An online parameter estimator for quick convergence and time-varying linear systems

A recursive algorithm called 3-OM is presented to estimate parameters and noise variances for discrete-time linear stochastic systems. The unprojected version of 3-OM is globally convergent with probability 1 to minima of the asymptotic negative log-likelihood function. 3-OM approximates the quick convergence attained by the optimal nonlinear filter used as a parameter estimator. The state-space form of 3-OM permits application to time-varying linear systems and to online tuning of a Kalman filter.     

Identification of time delays in linear stochastic systems

This paper presents a new approach to the explicit identification of an input time delay in continuous-time linear systems. The system model is converted to a discrete-time version, assuming that a digital computer is to be used for time delay estimation and control. A recursive identification algorithm based on parallel Kalman filtering and Bayes' estimation is developed. The sampling rate is adapted during the time delay estimation process using the most recent estimate of the time delay. This method assures that the estimate of the time delay approaches the true value with each successive iteration. The proposed method also has the advantage of a fast convergence rate because prior knowledge of the delay, if available, can be effectively utilized.     

Exact finite-dimensional nonlinear filters

A new nonlinear filter is derived for continuous-time processes with discrete-time measurements. The filter is exact, and it can be implemented in real time with a computational complexity that is comparable to the Kalman filter. This new filter includes both the Kalman filter and the discrete-time version of the Benes filter as special cases. Moreover, the new theory can handle a large class of nonlinear estimation problems that cannot be solved using the Kalman or discrete-time Benes filters. A simple approximation technique is suggested for practical applications in which the dynamics do not satisfy the required conditions exactly. This approximation is analogous to the so-called "extended Kalman filter" [10], and it represents a generalization of the standard linearization method.     

Comparison of six on-line identification algorithms

This paper discusses six popular parameter identification algorithms developed mainly for linear discrete-time dynamic systems. They are namely the Crosscorrelation technique, the first and second Stochastic Approximation methods, the Maximum Likelihood method, the Maximum a-posteriori probability filter, and the extended Kalman filter. Their computational properties are compared and their convergence is tested on two fourth order discrete-time systems. An overall evaluation of the methods is also presented.     

Convergence analysis of the extended Kalman filter used as anobserver for nonlinear deterministic discrete-time systems

In this paper, convergence analysis of the extended Kalman filter (EKF), when used as an observer for nonlinear deterministic discrete-time systems, is presented. Based on a new formulation of the first-order linearization technique, sufficient conditions to ensure local asymptotic convergence are established. Furthermore, it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified EKF significantly. The efficiency of this approach, compared to the classical version of the EKF, is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete-time systems     

The iterated Kalman filter update as a Gauss-Newton method

It is shown that the iterated Kalman filter (IKF) update is an application of the Gauss-Newton method for approximating a maximum likelihood estimate. An example is presented in which the iterated Kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate, whereas the extended Kalman filter update does not     

Optimal filtering for linear systems with state and observation delays

In this paper, the optimal filtering problem for linear systems with state and observation delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate, error variance, and various error covariances. As a result, the optimal estimate equation similar to the traditional Kalman–Bucy one is derived; however, it is impossible to obtain a system of the filtering equations, that is closed with respect to the only two variables, the optimal estimate and the error variance, as in the Kalman–Bucy filter. The resulting system of equations for determining the filter gain matrix consists, in the general case, of an infinite set of equations. It is however demonstrated that a finite set of the filtering equations, whose number is specified by the ratio between the current filtering horizon and the delay values, can be obtained in the particular case of equal or commensurable (τ=qh, q is natural) delays in the observation and state equations. In the example, performance of the designed optimal filter for linear systems with state and observation delays is verified against the best Kalman–Bucy filter available for linear systems without delays and two versions of the extended Kalman–Bucy filter for time delay systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Stochastic stability of the unscented Kalman filter with intermittent observations

In this paper, the stochastic stability of the discrete-time unscented Kalman filter for general nonlinear stochastic systems with intermittent observations is proposed. It is shown that the estimation error remains bounded if the system satisfies some assumptions. And the statistical convergence property of the estimation error covariance is studied, showing the existence of a critical value for the arrival rate of the observations. An upper bound on this expected state error covariance is given. A numerical example is given to illustrate the effectiveness of the techniques developed.     

Reduced order state estimators for discrete-time stochastic systems

A reduced order, least squares, state estimator is developed for linear discrete-time systems having both input disturbance noise and output measurement noise with no output being free of measurement noise. The order reduction is achieved by using a Luenberger observer in connection with some of the system outputs and a Kalman filter to estimate the state of the Luenberger observer. The order of the resulting state estimator is reduced from the order of the usual Kalman filter system state estimator by the number of system outputs selected for use as inputs to the Luenberger Observer. The manner in which the noise associated with the selected system outputs affects the state estimation error covariance provides considerable insight into the compromise being attempted.     

基于双扩展卡尔曼滤波的电池荷电状态估计

以磷酸铁锂动力电池为研究对象,以精确估算电动汽车动力锂电池组在实际运行工况中的SOC为目的,基于Thevenin等效电路模型和扩展卡尔曼滤波算法,结合脉冲功率特性实验（HPPC Test）对模型参数进行辨识,采用双扩展卡尔曼滤波对SOC和模型参数进行在线估算,并分析算法在不同温度下的适应性和不同SOC初始值条件下的收敛特性。仿真结果表明,在不同的工况下,相比于单扩展卡尔曼滤波该算法具有更高的精度、更好的环境适应度和对初始误差的收敛性。     

基于EKF神经网络的扩频系统抗窄带干扰技术

针对消除扩频系统中的窄带干扰问题,文章提出了一种基于扩展卡尔曼滤波(EKF)的递归神经网络预测器(RNNP)。扩展卡尔曼滤波被用于反馈修改递归神经网络的权值系数,从而准确地估计干扰信号,具有收敛速度快、预测精度高和适用于非线性处理的优点。仿真结果表明:基于EKF学习算法的RNNP相对于自适应线性最小均方差(LMS)干扰预测器、自适应近似条件均值(ACM)干扰预测器和基于实时递推学习(RTRL)算法的RNNP在预测误差的均方误差、收敛速度、信噪比改善量方面上有不同程度的改进。     

A superposition principle for the Kalman filter

In this paper, decomposition formulas for the discrete-time Kalman filter are presented. Both the state estimate and the error covariance matrix are expressed as the sum of two terms, the first being the estimate corresponding to zero initial conditions, and the second being an explicit function of the initial values and P₀. The representation is updated in time by well-behaved finite complexity matrix recursions, and allows for a direct evaluation of the estimates for variable initial conditions. Applications to stochastic hybrid filtering are discussed.     

Discrete-time filtering for nonlinear polynomial systems over linear observations

This paper designs a discrete-time filter for nonlinear polynomial systems driven by additive white Gaussian noises over linear observations. The solution is obtained by computing the time-update and measurement-update equations for the state estimate and the error covariance matrix. A closed form of this filter is obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and the error covariance. As a particular case, a third-degree polynomial is considered to obtain the finite-dimensional filtering equations. Numerical simulations are performed for a third-degree polynomial system and an induction motor model. Performance of the designed filter is compared with the extended Kalman one to verify its effectiveness.     

自适应扩展卡尔曼滤波器在移动机器人定位中的应用

针对移动机器人定位过程中存在的误差积累问题,提出了采用自适应扩展卡尔曼滤波算法(AEKF).分析了扩展卡尔曼滤波(EKF)和AEKF两种算法, AEKF取采样时刻的各项泰勒级数,并利用Sage-Husa时变噪声估计器实时估计观测噪声,克服了线性化误差,增强了环境适应性;同时,对AEKF的收敛性及运算复杂度进行分析,并结合算法实验表明AEKF具有良好的速度精度综合性价比;最后对比分析两种算法实现机器人定位的效果并实验完成误差对比.结果表明AEKF具有更优的定位性能.     

Evolutionary-Programming-Based Kalman Filter for Discrete-Time Nonlinear Uncertain Systems

Some observations and improvements on the conventional Kalman filtering scheme to function properly are presented. The improvements can be achieved using the minimal principle evolutionary programming (EP) technique. A new linearization methodology is presented to obtain the exact linear models of a class of discrete-time nonlinear time-invariant systems at operating states of interest, so that the conventional Kalman filter can work for the nonlinear stochastic systems. Furthermore, a Kalman innovation filtering algorithm and such an algorithm based on the evolutionary programming optimal-search technique are proposed in this paper for discrete-time time-invariant nonlinear stochastic systems with unknown-but-bounded plant uncertainties and noise uncertainties to find a practically implementable “best” Kalman filter. The worst-case realization of the discrete-time nonlinear stochastic uncertain systems represented by the interval form with respect to the implemented “best” nominal filter is also found in this paper for demonstrating the effectiveness of the proposed filtering scheme.     

Algorithm of Gaussian Sum Filter Based on SGQF for Nonlinear Non-Gaussian Models

To improve the filtering effect of the sparse grid quadrature filter (SGQF) under non-Gaussian conditions, the Gaussian sum technique is introduced, and the Gaussian sum sparse grid quadrature filter (GSSGQF) is developed. We present a systematic formulation of the SGQF and extend it to the discrete-time nonlinear system with the non-Gaussian noise. The proposed algorithm approximates the non-Gaussian probability densities by a finite number of weighted sums of Gaussian densities, and takes the SGQF as the Gaussian sub-filter to conduct the time and measurement update for each Gaussian component. An application in the discrete-time nonlinear system with the non-Gaussian noise has been shown to demonstrate the accuracy of the GSSGQF. It outperforms the unscented Kalman filter (UKF), the cubature Kalman filter (CKF) and the SGQF. Theoretical analysis and simulation results prove that the GSSGQF provides significant performance improvement in the calculation accuracy for nonlinear non-Gaussian filtering problems.

     

Unbiased minimum-variance input and state estimation for linear discrete-time systems

This paper addresses the problem of simultaneously estimating the state and the input of a linear discrete-time system. A recursive filter, optimal in the minimum-variance unbiased sense, is developed where the estimation of the state and the input are interconnected. The input estimate is obtained from the innovation by least-squares estimation and the state estimation problem is transformed into a standard Kalman filtering problem. Necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed.     

一种基于非线性滤波的倒立摆控制方法研究

对于倒立摆这样的强非线性系统,采用传统的BP算法存在着收敛速度慢、易陷入局部极小值的缺陷,而采用卡尔曼滤波方法则会带来很大的模型误差。为了解决上述问题,提出了基于粒子滤波优化神经网络的方法。首先建立了倒立摆神经网络控制器的物理模型并将模型粒子化,而后用粒子滤波算法对粒子进行优化估计,将估计结果作为网络的权值应用到倒立摆控制中,采用离线训练方式,仿真比较了卡尔曼滤波和粒子滤波两种方法控制效果,结果表明,新算法较卡尔曼滤波方法在控制性能上有明显提高。