Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory

For Hammerstein output-error autoregressive systems, a decomposition based multi-innovation stochastic gradient (D-MISG) identification algorithm and a data filtering based multi-innovation stochastic gradient (F-MISG) identification algorithm are derived by means of the key-term separation principle and the multi-innovation identification theory. The D-MISG algorithm uses the decomposition technique to transform a Hammerstein system into two subsystems and requires less computational cost, and the F-MISG algorithm uses a linear filter to filter the input-output data and has a higher estimation accuracy for larger innovation lengths. The simulation results show that the proposed two algorithm can give satisfactory parameter estimates.     

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.     

基于辅助模型的多新息广义增广随机梯度算法

将辅助模型辨识思想与多新息辨识理论相结合,利用系统可测信忠建立一个辅助模型.分别用辅助模型输出和噪声估计值代替辨识模型信忠向量中未知真实输出变量和不可测噪声项,并引入新忠长度扩展标量新息为新息向量,提出了Box-lenkins模型的辅助模型多新忠广义增广随机梯度辨识方法.所提出方法重复使用系统数据,能够改善参数估计精度,加快算法的收敛速度.     

Two-stage multi-innovation stochastic gradient algorithm for multivariate output-error ARMA systems based on the auxiliary model

ABSTRACT

This paper investigates the parameter estimation problem for multivariate output-error systems perturbed by autoregressive moving average noises. Since the identification model has two different kinds of parameters, a vector and a matrix, the gradient algorithm cannot be used directly. Therefore, we decompose the original system model into two sub-models and proceed the identification problem by the collaboration between the two sub-models. By employing the gradient search and determining the optimal step-sizes, we present an auxiliary model based two-stage projection algorithm. However, in order to alleviate the sensitivity to the noise, we reselect the step-sizes and derive the auxiliary model based two-stage stochastic gradient (AM-2S-SG) algorithm. Based on the AM-2S-SG algorithm, an auxiliary model based two-stage multi-innovation stochastic gradient algorithm is proposed to generate more accurate estimates. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed algorithms.     

Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique

This paper considers the identification problems of Hammerstein finite impulse response moving average (FIR-MA) systems using the maximum likelihood principle and stochastic gradient method based on the key term separation technique. In order to improve the convergence rate, a maximum likelihood multi-innovation stochastic gradient algorithm is presented. The simulation results show that the proposed algorithms can effectively estimate the parameters of the Hammerstein FIR-MA systems.     

An algorithm for bounded-error identification of nonlinear systems based on DC functions

This paper presents a guaranteed method for the parameter estimation of nonlinear models in a bounded-error context. This method is based on functions which consists of the difference of two convex functions, called DC functions. The method considers DC representations of the functional form of the dynamic system to obtain an outer bound of the set of parameters that are consistent with the measurements, the system and the considered bounded error. At each iteration, the proposed algorithm solves several convex optimization problems to discard from the initial search region subregions that are proved not consistent. This operation is repeated while the obtained solution is improved. Four examples are provided to clarify the proposed identification algorithm.     

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.     

Event-triggered filtering and fault estimation for nonlinear systems with stochastic sensor saturations

This paper is concerned with the filtering problem for a class of nonlinear systems with stochastic sensor saturations and event-triggered measurement transmissions. An event-triggered transmission scheme is proposed with hope to ease the traffic burden and improve the energy efficiency. The measurements are subject to randomly occurring sensor saturations governed by Bernoulli-distributed sequences. Special effort is made to obtain an upper bound of the filtering error covariance in the presence of linearisation errors, stochastic sensor saturations as well as event-triggered transmissions. A filter is designed to minimise the obtained upper bound at each time step by solving two sets of Riccati-like matrix equations, and thus the recursive algorithm is suitable for online computation. Sufficient conditions are established under which the filtering error is exponentially bounded in mean square. The applicability of the presented method is demonstrated by dealing with the fault estimation problem. An illustrative example is exploited to show the effectiveness of the proposed algorithm.     

数值鲁棒的非线性滤波新方法

应用多维情形的二阶插值公式构造新型非线性滤波器。该滤波器不需非线性函数的偏导计算，便能代替常规的扩展卡尔曼滤波器，并有滤波精度高、数值计算稳定和适用范围宽等优点。仿真实例表明新滤波器具有较高的性能。     

Block adaptive shifting algorithm for filtering based on the Toeplitz preconditioned conjugate gradient technique

We present a new block adaptive algorithm as a variant of the Toeplitz-preconditioned block conjugate gradient (TBCG) algorithm. The proposed algorithm is formulated by combining TBCG algorithm with a data-reusing scheme that is realized by processing blocks of data in an overlapping manner, as in the optimum block adaptive shifting (OBAS) algorithm. Simulation results show that the proposed algorithm is superior to the block conjugate gradient shifting (BCGS), TBCG and Toeplitz-OBAS (TOBAS) algorithms in both convergence rate and tracking property of input signal conditioning.     

A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantum stochastic systems

This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Parthasarathy quantum stochastic differential equation driven by quantum Wiener processes of bosonic fields in vacuum state. The Hamiltonian and system-field coupling operators, as functions of the system variables, are assumed to be represented in a Weyl quantization form. Using the Wigner-Moyal phase-space framework, we obtain a stochastic integro-differential equation for the posterior quasi-characteristic function (QCF) of the system conditioned on the measurements. This equation is a spatial Fourier domain representation of the Belavkin-Kushner-Stratonovich stochastic master equation driven by the innovation process associated with the measurements. We discuss a specific form of the posterior QCF dynamics in the case of linear system-field coupling and outline a Gaussian approximation of the posterior quantum state.     

Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems

This paper combines the multi-innovation identification theory and the auxiliary model identification idea and presents an auxiliary model based multi-innovation stochastic gradient algorithm by expanding the scalar innovation to an innovation vector and introducing the innovation length. Convergence analysis in the stochastic framework indicates that the parameter estimates given by the proposed algorithm can fast converge to their true values. Finally, we illustrate and test the proposed algorithm with an example.     

基于人工免疫系统的RFID数据过滤模型研究*

为了避免感染计算机病毒或者包含恶意代码等不良信息的电子标签对RFID应用系统运行效率的影响,采用人工免疫系统的多层过滤机制建立了面向RFID数据中不良信息的过滤模型,模型的实施包括数据预处理、多层过滤器的生成与衰亡、过滤器的应用及进化。实验结果表明,该模型有较高的召回率和正确率,这说明了基于人工免疫系统的RFID数据过滤模型具有动态性和自适应强的优点,并为特定领域的信息分类问题解决提供了参考。     

改进的基于符号数据的协同过滤推荐算法

随着用户和资源种类的不断增加,评价矩阵的稀疏性问题越来越突出,严重影响了推荐系统的推荐质量。奇异值分解(SVD)是一种对数据进行降维处理的方法,符号数据分析(SDA)是一种处理海量数据的全新数据分析思路。提出一种改进的基于符号数据的协同过滤推荐算法,即将奇异值分解和符号数据分析方法结合起来运用到推荐系统中。在EachMovie 数据库集上的实验结果表明该算法在数据稀疏时的推荐质量明显优于传统的推荐算法。     

A state predictor for continuous-time stochastic systems

This work investigates the state prediction problem for nonlinear stochastic differential systems, affected by multiplicative state noise. This problem is relevant in many state-estimation frameworks such as filtering of continuous-discrete systems (i.e. stochastic differential systems with discrete measurements) and time-delay systems. A very common heuristic to achieve the state prediction exploits the numerical integration of the deterministic nonlinear equation associated to the noise-free system. Unfortunately these methods provide the exact solution only for linear systems. Instead here we provide the exact state prediction for nonlinear system in terms of the series expansion of the expected value of the state conditioned to the value in a previous time instant, obtained according to the Carleman embedding technique. The truncation of the infinite series allows to compute the prediction at future times with an arbitrary approximation. Simulations support the effectiveness of the proposed state-prediction algorithm in comparison to the aforementioned heuristic method.     

A noniterative neuro-fuzzy based identification method for Hammerstein processes

In this paper, a noniterative identification procedure for neuro-fuzzy based Hammerstein model is presented. The proposed method not only avoids the inevitable restrictions on static nonlinear function encountered by using the polynomial approach, but also overcomes the problems of initialization and convergence of the model parameters, which are usually resorted to trial and error procedure in the existing iterative algorithms used for the identification of Hammerstein model. To construct the neuro-fuzzy based model, a clustering algorithm is presented to estimate the centers and widths of the model, and an analytical solution is developed to calculate the weights of the model in a noniterative manner. Examples are used to illustrate the applicability of the proposed method and a comparison with polynomial approach is made.     

基于二阶插值滤波的粒子滤波改进算法研究

粒子退化等问题严重制约了粒子滤波的工程应用,通过对粒子滤波的分析与总结,提出一种基于二阶插值滤波的粒子滤波改进算法,利用二阶插值滤波器计算出更优的重要性函数,从而有效抑制粒子滤波的退化,降低了计算量,通过对导弹再入时的非线性导航参数估计问题进行实例仿真分析,所得结果验证了该算法的有效性.     

L2–L∞ filtering for nonlinear stochastic systems

A sufficient condition for a general nonlinear stochastic system to have L₂?L_∞ gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton–Jacobi inequality (HJI). Based on this criterion, the existence of an L₂?L_∞ filter is given by a second‐order nonlinear HJI, and the filter matrices can be obtained by solving such an HJI. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于正多胞体空间扩展滤波的时变参数系统辨识方法

针对未知但有界噪声时变参数系统,提出了一种基于正多胞体空间扩展滤波的参数辨识方法.采用有界误差方法对测量噪声和参数变化过程进行建模,通过选取最优扩展系数进而扩大正多胞体大小,使得正多胞体包含变化后的参数可行集,由时不变参数系统约束条件构造扩展系数方程,通过线性规划方法求解前k步扩展系数值,选取最大值作为最终扩展系数.采用扩展系数更新每一步时变参数正多胞体约束条件,求解全部参数的上下界得到包裹参数可行域的最紧致正多胞体.仿真示例说明该方法辨识时变参数的有效性和准确性.