A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems

The identification of nonlinear systems is a hot topic in the identification fields. In this paper, a data filtering based multi-innovation stochastic gradient algorithm is derived for Hammerstein nonlinear controlled autoregressive moving average systems by adopting the key-term separation principle and the data filtering technique. The proposed algorithm provides a reference to improve the identification accuracy of the nonlinear systems with colored noise. The simulation results show that the new algorithm can more effectively estimate the parameters of the Hammerstein nonlinear systems than the multi-innovation stochastic gradient algorithm.     

Parameter estimation for block‐oriented nonlinear systems using the key term separation

This article considers the parameter estimation problems of block‐oriented nonlinear systems. By using the key term separation, the system output is represented as a linear combination of unknown parameters. We give a key term separation auxiliary model gradient‐based iterative (KT‐AM‐GI) identification algorithm and propose a key term separation auxiliary model three‐stage gradient‐based iterative (KT‐AM‐3S‐GI) identification algorithm by using the hierarchical identification principle. Meanwhile, the multiinnovation theory is used to derived the key term separation auxiliary model three‐stage multiinnovation gradient‐based iterative (KT‐AM‐3S‐MIGI) algorithm. The analysis shows that compared with the KT‐AM‐GI algorithm, the KT‐AM‐3S‐GI algorithm can improve the parameter estimation accuracy and reduce the computational burden. In addition, the KT‐AM‐3S‐MIGI can give more accurate parameter estimates than the KT‐AM‐3S‐GI algorithm and can track time‐varying parameters based on the dynamical window data. This work provides a reference for improving the identification performance of multiinput nonlinear output‐error systems or multivariable nonlinear systems. The simulation results confirm the effectiveness of the proposed algorithm.     

Maximum likelihood‐based gradient estimation for multivariable nonlinear systems using the multiinnovation identification theory

This article considers the identification problems of multivariable input nonlinear systems with unmeasured disturbances. For the identification difficulty caused by the crossproducts between the parameters of the linear block and the nonlinear block, the key term separation technique is adopted to separate the parameters of the nonlinear block from the parameters of the linear block. By combining the model decomposition technique and the hierarchical identification principle, a key term separation‐based maximum likelihood recursive extended stochastic gradient algorithm with reduced computational complexity is presented to estimate all the parameters directly. By introducing the multiinnovation identification theory, a key term separation‐based maximum likelihood multiinnovation extended stochastic gradient algorithm is proposed to improve the parameter estimation accuracy. The simulation results illustrate the effectiveness of the proposed methods.     

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.     

Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering

This paper studies the joint state and parameter estimation problem for a linear state space system with time-delay. A multi-innovation gradient algorithm is developed based on the Kalman filtering principle. To improve the convergence rate, a filtering based multi-innovation gradient algorithm is proposed by using the filtering technique. The analysis indicates that the parameter estimates given by the proposed algorithms converge to their true values under the persistent excitation conditions. A simulation example is given to confirm that the proposed algorithms are effective.     

非均匀采样系统多新息随机梯度辨识性能分析

针对一类非均匀采样系统,提出了其输入输出表达的多新息随机梯度辨识方法．该方法将随机梯度算法中的新息项扩展为向量,有效利用了历史新息所包含的信息,从而提高辨识精度和算法的收敛速度,同时又保留了随机梯度算法计算量小的优点．仿真例子通过改变新息长度,验证了所提出辨识算法性能的优越性．     

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。     

Parameter estimation and system identification for continuously-observed quantum systems

This paper gives an overview of parameter estimation and system identification for quantum input–output systems by continuous observation of the output field. We present recent results on the quantum Fisher information of the output with respect to unknown dynamical parameters. We discuss the structure of continuous-time measurements as solutions of the quantum Zakai equation, and their relationship to parameter estimation methods. Proceeding beyond parameter estimation, the paper also gives an overview of the emerging topic of quantum system identification for black-box modelling of quantum systems by continuous observation of a travelling wave probe, for the case of ergodic quantum input–output systems and linear quantum systems. Empirical methods for such black-box modelling are also discussed.     

基于滤波的分段线性Hammerstein系统的递推辨识方法

Hammerstein模型具有结构简单、能很好地反映典型非线性特性等优点, 一直是控制领域的重要研究内容之一. 本文主要研究输出误差自回归Hammerstein系统的辨识问题, 系统的输入非线性部分采用分段线性函数拟合,并引入切换函数和位置函数将其表示为线性参数表达式. 为克服有色噪声的干扰, 本文通过关键项分离和数据滤波技术, 建立系统的滤波辨识模型. 在此基础上, 文中提出了基于滤波的遗忘梯度算法, 基于滤波的递推广义最小二乘算法和基于滤波的多新息遗忘梯度算法估计未知参数. 本文通过仿真实例验证了所提算法的有效性, 证明了多新息理论的应用可以有效地提高递推算法的辨识性能.     

Maximum likelihood-based recursive least-squares estimation for multivariable systems using the data filtering technique

For multivariable equation-error systems with an autoregressive moving average noise, this paper applies the decomposition technique to transform a multivariable model into several identification sub-models based on the number of the system outputs, and derives a data filtering and maximum likelihood-based recursive least-squares algorithm to reduce the computation complexity and improve the parameter estimation accuracy. A multivariable recursive generalised extended least-squares method and a filtering-based recursive extended least-squares method are presented to show the effectiveness of the proposed algorithm. The simulation results indicate that the proposed method is effective and can produce more accurate parameter estimates than the compared methods.     

基于改进差分进化算法的非线性系统模型参数辨识

针对非线性模型的参数估计寻优较为困难的问题,提出一种基于改进的差分进化算法的非线性系统模型参数辨识新方法。通过引入一个自适应变异率,随着迭代的进行自适应调整缩放因子,从而在初期保持种群多样性以避免早熟,并在后期逐步降低变异率,保留优良信息,避免最优解遭到破坏。交叉概率采用动态非线性增加的方法,提高了收敛速度。为了验证算法性能,针对几类典型的非线性模型参数辨识问题进行了仿真研究,并将其应用于一类发酵动力学模型参数的估计中。结果表明改进算法的参数辨识精度高,收敛速度也比较快,有效提高了模型建立的精度与效率,为解决实际系统中参数估计问题提供了一条可行的途径。     

A separated bias identification and state estimation algorithm for nonlinear systems

A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.     

State estimation and filtering in stochastic systems using adequate simplification

The method of order reduction in solving stochastic problems of state estimation and filtering is considered. The method presented concerns the case where mathematical models of objects being studied are defined by systems of nonstationary differential equations. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 98–102, September–October, 1999.     

基于统计学理论的参数模型运动估计方法

运动估计对视频编码十分重要,基于参数模型的运动估计方法也越来越受到人们的关注,参数模型的选择是该方法的关键。基于此,提出了基于统计学原理的模型选择方法,它以少量的图像数据流为基础,通过参数估计,并分析各近似模型的预测风险和误差,选出最优模型,它最符合预测对象的实际发展变化规律,进而利用该模型对未知对象进行运动估计。试验结果表明,在对实际图像序列进行运动估计时,这种方法是可靠并且实用的。     

Quantised polynomial filtering for nonlinear systems with missing measurements

This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-bounded coefficients. The transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a Bernoulli distributed sequence taking values on 0 or 1. Dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors, the quantisations as well as the missing measurements at each time instant. Such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations. The filter design algorithm is recursive and therefore applicable for online computation. An illustrative example is exploited to show the effectiveness of the proposed algorithm.     

Parameter identification for a class of abstract nonlinear parabolic distributed parameter systems

This paper studies the parameter identification problem of nonlinear abstract parabolic distributed parameter systems via variational method ^[1]. Based on the fundamental optimal control theory and the transposition method studied in ^[2], the existence of optimal parameter is proved, and the necessary condition for the optimal parameter is established.     

On Kalman filtering for conditionally Gaussian systems with random matrices

We consider linear stochastic systems with additive white Gaussian noise, with the added generality that the system matrices are random and adapted to the observation process. The main result of this paper is that in order for the standard Kalman filter to generate the conditional mean and conditional covariance of the conditionally Gaussian distributed state, it is sufficient for the random matrices to be finite with probability one at each time instant. This generalizes the best previous results available to date, to our knowledge, which require the more stringent hypothesis that the entries of the random matrices should possess finite second moments at each time instant.

A significant application of the results of this paper is to the problem of recursive identification of the unknown parameters of a controlled linear stochastic system. In such problems, the observation matrix is typically generated by complicated nonlinear feedback, as for example in adaptive control, and the finiteness of the second moments is difficult, if not impossible, to establish, while the finiteness with probability one has been established in many applications.     

非线性振动系统参数识别的迭代离散变分方法

针对存在干扰的非线性振动系统,本文提出了一种识别模型参数的时域迭代方法．首先,对于每一组包含随机干扰的测量数据样本,将待辨识参数对时间的导数引入到系统代价函数中,进而利用离散变分原理导出关于待辨识参数的差分方程,并与修改后的系统约束方程一同求解;通过迭代计算使待识别参数从给定的初始值收敛到稳定的真值．然后,对通过n组干扰样本得到的参数识别结果取平均值,并作为最终辨识结果．最后,利用本方法对一个四自由度非线性振动系统的模型参数进行了识别仿真,数值结果证明了该方法的有效性．     

Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model

This paper focuses on the parameter estimation problems of output error autoregressive systems and output error autoregressive moving average systems (i.e., the Box–Jenkins systems). Two recursive least squares parameter estimation algorithms are proposed by using the data filtering technique and the auxiliary model identification idea. The key is to use a linear filter to filter the input–output data. The proposed algorithms can identify the parameters of the system models and the noise models interactively and can generate more accurate parameter estimates than the auxiliary model based recursive least squares algorithms. Two examples are given to test the proposed algorithms.