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.

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.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

A New Recursive Parameter Estimation Algorithm of Multi－Variable Time－Varying AR Model

A new recursive algorithm of multi variable time varying AR model is proposed. By changing the form of AR model, the parameter estimation can be regarded as state estimation of state equations. Then the Kalman filter is used to estimate the variation of

A RECURSIVE ALGORITHM AND ITS CONVERGENCE FOR PARAMETER ESTIMATION OF CONVOLUTION MODEL

In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.

Recursive estimation algorithms for power controls of wireless communication networks

Power control problems for wireless communication networks are investigated in direct-sequence codedivision multiple-access （DS/CDMA） channels. It is shown that the underlying problem can be formulated as a constrained optimization problem in a stochastic framework. For effective solutions to this optimization problem in real time, recursive algorithms of stochastic approximation type are developed that can solve the problem with unknown system components. Under broad conditions, convergence of the algorithms is established by using weak convergence methods.

Fusion of Absolute and Recursive Information to Overcome Jitter and Occlusion in ARToolKit System

According to the most mature marker based augmented reality system ARToolKit only utilizes absolute information in pose estimation, a novel technique is presented in this paper. The proposed method embeds the recursive information as well to make ARToolKit system smoother by eliminating the jitter and more robust to occlusion conditions. Experiments on the jitter improvement has been performed, the results show that the proposed method is very effective.

BLOCK ADAPTIVE RECURSIVE ALGORITHM FOR VIDEO CONFERENCE CODING

This paper presents a new motion estimation algorithm for video conference signal coding. This type of algorithm is called block adaptive recursive algorithm (BARA). Simulation results show that this new algorithm has better performance than conventional ones.

Modified Recursive Least Squares Algorithm with Variable Parameters and Resetting for Time-Varying System

Based on the idea of the set-membership identification, a modified recursive least squares algorithm with variable gain, variable forgetting factor and resetting is presented. The concept of the error tolerance level is proposed. The selection criteria of the error tolerance level are also given according to the min-max principle. The algorithm is particularly suitable for tracing time-varying systems and is similar in computational complexity to the standard recursive least squares algorithm. The superior performance of the algorithm is verified ma simulation studies on a dynamic fermentation process.

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR A CLASS OF STOKES EQUATION

A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.

Distributed Dynamic Load in Structural Dynamics by the Impulse-Based Force Estimation Algorithm

This paper proposes a novel approach for identifying distributed dynamic loads in the time domain.Using polynomial andmodal analysis,the load is transformed intomodal space for coefficient identification.This allows the distributed dynamic load with a two-dimensional form in terms of time and space to be simultaneously identified in the form of modal force,thereby achieving dimensionality reduction.The Impulse-based Force Estimation Algorithm is proposed to identify dynamic loads in the time domain.Firstly,the algorithm establishes a recursion scheme based on convolution integral,enabling it to identify loads with a long history and rapidly changing forms over time.Secondly,the algorithm introduces moving mean and polynomial fitting to detrend,enhancing its applicability in load estimation.The aforementioned methodology successfully accomplishes the reconstruction of distributed,instead of centralized,dynamic loads on the continuum in the time domain by utilizing acceleration response.To validate the effectiveness of the method,computational and experimental verification were conducted.

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.

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.

Online LS-SVM for function estimation and classification

An online algorithm for training LS-SVM (Least Square Support VectorMachines) was proposed for the application of function estimation and classification. Online LS-SVMmeans that LS-SVM can be trained in an incremental way, and can be pruned to get sparseapproximation in a decremental way. When a SV (Support Vector) is added or removed, the onlinealgorithm avoids computing large-scale matrix inverse. Thus the computation cost is reduced. Onlinealgorithm is especially useful to realistic function estimation problem such as systemidentification. The experiments with benchmark function estimation problem and classificationproblem show the validity of this online algorithm.

Dynamic Event-triggered State Estimation for Nonlinear Coupled Output Complex Networks Subject to Innovation Constraints

Dear editor,This letter investigates the recursive state estimation(RSE)problem for a class of coupled output complex networks via the dynamic event-triggered communication mechanism(DETCM)and innovation constraints(ICs).Firstly,a DETCM is employed to regulate the transmission sequences.Then,in order to improve the reliability of network communication,a saturation function is introduced to constrain the measurement outliers.A new RSE method is provided such that,for all output coupling,DETCM and ICs,an upper bound of state estimation error covariance(SEEC)is presented in a recursive form,whose trace can be minimized via parameterizing the state estimator gain matrix(SEGM).Moreover,the theoretical analysis is given to guarantee that the error dynamic is uniformly bounded.Finally,a simulation example is illustrated to show the effectiveness of the proposed RSE method.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

An Adaptive Channel Estimation Technique in MIMO OFDM Systems

In this paper, an adaptive channel estimation for MIMO OFDM is proposed. A set of pilot tones first are placed in each OFDM block, then the channel frequency response of these pilot tones are adaptively estimated by reeursive least squares （RLS） directly in frequency domain not in time domain. Then after the estimation of the channel frequency response of pilot tones, to obtain the channel frequency response of data tones, a new interpolation method based on DFT different from traditional linear interpolation method according to adjacent pilot tones is proposed. Simulation results show good performance of the technique.

HMM-based noise estimator for speech enhancement

A noise estimator was presented in this paper by modeling the log-power sequence with hidden Markov model （HMM）. The smoothing factor of this estimator was motivated by the speech presence probability at each frequency band. This HMM had a speech state and a nonspeech state, and each state consisted of a unique Gaussian function. The mean of the nonspeech state was the estimation of the noise logarithmic power. To make this estimator run in an on-line manner, an HMM parameter updated method was used based on a first-order recursive process. The noise signal was tracked together with the HMM to be sequentially updated. For the sake of reliability, some constraints were introduced to the HMM. The proposed algorithm was compared with the conventional ones such as minimum statistics （MS） and improved minima controlled recursive averaging （IM- CRA）. The experimental results confirms its promising performance.

A SPECTRAL ESTIMATION ALGORITHM USING THE HOUSEHOLDER TRANSFORM

Householder transform is used to triangularize the data matrix, which is basedon the near prediction error equation. It is proved that the sum of squared residuals for eachAR order can be obtained by the main diagonal elements of upper triangular matrix, so thecolumn by column procedure can be used to develop a recursive algorithm for AR modeling andspectral estimation. In most cases, the present algorithm yields the same results as the covariancemethod or modified covariance method does. But in some special cases where the numerical ill-conditioned problems are so serious that the covariance method and modified covariance methodfail to estimate AR spectrum, the presented algorithm still tends to keep good performance. Thetypical computational results are presented finally.