稀疏距离扩展目标自适应检测及性能分析

在球不变随机向量杂波背景下,研究了稀疏距离扩展目标的自适应检测问题.基于有序检测理论, 利用协方差矩阵估计方法,分析了自适应检测器(Adaptive detector, AD).其中,基于采样协方差矩阵(Sample covariance matrix, SCM)和归一化采样协方差矩阵(Normalized sample covariance matrix, NSCM),分别建立了AD-SCM和AD-NSCM检测器.从恒虚警率特性和检测性能综合来看, AD-NSCM的性能优于AD-SCM和已有的修正广义似然比检测器.最后,通过仿真实验验证了所提方法的有效性.     

基于自适应重要采样UKF的SAR图像超分辨率方法

针对图像中的软边缘不能完全重建导致生成图像清晰度较低的问题,提出一种基于自适应重要采样无迹卡尔曼滤波(Unscented Kalman Filter,UKF)的SAR图像超分辨率方法.该方法利用协方差匹配技术实现自适应重要采样的UKF框架,通过将测量噪声协方差和处理噪声协方差自适应地调整到SAR图像超分辨率的强度估计框架中,恢复图像中的纹理细节.实验结果表明,当考虑观测和过程噪声协方差时,该方法的超分辨率在去噪、边缘锐化和特征保存方面的性能表现极佳.     

基于主动变采样周期方法的网络控制系统的H∞控制器设计

利用主动变采样周期方法, 本文研究了具有时延及丢包的网络控制系统的 H∞ 控制器设计问题, 其中采样周期在一个有限集合内切换. 提出了一个新的线性估计方法以补偿丢包的负面影响, 并利用多目标优化方法设计系统的 H∞ 控制器. 仿真结果表明了主动变采样周期方法及基于线性估计的丢包补偿方法的有效性.     

分维自适应稀疏网格积分非线性滤波器

针对含加性高斯噪声的非线性离散系统,提出了可分别根据各维状态及量测方程的非线性函数特性来确定采样点及其权重的积分滤波器.设计了基于嵌入式高斯采样积分和稀疏网格法则的自适应多变量采样积分方法,可在匹配函数高阶泰勒展开项时,利用低阶采样点,提出了高效的数据结构和遍历算法,便于采用该积分方法分别估计系统状态/量测的预测均值和协方差矩阵.该滤波器既能根据各维非线性函数的特性确定采样点,又实现了对采样值和权重的完全复用,保证了算法效率.理论分析和仿真表明,该滤波算法中自适应调整的运算量小于计算非线性函数采样值.该滤波器与无迹卡尔曼滤波相比,提高了滤波精度,与固定形式的稀疏网格滤波器相比,提高了采样效率,且该方法为两者的广义形式.仿真实验也验证了状态估计的精确性和函数采样的高效性.     

网络化不确定非线性时滞系统的状态估计

本文研究了离散不确定非线性时滞系统在网络传输不可靠情况下的状态估计问题.针对网络传输丢包问题,采用伯努利(Bernoulli)随机模型,建立了控制信号和输入信号的不可靠传输模型.本文通过状态扩展的方法处理不确定非线性项,得到了扩展状态系统.基于不可靠的控制和测量信息,设计了状态预测器和估计器,并给出相应的误差系统.通过设计最优估计器增益,本文给出了状态预测误差协方差的迭代公式.为了进一步提高状态估计器的精度,设计了一种新型的参数迭代优化方法.针对状态预测误差协方差,本文得到了其稳定性的判别准则.最后,通过一例数值仿真,验证了所得结论的有效性.     

基于序贯重点采样粒子滤波和Cholesky分解的分布估计算法

连续域分布估计算法一般假设数据服从Gauss分布,而且大多采用了单峰的概率模型,但是对于一些复杂的优化问题,单峰的Gauss分布模型不能有效地描述解在空间的分布.提出一种基于序贯重点采样粒子滤波的分布估计算法,采用带权粒子描述优选集样本服从的概率分布,Cholesky分解法分解收缩的协方差矩阵并利用其产生下一代样本,不需要假设样本服从Gauss分布.算法采用的概率模型是多峰的.变量之间的相关性通过采样时利用群体的协方差矩阵显式地予以考虑,并对协方差矩阵为零矩阵的情况进行了处理.仿真实验结果验证了方法的正确性和有效性.     

比例最小偏度单行采样的平方根UKF-SLAM算法

对于UKF-SLAM算法所存在的滤波增益矩阵计算失真,采用对称采样计算复杂度相对较高且易产生非局部效应等问题,提出基于比例最小偏度单行采样的平方根UKF-SLAM算法。改进后的算法采用协方差阵的平方根代替协方差阵带入迭代运算,并以比例最小偏度单行采样的方式优化采样策略。仿真结果表明,该算法能够有效地提高机器人位姿以及特征地图的估计精度,并降低了计算复杂度,提高算法的稳定性。     

双层无迹卡尔曼滤波

针对无迹卡尔曼滤波（Unscented Kalman fllter,UKF）在强非线性系统中估计效果差的问题,提出了双层无迹卡尔曼滤波（Double layer unscented Kalman filter,DLUKF）算法,该算法用带权值的采样点表征先验分布,而后用内层UKF算法对每个采样点进行更新,最后引入外层UKF算法的更新机制得到估计值和估计协方差.仿真结果表明,相比于传统算法,所提的DLUKF算法可以在较低计算负载下获得较高滤波估计精度.     

一类不确定线性系统鲁棒状态估计器设计

本文对一类不确定线性系统给出了一种鲁棒状态估计器设计方法，其主要思想是对允许的系统扰动，通过设计估计器参数矩阵使增广系统的极点位于左半复平面指定圆形区内或指定直线的左侧，且稳态误差协方差阵不超过给定上限，给出了鲁棒估计器存在条件及其解的一般表达式。     

基于二阶循环统计量的盲均衡算法

提出一种新的基于循环二阶统计量的盲均衡算法.通过对信道输出信号进行过采样,建立单输入多输出信道模型.由于过采样等效信道矩阵具有特殊结构,使得仅仅根据零延迟时的协方差矩阵所包含的信息就能实现信道估计,根据不同延迟下的协方差矩阵也可求得不同时延的均衡器矩阵,然后用最小均方误差MMSE准则来优化均衡器得到最佳延迟协方差矩阵.仿真结果表明了该算法的有效性.     

State estimation for stochastic time‐varying multisensor systems with multiplicative noises: Centralized and decentralized data fusion

In this paper, the state estimation problems, including filtering and one‐step prediction, are solved for uncertain stochastic time‐varying multisensor systems by using centralized and decentralized data fusion methods. Uncertainties are considered in all parts of the state space model as multiplicative noises. For the first time, both centralized and decentralized estimators are designed based on the regularized least‐squares method. To design the proposed centralized fusion estimator, observation equations are first rewritten as a stacked observation. Then, an optimal estimator is obtained from a regularized least‐squares problem. In addition, for decentralized data fusion, first, optimal local estimators are designed, and then fusion rule is achieved by solving a least‐squares problem. Two recursive equations are also obtained to compute the unknown covariance matrices of the filtering and prediction errors. Finally, a three‐sensor target‐tracking system is employed to demonstrate the effectiveness and performance of the proposed estimation approaches.     

On Robust H2 Estimation

The problem of state estimation for uncertain systems has attracted a recurring interest in the past decade. In this paper, we shall give an overview on some of the recent development in the area by focusing on the robust H2 (Kalman) filtering of uncertain discrete-time systems. The robust H2 estimation is concerned with the design of a fixed estimator for a family of plants under consideration such that the estimation error covariance is of a minimal upper bound. The uncertainty under consideration includes norm-bounded uncertainty and polytopic uncertainty. In the finite horizon case, we shall discuss a parameterized difference Riccati equation approach for systems with norm-bounded uncertainty and pinpoint the difference of state estimation between systems without uncertaintyand those with uncertainty. In the infinite horizon case, we shall deal with both the norm-bounded and polytopic uncertainties using a linear matrix inequality (LMI) approach. In particular, we shalldemonstrate how the conservatism of design can be improved using a slack variable technique. We also propose an iterative algorithm to refine a designed estimator. An example will be given to compareestimators designed using various techniques.     

Optimal state estimation using randomly delayed measurements without time stamping

This paper studies an optimal state estimation (Kalman filtering) problem under the assumption that output measurements are subject to random time delays caused by network transmissions without time stamping. We first propose a random time delay model which mimics many practical digital network systems. We then study the so‐called unbiased, uniformly bounded linear state estimators and show that the estimator structure is given based on the average of all received measurements at each time for different maximum time delays. The estimator gains can be derived by solving a set of recursive discrete‐time Riccati equations. The estimator is guaranteed to be optimal in the sense that it is unbiased with uniformly bounded estimation error covariance. A simulation example shows the effectiveness of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation of the autoregressive parameters of a mixed autoregressive moving-average time series

The problem of estimating the autoregressive parameters of a mixed autoregressive moving-average (ARMA) time series (of known order) using the output data alone is treated. This problem is equivalent to the estimation of the denominator terms of the scalar transfer function of a stationary, linear discrete time system excited by an unobserved unenrrelated sequence input by employing only the observations of the scalar output. The solution of this problem solves the problem of the identification of the dynamics of a white-noise excited continuous-time linear stationary system using sampled data. The latter problem was suggested by Bartlett in 1946. The problem treated here has appeared before in the engineering literature. The earlier treatment yielded biased parameter estimates. An asymptotically unbiased estimator of the autoregressive parameters is obtained as the solution of a modified set of Yule-Walker equations. The asymptotic estimator covariance matrix behaves like a least-squares parameter estimate of an observation set with unknown error covariances. The estimators are also shown to be unbiased in the presence of additive independent observation noise of arbitrary finite correlation time. An example illustrates the performance of the estimating procedures.     

Event-based input and state estimation for linear discrete time-varying systems

In this paper, the joint input and state estimation problem is considered for linear discrete-time stochastic systems. An event-based transmission scheme is proposed with which the current measurement is released to the estimator only when the difference from the previously transmitted one is greater than a prescribed threshold. The purpose of this paper is to design an event-based recursive input and state estimator such that the estimation error covariances have guaranteed upper bounds at all times. The estimator gains are calculated by solving two constrained optimisation problems and the upper bounds of the estimation error covariances are obtained in form of the solution to Riccati-like difference equations. Special efforts are made on the choices of appropriate scalar parameter sequences in order to reduce the upper bounds. In the special case of linear time-invariant system, sufficient conditions are acquired under which the upper bound of the error covariance of the state estimation is asymptomatically bounded. Numerical simulations are conducted to illustrate the effectiveness of the proposed estimation algorithm.     

Multi-rate optimal state estimation

This article formulates a multi-rate linear minimum mean squared error (LMMSE) state estimation problem, which includes four rates as follows: the state updating rate in the model, the measurement sampling rate, the estimate updating rate and the estimate output rate. This formulation is unique in two ways. First, the rate ratio between state measurement and state estimate is more general (a rational number), instead of just an integer or its reciprocal as considered in the existing literature. Second, state estimates are produced in blocks, which have never been considered before in the multi-rate estimator design. The multi-rate LMMSE estimation problem is solved by examining several distinctive cases for single-rate state estimation, obtained through the lifting technique. Also, sufficient conditions are given for asymptotic stability of the proposed multi-rate LMMSE estimators. An example in tracking a manoeuvering target is given to illustrate the proposed multi-rate state estimators.     

A New Approach To Optimal and Self‐Tuning Filtering,Smoothing and Prediction For Discrete‐Time Systems

A new approach to optimal and self‐tuning state estimation of linear discrete time‐invariant systems is presented, using projection theory and innovation analysis method in time domain. The optimal estimators are calculated by means of spectral factorization. The filter, predictor, and smoother are given in a unified form. Comparisons are made to the previously known techniques such as the Kalman filtering and the polynomial method initiated by Kucera. When the noise covariance matrices are not available, self‐tuning estimators are obtained through the identification of an ARMA innovation model. The self‐tuning estimator asymptotically converges to the optimal estimator.     

Design of distributed decentralized estimators for formations with fixed and stochastic communication topologies

This paper proposes a solution to the problem of synthesizing distributed decentralized estimators for a formation of agents. The collected dynamics of the formation are modeled by a discrete LTI system. In the considered estimation structure, each agent of the formation carries an estimate of the entire formation state. Agents of the formation can communicate information between each other through unidirectional links modeled with a fixed or a stochastic communication topology. The design procedures are based on a set of convex optimization problems with linear matrix inequalities and result in the suboptimal choice of estimator gains which stabilize the estimation error dynamics and minimize a norm of the estimation error correlation matrix.     

An ordinary differential equation technique for continuous-timeparameter estimation

An ordinary differential equation technique is developed via averaging theory and weak convergence theory to analyze the asymptotic behavior of continuous-time recursive stochastic parameter estimators. This technique is an extension of L. Ljung's (1977) work in discrete time. Using this technique, the following results are obtained for various continuous-time parameter estimators. The recursive prediction error method, with probability one, converges to a minimum of the likelihood function. The same is true of the gradient method. The extended Kalman filter fails, with probability one, to converge to the true values of the parameters in a system whose state noise covariance is unknown. An example of the extended least squares algorithm is analyzed in detail. Analytic bounds are obtained for the asymptotic rate of convergence of all three estimators applied to this example     

Robust Kalman filtering for uncertain systems

This paper studies the problem of Kalman filter design for uncertain systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in both the state and measurement matrices. The problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties. A Riccati equation approach is proposed to solve the above problem. Furthermore, a suboptimal covariance upper bound can be computed by a convex optimization.