A tutorial – game theory-based extended H infinity filtering approach to nonlinear problems in signal processing

In this paper, we provide a tutorial for the applications of “game-theory-based extended H infinity filtering (EHIF)” approach to various problems in disciplines of signal processing. The algorithm of this filtering approach is similar to that of the extended Kalman filtering (EKF). Since its invention, the Kalman filtering approach has been successfully and widely employed for many problems in scientific and engineering fields, e.g. target tracking, satellite systems, control, communications, etc. Therefore, the H infinity filtering approach also can be applied to all these problems. One big difference of EHIF from the EKF approach is that we apply it with unknown noise statistics of the state and measurement. In this tutorial, we introduce this non-well-known approach in spite of its practical usefulness, by providing the step by step algorithm with example problems of a number of signal processing disciplines. We also show that EHIF can outperform other approaches including the EKF that need to know the noise statistics in their applications, in some scenarios. By the contribution of this tutorial, we look forward to easy, and disseminative applications of EHIF to problems where, particularly, the EKF or particle filter could have been applied if noise statistics were known.     

Self-calibration of stationary non-rotating zooming cameras

This paper proposes a new method for self-calibrating a set of stationary non-rotating zooming cameras. This is a realistic configuration, usually encountered in surveillance systems, in which each zooming camera is physically attached to a static structure (wall, ceiling, robot, or tripod). In particular, a linear, yet effective method to recover the affine structure of the observed scene from two or more such stationary zooming cameras is presented. The proposed method solely relies on point correspondences across images and no knowledge about the scene is required. Our method exploits the mostly translational displacement of the so-called principal plane of each zooming camera to estimate the location of the plane at infinity. The principal plane of a camera, at any given setting of its zoom, is encoded in its corresponding perspective projection matrix from which it can be easily extracted. As a displacement of the principal plane of a camera under the effect of zooming allows the identification of a pair of parallel planes, each zooming camera can be used to locate a line on the plane at infinity. Hence, two or more such zooming cameras in general positions allow the obtainment of an estimate of the plane at infinity making it possible, under the assumption of zero-skew and/or known aspect ratio, to linearly calculate the camera's parameters. Finally, the parameters of the camera and the coordinates of the plane at infinity are refined through a nonlinear least-squares optimization procedure. The results of our extensive experiments using both simulated and real data are also reported in this paper.     

Performance of disturbance augmented control design in turbulent wind conditions

This paper investigates the use of disturbance models in the design of wind turbine individual pitch controllers. Previous work has used individual pitch control and disturbance models with the Multiblade Coordinate Transformation to design controllers that reduce the blade loads at the frequencies associated with the rotor speed. This paper takes a similar approach of using a disturbance model within the H_∞ design framework to account for periodic loading effects. The controller is compared with a baseline design that does not include the periodic disturbance model. In constant wind speeds, the disturbance model design is significantly better than the baseline design at canceling blade loads at the rotor frequencies. However, these load reduction improvements become negligible even under low turbulent wind conditions. The two controllers perform similarly in turbulent wind conditions because disturbance augmentation improves load reduction only at the multiples of the rotor frequency in the yaw and tilt moment channels whereas turbulence creates strong collective bending moments. In addition, turbulent wind contains energy across a broad frequency spectrum and improvements at multiples of the rotor frequency are less important in these conditions. Therefore inclusion of periodic disturbance models in the control design may not lead to the expected load reduction in fielded wind turbines.     

带对准光路的激光细胞穿孔显微物镜设计

针对近红外光谱可对活体组织进行无损伤穿孔,并解决在穿孔中需要重新对焦的问题,通过Zemax软件对7片式前置光阑显微物镜结构在0.48~1.48?m波长范围内进行了宽光谱消色差的优化设计。设计实现了像距为无限远的多光谱共焦成像,其放大倍率为40,数值孔径0.5,最大焦面漂移量仅为27?m,可见光波段在空间频率为350 lp/mm时,0.7视场的MTF>0.5,具有较高的分辨力。并且在波长1480 nm处,MTF值接近衍射极限,具有较高的能量,满足细胞穿孔的要求。文中还给出了实验结果,并预测其应用前景。     

基于扩展H∞滤波农业机器人滑移运动模型估计

针对履带式农业自动化机器人侧滑运动控制问题,提出了一种基于扩展H_∞滤波的滑移运动模型估计方法。首先,给出了机器人侧滑转向的速度瞬心(ICRs)运动模型,并针对不同的运行路况进行双模态并行估计实现。接着,针对不同路况进行了实现分析。固定路况下,采用扩展H_∞滤波(EHF)在线实时估计ICRs参数值;时变路况下,首先采用k均值聚类对运行路况进行类别划分,然后针对划分的类型进行EHF估计。仿真和实验结果表明,该估计方法在固定路况和时变路况下均能快速估计侧滑机器人的运动学模型,保持了较高的拟合精度。     

Dirichlet级数与随机Dirichlet级数的迭代级数

对于在左半平面σ <0内收敛的下侧Dirichlet级数所定义的解析函数f1(s)定义了下级 ,定义了在概率空间 (Ω ,A,P) 上的下侧随机Dirichlet级数的下级 (σ <0 ) ,研究了两类级数所定义的解析函数f1(s) ,f1(s,ω)的下级存在的条件 ;对两类由上、下侧级数迭代而成的关于无穷乘积的级数 ,讨论了它们与无穷乘积的收敛性 ,建立了它们的和函数f1[f(s) ]与f1[f(s,ω) ]在σ >0内的下级与其系数及指数之间的关系式     

Transmitting boundary and radiation conditions at infinity

Relationship between the radiation conditions at infinity and the transmitting boundary for numerical simulation of the near-field wave motion has been studied in this paper. The conclusion is that the transmitting boundary is approximately equivalent to the radiation conditions at infinity for a large class of infinite media. And the errors of the approximation are of the same order of magnitude as those of the finite elements or finite differences in numerical simulation of wave motion. This result provides a sound theoretical basis for the transmitting boundary used in the numerical simulation of the near-field wave motion and gives a complete explanation for the major experiences accumulated in applications of the transmitting boundary to the numerical simulation.     

On mind &; Turing’s machines

Turing’s notion of human computability is exactly right not only for obtaining a negative solution of Hilbert’s Entscheidungsproblem that is conclusive, but also for achieving a precise characterization of formal systems that is needed for the general formulation of the incompleteness theorems. The broad intellectual context reaches back to Leibniz and requires a focus on mechanical procedures; these procedures are to be carried out by human computers without invoking higher cognitive capacities. The question whether there are strictly broader notions of effectiveness has of course been asked for both cognitive and physical processes. I address this question not in any general way, but rather by focusing on aspects of mathematical reasoning that transcend mechanical procedures.Section 1 discusses Gödel’s perspective on mechanical computability as articulated in his [193?], where he drew a dramatic conclusion from the undecidability of certain Diophantine propositions, namely, that mathematicians cannot be replaced by machines. That theme is taken up in the Gibbs Lecture of 1951; Gödel argues there in greater detail that the human mind infinitely surpasses the powers of any finite machine. An analysis of the argument is presented in Section 2 under the heading Beyond calculation. Section 3 is entitled Beyond discipline and gives Turing’s view of intelligent machinery; it is devoted to the seemingly sharp conflict between Gödel’s and Turing’s views on mind. Their deeper disagreement really concerns the nature of machines, and I’ll end with some brief remarks on (supra-) mechanical devices in Section 4.