FAST RECURSIVE LEAST SQUARES LEARNING ALGORITHM FOR PRINCIPAL COMPONENT ANALYSIS

Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the proposed algorithm providing the capability of the fast convergence and high accuracy for extracting all the principal components. It is shown that all the information needed for PCA can be completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input-output product. The convergence performance of the proposed algorithm is briefly analyzed.The relation between Oja’s rule and the least squares learning rule is also established. Finally, a simulation example is given to illustrate the effectiveness of this algorithm for PCA.

CONVERGENCE AND STABILITY OF RECURSIVE DAMPED LEAST SQUARE ALGORITHM

The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. rt is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.

基于FFRLS和ASR-UKF滤波算法的锂电池SOC估计

锂电池在工作过程中,其内部参数易受多种因素影响,为提高锂电池在复杂环境下荷电状态(SOC)估计精度,以二阶戴维宁(Thevenin)等效模型为基础,结合遗忘因子递推最小二乘法(FFRLS)对模型参数进行在线辨识。针对传统卡尔曼滤波算法高度非线性及系统噪声不确定性等缺点,提出了一种自适应平方根无迹卡尔曼滤波(ASR-UKF)算法,该算法利用平方根算法处理均值和协方差,确保了状态协方差的半正定性和稳定性,并引入自适应滤波算法对噪声进行实时修正,消除了系统时变噪声影响。结果表明,FFRLS能有效解决数据饱和及算法矩阵计算量大的问题,等效模型精度高达98%。在混合动力脉冲特性(HPPC)测试和北京公交动态测试工况(BBDST)下,ASR-UKF算法SOC估计最大误差分别为3.264%和0.572%,具备更好的跟踪效果,验证了改进算法良好的收敛性与自适应性。

NEW EFFICIENT ORDER-RECURSIVE LEAST-SQUARES ALGORITHMS

Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.

基于FFRLS-SRUKF算法的锂电池SOC估计研究

传统无迹卡尔曼滤波在荷电状态(SOC)估计时主要面临两个问题:一是电池模型参数固定导致SOC估计精度低;二是协方差矩阵出现非正定时导致SOC估计失败。提出了遗忘因子递推最小二乘(FFRLS)算法结合平方根无迹卡尔曼滤波(SRUKF)的SOC估计算法。首先,建立二阶阻容(RC)等效电路模型。其次,利用FFRLS算法对电路模型参数在线辨识并实时修正电池等效电路模型,在此基础上使用SRUKF算法估计SOC。最后,通过间歇恒流脉冲放电和动态应力测试工况对所提算法进行验证。试验结果表明,该算法的平均绝对值误差低于0.0115、均方根误差低于0.012。与SRUKF算法相比,FFRLS-SRUKF算法具有更好的SOC估计性能,为电池管理系统解决锂电池的不一致性提供了可靠依据。

Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition

In this paper,a new recursive least squares(RLS)identification algorithm with variable-direction forgetting(VDF)is proposed for multi-output systems.The objective is to enhance parameter estimation performance under non-persistent excitation.The proposed algorithm performs oblique projection decomposition of the information matrix,such that forgetting is applied only to directions where new information is received.Theoretical proofs show that even without persistent excitation,the information matrix remains lower and upper bounded,and the estimation error variance converges to be within a finite bound.Moreover,detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition(VDF-ED).It is revealed that under non-persistent excitation,part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data,which could produce a more ill-conditioned information matrix than our proposed algorithm.Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.

Prediction of Time Series Empowered with a Novel SREKRLS Algorithm

For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.

A RESEARCH OF UWB RAKE RECEIVER BASED ON NOVEL RLS ADAPTIVE ALGORITHM

A modified RAKE receiver based on novel Recursive Least Squares （RLS） adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance of multipath receiving. It can also track the amplitude of the received signal to form a real-time amplitude estimation which is correlated with the power of excess delay bin. The simulation results based on the IEEE UltraWide Band （UWB） channel models （CMI to CM4） show that the novel RLS algorithm can alter the attenuation estimation with the finger＇s power delay profile, and RAKE receiver with few fingers can be employed to get high performance.

一种改进型KB-RLS算法在自适应干扰对消中的仿真分析

针对目前电子一体化平台收发系统间强自干扰在数字域的抑制问题,讨论了目前已有解决方案的可行性。同时基于经典递归最小二乘法(RLS)算法,将收敛因子改为关于误差的函数,提高了算法的精度;此外,在自相关矩阵的迭代过程中添加了自干扰项。仿真结果表明,该算法针对信噪比20 dB的100 MHz带宽的线性调频(LFM)信号,能取得23.03 dB的对消效果,相比经典RLS算法,该方法能更好地兼顾实际需求中收敛速度、收敛精度与算法适应性等要求。

TPC-BASED STBC MULTIUSER DETECTION WITH LSE-RLS ALGORITHM

The Bit Error Rate （BER） performance of a Turbo Product Code （TPC） based Space-Time Block Coding （STBC） multiuser wireless system in the frequency-selective channels has been investigated. Both of the good error correcting capability of TPC and the large diversity gain of STBC can be achieved simultaneously. A Least Square Error-Recursive Least Square （LSE-RLS） algorithm is applied to estimate the channel and cancel the interference. Simulations show that the proposed system can obtain about 2.7dB gain in Es/N0 at the BER of 10^-3.

Analysis and implementation of FURLS algorithm for active vibration control system with positive feedback

While positive feedback exists in an active vibration control system, it may cause instability of the whole system. To solve this problem, a feedforward adaptive controller is proposed based on the Fihered-U recursive least square （FURLS） algorithm. Algorithm development process is presented in this paper. Real time active vibration control experimental tests were done. The experiment resuits show that the active control algorithm proposed in this paper has good control performance for both narrow band disturbances and broad band disturbances.

Blind cancellation for frequency offset in OFDM system based on MCMA-RLS algorithm

Modified constant modulus and recursive least squares （MCMA-RLS） algorithm is proposed to cancel interference caused by the variable frequency offset （FO） in the orthogonal frequency division multiplexing （OFDM） system. The MCMA-RLS algorithm is composed of two stages including MCMA scheme and RLS scheme. MCMA is selected to pre-cancel the variable frequency offset firstly, and then the residual interference has been canceled by the RLS scheme. BR error rate is simulated to demonstrate that the proposed method is robust for canceling the variable frequency offset.

基于改进RLS算法的故障电流参数估计

由于故障电流中直流衰减分量的影响,快速准确地估计出故障电流参数并预测出可用的过零点成为故障电流相控开断的关键。将故障电流方程中指数项进行泰勒级数展开,保留前2项,并基于递推最小二乘法,估计电流参数。分析由泰勒级数展开引起的截断误差,提出时间常数补偿公式。利用Matlab软件对不含谐波和含有谐波两种情况下的故障进行仿真,结果表明:算法可在15 ms内得到足够精度的故障电流参数,电流过零点的预测精度在?0.2 ms以内。最后对故障录波数据的仿真结果证实了算法的效果。

一种改进RLS算法及其在SINS快速对准中的应用

在传统递推最小二乘算法(RLS)中,人为设置的递推初始值将导致状态估计的有偏性,也就丧失了最优性,当量测数据次数较小时尤为严重。摒弃了传统RLS算法"新估计值=旧估计值+修正值"的递推结构,提出了借助中间量进行递推,再由中间量直接作状态估计的改进算法。改进RLS算法状态估计结果与批处理LS算法完全一致,且无需初始状态的任何信息。将改进RLS算法应用于捷联惯导系统(SINS)初始对准。对于一定的初始对准精度要求,理论上改进RLS算法所需的初始对准时间是最短的。最后,SINS初始对准数值仿真结果验证了所提算法的正确性。

基于RLS的嵌入式永磁同步电机参数辨识技术

电机参数变化影响电机控制性能,因而需要对电机参数进行在线辨识,基于嵌入式永磁同步电机在两相坐标系里的动态状态方程,通过检测电机的定子电压、电流和转子转速信号,利用递推最小二乘法算法对嵌入式永磁同步电机参数进行辨识,由于该方法所用的信号均可检测到,从而减少了其他干扰对电机参数辨识的影响,提高了参数辨识的准确性。仿真结果和实验验证了辨识方案的有效性。

一种具有快速跟踪能力的改进RLS算法研究

为了改善固定遗忘因子递推最小二乘(RLS)算法在时变系统中的跟踪性能,提出一种改进的RLS算法。改进的可变遗忘因子RLS算法,不仅克服了固定遗忘因子RLS算法中跟踪速度和参数失调的矛盾,而且避免了当参数估值趋于参数真值时,卡尔曼增益趋于零,RLS算法失去对时变系统的跟踪能力的问题。最后,在MATLAB仿真平台下,对改进的RLS算法性能进行仿真验证。仿真结果表明,改进的算法能够获得快速的跟踪能力,也具有较快的收敛速度和较小的稳态误差。

基于RLS算法的并联型APF全局积分滑模变结构控制

针对并联型有源电力滤波器(active power filter,APF)谐波检测环节的延时和谐波电流跟踪环节的鲁棒性差、跟踪精度不高的问题,建立了系统解耦后的数学模型,提出了基于递归最小二乘(recursive least squares,RLS)算法的并联型APF全局积分滑模变结构控制策略。谐波检测环节采用改进的瞬时无功功率理论的id-iq法,用RLS自适应滤波器替换传统的Butterworth低通滤波器,解决了传统的Butterworth低通滤波器因延时而导致的一个基波周期(20 ms)内检测盲区问题。谐波电流跟踪环节采用全局积分滑模变结构控制方法,引入了全局积分滑模面,运用Lyapunov稳定性理论导出的控制律兼顾了全局滑模的快速性和积分滑模的准确性。在解决了谐波检测环节延时的情况下,将全局积分滑模控制策略与传统的PI控制和滞环控制对比,仿真实验结果表明:全局积分滑模控制对指令电流具有更高的跟踪精度,且具有更低的电网侧电流总谐波畸变率(total harmonic distortion,THD)。

基于小波变换的RLS波束成形算法研究

为了解决递归最小二乘算法(RLS)在较低信噪比(SNR)、遗忘因子较小的环境中,对噪声敏感、收敛时参数估计误差大的问题,引入小波变换去噪思想,提出了基于小波变换的RLS波束成形算法。该算法利用小波变换软阈值法进行信号去噪,再采用RLS算法进行波束成形。最后对实验进行仿真,仿真结果表明,与传统的RLS算法相比,该算法具有较小的稳态误差和较快的跟踪速度和收敛速度,并且波束成形效果好。

基于距离和DF-RLS的时间序列异常检测

为能同时检测时间序列中的附加异常和革新异常,改进自回归模型,提出距离因子递推最小二乘(DF-RLS)线性预测算法。在此基础上,给出一种基于距离和DF-RLS的联合异常检测方法——DDR-OD。实验结果表明,与当前其他时间序列异常检测方法相比,DDR-OD的检测效果较优。

基于RLS与EKF算法的锂电池SOC估计

准确估计荷电状态是电池管理系统高效和安全运行的关键因素之一。以Thevenin模型为基础,运用递推最小二乘法,对模型参数进行估计并且定期更新。采用扩展卡尔曼滤波算法实现了对锂电池荷电状态的估算。仿真结果表明,该估算策略能保持很高的精度,并对观测噪声有很强的抑制作用。