Adaptive parameter estimation for a general dynamical system with unknown states

This paper is concerned with the design of a state filter for a time‐delay state‐space system with unknown parameters from noisy observation information. The key is to investigate new identification algorithms for interactive state and parameter estimation of the considered system. Firstly, an observability canonical state‐space model is derived from the original model by linear transformation for the purpose of simplifying the model structure. Secondly, a direct state filter is formulated by minimizing the state estimation error covariance matrix on the basis of the Kalman filtering principle. Thirdly, once the unknown states are estimated, a state filter–based recursive least squares algorithm is proposed for parameter estimation using the least squares principle. Then, a state filter–based hierarchical least squares algorithm is derived by decomposing the original system into several subsystems for improving the computational efficiency. Finally, the numerical examples illustrate the effectiveness and robustness of the proposed algorithms.     

Fast parametric imaging algorithm for dual-input biomedical system parameter estimation

Medical parametric imaging with dynamic positron emission tomography (PET) plays an increasingly potential role in modern biomedical research and clinical diagnosis. The key issue in parametric imaging is to estimate parameters based on sampled data at the pixel-by-pixel level from certain dynamic processes described by valid mathematical models. Classic nonlinear least squares (NLS) algorithm requires a "good" initial guess and the computational time-complexity is high, which is impractical for image-wide parameter estimation. Although a variety of fast parametric imaging techniques have been developed, most of them focus on single input systems, which do not provide an optimal solution for dual-input biomedical system parameter estimation, which is the case of liver metabolism. In this study, a dual-input-generalized linear least squares (D-I-GLLS) algorithm was proposed to identify the model parameters including the parameter in the dual-input function. Monte Carlo simulation was conducted to examine this novel fast algorithm. The results of the quantitative analysis suggested that the proposed technique could provide comparable reliability of the parameter estimation with NLS fitting and accurately identify the parameter in the dual-input function. This method may be potentially applicable to other dual-input biomedical system parameter estimation as well.     

A demonstration of pharmacokinetics and physiological modelling using a microcomputer for data capture and analysis

We describe a simple and inexpensive demonstration of mass transport and exchange using dye clearance from a hydrodynamic model. A microcomputer was used for data acquisition and storage, non-linear least squares curve fitting, compartmental analysis and parameter estimation. The system is useful for demonstrating the indicator-dilution technique for fluid volume measurement and compartmental analysis in pharmacokinetics.     

Polynomial (linear in parameters) least squares analysis when all experimental data are subject to random errors

An iterative method for the least squares fitting of experimental data to polynomial (linear in parameters) models without initial parameter guesses and with the true least squares solution, including the variance-covariance matrix, is presented. The algorithm does not require any linearization of model or normal equations and prevents oscillation and divergence in the solutions.     

联合ADS-B的最小二乘雷达系统误差估计方法

为了解决两坐标雷达系统误差估计问题,提出一种联合ADS-B的最小二乘雷达系统误差估计方法.提出方法首先将ADS-B量测从地理坐标系转换到雷达局部直角坐标系,建立统一的配准空间;其次以雷达航迹的采样时间为基准,对ADS-B航迹进行插值,构造新的ADS-B航迹;然后采用直线拟合算法分别计算雷达航迹和ADS-B航迹的直线方程,并计算两条直线的夹角,再利用该夹角补偿雷达航迹的航向角数据;最后采用最小二乘算法估计雷达系统误差.实测数据实验结果表明,与传统直线拟合方法和最小二乘方法相比,提出方法能够更有效地估计雷达系统误差;经过提出方法配准处理后,雷达航迹数据的平均斜距离误差和方位角误差分别降低71.7%和52.7%.     

全最小二乘法及其在参数估计中的应用

本文介绍了全最小二乘法的基本原理及其在参数估计中的应用.文中采用矩阵逼近和线 性空间分解的理论推导了全最小二乘法的解及其性质,并且证明了全最小二乘解对数据拟合 的残差平方和小于一般最小二乘解的残差平方和.仿真结果验证了理论,显示了全最小二乘 法的优越性.     

Time-varying parametric system multiresolution identification by wavelets

In this paper, the problem of time-varying parametric system identification by wavelets is discussed. Employing wavelet operator matrix representation, we propose a new multiresolution least squares (MLS) algorithm for time-varying AR (ARX) system identification and a multiresolution least mean squares (MLMS) algorithm for the refinement of parameter estimation. These techniques can achieve the optimal tradeoff between the over-fitted solution and the poorly represented identification. The main features of time-varying model parameters are extracted in a multiresolution way, which can be used to represent the smooth trends as well as track the rapidly changing components of time-varying parameters simultaneously and adaptively. Further, a noisy time-varying AR (ARX) model can also be identified by combining the total least squares algorithm with the MLS algorithm. Based on the proposed AR (ARX) model parameter estimation algorithm, a novel identification scheme for time-varying ARMA (ARMAX) system is presented. A higher-order time-varying AR (ARX) model is used to approximate the time-varying ARMA (ARMAX) system and thus obtain an initial parameter estimation. Then an iterative algorithm is applied to obtain the consistent and efficient estimates of the ARMA (ARMAX) system parameters. This ARMA (ARMAX) identification algorithm requires linear operations only and thus greatly saves the computational load. In order to determine the time-varying model order, some modified AIC and MDL criterions are developed based on the proposed wavelet identification schemes. Simulation results verify that our methods can track the rapidly changing of time-varying system parameters and attain the best balance between parsimonious modelling and accurate identification.     

带未知模型参数和衰减观测率系统自校正分布式融合估计

研究了带未知模型参数和衰减观测率多传感器线性离散随机系统的信息融合估计问题.在模型参数和衰减观测率未知的情形下,应用递推增广最小二乘(Recursive extend least squares,RELS)算法和加权融合估计算法提出了分布式融合未知模型参数辨识器;应用相关函数对描述衰减观测现象的随机变量的数学期望和方差...     

Adaptive Finite Element Methods for the Identification of Elastic Constants

In this paper, the elastic constants of a material are recovered from measured displacements where the model is the equilibrium equations for the orthotropic case. The finite element method is used for the discretization of the state equation and the Gauss–Newton method is used to solve the nonlinear least squares problem attained from the parameter estimation problem. A posteriori error estimators are derived and used to improve the accuracy by an appropriate mesh refinement. A numerical experiment is presented to show the applicability of the approach.     

多变量系统状态空间模型的递阶辨识

研究多变量系统状态空间模型的递阶辨识问题,推广了作者提出的标量系统状态和参数联合辨识算法.当状态可量测时,利用最小二乘原理直接辨识状态空间模型的参数矩阵;当状态不可测时,利用递阶辨识原理提出了状态空间模型递阶辨识方法,使用系统输入输出数据来估计系统的未知状态和参数.状态空间模型递阶辨识方法分为两步:首先假设系统状态是已知的(即参数估计算法中的未知系统状态用其估计代替),基于状态估计和系统输入输出数据递归计算系统参数估计;然后基于系统输入输出数据和获得的参数估计,递归计算系统的状态估计.     

On-line system identification algorithm combining stochastic approximation and pseudoinverse

A new algorithm for on-line system identification is presented combining stochastic approximation with the recursive pseudoinverse algorithm for least squares estimation. It is an extension of Clarke's generalized least squares method, and gives unbiased estimates of the parameters even in the presence of large noise. An example of a simulated second-order process compares the proposed method with three earlier methods.     

Identification of Neurofuzzy Models Using GTLS Parameter Estimation

In this paper, nonlinear system identification utilizing generalized total least squares (GTLS) methodologies in neurofuzzy systems is addressed. The problem involved with the estimation of the local model parameters of neurofuzzy networks is the presence of noise in measured data. When some or all input channels are subject to noise, the GTLS algorithm yields consistent parameter estimates. In addition to the estimation of the parameters, the main challenge in the design of these local model networks is the determination of the region of validity for the local models. The method presented in this paper is based on an expectation–maximization algorithm that uses a residual from the GTLS parameter estimation for proper partitioning. The performance of the resulting nonlinear model with local parameters estimated by weighted GTLS is a product both of the parameter estimation itself and the associated residual used for the partitioning process. The applicability and benefits of the proposed algorithm are demonstrated by means of illustrative examples and an automotive application.      

Robust adaptive-scale parametric model estimation for computer vision

Robust model fitting essentially requires the application of two estimators. The first is an estimator for the values of the model parameters. The second is an estimator for the scale of the noise in the (inlier) data. Indeed, we propose two novel robust techniques: the two-step scale estimator (TSSE) and the adaptive scale sample consensus (ASSC) estimator. TSSE applies nonparametric density estimation and density gradient estimation techniques, to robustly estimate the scale of the inliers. The ASSC estimator combines random sample consensus (RANSAC) and TSSE, using a modified objective function that depends upon both the number of inliers and the corresponding scale. ASSC is very robust to discontinuous signals and data with multiple structures, being able to tolerate more than 80 percent outliers. The main advantage of ASSC over RANSAC is that prior knowledge about the scale of inliers is not needed. ASSC can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model. Experiments on synthetic data show that ASSC has better robustness to heavily corrupted data than least median squares (LMedS), residual consensus (RESC), and adaptive least Kth order squares (ALKS). We also apply ASSC to two fundamental computer vision tasks: range image segmentation and robust fundamental matrix estimation. Experiments show very promising results.     

Fitting smooth curves to noisy indicator-dilution and other unimodal data.

A linear least squares method for fitting noisy unimodal functions such as indicator-dilution curves with piecewise stretched exponential functions is described. Stretched exponential functions have the form z(t) = alpha t beta e gamma t, where alpha, beta, and gamma are constants. These functions are particularly useful for fitting experimental data that spans several orders of magnitude is non-Gaussian, high skewed, and long tailed. In addition, the method allows for specifying external restrictions on the smooth curve that might be required by physical constraints on the data. These constraints can take the form of restrictions on the value of the fitting function at certain points or the value of the derivatives in certain regions. To determine the necessary constants in the fitting functions, a linear least squares problem with linear equality and inequality constraints is solved.     

A majorization algorithm for simultaneous parameter estimation in robust exploratory factor analysis

A new approach for fitting the exploratory factor analysis (EFA) model is considered. The EFA model is fitted directly to the data matrix by minimizing a weighted least squares (WLS) goodness-of-fit measure. The WLS fitting problem is solved by iteratively performing unweighted least squares fitting of the same model. A convergent reweighted least squares algorithm based on iterative majorization is developed. The influence of large residuals in the loss function is curbed using Huber’s criterion. This procedure leads to robust EFA that can resist the effect of outliers in the data. Applications to real and simulated data illustrate the performance of the proposed approach.     

基于辅助模型和数据滤波的伪线性回归系统参数估计方法

针对伪线性输出误差回归系统的辨识模型新息信息向量存在不可测变量的问题,首先通过构造一个辅助模型,用辅助模型的输出代替未知中间变量,推导得到的基于辅助模型的递推最小二乘参数估计算法计算量较大,但算法的辨识效果不佳。进一步采用估计的噪声模型对系统观测数据进行滤波,使用滤波后的数据进行参数估计,从而推导提出了基于数据滤波的递推最小二乘参数估计算法。仿真结果表明,所提算法能够有效估计伪线性回归线性输出误差系统的参数。     

A new bias-compensating LS method for continuous system identification in the presence of coloured noise

A new bias-compensating least squares (LS) method is presented for the parameter estimation of linear single-input single-output (SISO) continuous-time systems. A discrete-time model obtained by using the linear integral filter is augmented by introducing a pre-filter on the input and then the parameters of the augmented model are estimated by the conventional LS method. The distinct characteristic roots of the pre-filter are used to estimate the bias in the LS estimate. The pre-filter should be chosen so that its frequency bandwidth is wider than those of the system and the input signals. Since the new method requires minimal information on the noise characteristics, it is easily applicable to the case of coloured noise.     

多变量CARMA模型的结构辨识

本文提出了多变量受控的自回归滑动平均(CARMA)模型结构辨识的新方法.根据模型参 数的递推增广最小二乘法(RELS)估计,给出了确定模型的阶、子阶和时滞的F检验判决器, 且可得到节省参数模型.本方法推广和改进了Bokor和Kevizky的结构辨识方法, 数值模拟例子证明了所提出方法的有效性.     

Jackknife and bootstrap methods in the identification of dynamic models

A new criterion based on a Jackknife or a Bootstrap statistic is proposed for identifying non-parsimonious dynamic models (FIR, ARX). It is applicable for selecting the number of components in latent variable regression methods or the constraining parameter in regularized least squares regression methods. These meta parameters are used to overcome ill-conditioning caused by model over-parameterization, when fitted using prediction error or least squares methods. In all cases studied, using PLS for parameter estimation, the proposed criterion led to the selection of better models, in the mean square error sense, than when selected via cross-validation. The methodology also provides approximate confidence intervals for the model parameters and the step and impulse response of the system.