哈默斯坦非线性时变系统的加权学习辨识方法

针对有限区间哈默斯坦(Hammerstein)非线性时变系统,该文提出一种加权迭代学习算法用以估计系统时变参数。首先将Hammerstein系统输入非线性部分进行多项式展开,采用迭代学习最小二乘算法辨识系统的时变参数。为了防止数据饱和,采用带遗忘因子的迭代学习最小二乘算法,进而引入权矩阵,采用加权迭代学习最小二乘算法改进系统跟踪误差,以提高辨识精度。该文分别给出3种算法的推导过程并进行仿真验证。结果表明,与迭代学习最小二乘算法和带遗忘因子迭代学习最小二乘算法相比,加权迭代学习最小二乘算法具有辨识精度高、跟踪误差小以及迭代次数少等优点。     

一类 Wiener 非线性时变系统的迭代学习辨识

针对Wiener非线性时变系统的参数辨识问题,该文提出一种基于重复轴的迭代学习算法来实现对时变甚至突变参数的估计。文中将维纳系统输出非线性部分的反函数进行多项式展开,进而构造了回归模型,未知参数及中间变量用其估计替代,分别给出了采用迭代学习梯度算法和迭代学习最小二乘算法实现时变参数辨识的方法。仿真结果表明,与带遗忘因子的递推算法和迭代学习梯度算法相比,迭代学习最小二乘算法更具有参数估计收敛速度快,辨识精度高,系统输出误差小等优势,验证了所提学习算法的有效性。     

非均匀周期采样多率系统的一种辨识方法

本文利用提升技术,推导了非均匀采样多率系统的提升状态空间模型.对于状态可测量的多率系统,利用最小二乘原理,给出了模型参数矩阵辨识方法;对于状态不可测的未知参数多率系统,利用递阶辨识原理,在考虑提升模型的因果约束下,将提升系统分解为子系统进行辨识,形成了状态空间模型递阶辨识方法.仿真例子表明,本文提出的递阶辨识方法是有效的.     

Recursive Parameter Estimation Algorithms and Convergence for a Class of Nonlinear Systems with Colored Noise

Parameter estimation is important for controller design of linear systems and nonlinear systems. The parameters of the systems can be estimated through some identification algorithms. This paper presents a recursive generalized extended least squares algorithm and a generalized extended stochastic gradient (GESG) algorithm for identifying the parameters of a class of nonlinear systems. Furthermore, a multi-innovation GESG algorithm is derived to improve the estimation accuracy. The simulation example is provided to test the effectiveness of the proposed algorithms.     

Recursive least squares identification methods for multivariate pseudo-linear systems using the data filtering

This paper concerns the parameter identification methods of multivariate pseudo-linear autoregressive systems. A multivariate recursive generalized least squares algorithm is presented as a comparison. By using the data filtering technique, a multivariate pseudo-linear autoregressive system is transformed into a filtered system model and a filtered noise model, and a filtering based multivariate recursive generalized least squares algorithm is developed for estimating the parameters of these two models. The proposed algorithm achieves a higher computational efficiency than the multivariate recursive generalized least squares algorithm, and the simulation results prove that the proposed method is effective.     

QR methods of O(N) complexity in adaptive parameter estimation

Recent attention in adaptive least squares parameter estimation has been focused on methods derived from the QR factorization owing to the fact that the QR-based algorithms are much more numerically stable and accurate than the traditional pseudo-inverse-based algorithms, also known as normal equation-based algorithms, even though the former is usually much slower than the latter. This paper presents a fast adaptive least squares algorithm for the parameter estimation of linear and some nonlinear time-varying systems. The algorithm is based on Householder transformations. As verified by simulation results, this algorithm exhibits good numerical stability and accuracy. In addition, the new algorithm requires computation and storage with order of O(N) rather than O(N²) where N is the number of unknown parameters to be estimated. This algorithm can be easily extended to construct other kinds of algorithms, such as the generalized adaptive least squares algorithm, the augmented matrix algorithm, and the maximum likelihood algorithm     

On adaptive HMM state estimation

New online adaptive hidden Markov model (HMM) state estimation schemes are developed, based on extended least squares (ELS) concepts and recursive prediction error (RPE) methods. The best of the new schemes exploit the idempotent nature of Markov chains and work with a least squares prediction error index, using a posterior estimates, more suited to Markov models than traditionally used in identification of linear systems. These new schemes learn the set of N Markov chain states, and the a posteriori probability of being in each of the states at each time instant. They are designed to achieve the strengths, in terms of computational effort and convergence rates, of each of the two classes of earlier proposed adaptive HMM schemes without the weaknesses of each in these areas. The computational effort is of order N. Implementation aspects of the proposed algorithms are discussed, and simulation studies are presented to illustrate convergence rates in comparison to earlier proposed online schemes     

Use of adaptive RLS, LMS, and NLMS algorithms for nonlinearity modeling in a modified laser interferometer

Laser heterodyne interferometer is one kind of nano-metrology systems which has been widely used in industry for high-accuracy displacement measurements. The accuracy of the nano-metrology systems based on the laser heterodyne interferometers can be effectively limited by the periodic nonlinearity. In this paper, we present the nonlinearity modeling of the nano-metrology interferometric system using some adaptive filters. The adaptive algorithms consist of the least mean squares (LMS), normalized least mean squares (NLMS), and recursive least squares (RLS). It is shown that the RLS algorithm can obtain optimal modeling parameters of nonlinearity.     

基于偏最小二乘的低复杂度数字预失真

在宽带场景下,传统的数字预失真(DPD)模型需要更高的阶次和更多的系数来校正功率放大器(PA)强非线性和记忆效应,这就会导致极高的计算复杂度和解算系数时的病态问题。文章围绕复杂DPD模型参数辨识和低复杂度DPD算法实现展开深入研究,提出了一种新的基于偏最小二乘(PLS)的低复杂度DPD方法。所提方法根据PA的前逆输入输出特性来获得常数转换矩阵,生成新的基函数矩阵实现模型系数降维。与现有的DPD系数降维方法相比,该方法能在几乎不损失性能的情况下大幅减少DPD模型系数维度和计算复杂度。实验验证了新方法能大幅降低复杂度且具有很好的线性化性能。     

Simplified recursive identifier for ARMA processes

Symmetrical behaviour of the covariance matrix and the positive-definite criterion are used to simplify identification of single-input/single-output systems using recursive least squares. Simulation results are obtained and these are compared with ordinary recursive least squares. The adaptive nature of the identifier is verified by varying the system parameters on convergence.     

Blind adaptive MIMO receivers for space-time block-coded DS-CDMA systems in multipath channels using the constant modulus criterion

We propose blind adaptive multi-input multi-output (MIMO) linear receivers for DS-CDMA systems using multiple transmit antennas and space-time block codes (STBC) in multipath channels. A space-time code-constrained constant modulus (CCM) design criterion based on constrained optimization techniques is considered and recursive least squares (RLS) adaptive algorithms are developed for estimating the parameters of the linear receivers. A blind space-time channel estimation method for MIMO DS-CDMA systems with STBC based on a subspace approach is also proposed along with an efficient RLS algorithm. Simulations for a downlink scenario assess the proposed algorithms in several situations against existing methods.     

Identification of Hammerstein systems with time-varying piecewise-linear characteristics

This brief deals with the recursive parameter identification of Hammerstein type nonlinear dynamic systems with time-varying piecewise-linear characteristics. A special form of the Hammerstein model, which is linear in parameters, is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables. This enables online estimation of the linear block parameters, the coefficients determining the partition of nonlinearity subdomains and the corresponding linear segment slopes. An illustrative example is included.     

Recursive parameter identification of constrained systems: anapplication to electrically stimulated muscle

In the application of real-time identification methods for diagnosis or adaptive control of biomedical systems, there is often known model information that is ignored. Constraints on the allowable values of parameters, which may be based on physical considerations, are often neglected because the information does "fit" easily into commonly used parameter-identification algorithms. In this paper a method of incorporating constraints on model parameters is developed. This method is applicable to most recursive parameter-identification algorithms. It enforces linear equality constraints on identified parameters. The use of this method for the real-time identification of autoregressive moving-average-type time series models, subject to parameter constraints, is described in detail. These constraints may be time varying. At each time step, the parameter estimate obtained by a recursive least squares estimator is orthogonally projected onto the constraint surface. This simple idea, when appropriately executed, enhances the output prediction accuracy of estimated parameters. Using constraint information in this way is important when we do not wish to destroy a "natural" parameterization of the model (by an initial projection to incorporate equality constraints), or when we cannot use a single initial model simplification (because the constraints are time varying or involve inputs and outputs). Because it improves output prediction at future times, this method is advantageous for use in predictive adaptive controllers. The use of this algorithm is demonstrated in the identification of electrically stimulated quadriceps muscles in paraplegic human subjects, using percutaneous intramuscular electrodes. The nonlinear steady-state force versus pulsewidth recruitment characteristic of the electrode-muscle system is identified simultaneously with the input-output muscle response dynamics, using a Hammerstein-type model. Knowledge of the recruitment curve's shape is translated into constraints on the identified parameters. This information improves the experimental predictive quality of the identified model.     

变遗忘因子递推最小二乘Hammerstein系统辨识算法

摘.要:本论文研究了单输入单输出非线性Hammerstein系统的辨识问题,提出了一种具有变遗忘因子的递推最小二乘算法.由于Hammerstein系统模型的非线性特征,传统的递推最小二乘算法无法直接用来解决该系统的辨识问题.为此,论文将Hammerstein系统参数进行了映射变换,使得变换后的系统参数与Hammerst...     

A class of square root and division free algorithms andarchitectures for QRD-based adaptive signal processing

The least squares (LS) minimization problem constitutes the core of many real-time signal processing problems, such as adaptive filtering, system identification and adaptive beamforming. Recently efficient implementations of the recursive least squares (RLS) algorithm and the constrained recursive least squares (CRLS) algorithm based on the numerically stable QR decomposition (QRD) have been of great interest. Several papers have proposed modifications to the rotation algorithm that circumvent the square root operations and minimize the number of divisions that are involved in the Givens rotation. It has also been shown that all the known square root free algorithms are instances of one parametric algorithm. Recently, a square root free and division free algorithm has also been proposed. In this paper, we propose a family of square root and division free algorithms and examine its relationship with the square root free parametric family. We choose a specific instance for each one of the two parametric algorithms and make a comparative study of the systolic structures based on these two instances, as well as the standard Givens rotation. We consider the architectures for both the optimal residual computation and the optimal weight vector extraction. The dynamic range of the newly proposed algorithm for QRD-RLS optimal residual computation and the wordlength lower bounds that guarantee no overflow are presented. The numerical stability of the algorithm is also considered. A number of obscure points relevant to the realization of the QRD-RLS and the QRD-CRLS algorithms are clarified. Some systolic structures that are described in this paper are very promising, since they require less computational complexity (in various aspects) than the structures known to date and they make the VLSI implementation easier     

Frequency-selective fading channel estimation with a polynomialtime-varying channel model

A rectangular-windowed least-squares estimator using a polynomial model of the time-varying channel taps is proposed for estimating the impulse response of a frequency-selective fading channel. This method provides a significant improvement in mean square identification error (MSIE) over the conventional least mean squares (LMS) and the exponentially weighted recursive least squares (EW-RLS) algorithms without a polynomial model. A detailed study of the effects of channel parameters, such as the fading rate and the signal-to-noise ratio, on the proposed method is carried out. The performance of the method depends on the window size of the least squares estimator and the polynomial order being used. Algorithms to obtain the approximately optimal window size and polynomial order are proposed and are shown to perform well     

Fast adaptive algorithms for multichannel filtering and systemidentification

Fast transversal and lattice least squares algorithms for adaptive multichannel filtering and system identification are developed. Models with different orders for input and output channels are allowed. Four topics are considered: multichannel FIR filtering, rational IIR filtering, ARX multichannel system identification, and general linear system identification possessing a certain shift invariance structure. The resulting algorithms can be viewed as fast realizations of the recursive prediction error algorithm. Computational complexity is then reduced by an order of magnitude as compared to standard recursive least squares and stochastic Gauss-Newton methods. The proposed transversal and lattice algorithms rely on suitable order step-up-step-down updating procedures for the computation of the Kalman gain. Stabilizing feedback for the control of numerical errors together with long run simulations are included     

基于ALS协同过滤及频繁项挖掘的混合推荐算法

在信息技术日益发展的当下,不同类型的推荐算法在互联网行业的各领域有着广泛的应用。在目前使用较多的推荐算法中,部分侧重于基于评分的预测,也有部分是基于关联排序生成的推荐序列。本文设计一种混合推荐算法,将交替最小二乘法(ALS)计算的具体评分与Fp-growth的置信度相结合,融合两种算法的优势,从而实现推荐结果优化。基于Spark计算框架的实验表明,在选取合适的算法参数的情况下,这种改进的算法与交替最小二乘法(ALS)的原始结果相比,效率有较明显的提高,能够更准确的为用户做出个性化推荐。     

Rotation-based RLS algorithms: unified derivations, numericalproperties, and parallel implementations

This work presents a unified derivation of four rotation-based recursive least squares (RLS) algorithms. They solve the adaptive least squares problems of the linear combiner, the linear combiner without a desired signal, the single channel, and the multichannel linear prediction and transversal filtering. Compared to other approaches, the authors' derivation is simpler and unified, and may be useful to readers for better understanding the algorithms and their relationships. Moreover, it enables improvements of some algorithms in the literature in both the computational and the numerical issues. All algorithms derived in this work are based on Givens rotations. They offer superior numerical properties as shown by computer simulations. They are computationally efficient and highly concurrent. Aspects of parallel implementation and parameter identification are discussed     

Performance analysis of estimation algorithms of nonstationary ARMA processes

The correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive (AR), moving average (MA), and ARMA systems. By using estimation residuals in place of unmeasurable noise terms in information vector or matrix, we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity, ergodicity, or existence of higher order moments. Furthermore, we derive the conditions for convergence of the parameter estimation. The simulation results validate the convergence theorems proposed.