Bias-compensated Least-squares Research Articles

Bias-compensated least squares and fuzzy PSO based hierarchical identification of errors-in-variables Wiener systems

This paper investigates the parameter estimation of errors-in-variables Wiener (EIV-W) nonlinear systems. In such nonlinear systems, both input and output contain interference noises, and some intermediate processes are also interfered by noises. The hierarchical technology is applied to decompose the whole system into two subsystems firstly. For the linear subsystem, in order to obtain unbiased estimates of model parameters, a bias compensation method is introduced. Then, the bias-compensated least squares (BLS) algorithm is proposed. For the nonlinear subsystem, on the basis of particle swarm optimisation (PSO), the fuzzy control technology is added to improve the ability of jumping out of the local optimum. Thus, a bias-compensated least squares and fuzzy PSO based hierarchical (BLS-FPSO-H) method is derived at last. In simulation, a numerical example and a case study about the carbon fibre stretching process are implemented. Results indicate that the BLS-FPSO-H algorithm can effectively identify EIV-W nonlinear systems, the convergence speed and identification accuracy are greatly improved than the basic PSO method and some other PSO variants.

BCLS Method for Stationary Systems in Closed Loop Environment

This paper proposes a bias-compensated least squares (BCLS) method in closed loop environment where the noise is assumed to be stationary. The feedback controller is assumed to be linear, time-inva...

Relations between Bias-Eliminating Least Squares, the Frisch scheme and Extended Compensated Least Squares methods for identifying errors-in-variables systems

There are many methods for identifying errors-in-variables systems. Among them Bias-Eliminating Least Squares (BELS), the Frisch scheme and Extended Compensated Least Squares (ECLS) methods are attractive approaches because of their simplicity and good estimation accuracy. These three methods are all based on a Bias-Compensated Least-Squares (BCLS) principle. In this paper, the relationships between them are considered. In particular, the set of nonlinear equations utilized in these three methods are proved to be equivalent under different noise conditions also for finite samples. It is shown that BELS, Frisch and ECLS methods have the same asymptotic estimation accuracy providing the same extended vector is used.

Bias-compensated Least Squares Method in Closed Loop Environment

In this paper, a bias-compensated least squares (BCLS) method in the closed loop environment is proposed. It is assumed that the observation noise is a white gaussinan signal while there are no process noises. It is also assumed that the plant is controlled by a linear time invariant controller and that the closed loop system is asymptotically stable. The proposed estimator is unbiased and it does not require the reference input be informative. An iterative redesign of the prefilters is also considered in order to achieve a minimum variance estimator. The proposed BCLS method is applied for the iterative redesign of the prefilters in order to reduce the computational cost.

Bias-compensation based method for errors-in-variables model identification

It is well known that least-squares (LS) method gives biased parameter estimates when the input and output measurements are corrupted by noise. One possible approach for solving this bias problem is the bias-compensation based method such as the bias-compensated least-squares (BCLS) method. In this paper, a new bias-compnesation based method is proposed for identification of noisy input-output system. The proposed method is based on compensation of asymptotic bias on the instrumental variables type (IV-type) estimates by making use of noise covariances estimates. In order to obtain the noise covariances estimates, an overdetermined system of equations is introduced, and the noise covariances estimation algorithm is derived by solving this overdetermined system of equations. From the combination of the parameter estimation algorithm and the noise covariances estimation algorithm, the proposed bias-compensated instrumental variables type (BCIV-type) method can be established. The results of a simulated example indicate that the proposed algorithm provides good estimates.

A Bias-Compensated Identification Approach for Noisy FIR Models

A new bias-compensated least-squares method for identifying finite impulse response (FIR) models whose input and output are affected by additive white noise is proposed. By exploiting the statistical properties of the equation error of the noisy FIR system, an estimate of the input noise variance is obtained and the noise-induced bias is removed. The results obtained by means of Monte Carlo simulations show that the proposed algorithm outperforms other bias-compensated approaches and allows to obtain an estimation accuracy comparable to that of total least-squares without requiring the a priori knowledge of the input-output noise variance ratio.

閉ループ環境におけるバイアス補償型最小二乗法

In this paper, bias-compensated least squares(BCLS) method is proposed in order to estimate a plant under feedback control when the noise is colored. The feedback controller is a ssumed to be linear time invariant discrete-time system and the feedback system is assumed to be a symptotically stable. The aim of the proposed method is to reduce the computational cost which will be required for the conventional method.

On Bias-Compensated Least-Squares Methods Using α-filter and β-filter

On Bias-Compensated Least-Squares Methods Using α-filter and β-filter

IDENTIFICATION OF NOISY INPUT-OUTPUT SYSTEM USING BIAS-COMPENSATED LEAST-SQUARES METHOD

In this paper, a new bias-compensated least-squares (BCLS) based algorithm is proposed for identification of noisy input-output system. It is well known that BCLS method is based on compensation of asymptotic bias on the least-squares (LS) estimates by making use of noise variances estimates. The main feature of the proposed algorithm is to introduce a generalized least-squares type estimator in order to obtain the good estimates of noise variances. The results of a simulated example indicate that the proposed algorithm provides good estimates.

A NEW ESTIMATION APPROACH FOR AR MODELS IN PRESENCE OF NOISE

This paper considers the problem of estimating the parameters of an autoregressive (AR) process in presence of additive white noise and proposes a new identification method, based on theoretical results originally developed in errors-in-variables contexts. This approach allows to estimate the AR parameters, the driving noise variance and the variance of the additive noise in a congruent way in that these estimates assure the positive definiteness of the autocorrelation matrix. The performance of the proposed algorithm is compared with that of bias-compensated least-squares methods by means fo Monte Carlo simulations. The results show the effectivenesss of the new method also in presence of high amounts of noise.

On the Parameter Estimation of Pulse Transfer Function In the Presence of Input and Output Noise

Many identification methods are based on the assumption that input measurement is noise-free. However, this condition is not satisfied in most practical situations. In the presence of input noise, those methods have been shown to give erroneous results. Bias-compensated least-squares method is a consistent estimation method for unknwon parameters of pulse transfer function in the presence of input and output noise. The method is based on compensation of asymptotic bias on the least-squares estimates by making use of noise variances estimates. In this paper, a new type of noise variances estimation method is proposed to overcome drawbacks of previously proposed methods. The main feature of proposed method is to introduce a generalized least-squares type estimator in order to estimate noise variances. The results of a simulated example indicate that the proposed method provides good estimates.

Bias-Compensated Least-Squares Estimation and Parameter Transformation in Identification with Over-Parameterized Models

For the problem of estimating unknown parameters of the transfer function model from input and output (I/O) data contaminated by colored measurement noise, a three-step estimation procedure has been previously proposed to exploit the I/O correlation information with respect to the correlation time. This paper analyzes this procedure from the compatibility between the parameter transformation and the bias-compensated least-squares (BCLS) estimation used in the third step. The transformation is made from the over-parameterized model in the first and second steps to the final model with the true order in the final step, and is based on the minimization of the mean square error (MSE) between the outputs of the two models. The BCLS estimation is based on the minimization of MSE between the final model output and the process output. It is verified that the condition for compatibility, i.e. the equivalence of two minimizations, is a consequence of the two over-parameterized estimation equations in the first two steps, and that the over-parameterization assures an inclusive expansion of the I/O correlation information. Simulation results are presented to demonstrate the equivalence.

A Three-Step Estimation Procedure for the Pulse Transfer Function from the Viewpoint of a Reductive Parameter Transformation

The problem is considered of estimating unknown parameters in the pulse transfer function by using estimates of the noise auto-correlation function, from input and output data corrupted by colored noise. The three-step estimation procedure has already been proposed to obtain improved parameter estimates in the final step, by making good use of the extended input/output correlation functions. For quantitatively evaluating this procedure, the reductive parameter transformation from the first step to the final step is introduced. Then, the final parameter estimates hold the good properties of satisfying the minimum error criteria not only for the parameter transformation but also for the bias-compensated least-squares estimation.

Identification of Continuous Systems from Noisy Sampled Input-Output Data

The problem of identification of continuous systems is considered when both the discrete input and output measurements are contaminated by white noises. Using a pre-designed digital filter, a discrete-time estimation model is constructed easily without direct approximations of system signal derivatives. If the pass-band of the filter is designed so that it includes the main frequencies of both the system input and output signals in some range, the noise effects are sufficiently reduced, accurate estimates can be obtained by least squares(LS) algorithm in the presence of low measurement noises. Two classes of filters (infinite impulse response(IIR) filter and finite impulse response(FIR) filter) are employed. The former requires less computational burden and memory than the latter while the latter is suitable for the bias compensated least squares(BCLS) method, which compensates the bias of the LS estimate by the estimates of the input-output noise variances and thus yields unbiased estimates in the presence of high noises.

On the Bias-Compensated Least-Squares Estimation for Identification of Continuous Systems

For the identification of continuous-time systems from sampled data, digital filters(IIR filter or FIR filter) have been introduced to avoid direct approximations of system signal derivatives. The filter, however, will cause a computational difficulty in the bias compensation algorithm. In this paper, an analytical expression for the asymptotic biases of least squares estimates is given for the case where the IIR digital filter is used. The feasibility of the bias compensated least squares (BCLS) algorithm with the expression is shown by a simulation study.

Identification of Pulse Transfer Function in the Presence of Input and Output Noise

The numerical instabilities of the bias compensated least-squares (BCLS) algorithm are discussed in the case where input and output measurements are corrupted by white noise. For improving the stability of BCLS algorithm, an estimator constructed by filtered data vectors is developed. The identifiability in the special case where input signal is white is also discussed. Some simulation results are presented to demonstrate the numerical robustness of the proposed BCLS algorithm

Parameter Estimation of AR Process via Bias Compensated Least Squares Method

A new algorithm is proposed to estimate parameters of autoregressive (AR) processes with output data corrupted by white noise. This algorithm is based on the bias compensated least-squares (BCLS) principle which is introduced by Sagara and Wada for estimation of pulse transfer function models. The BCLS method requires the estimate of the unknown variance of the noise to compensate the biases of the LS estimates. For this end, a variance estimation algorithm is developed to obtain the consistent estimate. This algorithm is joined with the BCLS algorithm to provide consistent estimates of the AR parameters. The algorithm proposed here is a modified version of Sakai and Arase's algorithm which often gives negative values of the variance estimate. Several simulation results indicate that the proposed algorithm is more effective than Sakai and Arase's from statistical and computational points of view.