. We prove that under certain conditions the approximated conditional density of the state converges to the true conditional density. In the realistic setting where the conditional density does not lie in an exponential family but stays close to it, we show that under certain assumptions the error of the estimate given by an approximate nonlinear filter (which we call the projection particle filter), is bounded. We use projection particle filtering in state estimation for a combination of inertial navigation system (INS) and global positioning system (GPS), referred to as integrated INS/GPS. We illustrate via numerical experiments that projection particle filtering outperforms regular particle filtering in navigation performance, and extended Kalman filter as well when satellite loss-of-lock occurs.     

On model and filter sensitivity

It is shown that there is a stochastic version of the fact that the standard IIR, AR, ARX and ARMAX model and filter parametrizations suffer from a worst-case exponential growth of the required relative coefficient accuracy to preserve model and filter stability. This means that, inevitably, such standard model and filter parametrizations become infeasible to use for a subclass of order n filters and models when n is not small.     

Approximation of an arbitrary filter and its recursive implementation

Filtering is one of the important techniques in computer vision. It has been widely used in edge detection, image restoration, range image segmentation, etc. However, the efficient implementation of an arbitrary filter has been a challenging problem until now. In this paper, a novel method is proposed to implement an arbitrary filter. Firstly, an efficient recursive structure is proposed to implement any (polynomial) × (exponential)-type (PET) filter. The computational complexity and structure are independent of its filter mask size or its bandwidth. Secondly, a new method is proposed—Lagurre spectrum decomposition method—to obtain the PET approximation of any filters. As an example, the above method is applied to the approximation and implementation of Gaussian filters and experiments have shown that a perfect approximation can be obtained with only third-order Lagurre bases, and therefore only a fourth-order recursive filter is needed to implement Gaussian filters. Finally, the comparison of the present method with the known ones shows that (1) Lagurre polynomial bases are orthogonal with each other, so the filter approximation is simple, (2) the bases are complete and the completeness guarantees the approximation error can be reduced to zero, (3) the method can be used to design both Gaussian and any other filters.     

Filtering on nonlinear time-delay stochastic systems

In this paper, we address the filtering problem for a general class of nonlinear time-delay stochastic systems. The purpose of this problem is to design a full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square. Both filter analysis and synthesis problems are considered. Sufficient conditions are proposed for the existence of desired exponential filters, which are expressed in terms of the solutions to algebraic Riccati inequalities involving scalar parameters. The explicit characterization of the desired filters is also derived. A simulation example is given to illustrate the design procedures and performances of the proposed method.     

Optimal structurally partitioned filter for undisturbable stochastic systems Part II. Stability and its asymptotic behaviour

This paper investigates the stability of an optimal structurally partitioned filter and its asymptotic behaviour in undisturbable stochastic systems. In fact, these filters cannot assure the exponential asymptotic stability and therefore cannot proceed directly to the steady state problem because they include a fixed point smoother as one estimation mechanism in the parallel processors. It is shown, howover, that these types of estimator are asymptotically stable in the Lyapunov sense by introducing a generalized disturbability (or controllability) matrix (Anderson 1971). It is also shown that after analysing the asymptotic behaviour of such filters, a steady state partitioned filter, which takes the gains as the practical constant, is able to generate the unbiased estimate.     

State estimation of nonlinear dynamic systems using weighted variance-based adaptive particle swarm optimization

New heuristic filters are proposed for state estimation of nonlinear dynamic systems based on particle swarm optimization (PSO) and differential evolution (DE). The methodology converts state estimation problem into dynamic optimization to find the best estimate recursively. In the proposed strategy the particle number is adaptively set based on the weighted variance of the particles. To have a filter with minimal parameter settings, PSO with exponential distribution (PSO-E) is selected in conjunction with jDE to self-adapt the other control parameters. The performance of the proposed adaptive evolutionary algorithms i.e. adaptive PSO-E, adaptive DE and adaptive jDE is studied through a comparative study on a suite of well-known uni- and multi-modal benchmark functions. The results indicate an improved performance of the adaptive algorithms relative to original simple versions. Further, the performance of the proposed heuristic filters generally called adaptive particle swarm filters (APSF) or adaptive differential evolution filters (ADEF) are evaluated using different linear (nonlinear)/Gaussian (non-Gaussian) test systems. Comparison of the results to those of the extended Kalman filter, unscented Kalman filter, and particle filter indicate that the adopted strategy fulfills the essential requirements of accuracy for nonlinear state estimation.     

基于卡尔曼滤波的TDOA/AOA混合定位算法

提出了一种利用两次卡尔曼滤波实现非视距环境中TDOA/AOA混合定位方法。根据类正态分布密度曲线是最小二乘意义下对指数分布密度曲线的最优拟合的思想建立TDOA误差模型,先利用卡尔曼滤波对TOA测量值进行预处理以消除NLOS误差,再把经过预处理的TOA测量值输入到卡尔曼滤波器来实现TDOA/AOA混合定位。仿真结果表明,该方法的定位误差性能明显优于单纯的TDOA定位方法以及服从指数分布误差模型下的TDOA定位方法。     

Robust Ensemble Kalman Filter Based on Exponential Cost Function

This paper provides an alternative point of view to the robust estimation technique for nonlinear non Gaussian systems based on exponential quadratic cost function. The proposed method, named the risk sensitive ensemble Kalman filter (RSEnKF), is based on the ensemble Kalman filter (EnKF) which may be thought of as a Monte Carlo implementation of the Kalman filter for nonlinear estimation problems. The theory and formulation of the RSEnKF are presented in this paper. The proposed method is superior to the extended risk sensitive filter (ERSF) and the quadrature based risk sensitive filters in terms of estimation accuracy, and is faster than the risk sensitive particle filter (RSPF).     

投影滤波器原理在贝叶斯滤波中的应用

对于非线性滤波问题,给出一种有限维近似滤波算法。它利用统计流形上的微分几何方法,将关于概率密度的随机偏微分方程投影到有限维统计流形上,得到相关参数的有限维随机常微分方程。通过引入指数型概率密度模型,简化投影滤波算法的计算。再结合Bayes定理求解非线性系统状态的后验概率密度,最后应用于立体传感器系统的滤波问题。     

Exponential stability of discrete-time filters for bounded observation noise

This paper proves exponential asymptotic stability of discrete-time filters for the estimation of solutions to stochastic difference equations, when the observation noise is bounded. No assumption is made on the ergodicity of the signal. The proof uses the Hilbert projective metric, introduced into filter stability analysis by Atar and Zeitouni [1,2]. It is shown that when the signal noise is sufficiently regular, boundedness of the observation noise implies that the filter update operation is, on average, a strict contraction with respect to the Hilbert metric. Asymptotic stability then follows.     

Processes,characterizations, and system applications of color‐filter liquid‐crystal‐on‐silicon microdisplays

Abstract— A color‐filter liquid‐crystal‐on‐silicon (CF‐LCOS) microdisplay that integrates color filters on silicon for color will be presented. The color‐filter process on silicon was optimized to achieve fine resolution and precise alignment of the color filters on the pixel array, good adhesion to the silicon suface, and a flat surface for the liquid‐crystal cell assembly. Important optical and electrical parameters of the color filters were extracted to establish an electro‐optical model of the CF‐LCOS microdisplays for device simulation. Thermal, chemical, and light‐stability characterizations were performed to ensure the stabilty of the color filters and CF‐LCOS microdisplays. With color CF‐LCOS microdisplays already available, the projection or viewing optics is greatly simplified. This CF‐LCOS microdisplay is ideal for near‐to‐eye displays because of its low‐power consumption and compactness. The CF‐LCOS microdisplay could also withstand medium light illumination for medium‐sized projectors. A single‐panel projector based on one CF‐LCOS microdisplay of 1280 × 768 × RGB resolution was demonstrated.     

时域Wiener状态滤波新方法

基于稳态Kalman滤波器和射影理论,提出了统一和通用的时域Wiener状态滤波新方法,用它得到带非零均值相关噪声线性随机系统的渐近稳定的Wiener状态估值器和解耦Wiener状态估值器.它可统一处理状态滤波、预报和平滑问题.发现了Kalman滤波器和Wiener滤波器之间的变换关系,Wiener状态估值器可由Kalman估值器通过自回归滑动平均(ARMA)新息模型得到.一个仿真例子说明了其有效性.     

On the similarities between micro/nano lithography and topology optimization projection methods

The aim of this paper is to incorporate a model for micro/nano lithography production processes in topology optimization. The production process turns out to provide a physical analogy for projection filters in topology optimization. Blueprints supplied by the designers cannot be directly used as inputs to lithographic processes due to the proximity effect which causes rounding of sharp corners and geometric interaction of closely spaced design elements. Therefore, topology optimization is applied as a tool for proximity effect correction. Furthermore, it is demonstrated that the robust projection filter can be used to account for uncertainties due to lithographic production processes which results in manufacturable blueprint designs and eliminates the need for subsequent corrections.     

基于核自适应滤波器的时间序列在线预测研究综述

核自适应滤波器(Kernel adaptive filter, KAF)是时间序列在线预测的重点研究领域之一, 本文对核自适应滤波器的最新进展及未来研究方向进行了分析和总结. 基于核自适应滤波器的时间序列在线预测方法, 能较好地解决预测、跟踪问题. 本文首先概述了三类核自适应滤波器的基本模型, 包括核最小均方算法、核递归最小二乘算法和核仿射投影算法(Kernel affine projection algorithm, KAPA). 在此基础上, 从核自适应滤波器在线预测的内容和机理入手, 综述基于核自适应滤波器的时间序列在线预测方法. 最后, 本文将介绍这一领域潜在的研究方向和发展趋势, 并展望未来的挑战.     

Application of multiple regression analysis to identification of time-varying linear dynamic systems

A technique for determining the dynamic response characteristics of time-varying linear systems is presented. A model composed of a parallel connection of filters whose impulse responses are orthogonalized exponential functions is used. The input to the system is fed to each of the filters. The coefficients of linear regression of the system output on each of the filter outputs are determined. Time-varying characteristics are measured by determining successively the coefficients from short samples of the input and output signals of the system. Many of the statistical properties of regression coefficients are known and can be used to estimate the length of sample of input and output signals required to determine the coefficients with given variance. The measurement technique has been implemented on a high speed digital computer. Results obtained by applying the technique to measurement of a variety of digitally simulated filters and to measurement of human pilot control characteristics are presented.     

模型显著域上的形状调控和处理

基于3维数字模型的显著性度量和显著域处理技术,提出一种模型显著域上的形状调控和处理方法。该方法首先基于曲面上采样顶点处局部投影高度的Gaussian加权平均双边滤波定义数字模型的表面显著性;然后利用定义在模型显著域上的形状调控函数——显著域低通形状调控函数、显著域高通形状调控函数和显著域增强形状调控函数,使模型的显著特征得到有效抑制、提升和增强,实现了针对模型表面显著特征的形状调控和处理。实验结果表明,该方法能够方便快速地实现3维数字模型的不同形状造型效果。     

Boolean filters and positive implicative filters of residuated lattices

The aim of this paper is to introduce the notions of Boolean filters and positive implicative filters in residuated lattices and to investigate their properties. Several characterizations of Boolean filters and positive implicative filters are derived. The extension theorems of implicative filters and positive implicative filters are obtained. The relations among Boolean filters, implicative filters and positive implicative filters are investigated and it is proved that Boolean filters are equivalent to implicative filters, and that every Boolean filter is a positive implicative filter, but the converse may not be true. Furthermore, the conditions under which a positive implicative filter is a Boolean filter are established.     

Reduced-order ℓ2-ℓ∞ filtering for discrete-time T-S fuzzy systems with stochastic perturbation

This paper is concerned with the problem of ?₂-?_∞ filtering for discrete-time Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation. Firstly, a basis-dependent existence condition of desirable ?₂-?_∞ filters is proposed. Then by means of the convex linearisation technique, the derived condition is transformed into some strict linear matrix inequality (LMI) constraints, by which both full- and reduced-order filters can be designed. Moreover, for the reduced-order ?₂-?_∞ filter design, a novel analysis and design method with the projection lemma is also provided. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the proposed full- and reduced-order ?₂-?_∞ filter design methods.