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.

Modelling of wind power forecasting errors based on kernel recursive least-squares method

Forecasting error amending is a universal solution to improve short-term wind power forecasting accuracy no matter what specific forecasting algorithms are applied. The error correction model should be presented considering not only the nonlinear and non-stationary characteristics of forecasting errors but also the field application adaptability problems. The kernel recursive least-squares(KRLS) model is introduced to meet the requirements of online error correction. An iterative error modification approach is designed in this paper to yield the potential benefits of statistical models, including a set of error forecasting models. The teleconnection in forecasting errors from aggregated wind farms serves as the physical background to choose the hybrid regression variables. A case study based on field data is found to validate the properties of the proposed approach. The results show that our approach could effectively extend the modifying horizon of statistical models and has a better performance than the traditional linear method for amending short-term forecasts.

Natural gradient-based recursive least-squares algorithm for adaptive blind source separation

This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA), and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyses of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Non-Recursive Base Conversion Using a Deterministic Markov Process

We prove that non-recursive base conversion can always be implemented by using a deterministic Markov process. Our paper discusses the pros and cons of recursive and non-recursive methods, in general. And we include a comparison between non-recursion and a deterministic Markov process, proving that the Markov process is twice as efficient.

Poststack reverse-time migration using a non-reflecting recursive algorithm on surface relief

Presently the research based on the accurate seismic imaging methods for surface relief, complex structure, and complicated velocity distributions is of great significance. Reverse-time migration is considered to be one of highly accurate methods. In this paper, we propose a new non-reflecting recursive algorithm for reverse-time migration by introducing the wave impedance function into the acoustic wave equation and the algorithm for the surface relief case is derived from the coordinate transformation principle. Using the exploding reflector principle and the zero-time imaging condition of poststack reverse- time migration, poststack numerical simulation and reverse-time migration with complex conditions can be realized. The results of synthetic and real data calculations show that the method effectively suppresses unwanted internal reflections and also deals with the seismic imaging problems resulting from surface relief. So, we prove that this method has strong adaptability and practicality.

Calculation connectivity reliability of road networks based on recursive decomposition arithmetic

In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.

Least-Squares及Galerkin谱元方法求解环形区域内的泊松方程

为研究基于Least-Squares变分及Galerkin变分两种形式的谱元方法的求解特性,推导了极坐标系中采用两种变分方法求解环形区域内Poisson方程时对应的弱解形式,采用Chebyshev多项式构造插值基函数进行空间离散,得到两种谱元方法对应的代数方程组,由此分析了系数矩阵结构的特点。数值计算结果显示:Least-Squares谱元方法为实现方程的降阶而引入新的求解变量,使得代数方程组形式更为复杂,但边界条件的处理比Galerkin谱元方法更为简单;两种谱元方法均能求解极坐标系中的Poisson方程且能获得高精度的数值解,二者绝对误差分布基本一致;固定单元内的插值阶数时,增加单元数可减小数值误差,且表现出代数精度的特点,误差降低速度较慢,而固定单元数时,在一定范围内数值误差随插值阶数的增加而减小的速度更快,表现出谱精度的特点;单元内插值阶数较高时,代数方程组系数矩阵的条件数急剧增多,方程组呈现病态,数值误差增大,这一特点限制了单元内插值阶数的取值。研究内容对深入了解两种谱元方法在极坐标系中求解Poisson方程时的特点、进一步采用相关分裂算法求解实际流动问题具有参考价值。

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.

Recursive Least Square Vehicle Mass Estimation Based on Acceleration Partition

Vehicle mass is an important parameter in vehicle dynamics control systems. Although many algorithms have been developed for the estimation of mass, none of them have yet taken into account the different types of resistance that occur under different conditions. This paper proposes a vehicle mass estimator. The estimator incorporates road gradient information in the longitudinal accelerometer signal, and it removes the road grade from the longitudinal dynamics of the vehicle. Then, two different recursive least square method （RLSM） schemes are proposed to estimate the driving resistance and the mass independently based on the acceleration partition under different conditions. A 6 DOF dynamic model of four In-wheel Motor Vehicle is built to assist in the design of the algorithm and in the setting of the parameters. The acceleration limits are determined to not only reduce the estimated error but also ensure enough data for the resistance estimation and mass estimation in some critical situations. The modification of the algorithm is also discussed to improve the result of the mass estimation. Experiment data on asphalt road, plastic runway, and gravel road and on sloping roads are used to validate the estimation algorithm. The adaptability of the algorithm is improved by using data collected under several critical operating conditions. The experimental results show the error of the estimation process to be within 2.6%, which indicates that the algorithm can estimate mass with great accuracy regardless of the road surface and gradient changes and that it may be valuable in engineering applications. This paper proposes a recursive least square vehicle mass estimation method based on acceleration partition.

FOUR-PARAMETER AUTOMATIC TRANSMISSION TECHNOLOGY FOR CONSTRUCTION VEHICLE BASED ON ELMAN RECURSIVE NEURAL NETWORK

From the viewpoint of energy saving and improving transmission efficiency, the ZL50E wheel loader is taken as the study object. And the system model is analyzed based on the transmission system of the construction vehicle. A new four-parameter shift schedule is presented, which can keep the torque converter working in the high efficiency area. The control algorithm based on the Elman recursive neural network is applied, and four-parameter control system is developed which is based on industrial computer. The system is used to collect data accurately and control 4D180 power-shift gearbox of ZL50E wheel loader shift timely. An experiment is done on automatic transmission test-bed, and the result indicates that the control system could reliably and safely work and improve the efficiency of hydraulic torque converter. Four-parameter shift strategy that takes into account the power consuming of the working pump has important operating significance and reflects the actual working status of construction vehicle.

New recursive algorithm for matrix inversion

To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.

Piecewise linear recursive convolution FDTD method for magnetized plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method greatly improves accuracy over the original recursive convolution （RC） FDTD approach but retains its speed and efficiency advantages. A PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time is presented, enabled the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations the reflection and transmission coefficients through a magnetized plasma layer. The results show that the PLRC-FDTD method has significantly improved the accuracy over the original RC method.

Regularized least-squares migration of simultaneous-source seismic data with adaptive singular spectrum analysis

Simultaneous-source acquisition has been recog- nized as an economic and efficient acquisition method, but the direct imaging of the simultaneous-source data produces migration artifacts because of the interference of adjacent sources. To overcome this problem, we propose the regularized least-squares reverse time migration method （RLSRTM） using the singular spectrum analysis technique that imposes sparseness constraints on the inverted model. Additionally, the difference spectrum theory of singular values is presented so that RLSRTM can be implemented adaptively to eliminate the migration artifacts. With numerical tests on a fiat layer model and a Marmousi model, we validate the superior imaging quality, efficiency and convergence of RLSRTM compared with LSRTM when dealing with simultaneoussource data, incomplete data and noisy data.

Recursive Partitioning Analysis Classification and Graded Prognostic Assessment for Non-Small Cell Lung Cancer Patients with Brain Metastasis:A Retrospective Cohort Study

Objective：To assess prognostic factors and validate the effectiveness of recursive partitioning analysis （RPA） classes and graded prognostic assessment （GPA） in 290 non-small cell lung cancer （NSCLC） patients with brain metastasis （BM）.Methods：From Jan 2008 to Dec 2009,the clinical data of 290 NSCLC cases with BM treated with multiple modalities including brain irradiation,systemic chemotherapy and tyrosine kinase inhibitors （TKIs） in two institutes were analyzed.Survival was estimated by Kaplan-Meier method.The differences of survival rates in subgroups were assayed using log-rank test.Multivariate Cox＇s regression method was used to analyze the impact of prognostic factors on survival.Two prognostic indexes models （RPA and GPA） were validated respectively.Results：All patients were followed up for 1-44 months,the median survival time after brain irradiation and its corresponding 95% confidence interval （95% CI） was 14 （12.3-15.8） months.1-,2-and 3-year survival rates in the whole group were 56.0%,28.3%,and 12.0%,respectively.The survival curves of subgroups,stratified by both RPA and GPA,were significantly different （P0.001）.In the multivariate analysis as RPA and GPA entered Cox＇s regression model,Karnofsky performance status （KPS） ≥ 70,adenocarcinoma subtype,longer administration of TKIs remained their prognostic significance,RPA classes and GPA also appeared in the prognostic model.Conclusion：KPS ≥70,adenocarcinoma subtype,longer treatment of molecular targeted drug,and RPA classes and GPA are the independent prognostic factors affecting the survival rates of NSCLC patients with BM.

Recursive State-space Model Identification of Non-uniformly Sampled Systems Using Singular Value Decomposition

In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are considered for identification. In the case of state measurement, an identification algorithm based on the singular value decomposition(SVD) is developed to estimate the model parameter matrices by using the least-squares fitting. In the case of output measurement only, another identification algorithm is given by combining the SVD approach with a hierarchical identification strategy. An example is used to demonstrate the effectiveness of the proposed identification method.

Fast recursive algorithm for two-dimensional Tsallis entropy thresholding method

Recently, a two-dimensional （2-D） Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O（L2） from O（L4）. The effectiveness of the proposed algorithm is illustrated by experimental results.

Research on SINS Error Recursive Model of Ballistic Missile

The strap-down inertial navigation system (SINS) error of ballistic missile is generated by the mutual influence of gyroscope and accelerometer, and the recursive model is completely different from that of gimbaled INS. In the paper, a discrete error recursive model was obtained by studying the applied SINS error model of ballistic missile, and the discrete Kalman filtering simulation based on the model was carried out. The simulated results show that the model can depict the SINS error exactly and provide the advantages for research on integrated guidance and improved hit accuracy.

Single Point Positioning with Sequential Least-Squares Filter and Estimated Real-Time Stochastic Model

To obtain higher accurate position estimates, the stochastic model is estimated by using residual of observations, hence, the stochastic model describes the noise and bias in measurements more realistically. By using GPS data and broadcast ephemeris, the numerical results indicating the accurate position estimates at sub-meter level are obtainable.

Mixed-Weights Least-Squares Stable Predictive Control Algorithm with Soft and Hard Constraints

Mixed-weight least-squares (MWLS) predictive control algorithm, compared with quadratic programming (QP) method, has the advantages of reducing the computer burden, quick calculation speed and dealing with the case in which the optimization is infeasible. But it can only deal with soft constraints. In order to deal with hard constraints and guarantee feasibility, an improved algorithm is proposed by recalculating the setpoint according to the hard constraints before calculating the manipulated variable and MWLS algorithm is used to satisfy the requirement of soft constraints for the system with the input constraints and output constraints. The algorithm can not only guarantee stability of the system and zero steady state error, but also satisfy the hard constraints of input and output variables. The simulation results show the improved algorithm is feasible and effective.