Bias-eliminated Least-squares Method Research Articles

Realizations of BELS as WIV method in both direct and indirect closed-loop system identification

The bias eliminated least squares (BELS) method, which is known as efficient for unknown parameter estimation of transfer function in the correlated noise case, has been developed and applied effectively to the closed-loop system identification. In this paper, under the general settings, the realizations of the BELS method as a weighted instrumental variables (WIV) method in both direct and indirect closed-loop system identification are established through constructing an appropriate weighting matrix in the WIV method. The constructed structures are similar in both cases, which reveals that all the proof procedures of the two realizations are the same. Thus, the unified realizations of the BELS as the WIV method for the closed-loop system identification can be built. A simulation example is given to validate our theoretical analysis.

Least-squares parameter estimation of linear systems with noisy input–output data

This paper studies the computational efficiency of the bias-eliminated least-squares (BELS) method recently proposed for estimating linear systems in the presence of input and output noises. It is found that the BELS method based on expanding the denominator polynomial of the system transfer function by two dimensions may involve some redundant computations due to its handling of an augmented system model in its estimation scheme. To improve the computational efficiency, a direct estimation scheme is proposed to identify the underlying noisy input–output system. Numerical results show that the computational cost can be considerably reduced using such a new estimation scheme.

On the relation between a bias-eliminated least-squares (BELS) and an IV estimator in closed-loop identification

A bias-correction method for closed-loop identification, introduced in the literature as the bias-eliminated least-squares (BELS) method (Zheng & Feng, Automatica 31 (1995) 1019), is shown to be equivalent to a basic instrumental variable estimator applied to a predictor for the closed-loop system. This predictor is a function of the plant parameters and the known controller. Corresponding to the related method using a least-squares criterion, the method is referred to as the tailor-made IV method for closed-loop identification. The indicated equivalence greatly facilitates the understanding and the analysis of the BELS method.

On BELS parameter estimation method of transfer functions

Least squares (LS) method is the most widely used method for the parameter estimation. However when applying directly the LS method to estimate transfer function parameters in the presence of noise, the LS method becomes an asymptotically biased estimator and is unable to be a consistent estimator. There have been many studies to solve the problem of bias and one of them is bias-eliminated least-squares (BELS) method. BELS method is one of consistent estimation methods for unknown parameters of transfer functions. In this paper, we discuss the equivalence of BELS method and IV method under certain condition.

A bias-eliminated least-squares method for continuous-time model identification of closed-loop systems

Schemes for system identification based on closed-loop experiments have attracted considerable interest lately. However, most of the existing approaches have been developed for discrete-time models. In this paper, the problem of continuoustime model identification is considered. A bias correction method without noise modelling associated with the Poisson moment functionals approach is presented for indirect identification of closed-loop systems. To illustrate the performances of the proposed method, the bias-eliminated least-squares algorithm is applied to the parameter estimation of a simulated system via Monte Carlo simulations.

Identification of a class of dynamic errors‐in‐variables models

AbstractDynamic errors‐in‐variables (EV) models are a new type of linear system models and have found extensive practical applications. One common and important concern with EV models is how to remove noise‐induced bias in parameter estimators. In this paper some significant extensions to the newly established bias‐eliminated least‐squares (BELS) method are made, so that this BELS method can be applied to unbiased identification of a general class of dynamic EV models where input noise is white noise and output noise is correlated noise but the noise statistics are unknown a priori. Though still based on the bias correction principle, this method is very meaningful in that it presents a novel and efficient way of utilizing signal‐processing techniques to draw much more useful information from sampled data in order to get desirable identification results. The performance of the proposed method is illustrated by numerical examples.

Unbiased parameter estimation of linear systems in the presence of input and output noise

AbstractIt is well known that in practical situations the observed input‐output data of an identified plant are usually corrupted by measurement noise. In this case the ordinary least‐squares estimator of the system parameters is biased. In order to obtain a consistent estimator, a new type of modified least‐squares estimation method, which is called the bias‐eliminated least‐squares (BELS) method, is presented in this paper. It is shown that the estimation bias can be determined if the variance of the white measurement noise can be obtained accurately. A designed first‐order prefilter is connected in parallel to the input of the identified system. Based on asymptotic analysis, the noise variance can be estimated correctly by using the processed sampled data. Both a batch algorithm and a recursive algorithm are presented. It is shown that the presented BELS method gives a consistent estimate without a priori knowledge of the variance of the white input and output noise. Simulation results are presented to support the theoretical discussions.