Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms

In this paper, a new parallel adaptive self-tuning recursive least squares (RLS) algorithm for time-varying system identification is first developed. Regularization of the estimation covariance matrix is included to mitigate the effect of non-persisting excitation. The desirable forgetting factor can be self-tuning estimated in both non-regularization and regularization cases. We then propose a new matrix forgetting factor RLS algorithm as an extension of the conventional RLS algorithm and derive the optimal matrix forgetting factor under some reasonable assumptions. Simulations are given which demonstrate that the performance of the proposed self-tuning and matrix RLS algorithms compare favorably with two improved RLS algorithms recently proposed in the literature.     

Bacterial foraging optimization and adaptive version for economically optimum sitting,sizing and harmonic tuning orders setting of LC harmonic passive power filters in radial distribution systems with linear and nonlinear loads

This paper presents bacterial foraging optimization (BFO) algorithm and its adaptive version to optimize the planning of passive harmonic filters (PHFs).The important problem of using PHFs is determining location, size and harmonic tuning orders of them, which is reach standard levels of harmonic distortion with applying minimum cost of passive filters.In this study to optimize the PHFs location, size and setting the harmonic tuning orders in the distribution system, considered objective function includes the reduction of power loss and investment cost of PHFs. At the same time, constraints include voltage limits, number/size of installed PHFs, limit candidate buses for PHFs installation and the voltage total harmonic distortion (THDv) in all buses. The harmonic levels of system are obtained by current injections method and the load flow is solved by the iterative method of power sum, which is suitable for the accuracy requirements of this type of study. It is shown that through an economical placement and sizing of PHFs the total voltage harmonic distortion and active power loss could be minimized simultaneously.The considered objective function is of highly non-convex manner, and also has several constraints. On the other hand due to significant computational time reduction and faster convergence of BFO in comparison with other intelligent optimization approach such as genetic algorithm (GA), particle swarm optimization (PSO) and artificial bee colony (ABC) the simple version of BFO has been implemented. Of course other versions of BFO such as Adaptive BFO and combination of BFO with other method due to complexity of harmonic optimization problem have not considered in this research.The simulation results for small scale test system with 10 buses, showed the significant computational time reduction and faster convergence of BFO in comparison with GA, PSO and ABC. Therefore in large scale radial system with 34 buses, the proposed method is solved using BFO.The simulation results for a 10-bus system as a small scale and 34-bus radial system as a large scale show that the proposed method is efficient for solving the presented problem.     

基于AKF和RLS的车辆簧载质量辨识研究

实际应用中,车辆负载会随着乘客和货物的变化而发生显著改变.提出结合自适应卡尔曼滤波器(AKF)与递推最小二乘算法(RLS)进行车辆簧载质量的在线辨识.首先,采集四分之一车辆悬架的簧载振动加速度、动行程及车轮垂向加速度信号,对车辆悬架系统中的簧载质量和车轮的绝对速度进行估计,进而由遗忘因子递推最小二乘算法辨识车辆簧载质量.分析了在不同路面等级下,卡尔曼滤波器的过程噪声协方差和测量噪声协方差对悬架状态估计精度的影响.仿真结果显示,在选取与车辆行驶路面等级匹配的过程噪声协方差和测量噪声协方差时,车辆悬架状态参数的估计精度较高,并能够在线准确地辨识得到车辆的簧载质量值.     

多算法结合的汽车参数和状态估计方法研究

为实时准确获取汽车参数及状态信息以提高汽车主动安全性能,提出了一种多算法结合的自适应估计算法。该算法将递推最小二乘算法、蚁群优化算法及容积卡尔曼滤波算法进行有效结合,同时将含有不准确模型参数及未知时变噪声的三自由度非线性整车模型作为标称模型。采用递推最小二乘算法实时估计汽车参数,引入蚁群优化算法实时跟踪容积卡尔曼滤波器的过程噪声及量测噪声,根据目标函数对噪声协方差进行寻优,以解决系统的噪声时变问题,从而获取汽车状态的准确估计。基于CarSim/Simulink的仿真实验结果表明,该算法的状态估计精度高,且具备汽车模型参数校正能力,可以满足系统的控制需要。     

Fault-Tolerant Recursive Least-Squares Computations on a Mesh-Connected Parallel Processor

Recursive least squares (RLS) is a popular iterative method used for the modeling of systems while in operation. RLS provides an estimate for unknown parameters of a system based on some known parameters and inputs and outputs of that system. This technique is used frequently in digital signal processing and control applications, where it is not possible to completely determine the current state of the system. The RLS procedure incurs intensive computations in every iteration of the algorithm. To implement RLS in situ at a reasonable sampling rate, the complexity of the system's model must be reduced, or the available computing power must be increased. This paper examines methods for increasing the computing power by implementing RLS algorithms on a parallel processing platform. While there has been a large body of research on using parallel processors for the computation of adaptive algorithms, little of this research has examined fault tolerant aspects. As fault tolerance is a critical aspect of any real-time system, this work will examine some factors that should be considered when implementing a real-time adaptive algorithm on a parallel processor system.     

TH-UWB系统中基于自适应算法的接收机研究

提出了一种适用于跳时超宽带(TH-UWB)系统中的RAKE接收机方案。该方法利用基于梯度的可变遗忘因子的改进递推最小二乘(RLS)算法进行信道估计,并与基于经典RLS算法和基于最大似然概率(ML)算法的接收机方案进行对比。结果表明,这种新型RAKE接收机方案能够更有效地跟踪时变衰落信道的变化;在相同条件下,该方案能够提高系统性能,获得更小的误码率(BER)。     

Bio-inspired fuzzy logic based tuning of power system stabilizer

In this paper, bacteria foraging optimization (BFO) – a bio-inspired technique, is utilized to tune the parameters of both single-input and dual-input power system stabilizers (PSSs). Conventional PSS (CPSS) and the three dual-input IEEE PSSs (PSS2B, PSS3B, and PSS4B) are optimally tuned to obtain the optimal transient performances. A comparative performance study of these four variants of PSSs is also made. It is revealed that the transient performance of dual-input PSS is better than single-input PSS. It is, further, explored that among dual-input PSSs, PSS3B offers superior transient performance. A comparison between the results of the BFO and that of genetic algorithm (GA) is conducted in this study. The comparison reveals that BFO is more effective than GA in finding the optimal transient performance. For on-line, off-nominal operating conditions Sugeno fuzzy logic (SFL) based approach is adopted. On real time measurements of system operating conditions, SFL adaptively and very fast yields on-line, off-nominal optimal stabilizer parameters.     

System Identification for a Miniature Helicopter at Hover Using Fuzzy Models

The objective of this paper is to present a system identification method suitable for miniature rotorcrafts under hovering. The proposed model to be identified is a Takagi-Sugeno fuzzy system, representing translational and rotational velocity dynamics. For parameter estimation of the Takagi-Sugeno system a classical Recursive Least Squares (RLS) algorithm is used, which allows identification to take place on-line since parameter updates are produced whenever a new measurement becomes available. The validity of this approach is tested using the X-Plane ^© flight simulator. Data obtained offer justification for the applicability of the approach in real-time applications.     

Recursive estimation methods for discrete systems

In system identification, the error evolution is composed of two decoupled parts: one is the identifying information on the current estimation residual, while the other is past arithmetic errors. Previous recursive algorithms only considered how to update current prediction errors. Up to now, research has mostly been based on recursive least-squares (RLS) methods. In this note, a general recursive identification method is proposed for discrete systems. Using this new algorithm, a recursive empirical frequency-domain optimal parameter (REFOP) estimate is established. The REFOP method has the advantage of resisting disturbance noise. Some simulations are included to illustrate the new method's reliability.     

State estimation in high-mix semiconductor manufacturing

The traditional way of state estimation in semiconductor manufacturing, known as “threaded” state estimation, segregates the process data into different bins and uses the ones that match the current event of the specific context information (such as tools, layers, products) to update the process state. The limitation of threaded state estimation is that a narrowly defined process stream can result in too many different threads and insufficient data for each thread. This limitation becomes more severe in high-mix manufacturing, where there can be many products and many tools. Hence there is great interest in estimation methods that utilize all available data in the analysis. In this work, the characteristics inherent in state estimation of high-mix semiconductor manufacturing processes are analyzed, and a general framework is introduced for the non-threaded state estimation methods, i.e., state estimation without segregating the process data into different bins. The framework is based on the best linear unbiased estimate (BLUE) of a simplified stationary singular Gauss–Markov process, and non-threaded state estimation methods based on the Kalman filter, least squares and recursive least squares (RLS) are analyzed using the general framework. Simulation examples are presented to illustrate the equivalence between different algorithms. As real processes are rarely stationary, modifications to the Kalman filter and RLS are discussed. We show that in non-threaded state estimation, how to regulate the estimate covariance plays a significant role in estimation performance. To handle nonstationary disturbances that often occur in semiconductor processes, Bayesian-enhanced adaptive versions of the Kalman filter and RLS are proposed. Both simulated and industrial nonstationary processes are used to demonstrate the effectiveness of the proposed adaptive methods.     

Accelerated Genetic Programming of Polynomials

An accelerated polynomial construction technique for genetic programming is proposed. This is a horizontal technique for gradual expansion of a partial polynomial during traversal of its tree-structured representation. The coefficients of the partial polynomial and the coefficient of the new term are calculated by a rapid recurrent least squares (RLS) fitting method. When used for genetic programming (GP) of polynomials this technique enables us not only to achieve fast estimation of the coefficients, but also leads to power series models that differ from those of traditional Koza-style GP and from those of the previous GP with polynomials STROGANOFF. We demonstrate that the accelerated GP is sucessful in that it evolves solutions with greater generalization capacity than STROGANOFF and traditional GP on symbolic regression, pattern recognition, and financial time-series prediction tasks.     

Bacterial Foraging Optimization Approach to Portfolio Optimization

In this paper we propose a heuristic approach based on bacterial foraging optimization (BFO) in order to find the efficient frontier associated with the portfolio optimization (PO) problem. The PO model with cardinality and bounding constraints is a mixed quadratic and integer programming problem for which no exact algorithms can solve in an efficient way. Consequently, various heuristic algorithms, such as genetic algorithms and particle swarm optimization, have been proposed in the past. This paper aims to examine the potential of a BFO algorithm in solving the PO problem. BFO is a new swarm intelligence technique that has been successfully applied to several real world problems. Through three operations, chemotaxis, reproduction, and elimination-dispersal, the proposed BFO algorithm can effectively solve a PO problem. The performance of the proposed approach was evaluated in computational tests on five benchmark data sets, and the results were compared to those obtained from existing heuristic algorithms. The proposed BFO algorithm is found to be superior to previous heuristic algorithms in terms of solution quality and time.     

A revisit to block and recursive least squares for parameter estimation

In this paper, the classical least squares (LS) and recursive least squares (RLS) for parameter estimation have been re-examined in the light of the present day computing capabilities. It has been demonstrated that for linear time-invariant systems, the performance of blockwise least squares (BLS) is always superior to that of RLS. In the context of parameter estimation for dynamic systems, the current computational capability of personal computers are more than adequate for BLS. However, for time-varying systems with abrupt parameter changes, standard blockwise LS may no longer be suitable due to its inefficiency in discarding “old” data. To deal with this limitation, a novel sliding window blockwise least squares approach with automatically adjustable window length triggered by a change detection scheme is proposed. Two types of sliding windows, rectangular and exponential, have been investigated. The performance of the proposed algorithm has been illustrated by comparing with the standard RLS and an exponentially weighted RLS (EWRLS) using two examples. The simulation results have conclusively shown that: (1) BLS has better performance than RLS; (2) the proposed variable-length sliding window blockwise least squares (VLSWBLS) algorithm can outperform RLS with forgetting factors; (3) the scheme has both good tracking ability for abrupt parameter changes and can ensure the high accuracy of parameter estimate at the steady-state; and (4) the computational burden of VLSWBLS is completely manageable with the current computer technology. Even though the idea presented here is straightforward, it has significant implications to virtually all areas of application where RLS schemes are used.     

基于RLS和EKF算法的全钒液流电池SOC估计

针对全钒液流电池的荷电状态(SOC)估计精度低、估计成本较高等问题,提出一种基于递推最小二乘算法(RLS)与扩展卡尔曼滤波算法(EKF)相结合的估计方法.该方法通过RLS算法辨识所建立的钒电池数学模型参数,通过EKF算法估计钒电池的SOC,将二者结合实现电池参数发生变化时准确估计钒电池的SOC.以5kW/ 30kWh的钒电池为对象,应用所提出的算法实现钒电池的SOC估计.结果表明,该算法可以准确估计钒电池的SOC,且可节省额外增加单片检测电池测量SOC的费用.     

基于可变遗忘因子RLS的盲多用户检测

对于直扩码分多址系统,本文提出了一种新的基于可变遗忘因子RLS的自适应盲多用户检测器,它能够自适应地估计检测向量,既具有对时变信道的快速跟踪能力,又具有较小的估计误差。最后通过仿真验证了该方法的有效性,与固定遗忘因子RLS盲多用户检测器相比,新算法具有更高的输出信干比,并且动态环境下的跟踪能力明显提高。另外还研究了参数对性能的影响,为参数的选择作出参考。     

Recursive subspace identification subject to relatively slow time-varying load disturbance

In this paper, a recursive subspace identification method is proposed to identify linear time-invariant systems subject to load disturbance with relatively slow dynamics. Using the linear superposition principle, the load disturbance response is decomposed from the deterministic-stochastic system response in the form of a time-varying parameter. To ensure unbiased estimation of the deterministic system matrices, a recursive least-squares (RLS) identification algorithm is established with a fixed forgetting factor, while another RLS algorithm with an adaptive forgetting factor is constructed based on the output prediction error to quickly track the time-varying parameter of load disturbance response. By introducing a deadbeat observer to represent the deterministic system response, two extended observer Markov parameter matrices are constructed for recursive estimation. Consequently, the deterministic matrices are retrieved from the identified system Markov parameter matrices. The convergence of the proposed method is analysed with a proof. Two illustrative examples are shown to demonstrate the effectiveness and merit of the proposed identification method.     

A new information-weighted recursive algorithm for time-varying systems: application to UAV system identification

This paper presents a new recursive identification method which can efficiently estimate time-varying parameters in discrete time systems and has significant advantages over standard recursive least-squares (RLS) method. This new information-weighted recursive algorithm for time-varying systems has three novel features, discounting of inaccurate estimates through weighting by the Information matrix, using the reuse of past data in computing current parameter estimates, a new tuneable damping factor parameter and a precisely designed compensation term to neutralise the estimation error caused by time-varying coefficients. A rigorous proof of convergence is also provided. Simulations show that the new algorithm significantly outperforms standard RLS, exhibiting better tracking performance and faster convergence. Flight tests on a T-REX 800 helicopter Unmanned Aerial Vehicle platform show that it gives system parameter estimates that are accurate enough and converge quickly enough that flight controllers can be designed in real-time based on the online identified model.     

改进的小波神经网络算法对变流器的故障诊断方法

变流器是双馈风力发电系统中的枢纽设备,其运行可靠性直接关系到发电系统的安全与稳定。针对基于递推最小二乘(RLS)算法的离散小波神经网络(DWNN)存在收敛速度慢、收敛精度不高、搜索局部极小等不足,以变流器的电流为分析对象,提出一种采用变加权和变学习率改进算法的小波神经网络的变流器故障诊断方法。选择变流器电流作为离散小波神经网络训练及故障识别样本,对训练过程和仿真结果进行对比分析。实验结果表明:较之RLS算法,改进的小波神经网络故障诊断方法在故障识别准确率和收敛时间方面表现更优。     

基于序贯最小二乘的多传感器误差配准方法

为实时估计多传感器系统偏差,针对广义最小二乘(GLS)配准方法不能实时估计传感器偏差的问题,提出了基于序贯最小二乘的多传感器误差估计方法,该方法在GLS配准模型基础上,采用最小二乘的序贯方法来估计系统偏差,不必存储过去的测量数据,能够实时估计系统偏差。仿真结果表明了该方法的有效性。     

TD-LTE下行发射分集自适应信道估计研究分析*

为了研究适用于TD-LTE系统下行信道发射分集模式下的信道估计算法,在基于离散分布的小区专用参考信号基础上分析了最小二乘（LS）和递归最小二乘（RLS）信道估计算法。为了简化MIMO信号检测的复杂度,针对发射分集模式提出了两种信道响应值的修正方法,改善的信道响应修正算法利用了时频域相关特性可以更好地跟踪信道变化。通过MATLAB在瑞利衰落信道下的仿真,表明RLS信道估计性能优于LS信道估计算法,而改善的信道响应修正算法能够进一步提高传统修正算法的性能。