New results in Sridhar filtering theory: The discrete case

A nonlinear time-varying adaptive filter is introduced, and its derivation using optimal control concepts is given in detail. The filter, which is called the discrete Pontryagin filter, is basically an extension to Sridhar filtering theory. The proposed approach can easily replace the conventional methods of autoregressive (AR) and autoregressive moving average (ARMA) models in their many applications. Instead of using a large number of time-invariant parameters to describe the signal or the time series, a single time-varying function is enough. This function is estimated using optimization techniques. Many features are gained using this approach, such as simpler and compact filter equations and better overall accuracy. The statistical properties of the filter are given, and it is shown that the signal estimate will converge in thepth mean to the true value.     

一维常系数双曲型方程每步过滤解法的稳定性与误差分析

考虑一维常系数双曲型方程的高阶数值解法，引进了一种稳定性过滤算子FN，最后从理论和数值实验上分析了该过滤算子对数值解稳定性和精度的影响．     

最优控制在车载惯性平台稳定回路中的应用

在分析车载惯性平台数学模型的基础上,针对平台的扰动特性，提出了稳定伺服回路的一种改进型线性二次高斯 (LQG) 控制方法。该方法在反馈中加入了积分项，可以消除稳态偏差，并且依据滤波器收敛性的判据，分别利用Sage Husa自适应滤波算法和强跟踪Kalman滤波器进行状态估计,既保证了估计精度，又具有跟踪突变状态的能力。仿真和实验表明：该方法在一定程度上降低了对系统模型误差和噪声统计特性误差的要求。     

红外图像空间噪声分析和预处理方法改进

讨论了基于天空背景下红外图像空间噪声组成，分析了各种空间噪声的形成原因,给出了红外图像噪声类型及其对图像质量的不同影响。分析结果认为红外图像空间噪声主要为高斯噪声和椒盐噪声。综合考虑均值法和中值法在处理噪声类型上的不同，提出了一种基于简单阈值的改进型中值法。对于不同的阈值，其算子有所不同。而M×N处理区域内每一点算子的权值取决于区域灰度中值，该点灰度越接近中值权值越大。处理后的图像背景更平滑，信噪比和改进的峰值信噪比提高了1.2dB以上，表明改进型中值法优于传统滤波方法。     

用于数字条纹轮廓术的一种基于广义分析模型的后滤波方法

由于数字投影和采集系统的非线性失真,传统的方法通常需对采集到的条纹进行低通或带通滤波从而抑制高次谐波并获取基频分量。基于广义分析模型针对数字条纹轮廓术提出一种对测量后的物体形貌进行后滤波的算法,消除了非线性失真对测量结果所造成的影响并提高了数字条纹轮廓术的测量精度。论述了条纹轮廓术的原理和广义分析模型,分析推导出后滤波算法。仿真和实验结果表明,后滤波方法能够快速准确地实现基于数字投影的三维形貌重建。     

Sampling the posterior: An approach to non-Gaussian data assimilation

The viewpoint taken in this paper is that data assimilation is fundamentally a statistical problem and that this problem should be cast in a Bayesian framework. In the absence of model error, the correct solution to the data assimilation problem is to find the posterior distribution implied by this Bayesian setting. Methods for dealing with data assimilation should then be judged by their ability to probe this distribution. In this paper we propose a range of techniques for probing the posterior distribution, based around the Langevin equation; and we compare these new techniques with existing methods.

When the underlying dynamics is deterministic, the posterior distribution is on the space of initial conditions leading to a sampling problem over this space. When the underlying dynamics is stochastic the posterior distribution is on the space of continuous time paths. By writing down a density, and conditioning on observations, it is possible to define a range of Markov Chain Monte Carlo (MCMC) methods which sample from the desired posterior distribution, and thereby solve the data assimilation problem. The basic building-blocks for the MCMC methods that we concentrate on in this paper are Langevin equations which are ergodic and whose invariant measures give the desired distribution; in the case of path space sampling these are stochastic partial differential equations (SPDEs).

Two examples are given to show how data assimilation can be formulated in a Bayesian fashion. The first is weather prediction, and the second is Lagrangian data assimilation for oceanic velocity fields. Furthermore the relationship between the Bayesian approach outlined here and the commonly used Kalman filter based techniques, prevalent in practice, is discussed. Two simple pedagogical examples are studied to illustrate the application of Bayesian sampling to data assimilation concretely. Finally a range of open mathematical and computational issues, arising from the Bayesian approach, are outlined.     

稀疏孔径光学系统成像恢复算法研究

分析了传统小波阈值去噪方法,给出改进去噪算法.先对稀疏孔径光学系统含噪成像,通过改进小波阈值去噪,提高信噪比,最大程度得到较为理想成像结果,参考修正维纳滤波方法,对去噪结果经过修正维纳滤波实现成像恢复.在实验中,考虑结构非冗余性,利用光学设计软件ZEMAX设计Golay6结构不同填充因子的稀疏孔径光学系统,以本算法进行成像恢复.实验结果表明本文算法优于单独使用维纳滤波或修正维纳滤波方法.     

基于FPGA的实时中值滤波器设计

在图像生成和采集过程中引入的各种噪声会使图像质量变差。为了实现对图像的实时预处理，首先介绍中值滤波器的基本原理和算法，然后在现场可编程门阵列（FPGA）上根据中值滤波的根基数算法，采用流水技术设计一种快速实时中值滤波器，给出按行输出的图像处理过程中存储前2行图像数据的方法。仿真结果表明：该中值滤波器可实时完成CCD输出图像的预处理，达到了抑制噪声及保持图像细节的目的。     

GEKF, GUKF and GGPF based prediction of chaotic time-series with additive and multiplicative noises

On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.     

Lanczos-Like σ-Factors for Reducing the Gibbs Phenomenon in General Orthogonal Expansions and Other Representations

The first attempt for reducing the Gibbs phenomenon in an orthogonalexpansion, besides the usual one of Fourier series, is due to Cooke in1927–1928 for the Fourier Bessel series.However, his work was limited tothe well-known Fejer averaging of the series. For the past 10 years or so,we have tried a parallel to the more effective Lanczos-type localaveraging method of the Fourier series. As expected, such efforts werehindered by the lack of realizable tools for the general orthogonalexpansion that parallels the familiar simple ones of the Fourier seriesand transforms. During the past 3 years, we have succeeded in developinga simple direct method of filtering the Gibbs phenomenon in Fourier--Besselseries, Hankel transforms representation, and a number of orthogonalpolynomials series expansions. This parallels the equivalent result ofLanczos, which he obtained for his local averaging with the help ofthe (Fourier) convolution theorem.