A note on estimation algebras on nonlinear filtering theory

The idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed by Brockett and Mitter independently. It turns out that the concept of estimation algebra plays a crucial role in the investigation of finite dimensional nonlinear filters. In his talk at the International Congress of Mathematicians in 1983, Brockett proposed to classify all finite dimensional estimation algebras. In this paper we consider some filtering systems. In a special filtering system: (1) We have some structure results. (2) For any arbitrary finite dimensional state space, under the condition that the drift term is a linear vector field plus a gradient vector field, we classify all finite dimensional estimation algebras with maximal rank. (3) We classify all finite dimensional estimation algebras with maximal rank if the dimension of the state space is less than or equal to three. A more general filtering system is considered. The above three results can be ‘used’ locally. Therefore from the algebraic point of view, we have now understood generically some finite dimensional filters.     

Research on Permeability of Multiphase Medium of Middle to High-Rank Coals

1　 IntroductionCoal reservoir permeability is one of the keyfactors to restrict coalbed methane ( CBM) recoveryon the ground in China.Although some domesticscholars investigated single- phase permeability ofgas- saturated and water- saturated coal samples aim-ing atthe prevention of gas outburst or the preven-tion of smut by water injection[1-3 ] ,the research onrelative permeability of double- phase medium underconfining stress has not been reported.Butsome o-versea scholars,such as Gash (…     

Serial Mechanisms in Lexical Access: The Rank Hypothesis.

There is general agreement that the effect of frequency on lexical access time is roughly logarithmic, although little attention has been given to the reason for this. The authors argue that models of lexical access that incorporate a frequency-ordered serial comparison or verification procedure provide an account of this effect and predict that the underlying function directly relates access time to the rank order of words in a frequency-ordered set. For both group data and individual data, it is shown that rank provides a better fit to the data than does a function based on log frequency. Extensions to a search model are proposed that account for error rates and latencies and the effect of age of acquisition, which is interpreted as an effect of cumulative frequency. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Rank Conditions on the Multiple-View Matrix

Geometric relationships governing multiple images of points and lines and associated algorithms have been studied to a large extent separately in multiple-view geometry. The previous studies led to a characterization based on multilinear constraints, which have been extensively used for structure and motion recovery, feature matching and image transfer. In this paper we present a universal rank condition on the so-called multiple-view matrix M for arbitrarily combined point and line features across multiple views. The condition gives rise to a complete set of constraints among multiple images. All previously known multilinear constraints become simple instantiations of the new condition. In particular, the relationship between bilinear, trilinear and quadrilinear constraints can be clearly revealed from this new approach. The theory enables us to carry out global geometric analysis for multiple images, as well as systematically characterize all degenerate configurations, without breaking image sequence into pairwise or triple-wise sets of views. This global treatment allows us to utilize all incidence conditions governing all features in all images simultaneously for a consistent recovery of motion and structure from multiple views. In particular, a rank-based multiple-view factorization algorithm for motion and structure recovery is derived from the rank condition. Simulation results are presented to validate the multiple-view matrix based approach.     

两个组合恒等式

文章通过对国际象棋棋盘上的一类修剪盘的"互不捉吃车问题"的讨论,利用母函数的方法证明了两个组合恒等式:①∑1≤i1相似文献   

广义特征向量与过渡矩阵

介绍了矩阵A的广义特征向量及利用A的特征向量ζ通过方程(A-λE)x=ζ逐次由秩数低的广义特征向量求出A的秩数高的广义特征向量;首次证明了矩阵A的按此法求得的这些广义特征向量是线性无关的;同时也证明了n阶矩阵恰有n个线性无关的广义特征向量;并给出了用这些广义特征向量为列来构造过渡矩阵P,使P-1AP为A的约当标准形的方法。     

Rank and select revisited and extended

The deep connection between the Burrows–Wheeler transform (BWT) and the so-called rank and select data structures for symbol sequences is the basis of most successful approaches to compressed text indexing. Rank of a symbol at a given position equals the number of times the symbol appears in the corresponding prefix of the sequence. Select is the inverse, retrieving the positions of the symbol occurrences. It has been shown that improvements to rank/select algorithms, in combination with the BWT, turn into improved compressed text indexes.     

Fast robust regression algorithms for problems with Toeplitz structure

The problem of computing an approximate solution of an overdetermined system of linear equations is considered. The usual approach to the problem is least squares, in which the 2-norm of the residual is minimized. This produces the minimum variance unbiased estimator of the solution when the errors in the observations are independent and normally distributed with mean 0 and constant variance. It is well known, however, that the least squares solution is not robust if outliers occur, i.e., if some of the observations are contaminated by large error. In this case, alternate approaches have been proposed which judge the size of the residual in a way that is less sensitive to these components. These include the Huber M-function, the Talwar function, the logistic function, the Fair function, and the ?₁ norm. New algorithms are proposed to compute the solution to these problems efficiently, in particular, when the matrix A has small displacement rank. Matrices with small displacement rank include matrices that are Toeplitz, block-Toeplitz, block-Toeplitz with Toeplitz blocks, Toeplitz plus Hankel, and a variety of other forms. For exposition, only Toeplitz matrices are considered, but the ideas apply to all matrices with small displacement rank. Algorithms are also presented to compute the solution efficiently when a regularization term is included to handle the case when the matrix of the coefficients is ill-conditioned or rank-deficient. The techniques are illustrated on a problem of FIR system identification.     

高频雷达回波信号去电离层污染

高频雷达回波信号受到电离层污染从而影响了雷达的探测性能，因此需要进行去污染处理。该文通过对高频雷达信号处理过程的分析，阐明了电离层扰动对回波信号污染的机理。根据电离层污染具有高度空间相关性的特点，将成像雷达中的秩-相位误差估计聚焦方法适当修正后应用于高频雷达回波信号去电离层扰动污染。仿真研究证明了该文方法的良好去污染效果。