Optimal Recurrent Nonlinear Filter of a Large Order for Jump Diffusion Markov Signals

Journal of Computer and Systems Sciences International - In this paper, we consider the problem of the root-mean-square optimal estimation of the current state of a continuous stochastic object of...     

Pipelined Chebyshev Functional Link Artificial Recurrent Neural Network for Nonlinear Adaptive Filter

A novel nonlinear adaptive filter with pipelined Chebyshev functional link artificial recurrent neural network (PCFLARNN) is presented in this paper, which uses a modification real-time recurrent learning algorithm. The PCFLARNN consists of a number of simple small-scale Chebyshev functional link artificial recurrent neural network (CFLARNN) modules. Compared to the standard recurrent neural network (RNN), those modules of PCFLARNN can simultaneously be performed in a pipelined parallelism fashion, and this would lead to a significant improvement in its total computational efficiency. Furthermore, contrasted with the architecture of a pipelined RNN (PRNN), each module of PCFLARNN is a CFLARNN whose nonlinearity is introduced by enhancing the input pattern with Chebyshev functional expansion, whereas the RNN of each module in PRNN utilizing linear input and first-order recurrent term only fails to utilize the high-order terms of inputs. Therefore, the performance of PCFLARNN can further be improved at the cost of a slightly increased computational complexity. In addition, due to the introduced nonlinear functional expansion of each module in PRNN, the number of input signals can be reduced. Computer simulations have demonstrated that the proposed filter performs better than PRNN and RNN for nonlinear colored signal prediction, nonstationary speech signal prediction, and chaotic time series prediction.      

An Optimal Recurrent Logical-Dynamical Filter of a High Order and Its Covariance Approximations

Journal of Computer and Systems Sciences International - The problem of logical recognition of the operating mode and dynamic estimation of the intra-mode state vector of a discrete-time stochastic...     

Finite Horizon Minimax Optimal Control of Nonlinear Continuous Time Systems with Stochastic Uncertainty

This paper develops a general continuous-time stochastic framework for robustness analysis and robust control synthesis. We consider a stochastic minimax optimization problem for general stochastic uncertain systems. A general method is presented for converting problems of performance analysis or controller synthesis into unconstrained optimization problems.     

Nonlinear Filter Design Using Envelopes

Machine design of a signal or image operator involves estimating the optimal filter from sample data. The optimal filter is the best filter, relative to the error measure used; however, owing to design error, the designed filter might not perform well. In general it is suboptimal. The envelope constraint involves using two humanly designed filters that form a lower and upper bound for the designed operator. The method has been employed for binary operators. This paper considers envelope design for gray-scale filters, in particular, aperture filters. Some basic theoretical properties are stated, including optimality of the design method relative to the constraint imposed by the envelope. Examples are given for noise reduction and de-blurring.     

Finite Memory Loading in Hairy Neurons

This paper presents a method to expand the basins of stable patterns in associative memory. It examines fully-connected associative memory geometrically and translate the learning process into an algebraic optimization procedure. It finds that locating all the patterns at certain stable corners of the neurons’ hypercube as far from the decision hyperplanes as possible can produce excellent error tolerance. It then devises a method based on this finding to develop the hyperplanes. This paper further shows that this method leads to the hairy model, or the deterministic analogue of the Gibb’s free energy model. Through simulations, it shows that this method gives better error tolerance than does the Hopfield model and the error-correction rule in both synchronous and asynchronous modes.     

非线性系统的神经网络自适应滤波器

针对一类具有未知非线性函数和未知虚拟系数的二阶非线性系统,提出了一种神经网络自适应滤波跟踪方法,用RBF神经网络估计出系统中不确定项,将神经网络与滑模控制方法相结合,用李雅普诺夫稳定性分析方法证明了滤波器内的所有信号均有界,选择的神经网络权值调整规律可以消除颤振,抑制外部随机干扰。     

Optimal External Memory Planar Point Enclosure

In this paper we study the external memory planar point enclosure problem: Given N axis-parallel rectangles in the plane, construct a data structure on disk (an index) such that all K rectangles containing a query point can be reported I/O-efficiently. This problem has important applications in e.g. spatial and temporal databases, and is dual to the important and well-studied orthogonal range searching problem. Surprisingly, despite the fact that the problem can be solved optimally in internal memory with linear space and O(log N+K) query time, we show that one cannot construct a linear sized external memory point enclosure data structure that can be used to answer a query in O(log  _B N+K/B) I/Os, where B is the disk block size. To obtain this bound, Ω(N/B ^1−ε ) disk blocks are needed for some constant ε>0. With linear space, the best obtainable query bound is O(log ₂ N+K/B) if a linear output term O(K/B) is desired. To show this we prove a general lower bound on the tradeoff between the size of the data structure and its query cost. We also develop a family of structures with matching space and query bounds. An extended abstract of this paper appeared in Proceedings of the 12th European Symposium on Algorithms (ESA’04), Bergen, Norway, September 2004, pp. 40–52. L. Arge’s research was supported in part by the National Science Foundation through RI grant EIA–9972879, CAREER grant CCR–9984099, ITR grant EIA–0112849, and U.S.-Germany Cooperative Research Program grant INT–0129182, as well as by the US Army Research Office through grant W911NF-04-01-0278, by an Ole Roemer Scholarship from the Danish National Science Research Council, a NABIIT grant from the Danish Strategic Research Council and by the Danish National Research Foundation. V. Samoladas’ research was supported in part by a grant co-funded by the European Social Fund and National Resources-EPEAEK II-PYTHAGORAS. K. Yi’s research was supported in part by the National Science Foundation through ITR grant EIA–0112849, U.S.-Germany Cooperative Research Program grant INT–0129182, and Hong Kong Direct Allocation Grant (DAG07/08).     

On Optimal Signal–Filter Pairs

We extend the notion of an optimal signal–filter pair to the case where n-convolution is used instead of cyclic convolution. We construct n-optimal n-adic signals for all n = 2, 3, . . ..     

A Lattice-Based Minimal Gray-Scale Switching Algorithm for Obtaining the Optimal Increasing Filter from the Optimal Filter

For binary window-based filters, the optimal increasing filter is often derived from the optimal unconstrained (nonincreasing) filter by iteratively switching the filter values at pixels from 0 to 1 or from 1 to 0 so as to make the resulting filter be the optimal increasing filter. This paper gives a corresponding switching algorithm for gray-scale nonlinear filters, and it does so in the context of finite lattices, which makes the algorithm applicable to computational morphology on lattices. The algorithm is minimal in the sense that it involves a minimal search if one wishes to be certain to obtain the optimal increasing filter when beginning with the optimal unconstrained filter.     

Learning Sequence Representations by Non-local Recurrent Neural Memory

International Journal of Computer Vision - The key challenge of sequence representation learning is to capture the long-range temporal dependencies. Typical methods for supervised sequence...     

非线性状态空间模型遗忘性研究

动态系统的遗忘性是描述系统行为主要取决于其近期输入的概念，与系统的稳定性、鲁棒性等密切相关。对于非线性状态空间模型，遗忘性在很弱的条件下与整体一致非常吸引等价。系统在凸集或不变区集上的遗忘性可由一类特殊Ｌｙａｐｕｎｏｖ函数的存在性保证。遗忘区域的大小可利用矩阵不等式来估计。     

基本样条循环神经网络及其非线性建模

提出一种新的基于基本样条逼近的循环神经网络,该网络易于训练且收敛速度快。此外为克服定长学习步长训练速度慢的问题,提出一种用于该网络训练的自适应权值更新算法,给出了学习步长的最优估计。该最优学习步长的选择可用于基本样条循环神经网络的训练以及对非线性系统的建模。     

IMC系统的优化滤波器研究

推荐两种滤波器作为ＩＭＣ系统的滤波器。一种是ＩＴＡＥ滤波器,它符合时间乘绝对误差积分值最小的优化原则,即Ｊ＝│ｅ│ｔｄｔ→ｍｉｎ。另一种是Ｂｕｔｔｅｒｗｏｒｔｈ滤波器,它具有很好的理想低通滤波器特性。由于这两种滤波器的全部结构极点均处于Ｓ复平面的高稳定性区域,又是按最优原理确定其参数,因此,采用这两种滤波器可以抑制模型失配导致的不良影响,使得ＩＭＣ系统的鲁棒性更加有保证。本文列举一个工业过程控制例     

Training Recurrent Neurocontrollers for Robustness With Derivative-Free Kalman Filter

We are interested in training neurocontrollers for robustness on discrete-time models of physical systems. Our neurocontrollers are implemented as recurrent neural networks (RNNs). A model of the system to be controlled is known to the extent of parameters and/or signal uncertainties. Parameter values are drawn from a known distribution. For each instance of the model with specified parameters, a recurrent neurocontroller is trained by evaluating sensitivities of the model outputs to perturbations of the neurocontroller weights and incrementally updating the weights. Our training process strives to minimize a quadratic cost function averaged over many different models. In the end, the process yields a robust recurrent neurocontroller, which is ready for deployment with fixed weights. We employ a derivative-free Kalman filter algorithm proposed by Norgaard and extended by Feldkamp (2001) and Feldkamp (2002) to neural network training. Our training algorithm combines effectiveness of a second-order training method with universal applicability to both differentiable and nondifferentiable systems. Our approach is that of model reference control, and it extends significantly the capabilities proposed by Prokhorov (2001). We illustrate it with two examples     

Stochastic Resonance in Recurrent Neural Network with Hopfield-Type Memory

Stochastic resonance (SR) is known as a phenomenon in which the presence of noise helps a nonlinear system in amplifying a weak (under barrier) signal. In this paper, we investigate how SR behavior can be observed in practical autoassociative neural networks with the Hopfield-type memory under the stochastic dynamics. We focus on SR responses in two systems which consist of three and 156 neurons. These cases are considered as effective double-well and multi-well models. It is demonstrated that the neural network can enhance weak subthreshold signals composed of the stored pattern trains and have higher coherence abilities between stimulus and response.     

基于变分PDE的非线性数字混合滤波器

从局部扩散角度分析了经典变分PDE复原模型的不足,给出一种基于全变差模型和调和模型的混合图像复原模型,并导出了相应的数字混合滤波器.该滤波器可以根据图像的局部梯度特征自适应选取滤波器系数,能在去噪的同时保留边缘,并削弱平滑区域的阶梯效应,具有较好的综合性能.针对该混合滤波器,还设计出相应的图像修补和放大算法.大量仿真实验表明,该滤波器可以很好地应用于图像的去噪、修补和放大.     

基于改进UKF的GPS非线性动态滤波研究

为了提高动态定位精度,将一种改进的UKF(Unscented galman Filter)算法应用在GPS非线性动态定位解算中.将UKF算法与IEKF(Iterated Improved Kalman Filter)算法相结合,因此保持了基本UKF算法易于实现和收敛速度快的优点,同时由于滤波值是通过迭代扩展的卡尔曼滤波机制得到,进而更新值能更准确的逼近非线性系统状态概率密度函数,具有更高的精度.应用于GPS非线性动态滤波定位中,仿真结果表明:与UKF算法相比,算法能够明显提高定位精度.