Adaptive Gaussian filters for nonlinear state estimation with one-step randomly delayed measurements

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one-step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off-line harmonics estimation problem with real data.     

带不确定量测和未知虚警概率的粒子滤波器

为了解决带不确定量测和未知虚警概率的非线性非高斯系统状态估计问题,本文提出了一种新的粒子滤波方法,利用随机不确定量测模型来更新粒子和权值,并基于极大似然准则来辨识未知的虚警概率.本文所提出的带不确定量测和已知虚警概率的粒子滤波方法与现有标准的粒子滤波方法具有几乎一致的计算复杂度,但是更适合用于处理带不确定量测的非线性非高斯系统状态估计问题.此外,在状态转移密度函数被选择为建议密度函数时,本文证明了基于所提出的虚警概率辨识方法的极大似然估计唯一,从而为精确辨识虚警概率提供了理论保证.单变量非平稳增长模型和纯方位跟踪的数值仿真验证了所提出粒子滤波方法的有效性和与现有方法相比的优越性.     

state estimation with fading measurements,randomly varying nonlinearities and probabilistic distributed delays

In this paper, the state estimation problem is investigated for a class of discrete‐time stochastic systems in simultaneous presence of three network‐induced phenomena, namely, fading measurements, randomly varying nonlinearities and probabilistic distributed delays. The channel fading is characterized by the ?th‐order Rice fading model whose coefficients are mutually independent random variables with given probability density functions. Two sequences of random variables obeying the Bernoulli distribution are utilized to govern the randomly varying nonlinearities and probabilistic distributed delays. The purpose of the problem addressed is to design an state estimator such that the dynamics of the estimation errors is stochastically stable and the prespecified disturbance rejection attenuation level is guaranteed. Through intensive stochastic analysis, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimization one that can be solved via the semi‐definite program method. Finally, a simulation example is provided to show the usefulness of the proposed state estimation scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Multi-target state-estimation technique for the particle probability hypothesis density filter

A simple yet effective state-estimation algorithm is presented and demonstrated to have advantages over previous standard clustering techniques used for the particle probability hypothesis density filter.The idea behind the proposed algorithm is that it uses the latest available information(i.e.,the measurements) to direct particle clustering.The particle likelihood and target number estimation,computed during probability hypothesis density recursion,are both used to partition particles into clusters,and the center of each cluster gives the state estimation of an individual target.Simulation results indicate that the proposed algorithm outperforms the standard clustering approach using the k-means algorithm,achieving higher accuracy and shorter computational time.     

带随机量测时滞和随机丢包的改进无迹卡尔曼滤波

经典卡尔曼滤波要求量测值可实时获取,且仅适用于线性系统.然而,在工程实际应用中,系统多为非线性系统,量测值也会发生滞后或者丢失等现象,此时经典卡尔曼滤波已不适用.因此,本文针对一类带有随机量测一步时滞和随机丢包的非线性离散系统的状态估计问题,用两个满足伯努利分布的独立随机变量来描述随机量测一步滞后和随机丢包的现象.当量测丢失时,用量测值的一步预测值来代替零输入进行补偿.在此基础上应用正交投影理论和无迹变换的方法提出了一种改进的无迹卡尔曼滤波算法.最后,通过仿真例子验证在考虑随机量测一步时滞和随机丢包的情况下,所提出的改进算法相比于经典无迹卡尔曼滤波算法具有更高的精度.     

State estimation for complex systems with randomly occurring nonlinearities and randomly missing measurements

This paper is concerned with the state estimation problem for the complex networked systems with randomly occurring nonlinearities and randomly missing measurements. The nonlinearities are included to describe the phenomena of nonlinear disturbances which exist in the network and may occur in a probabilistic way. Considering the fact that probabilistic data missing may occur in the process of information transmission, we introduce the randomly data missing into the sensor measurements. The aim of this paper is to design a state estimator to estimate the true states of the considered complex network through the available output measurements. By using a Lyapunov functional and some stochastic analysis techniques, sufficient criteria are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the state estimator gain is also obtained. Finally, a numerical example is employed to illustrate the effectiveness of the proposed state estimation conditions.     

Particle Smoother for Nonlinear Systems With One‐Step Randomly Delayed Measurements

In this paper, a new particle smoother based on forward filtering backward simulation is developed to solve the nonlinear and non‐Gaussian smoothing problem when measurements are randomly delayed by one sampling time. The heart of the proposed particle smoother is computation of delayed posterior filtering density based on stochastic sampling approach, whose particles and corresponding weights are updated in Bayesian estimation framework by considering the one‐step randomly delayed measurement model. The superior performance of the proposed particle smoother as compared with existing methods is illustrated in a numerical example concerning univariate non‐stationary growth model.     

考虑随机量测时滞和同步相关噪声的改进高斯滤波算法

经典高斯滤波算法存在量测信息实时获取,以及过程噪声和量测噪声相互独立的假设条件.然而,在工程实际应用中该假设条件有时难以满足.本文针对一类具有随机量测时滞和同步相关噪声的高斯系统的状态估计问题,设计了一种高斯滤波框架形式的最优估计算法,并给出了所设计算法的三阶球径容积法则的次优实现形式-考虑随机量测时滞和同步相关噪声的容积卡尔曼滤波器(CKF–RDSCN).其借助Bernoulli随机序列,来描述系统中可能存在的量测时滞现象,并利用高斯条件分布性质来解决噪声相关问题,在此基础上构建所提出的最优估计算法.仿真结果表明,相比于扩展卡尔曼滤波(EKF),无迹卡尔曼滤波(UKF)以及容积卡尔曼滤波(CKF),在含有随机量测时滞和噪声同步相关的状态估计问题中,CKF–RDSCN具有更高的精度和更好的数值稳定性.     

基于粒子滤波的非线性系统静态参数估计方法*

针对基于滤波方法的最大似然参数估计步长序列过于单一,算法收敛缓慢并很容易收敛于局部最优解的问题,提出了基于似然权值的在线EM参数估计算法(LWOEM)。通过粒子滤波方法实时估计系统的状态值变化,结合最大似然方法计算静态参数的点估计,然后通过计算更新参数的似然值来动态更新步长序列.与在线EM参数估计算法(OEM)的实验结果比较,表明该算法具有更好的适应性和收敛效果。     

Kalman filter-based identification for systems with randomly missing measurements in a network environment

We consider the problem of parameter estimation and output estimation for systems in a transmission control protocol (TCP) based network environment. As a result of networked-induced time delays and packet loss, the input and output data are inevitably subject to randomly missing data. Based on the available incomplete data, we first model the input and output missing data as two separate Bernoulli processes characterised by probabilities of missing data, then a missing output estimator is designed, and finally we develop a recursive algorithm for parameter estimation by modifying the Kalman filter-based algorithm. Under the stochastic framework, convergence properties of both the parameter estimation and output estimation are established. Simulation results illustrate the effectiveness of the proposed algorithms.     

Dissipative control for state-saturated discrete time-varying systems with randomly occurring nonlinearities and missing measurements

In this paper, the dissipative control problem is investigated for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements. In order to render more practical significance of the system model, some Bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements. The purpose of the addressed problem is to design a time-varying output-feedback controller such that the dissipativity performance index is guaranteed over a given finite-horizon. By introducing a free matrix with its infinity norm less than or equal to 1, the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities. A novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when the state saturation is partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed controller design approach.     

采用概率密度分布和粒子滤波的室内跟踪算法

提出了一种新的室内定位跟踪算法,采用了直方图法和核函数法估计参考点处的接收信号强度的概率分布,并将其作为该参考点的位置指纹,描述了该参考点处无线信道的特性;利用粒子滤波解决了非线性状态空间模型下的在线跟踪问题,仿真结果表明基于概率密度分布和粒子滤波的跟踪算法收敛速度快,且对环境变化不敏感,性能优于卡尔曼滤波算法。     

一种带多步随机延迟量测高斯滤波器的一般框架解

提出了一种适用于线性和非线性系统的带多步随机延迟量测高斯滤波器的一般框架解. 为了完成状态的递归更新估计, 噪声向量和先前时刻状态向量被扩展到当前时刻状态向量中. 然后基于贝叶斯方法推导了扩展后状态向量的一般框架解. 对于非线性系统, 通过利用不同的数值计算方法计算贝叶斯解中的高斯加权积分可以推导获得不同的高斯近似滤波器. 最后本文利用三阶球径容积准则来实施提出的方法, 并通过量测被随机延迟多步的目标跟踪模型对所提出的方法进行了仿真, 仿真结果验证了提出方法的有效性和优点.     

Optimal state estimation for networked systems with random parameter matrices,correlated noises and delayed measurements

In this paper, the optimal least-squares state estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with state transition and measurement random parameter matrices and correlated noises. It is assumed that at any sampling time, as a consequence of possible failures during the transmission process, one-step delays with different delay characteristics may occur randomly in the received measurements. The random delay phenomenon is modelled by using a different sequence of Bernoulli random variables in each sensor. The process noise and all the sensor measurement noises are one-step autocorrelated and different sensor noises are one-step cross-correlated. Also, the process noise and each sensor measurement noise are two-step cross-correlated. Based on the proposed model and using an innovation approach, the optimal linear filter is designed by a recursive algorithm which is very simple computationally and suitable for online applications. A numerical simulation is exploited to illustrate the feasibility of the proposed filtering algorithm.     

Development of soft sensor by incorporating the delayed infrequent and irregular measurements

Originated from challenging industrial applications, this paper addresses a soft sensor development problem for linear systems with two types of measurements. One is fast, regular and delay-free measurements. The other is infrequent, irregular measurements with time-varying delays. The approach to be taken is based on the Kalman filter and data fusion technique, avoiding running the full augmented state Kalman filter, and leading to a considerably lower implementation cost. Although it is suboptimal, the loss in performance is minor compared to the optimal filter. Two simulation examples demonstrate the advantages of the proposed approach. An industrial soft sensor application example is also used to demonstrate its practicality.     

Recursive filtering for state‐saturated systems with randomly occurring nonlinearities and missing measurements

This paper deals with the filtering problem for a class of discrete‐time state‐saturated systems subject to randomly occurring nonlinearities and missing measurements. A set of mutually independent Bernoulli random variables is used to describe the random occurrence of the missing measurements. Due to the simultaneous consideration of the state saturation, the randomly occurring nonlinearities, and the missing measurements, it is extremely hard to calculate the actual filtering error covariance in a closed form. As such, the objective of this paper is to construct an upper bound for the filtering error covariance and then design the filter parameters to minimize such an upper bound. The performance of the proposed filters is analyzed in terms of boundedness and monotonicity. Specially, we have shown that the minimum upper bound is always bounded under a mild assumption. Moreover, the relationship between the estimator performance and the arrival probability of the measurements is discussed. A numerical simulation is used to demonstrate the effectiveness of the filtering method.     

Adaptive state observation of linear time-varying systems with delayed measurements and unknown parameters

In this article, we address the problem of adaptive state observation of linear time-varying systems with delayed measurements and unknown parameters. Our new developments extend the results reported in our recently works. The case with known parameters has been studied by many researchers. However in this article we show that the generalized parameter estimation-based observer design provides a very simple solution for the unknown parameter case. Moreover, when this observer design technique is combined with the dynamic regressor extension and mixing estimation procedure the estimated state and parameters converge in fixed-time imposing extremely weak excitation assumptions.     

进化粒子滤波算法及其应用

样本贫化现象是应用粒子滤波算法的一个主要障碍,对估计长时间维持不变量的影响尤为严重.通过分析产生该现象的原因,本文引入进化规划算子构成进化粒子滤波算法,增加样本集的多样性而缓解样本贫化现象的影响,改善其估计与跟踪能力,仿真结果显示所提出的算法是可行的.     

带一步随机延迟量测非线性序列贝叶斯估计的条件后验克拉美罗下界

为了解决带一步随机延迟量测非线性状态估计器可获得最优性能的评价问题,提出了一种适用于带一步随机延迟量测非线性系统的条件后验克拉美罗下界(Conditional posterior Cramr-Rao lower bound, CPCRLB),且现有的CPCRLB仅是所提出的CPCRLB在延迟概率为零时的一种特例. 为了递归地计算提出的CPCRLB,本文提出了一种带一步随机延迟量测的粒子滤波器(Particle filter, PF),继而推导了提出的CPCRLB 一般近似解和在高斯噪声情况下的特殊近似解. 单变量非平稳增长模型、纯方位跟踪和频率调制信号模型的数值仿真证明了本文提出方法与现有方法相比的有效性和优越性.