Sampling strong tracking nonlinear unscented Kalman filter and its application in eye tracking

The unscented Kalman filter is a developed well-known method for nonlinear motion estimation and tracking. However, the standard unscented Kalman filter has the inherent drawbacks, such as numerical instability and much more time spent on calculation in practical applications. In this paper, we present a novel sampling strong tracking nonlinear unscented Kalman filter, aiming to overcome the difficulty in nonlinear eye tracking. In the above proposed filter, the simplified unscented transform sampling strategy with n+2 sigma points leads to the computational efficiency, and suboptimal fading factor of strong tracking filtering is introduced to improve robustness and accuracy of eye tracking. Compared with the related unscented Kalman filter for eye tracking, the proposed filter has potential advantages in robustness, convergence speed, and tracking accuracy. The final experimental results show the validity of our method for eye tracking under realistic conditions.     

A Bayesian tutorial for data assimilation

Data assimilation is the process by which observational data are fused with scientific information. The Bayesian paradigm provides a coherent probabilistic approach for combining information, and thus is an appropriate framework for data assimilation. Viewing data assimilation as a problem in Bayesian statistics is not new. However, the field of Bayesian statistics is rapidly evolving and new approaches for model construction and sampling have been utilized recently in a wide variety of disciplines to combine information. This article includes a brief introduction to Bayesian methods. Paying particular attention to data assimilation, we review linkages to optimal interpolation, kriging, Kalman filtering, smoothing, and variational analysis. Discussion is provided concerning Monte Carlo methods for implementing Bayesian analysis, including importance sampling, particle filtering, ensemble Kalman filtering, and Markov chain Monte Carlo sampling. Finally, hierarchical Bayesian modeling is reviewed. We indicate how this approach can be used to incorporate significant physically based prior information into statistical models, thereby accounting for uncertainty. The approach is illustrated in a simplified advection–diffusion model.     

强背景下混响时间的非线性滤波M序列相关测量

本文提出采用非线性滤波抑制在强背景噪声环境中用Ｍ－序列相关法得到的房间脉冲响应中的残余噪声影响，以扩大混响衰减曲线的动态范围，从而达到能够在强背景噪声环境下准确测量混响时间的目的。首先讨论了影响Ｍ序列相关法测量混响时间的几个因素。其次，采用非线性滤波进一步抑制背景噪声的影响。结果表明，非线性滤波的效果相当显著。本文还在非白噪声背景条件下用该法进行强背景下的混响时间测量，结果与传统测量结果符合得很好     

A numerical formulation for nonlinear ultrasonic waves propagation in fluids

A finite-difference algorithm is developed for analysing the nonlinear propagation of pulsed and harmonic ultrasonic waves in fluid media. The time domain model allows simulations from linear to strongly nonlinear plane waves including weak shock. Effects of absorption are included. All the harmonic components are obtained from only one solving process. The evolution of any original signal can be analysed. The nonlinear solution is obtained by the implicit scheme via a fast linear solver. The numerical model is validated by comparison to analytical data. Numerical experiments are presented and commented. The effect of the initial pulse shape on the evolution of the pressure waveform is especially analysed.     

小角度衍射噪声光栅滤波方法研究

针对因衍射等原因引起的小角度差光噪声信号,探讨了利用闪耀光栅的2级闪耀,实现角度差放大,提高空间低通滤波器适应性的滤波新方法。理论分析和模拟仿真表明,对于小于5°的角度差,可实现3倍以上放大。放大所需闪耀光栅的频率与入射单色波长成反比,波长越长,所需光栅频率越低。与正的斜入射角相比,负斜入射角度差的放大倍数更大。当负斜入射角超过一定值时,会因为全反射角的限制而导致斜入射2级闪耀不存在,只保留了有效信号的2级闪耀,滤波效果更好。     

扩展Kalman滤波器同时测定苯酚和邻氯苯酚

提出了苯酚和邻氯苯酚混合体系非线性吸光度表示式。即非线性吸光度由两组分各自对吸光度的贡献、由于混合而导致的两组分各自贡献的改变以及交互作用项三部分构成。依据该式,利用非线性Kalman滤波紫外分光光度法同时测量了苯酚和邻氯苯酚混合体系。在250～290 nm 区间测量了32组浓度各自在1～15 mg·L-1范围的苯酚和邻氯苯酚标准混合溶液紫外吸收光谱图。利用偏最小二乘法,将其制作成扩展Kalman滤波标准工作系数矩阵。通过对非线性吸光度关系式Taylor级数展开进行线性化处理,得到其向量函数的Jacobi矩阵,从而完成了非线性Kalman滤波器的设置。回收实验显示出,扩展Kalman滤波同时测量苯酚和邻氯酚双组分体系是准确、稳定的。     

相干噪声快速去除算法及其在声源定位中的应用

针对相干噪声干扰声源辨识问题,将强跟踪滤波器理论与阵列-信号采集模型相结合,发展了一种快速估计相位变化的算法。算法引入多重次优渐消因子,能够进一步提取相位残差中的有用信息,使输出残差序列处处正交,且该因子能根据噪声相位差变化自动调节。通过仿真对连续相位突变进行跟踪表明,在参数失配条件下该算法实现了相位差的准确估计,且其性能在宽频范围具有稳定性。通过音箱实验给出了宽频范围内的成像结果,与已有算法对比表明,该算法不仅能够实时消除噪声干扰并可将收敛速度提高一倍以上。本研究实现了对随机变化相位的准确估计,提升了传声器阵列在相干噪声干扰下的声源实时定位能力。     

Convex combination of nonlinear adaptive filters for active noise control

This paper proposes a nonlinear active noise control (ANC) system based on convex combination of a functional link artificial neural network (FLANN) and a Volterra filter. Simulation study reveals enhanced noise cancelation performance of the proposed ANC system over the ones based on its component filters.     

Rapid numerical difference recurrent formula of nonlinear Schrödinger equation and its application

In this paper, a rapid numerical difference recurrent formula, in which it has been taken that the chromatic dispersion and the nonlinearity act together along each fiber segment, is established in the time domain by applying a Maclaurin expansion to the differential form of the nonlinear Schrödinger equation (NLSE) in the frequency domain. The calculated results by using the established formula are contrasted with the known analytical results and the results of the split-step Fourier method (SSFM) and indicated that the rapid numerical difference recurrent formula is very accurate and more reasonable because it abandons an assumption that the dispersive and nonlinear effects can be assumed to act independently as the optical field propagates over each fiber segment. It has been concluded that the established formula in this paper is a scientific, reasonable and effective numerical method for the study of light pulse propagation in a nonlinear optical medium.     

A Maximum Entropy Method for Particle Filtering

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.     

A comparative numerical study of soliton switching in a nonlinear directional coupler with saturating nonlinearity

A detailed numerical study of soliton switching in a nonlinear directional coupler with saturating nonlinearity is carried out. All commonly used models have been studied. Relevant physical characteristics for switching have been determined, compared and discussed.     

一种基于场景的红外焦平面阵列非均匀性校正算法

针对IRFPA器件在工程使用中固定图案噪音会发生漂移及探测元响应呈现非线性的特征,提出了一种以二次方程表征的响应特性数学模型,并利用场景数据的卡尔曼滤波算法,对其实施双校正。本算法较基于线性模型的非均匀性校正算法具有更好的校正效果,仿真实验结果验明了算法的优越性.     

A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media

We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics.     

一种多滤波器组合导航数据融合方法

针对组合导航系统中使用单天线GPS接收机时导致姿态角不易收敛的问题,提出了一种互补滤波器和卡尔曼滤波器相结合的数据融合算法。该方法首先通过MEMS惯性传感器与磁强计设计了一种互补滤波算法。针对载体在变速运动过程中加速度计的倾角测量值有较大误差,影响互补滤波器输出精度的问题,通过GPS接收机和加速度计设计了卡尔曼滤波模型,将卡尔曼滤波器输出速度的微分量反馈给互补滤波器,实现了对互补滤波器中载体运动加速度的补偿。基于以上解算方法,以FPGA为核心处理器设计了组合导航系统并进行了车载实验。实验中,该方法有效补偿了汽车变速过程中的倾角测量误差,证明了该方法的有效性。     

单自由度非线性保守系统作大振幅振动时周期的计算方法

简要介绍了单自由度非线性保守系统作大振幅振动时周期的计算方法,并给出了几个常见典型振动问题的周期公式．     

流动管道内利用旁通管反声降噪非线性问题的数值模拟

具有流动的管道内的降噪工作是很有用的工程实际问题,当噪声源很强时就成为非线性问题。本文提出了一种非线性方法,可用来数值计算有流动时分通管对强噪声源的降噪影响。难点是建立并求解了连接点处的流动关系。数值算例表明,这种方法对线性和非线性情况下有流动的管道内利用旁通管的反声降噪问题都可适用。     

Analytical and numerical study of coupled atomistic-continuum methods for fluids

The stability and convergence rate of coupled atomistic-continuum methods are studied analytically and numerically. These methods couple a continuum model with molecular dynamics through the exchange of boundary conditions in the continuum-particle overlapping region. Different coupling schemes, including velocity–velocity, flux–velocity, velocity–flux and flux–flux, are studied. It is found that the velocity–velocity and flux–velocity schemes are stable. The flux–flux scheme is weakly unstable. The stability of the velocity–flux scheme depends on the parameter T_c which is the length of the time interval between successive exchange of boundary conditions. It is stable when T_c is small and unstable when T_c is large. For steady-state problems, the flux–velocity scheme converges faster than the other coupling schemes.     

A nonextensive maximum entropy approach to a family of nonlinear reaction–diffusion equations

We consider a monoparametric family of reaction–diffusion equations endowed with both a nonlinear diffusion term and a nonlinear reaction one that possess exact time-dependent particular solutions of the Tsallis’ maximum entropy (MaxEnt) form. The evolution of these solutions is governed by a system of three coupled nonlinear ordinary differential equations that are integrated numerically. A simple population dynamics interpretation provides a qualitative understanding of the behaviour of the q-MaxEnt solutions. When the reaction term vanishes the time-dependent distributions studied here reduce to the previously known Tsallis’ MaxEnt solutions for the nonlinear diffusion equation.     

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers. We discuss the effectiveness and conditioning of the proposed discretization, and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation/film precursor, several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows, using just a few hundred grid points.