Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models

A maximum likelihood parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) models based on the maximum likelihood principle. In this derivation, we use an estimated noise transfer function to filter the input–output data. The simulation results show that the proposed estimation algorithm can effectively estimate the parameters of such class of CARAR systems and give more accurate parameter estimates than the recursive generalized least-squares algorithm.     

有理模型辨识的两类新方法——混合迭代与柔性最小二乘法

针对有理模型提出两类辨识方法.首先提出基于递阶辨识思想的混合辨识方法,将模型分解为分子和分母两个子模型,分别用最小二乘法辨识分子参数,用粒子群算法和智能多步长梯度迭代算法辨识分母参数.由于降低了模型维数,且信息向量与噪声不相关,相对于传统的偏差补偿最小二乘算法,混合迭代法可以提高辨识精度并降低计算量.然后,为消除模型结构已知的假设,且充分利用最新数据更新系统参数,提出柔性递推最小二乘辨识方法,将有理模型转化为时变参数系统,进而辨识出时变系统的参数.仿真例子验证了所提出方法的有效性.     

Maximum likelihood least squares‐based iterative methods for output‐error bilinear‐parameter models with colored noises

This article is concerned with the parameter identification of output‐error bilinear‐parameter models with colored noises from measurement data. An auxiliary model least squares‐based iterative method is developed through the overparameterization model. It examines the difficulty of estimating the overparameterized vector, which usually presents a heavy computational burden in the identification process. To overcome this drawback, a parameter separation technique is introduced and the nonlinear model is reformulated as a refined identification model through eliminating the crossmultiplying terms. In this regard, a parameter separation least squares‐based iterative (PS‐LSI) algorithm is derived by avoiding estimating the redundant parameters. On the basis of the PS‐LSI algorithm, we derive a maximum likelihood least squares‐based iterative method to further improve the numerical accuracy. The identification is dependent on the formulation of a pseudolinear regression relationship, which contains two linear prefilters constructed from the system and noise models. The performance of this proposed method is confirmed by the numerical simulations as well as direct comparisons with other existing algorithms.     

Maximum likelihood identification of Wiener models

The Wiener model is a block oriented model, having a linear dynamic system followed by a static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. We show that this will, in general, lead to biased estimates if there are other disturbances present than measurement noise. The implications of Bussgang’s theorem in this context are also discussed. For the case with general disturbances, we derive the Maximum Likelihood method and show how it can be efficiently implemented. Comparisons between this new algorithm and the traditional approach, confirm that the new method is unbiased and also has superior accuracy.     

General模型辅助变量辨识方法的研究

对于存在相关噪声干扰的General系统,研究了一种新的辨识方法。首先系统模型用一个有限的脉冲响应（FIR）模型逼近,得到一个Box Jenkins模型,再使用辅助变量法辨识系统参数,最后根据模型等价原理确定原系统的参数估计。仿真结果表明：在这种近似下递推辅助变量法(RIV)比递推广义增广最小二乘法(RGELS)可以得到更好的参数估计。     

Recursive identification for multivariate autoregressive equation-error systems with autoregressive noise

This paper considers the recursive identification problems for a class of multivariate autoregressive equation-error systems with autoregressive noise. By decomposing the system into several regressive identification subsystems, a maximum likelihood recursive generalised least squares identification algorithm is proposed to identify the parameter vectors in each subsystem. In addition, a multivariate recursive generalised least squares algorithm is derived as a comparison. The numerical simulation results indicate that the maximum likelihood recursive generalised least squares algorithm can effectively estimate the parameters of the multivariate autoregressive equation-error autoregressive systems and get more accurate parameter estimates than the multivariate recursive generalised least squares algorithm.     

基于最大伪似然准则估计的故障链路诊断*

识别网络内部的故障链路对提升网络性能具有重要参考价值。研究了树型拓扑下基于端到端测量的故障链路诊断问题,提出一种最大伪似然估计方法估计链路先验故障概率,把树型拓扑划分为一系列具有两个叶节点的子树,并使用期望最大化(EM)算法最大化每个子树的似然函数,求出链路先验概率。仿真实验表明,该方法与现有的联立方程组求解方法估计精度相当,但是大大降低了算法时间复杂度,证明了该方法的有效性。     

Maximum likelihood estimation for continuous-time autoregressive models by relaxation on residual variances ratio parameters

In this paper we derive an explicit expression for the log likelihood function of a continuous-time autoregressive model. Then, using earlier results relating the autoregressive coefficients to the set of positive parameters called residual variances ratios, we develop an iterative algorithm for computing the maximum likelihood estimator of the model, similar to one in the discrete-time case. A simple noniterative estimation method, which can be used to produce an initial estimate for the algorithm, is also proposed.     

Maximum likelihood estimation for generalized semi-markov processes

Parametric statistical inference for generalized semi-Markov processes is addressed. This class of processes encompasses a large number of real-world discrete-event stochastic systems. Because of its properties (e.g., consistency, asymptotic normality, etc.), maximum likelihood estimation is considered here. Under reasonable conditions on the process, we show that a maximum likelihood estimator exists, and that it converges to the true parameter at ratet ^–1/2, wheret is the length of the observation period. A related estimator, which is typically easier to compute, is also introduced. We show that the use of this estimator results in no loss of statistical efficiency. It is also shown that the estimation problem does decouple into separate subproblems when the process' transition probabilities and event distributions depend on different parameters.     

Maximum likelihood estimation for constrained parameters of multinomial distributions—Application to Zipf-Mandelbrot models

A numerical maximum likelihood (ML) estimation procedure is developed for the constrained parameters of multinomial distributions. The main difficulty involved in computing the likelihood function is the precise and fast determination of the multinomial coefficients. For this the coefficients are rewritten into a telescopic product. The presented method is applied to the ML estimation of the Zipf-Mandelbrot (ZM) distribution, which provides a true model in many real-life cases. The examples discussed arise from ecological and medical observations. Based on the estimates, the hypothesis that the data is ZM distributed is tested using a chi-square test. The computer code of the presented procedure is available on request by the author.     

Robust maximum likelihood estimation for stochastic state space model with observation outliers

The objective of this paper is to develop a robust maximum likelihood estimation (MLE) for the stochastic state space model via the expectation maximisation algorithm to cope with observation outliers. Two types of outliers and their influence are studied in this paper: namely,the additive outlier (AO) and innovative outlier (IO). Due to the sensitivity of the MLE to AO and IO, we propose two techniques for robustifying the MLE: the weighted maximum likelihood estimation (WMLE) and the trimmed maximum likelihood estimation (TMLE). The WMLE is easy to implement with weights estimated from the data; however, it is still sensitive to IO and a patch of AO outliers. On the other hand, the TMLE is reduced to a combinatorial optimisation problem and hard to implement but it is efficient to both types of outliers presented here. To overcome the difficulty, we apply the parallel randomised algorithm that has a low computational cost. A Monte Carlo simulation result shows the efficiency of the proposed algorithms.     

Maximum likelihood identification of noisy input-output models

This work deals with the identification of errors-in-variables models corrupted by white and uncorrelated Gaussian noises. By introducing an auxiliary process, it is possible to obtain a maximum likelihood solution of this identification problem, by means of a two-step iterative algorithm. This approach allows also to estimate, as a byproduct, the noise-free input and output sequences. Moreover, an analytic expression of the finite Cràmer-Rao lower bound is derived. The method does not require any particular assumption on the input process, however, the ratio of the noise variances is assumed as known. The effectiveness of the proposed algorithm has been verified by means of Monte Carlo simulations.     

一种基于量子遗传算法的扩展T-S 模型辨识

在传统T-S模型的基础上,提出一种扩展T-S模型。该模型由一组模糊规则组成,由规则前件实现输入空间的划分,将成员函数及其函数变换引入规则后件以实现对输入子空间的非线性映射。对于该模型的建立,使用改进量子遗传算法优化规则前件,递推最小二乘法确定规则后件参数。通过对两个典型非线性系统辨识,仿真结果表明了该模型可以显著提高辨识精度,且具有很好的泛化性能。     

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.     

基于无线传感器网络的极大似然定位法的分析

对现在普遍应用的极大似然估计定位方法进行了分析,发现极大似然估计法参考方程(第n个方程)的锚节点(参照锚节点)测距误差和参照锚节点在定位区域内的位置对定位误差有重要影响:参照锚节点的测距误差越小,计算得到的定位精度越高;当所有方程所含误差相同时,参照锚节点在定位区域中心时定位误差小,在定位区域边缘时定位误差大;当参照锚...     

基于辅助模型的递推增广最小二乘辨识方法

针对有色噪声干扰的输出误差滑动平均系统, 将辅助模型与递推增广最小二乘算法相结合: 用辅助模型的输出代替辨识模型信息向量中的未知真实输出项, 用估计残差代替信息向量中的不可测噪声项, 从而提出了基于辅助模型的递推增广最小二乘辨识方法. 为了展示所提方法的特点, 文中还给出了经过模型变换的递推增广最小二乘算法. 理论分析和仿真研究表明, 提出的方法原理简单、计算量小, 可以给出高精度参数估计, 且能够用于在线辨识.     

Maximum likelihood and prediction error methods

The basic ideas behind the parameter estimation methods are discussed in a general setting. The application to estimation or parameters in dynamical systems is treated in detail using the prototype problem of estimating parameters in a continuous time system using discrete time measurements. Computational aspects are discussed. Theoretical results in consistency, asymptotic normality and efficiency are covered. Model validation and selection of model structures are discussed. An example is given which illustrates some properties of the methods and shows the usefulness of interactive computing. Additional examples illustrate what happens when the data has different artefacts.     

基于最大似然估计与朴素贝叶斯的WSN故障检测

WSN中的故障节点导致网络的数据传递延迟与能耗增加,同时可引起网络拥塞等问题,对此提出一种基于最大似然估计与朴素贝叶斯分析器的WSN故障节点诊断与定位算法。首先,从数据包的协议部分提取大量特征作为训练数据集,从中估算边际概率并建立朴素贝叶斯分类器,使用最大似然估计估算条件概率。检测阶段则通过判断传输延迟是否满足阈值条件来决定可疑节点,然后使用朴素贝叶斯分类器检测故障节点,最终将节点成功进行分类。     

Box-Jenkins模型偏差补偿方法与其他辨识方法的比较

对于存在相关噪声干扰的Box—Jenkins系统,本文借助于偏差补偿原理,推导了一个偏差补偿最小二乘(BCLS)辨识方法;理论分析说明BCLS方法能够给出系统模型参数的无偏估计,并将提出的方法与递推增广最小二乘算法和递推广义增广最小二乘算法进行了比较研究;用仿真试验分析了这些算法的各自特点和适用范围。     

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.