有理模型辨识的两类新方法-----混合迭代与柔性最小二乘法

针对有理模型提出两类辨识方法.首先提出基于递阶辨识思想的混合辨识方法,将模型分解为分子和分母两个子模型,分别用最小二乘法辨识分子参数,用粒子群算法和智能多步长梯度迭代算法辨识分母参数.由于降低了模型维数,且信息向量与噪声不相关,相对于传统的偏差补偿最小二乘算法,混合迭代法可以提高辨识精度并降低计算量.然后,为消除模型结构已知的假设,且充分利用最新数据更新系统参数,提出柔性递推最小二乘辨识方法,将有理模型转化为时变参数系统,进而辨识出时变系统的参数.仿真例子验证了所提出方法的有效性.     

差分模型参数递推估计的Householder变换法

本文提出了利用Householder变换进行差分模型参数递推估计的新方法.并由该方法导 出了新的递推最小二乘法、递推增广矩阵法、递推广义最小二乘法、递推极大似然法. 文中分单变量、多变量两种情况重点讨论了新递推最小二乘法及其与传统递推最小二乘 法的比较,并给出了计算实例.     

协方差重置的两阶段递推贝叶斯参数辨识算法

为了在有色噪声干扰情况下获得无偏估计,基于辅助模型思想和分解技术,提出了一种带协方差重置的两阶段递推贝叶斯辨识算法。该算法首先把待辨识模型分解成两个虚拟子模型,然后分别辨识;同时,把估计到的噪声方差引入算法,并加入了一种新的协方差重置方法。计算量分析表明,与带协方差重置的最小二乘算法相比,所提算法可以减少计算量。仿真结果显示,所提算法的估计误差比传统最小二乘算法要小。实例建模证明了算法的有效性。     

Input–output data filtering based recursive least squares identification for CARARMA systems

This paper uses an estimated noise transfer function to filter the input–output data and presents filtering based recursive least squares algorithms (F-RLS) for controlled autoregressive autoregressive moving average (CARARMA) systems. Through the data filtering, we obtain two identification models, one including the parameters of the system model, and the other including the parameters of the noise model. Thus, the recursive least squares method can be used to estimate the parameters of these two identification models, respectively, by replacing the unmeasurable variables in the information vectors with their estimates. The proposed F-RLS algorithm has a high computational efficiency because the dimensions of its covariance matrices become small and can generate more accurate parameter estimation compared with other existing algorithms.     

Recursive identification for multivariate autoregressive equation-error systems with autoregressive noise

This paper considers the recursive identification problems for a class of multivariate autoregressive equation-error systems with autoregressive noise. By decomposing the system into several regressive identification subsystems, a maximum likelihood recursive generalised least squares identification algorithm is proposed to identify the parameter vectors in each subsystem. In addition, a multivariate recursive generalised least squares algorithm is derived as a comparison. The numerical simulation results indicate that the maximum likelihood recursive generalised least squares algorithm can effectively estimate the parameters of the multivariate autoregressive equation-error autoregressive systems and get more accurate parameter estimates than the multivariate recursive generalised least squares algorithm.     

模糊熵的区域合并和图割的快速矿岩分割

目的 针对现有区域合并和图割的结合算法没有考虑矿岩图像模糊特性,导致分割精度和运行效率较低,模糊边缘无法有效分割的问题,利用快速递推计算的最大模糊2-划熵信息设置以区域为顶点的图割模型似然能来解决。方法 首先利用双边滤波器和分水岭算法对矿岩图像进行预处理,并将其划分为若干一致性较好的区域;然后利用图像在计算最大模糊2-划分熵时,目标和背景的模糊隶属度函数来设计图割能量函数似然能,使得能量函数更接近模糊图像的真实情况,期间为了提高最大模糊2-划分熵值的搜索效率,提出了时间复杂度为O（n²）的递推算法将模糊熵的计算转化为递推过程,并保留不重复的递推结果用于后续的穷举搜索;最后利用设计的图割算法对区域进行标号,以完成分割。结果 本文算法的分割精度较其他区域合并和图割结合算法提高了约23%,分割后矿岩颗粒个数的统计结果相对于人工统计结果,其误差率约为2%,运行时间较其他算法缩短了约60%。结论 本文算法确保精度同时,有效提高矿岩图像的分割效率,为自动化矿岩图像高效分割的工程实践提供重要指导依据。     

Maximum likelihood least squares‐based iterative methods for output‐error bilinear‐parameter models with colored noises

This article is concerned with the parameter identification of output‐error bilinear‐parameter models with colored noises from measurement data. An auxiliary model least squares‐based iterative method is developed through the overparameterization model. It examines the difficulty of estimating the overparameterized vector, which usually presents a heavy computational burden in the identification process. To overcome this drawback, a parameter separation technique is introduced and the nonlinear model is reformulated as a refined identification model through eliminating the crossmultiplying terms. In this regard, a parameter separation least squares‐based iterative (PS‐LSI) algorithm is derived by avoiding estimating the redundant parameters. On the basis of the PS‐LSI algorithm, we derive a maximum likelihood least squares‐based iterative method to further improve the numerical accuracy. The identification is dependent on the formulation of a pseudolinear regression relationship, which contains two linear prefilters constructed from the system and noise models. The performance of this proposed method is confirmed by the numerical simulations as well as direct comparisons with other existing algorithms.     

2维最大类间平均离差阈值选取快速递推算法

阈值分割是广泛使用的最为有效的图像分割方法之一。阈值选取是阈值分割的关键。Otsu提出的基于L2范数的最大类间方差法是备受关注的一种方法,而基于L1范数的最大类间平均离差法则更为简捷,效果很好。2维最大类间平均离差阈值选取方法分割精确、抗噪性能好,其效果优于2维最大类间方差法,但存在计算量大、难以实用等缺点。提出了2维最大类间平均离差阈值选取的两种不同的快速递推算法,都可将计算复杂性由O(L4)减少为O(L2)。给出了2维最大类间平均离差两种快速递推算法的分割结果及运行时间,并与原始算法及原有的快速算法进行了分析和比较。实验结果表明,这两种递推算法都可以大幅度地提高运算速度,运行时间可减少到原始算法的0.1%,使2维最大类间平均离差阈值分割方法更为实用,目前已被应用于红外目标、车牌、指纹等自动识别系统中。     

Fitting generalized linear models and their nonlinear extensions with least squares calculations

A class of maximum likelihood algorithms called NRL algorithms that can be implemented with a sequence of least squares calculations is developed. When applied to generalized linear models and their nonlinear extensions, this class includes several algorithms that have been previously proposed. Properties of the algorithms are examined both in the initial iterations and also near the maximum likelihood estimate; different types of algorithm often perform best in these two situations. A strategy for switching between two such NRL algorithms is presented.     

Detection techniques in least squares identification

Parameter estimation schemes based on least squares identification and detection ideas are proposed for ease of computation, reduced numerical difficulties, and bias reduction in the presence of colored noise correlated with the states of the signal generating system. The algorithms are simpler because in the calculations, the state vector is at one point replaced by a quantized version. This technique avoids to some extent numerical difficulties associated with ill-conditioning in least squares schemes and thus obviates the need for square root algorithms and the need for high order precision calculations. In recursive form, the schemes are designed to yield parameter estimates with negligible bias without the additional computational effort or instability risks associated with generalized and extended least squares, recursive maximum likelihood schemes, or the method of instrumental variables. Nonrecursive schemes are designed to minimize computational effort in a batch processing situation while at the same time giving some reduction of bias in the state dependent colored noise situation.

The novel algorithms have the limitation that they are suboptimal and there is thus a consequent reduction in the speed of convergence for some applications. The merits of the proposed schemes are assessed via simulation studies in this paper and an adaptive equalization application in a companion paper.     

Received signal strength based positioning for multiple nodes in wireless sensor networks

We address the problem of locating multiple nodes in a wireless sensor network with the use of received signal strength (RSS) measurements. In RSS based positioning, transmit power and path-loss factor are two environment dependent parameters which may be uncertain or unknown. For unknown transmit powers, we devise two-step weighted least squares (WLS) and maximum likelihood (ML) algorithms for node localization. The mean square error of the former is analyzed in the presence of zero-mean white Gaussian disturbances. When both transmit powers and path-loss factors are unavailable, two nonlinear least squares estimators, namely, the direct ML approach and combination of linear least squares and ML algorithm, are developed. Numerical examples are also included to evaluate the localization accuracy of the proposed estimators by comparing with two existing node positioning methods and the Cramér–Rao lower bound.     

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.     

基于数据滤波的带协方差重置的递推贝叶斯算法

针对传统最小二乘算法计算量大、在有色噪声干扰下估计有误差的问题,提出了一种基于滤波技术的带协方差重置的递推贝叶斯算法。该算法首先使用一个动态非线性滤波器对输入输出数据进行滤波,然后使用贝叶斯方法进行参数估计。同时,为了加快参数的收敛速度,在算法中加入了一种新型的协方差重置策略。计算量分析表明,当过程模型和噪声模型的阶数分别为6和4的时候,所提算法可以减少约62.35%的计算量。仿真结果显示,所提算法与传统最小二乘算法在采样数据长度为3000时的估计误差分别为0.771%和1.118%。因此,所提算法具有较高的计算效率,并且可以给出精度较高的参数估计值。     

A theoretical analysis of recursive identification methods

In this paper five different recursive identification methods will be analyzed and compared, namely recursive versions of the least squares method, the instrumental variable method, the generalized least squares method, the extended least squares method and the maximum likelihood method. They are shown to be similar in structure and need of computer storage and time. Making use of recently developed theory for asymptotic analysis of recursive stochastic algorithms, these methods are examined from a theoretical viewpoint. Possible convergence points and their global and local convergence properties are studied. The theoretical analysis is illustrated and supplemented by simulations.     

MIMO系统中基于代价函数和排序模式的MMSE SIC检测器

针对多输入多输出空间多路复用系统,提出了一种基于代价函数和排序模式的多个并行分支的最小均方误差连续干扰消除检测器;具体而言,设计了选择规则来选择代价函数性能最好的分支,并通过利用不同的检测排序模式使得每个分支中的SIC算法按照信号干扰噪声比由高到低来检测信号,从而实现完全检测分集;为了进一步降低算法的计算复杂度,还提出了一种采用递归最小二乘算法的有效自适应接收机来更新滤波器权值向量,从而获得基于递归最小二乘算法的MB-SIC接收机的自适应实现;此外,还对提出的检测器在比特差错概率性能方面进行了分析;仿真结果表明,相比于现有的检测算法,提出的算法不仅具有较低的计算复杂度,而且能获得更好的误码率性能。     

Stepwise-then-intelligent algorithm (STIA) for optimizing remotely sensed image rectification

ABSTRACT

To address the problems of parameter selection and accuracy optimization of models in image rectification, this article first proposes a novel stepwise-then-intelligent algorithm (STIA) for image rectification optimization, which includes the following steps. First, stepwise regression is suggested to simultaneously solve the over-parameterization problem and select the optimum parameters of the polynomial model and rational function model according to different terrains. Second, intelligent algorithms, e.g. the genetic algorithm (GA) and particle swarm optimization (PSO), are proposed to search for better results based on an innovative search range determined by the uncertainty propagation and 3-sigma rule. The experimental results show that the proposed STIA can achieve higher accuracy than conventional methods; and in most cases, the PSO algorithm used in STIA is superior to the GA used in STIA in measures of time and accuracy. Moreover, stepwise-then-PSO algorithm exhibits the best performance of all compared methods, including least squares, stepwise regression, total least squares and partial least squares.     

A Fast Nonlinear Model Identification Method

The identification of nonlinear dynamic systems using linear-in-the-parameters models is studied. A fast recursive algorithm (FRA) is proposed to select both the model structure and to estimate the model parameters. Unlike orthogonal least squares (OLS) method, FRA solves the least-squares problem recursively over the model order without requiring matrix decomposition. The computational complexity of both algorithms is analyzed, along with their numerical stability. The new method is shown to require much less computational effort and is also numerically more stable than OLS.     

Fast Blind Equalization Using Complex-Valued MLP

The blind equalizers based on complex valued feedforward neural networks, for linear and nonlinear communication channels, yield better performance as compared to linear equalizers. The learning algorithms are, generally, based on stochastic gradient descent, as they are simple to implement. However, these algorithms show a slow convergence rate. In the blind equalization problem, the unavailability of the desired output signal and the presence of nonlinear activation functions make the application of recursive least squares algorithm difficult. In this letter, a new scheme using recursive least squares algorithm is proposed for blind equalization. The learning of weights of the output layer is obtained by using a modified version of constant modulus algorithm cost function. For the learning of weights of hidden layer neuron space adaptation approach is used. The proposed scheme results in faster convergence of the equalizer.     

An efficient hierarchical identification method for general dual-rate sampled-data systems

For the lifted input–output representation of general dual-rate sampled-data systems, this paper presents a decomposition based recursive least squares (D-LS) identification algorithm using the hierarchical identification principle. Compared with the recursive least squares (RLS) algorithm, the proposed D-LS algorithm does not require computing the covariance matrices with large sizes and matrix inverses in each recursion step, and thus has a higher computational efficiency than the RLS algorithm. The performance analysis of the D-LS algorithm indicates that the parameter estimates can converge to their true values. A simulation example is given to confirm the convergence results.     

Design for Self-Organizing Fuzzy Neural Networks Based on Genetic Algorithms

A novel hybrid learning algorithm based on a genetic algorithm to design a growing fuzzy neural network, named self-organizing fuzzy neural network based on genetic algorithms (SOFNNGA), to implement Takagi-Sugeno (TS) type fuzzy models is proposed in this paper. A new adding method based on geometric growing criterion and the epsiv-completeness of fuzzy rules is first used to generate the initial structure. Then a hybrid algorithm based on genetic algorithms, backpropagation, and recursive least squares estimation is used to adjust all parameters including the number of fuzzy rules. This has two steps: First, the linear parameter matrix is adjusted, and second, the centers and widths of all membership functions are modified. The GA is introduced to identify the least important neurons, i.e., the least important fuzzy rules. Simulations are presented to illustrate the performance of the proposed algorithm