三种高效快速的量子态滤波和估计优化算法

针对不同干扰和噪声情况下的量子状态估计和滤波问题,分别提出相应的高效量子状态密度矩阵重构凸优化算法.对于稀疏状态干扰和测量噪声同时存在的情况,提出量子状态滤波算法.对分别存在稀疏状态干扰和测量噪声的情况,提出相应两种不同的量子状态估计算法.在5量子位的状态密度矩阵估计仿真实验中分析不同采样率下的3种算法性能.实验表明,3种算法均具有较低的计算复杂度、较快的收敛速度和较低的估计误差.     

基于粒子滤波算法的混合系统监测与诊断

利用粒子滤波算法具有同时估计连续状态和离散状态的特点,提出一种可用于混合系 统状态监测与诊断的新方法.给出了该方法的理论推导和设计步骤,讨论了在诊断应用中粒子滤 波器所遇到的问题,并给出了改善的措施.仿真结果证明用粒子滤波器对混合系统进行监测与诊 断是可行的,所提的方法对估计结果有比较好的改善.     

量子投影滤波

量子滤波器基于贝叶斯原理,利用连续弱测量数据给出当前时刻量子系统状态的最优估计,是量子计算和量子调控技术中极为重要的一环.然而,随着量子系统能级数提高,量子滤波器的实时计算复杂度呈二次型增长.本文介绍了一种量子投影滤波方法,用于减少量子滤波器的实时计算复杂度.基于量子信息几何方法,量子轨迹被限制在了一个由一类非归一化量子密度矩阵组成的子流形中.量子态从而可通过计算子流形的坐标系统来近似获得.仿真实验说明了投影滤波方法的有效性.     

基于OBE算法的自适应集员状态估计

研究了具有椭球集合描述的离散时间动态线性系统的状态估计问题.从提高计算的有 效性和可实现性的角度出发,通过在不同的更新阶段采用优化定界椭球(OBE)算法,提出了一 种新颖的解决状态估计的方法.通过与ROBP(recursive state bounding by parallelotopes)算法 和Kalman滤波的仿真比较,验证了本方法的性能.     

改进的迭代收缩阈值算法及其在量子状态估计中的应用

本文将含有稀疏干扰的量子状态估计问题, 转化为考虑量子状态的约束条件下, 分别求解密度矩阵的核范 数, 以及稀疏干扰l1范数的两个子问题的优化问题. 针对迭代收缩阈值算法(ISTA)所存在的收敛速度慢的问题, 通 过在两个子问题的迭代估计中, 引入一个加速算子, 对当前值与前一次值之差进行进一步的补偿, 来提高算法的迭 代速度(FISTA). 并将FISTA算法应用于求解含有稀疏干扰的量子状态估计中. 针对5个量子位的状态估计的仿真实 验, 将FISTA分别与ISTA、交替方向乘子法(ADMM)、不动点方程的ADMM算法(FP–ADMM), 以及非精确的ADMM 算法(I–ADMM)4种优化算法进行性能对比. 实验结果表明, FISTA算法具有更加优越的收敛速度, 并且能够得到更 小的量子状态估计误差.     

通讯约束下的线性系统状态降维与估计

本文面向状态估计, 考察了通讯功率受限时线性动态系统状态的降维问题. 为了满足平行信道传输数据的维数限制和通讯功率约束, 采取降低状态维数的方法, 通过传输信号的新息, 提高传输效率, 利用有限的通信资源, 使得接收端的状态估计达到最优. 本文采用差分脉冲编码调制系统(DPCM), 基于最小误差熵估计准则和Kalman估计算法, 得出了最优的状态降维矩阵的设计方法, 并且对随机系统的可估计性以及对相应确定性系统的能观性进行了分析. 分析和仿真结果表明, 这种设计方法在传输信号满足通讯功率限制的条件下可以使接收端的状态估计性能达到最优.     

基于深度学习LDAMP网络的量子状态估计

设计出一种基于学习去噪的近似消息传递(Learned denoising-based approximate message passing, LDAMP)的深度学习网络,将其应用于量子状态的估计.该网络将去噪卷积神经网络与基于去噪的近似消息传递算法相结合,利用量子系统输出的测量值作为网络输入,通过设计出的带有去噪卷积神经网络的LDAMP网络重构出原始密度矩阵,从大量的训练样本中提取各种不同类型密度矩阵的结构特征,来实现对量子本征态、叠加态以及混合态的估计.在对4个量子位的量子态估计的具体实例中,分别在无和有测量噪声干扰情况下,对基于LDAMP网络的量子态估计进行了仿真实验性能研究,并与基于压缩感知的交替方向乘子法和三维块匹配近似消息传递等算法进行估计性能对比研究.数值仿真实验结果表明,所设计的LDAMP网络可以在较少的测量的采样率下,同时完成对4种量子态的更高精度估计.     

基于两步测量方法及其最少观测次数的任意量子纯态估计

量子状态层析所需要的完备观测次数d~2(d=2~n)随着状态的量子位数n的增加呈指数增长,这使得对高维量子态的层析变得十分困难.本文提出一种基于两步测量的量子态估计方法,可以对任意量子纯态的估计提供最少的观测次数.本文证明:当选择泡利观测算符,采用本文所提出的量子态估计方法对d=2n维希尔伯特空间中的任意n量子位纯态进行重构时,如果为本征态,那么所需最少观测次数memin仅为memin=n;对于包含l(2 6 l 6 d)个非零本征值的叠加态,重构所需最少观测次数msmin满足msmin=d+2l..3,此数目远小于压缩传感理论给出的量子态重构所需测量配置数目O(rd log d),以及目前已发表论文给出的纯态唯一确定所需最少观测次数4d..5.同时给出最少观测次数对应的最优观测算符集的构建方案,并通过仿真实验对本文所提出的量子态估计方法进行验证,实验中重构保真度均达到97%以上.     

线性离散随机系统输入和状态的多步估计方法及应用

具有未知输入的系统的状态估计问题已经在过去几十年里引起了相当的关注.本文对于线性离散随机系统提出了一种基于多步信息的输入和状态同步估计方法.首先,采用多步信息的最小方差方法来获得未知输入.由于引入了包含多个时间步骤的扩张状态和测量向量而计算多步信息,使估计结果与一步估计相比减少了对噪声的敏感性.其次,利用输入估计值和卡尔曼滤波估计过去和当前的状态.该方法在未知输入维数等于状态维数时仍然有良好的估计效果.数值仿真验证了提出的估计方法的有效性.最后,该方法应用于厌氧消化过程反应罐中的溶解甲烷和二氧化碳的浓度估计以验证方法的实用性.     

网络攻击下的信息物理系统安全状态估计研究综述

近年来,信息物理系统在工业界的广泛应用引起了人们对系统安全问题的极大关注.信息物理系统对通信网络的深度依赖,使得网络攻击成为其中最为严峻的威胁之一,特别是那些能够干扰系统状态认知的攻击,因此,安全状态估计(即在遭受攻击时正确估计系统状态)已成为各界广泛关注的安全问题之一.此文旨在总结网络攻击下信息物理系统安全状态估计研究的进展.首先,介绍典型的网络攻击,并详细阐述在稀疏攻击下的安全状态估计问题.其次,探讨集中式安全状态估计和分布式安全状态估计的研究现状.在考虑稀疏攻击下安全状态估计问题的难点时,关键在于如何快速找到受到攻击的信道集合(这可能涉及到高计算复杂度).因此,将安全状态估计方法分为遍历搜索和非遍历搜索两大类,并对现有方法的优缺点进行归纳总结和详细阐述.然后,介绍稀疏攻击下信息物理系统安全状态能观性分析的研究现状.现有的研究结果表明:增加检测机制或先验知识可以缓解在稀疏攻击下安全状态估计所需的基础冗余度要求;同时,通过区分攻击和故障,也能有效降低传感器冗余度要求.最后,对信息物理系统安全状态估计仍然存在的问题进行展望,并提出一些可能的解决方向.     

量子态估计简介及其在超导电路电动力学系统中的应用

量子态估计是量子计算以及量子调控的基础,一般分为量子态层析,即对未知量子态(或过程的初态)进行估计,以及量子滤波,即对量子态进行实时的估计.本文首先介绍了近年来量子态层析技术新的进展,内容包括极大似然方法,压缩感知方法和线性回归方法,并分析了它们的适用范围及各自的优缺点.进一步,基于量子计算的成熟载体超导电路电动力学系统,介绍了基于连续弱测量对量子态进行实时估计的贝叶斯方法,并分析了贝叶斯估计的适用情形.进一步,通过仿真实现了量子贝叶斯估计,可以很容易发现贝叶斯方法能够精确地实时追踪量子态的演化.     

Distributed bounded-error state estimation based on practical robust positive invariance

We propose a state estimator for linear discrete-time systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state estimator that exploits suitable pieces of information from parent subsystems. Furthermore, each local estimator reconstructs the state of the corresponding subsystem only. Different from methods based on moving horizon estimation, our approach does not require the online solution to optimisation problems. Our state estimation scheme, which is based on the notion of practical robust positive invariance, also guarantees satisfaction of constraints on local estimation errors and it can be updated with a limited computational effort when subsystems are added or removed.     

Improved state estimator in the face of unreliable parameters

The improvement in state estimation based on independently estimated parameter values can be marginal when these parameter values are in error. A measure of uncertainty in the parameters is their error covariance, which most parameter estimation methods do not yield reliably. This work develops a new approach that obviates reliance on incorrect error covariance of the parameters. Uncertainty in the parameter values is assessed on the basis of errors in a priori predictions over a certain time horizon. This uncertainty measure is incorporated into the state estimator, modifying the state gains to account for errors in the parameter values used.     

Humanoid state estimation using a moving horizon estimator

In this research, a new state estimator based on moving horizon estimation theory is suggested for the humanoid robot state estimation. So far, there are almost no studies on the moving horizon estimator (MHE)-based humanoid state estimator. Instead, a large number of humanoid state estimators based on the Kalman filter (KF) have been proposed. However, such estimators cannot guarantee optimality when the system model is nonlinear or when there is a non-Gaussian modeling error. In addition, with KF, it is difficult to incorporate inequality constraints. Since a humanoid is a complex system, its mathematical model is normally nonlinear, and is limited in its ability to characterize the system accurately. Therefore, KF-based humanoid state estimation has unavoidable limitations. To overcome these limitations, we propose a new approach to humanoid state estimation by using a MHE. It can accommodate not only nonlinear systems and constraints, but also it can partially cope with non-Gaussian modeling error. The proposed estimator framework facilitates the use of a simple model, even in the presence of a large modeling error. In addition, it can estimate the humanoid state more accurately than a KF-based estimator. The performance of the proposed approach was verified experimentally.     

Nonlinear Bayesian Estimation: From Kalman Filtering to a Broader Horizon

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date, one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective, which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics (e.g., mean and covariance) conditioned on a system's measurement data. This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering (KF) techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.      

Distributed moving horizon state estimation for nonlinear systems with bounded uncertainties

In this work, we propose a distributed moving horizon state estimation (DMHE) design for a class of nonlinear systems with bounded output measurement noise and process disturbances. Specifically, we consider a class of nonlinear systems that are composed of several subsystems and the subsystems interact with each other via their subsystem states. First, a distributed estimation algorithm is designed which specifies the information exchange protocol between the subsystems and the implementation strategy of the DMHE. Subsequently, a local moving horizon estimation (MHE) scheme is designed for each subsystem. In the design of each subsystem MHE, an auxiliary nonlinear deterministic observer that can asymptotically track the corresponding nominal subsystem state when the subsystem interactions are absent is taken advantage of. For each subsystem, the nonlinear deterministic observer together with an error correction term is used to calculate a confidence region for the subsystem state every sampling time. Within the confidence region, the subsystem MHE is allowed to optimize its estimate. The proposed DMHE scheme is proved to give bounded estimation errors. It is also possible to tune the convergence rate of the state estimate given by the DMHE to the actual system state. The performance of the proposed DMHE is illustrated via the application to a reactor-separator process example.     

人工智能技术在电力系统状态估计的应用研究

为了有效地提高状态估计的计算精度和鲁棒性,将人工智能技术与电网数据相结合,提出了基于偏最小二乘(PLS)和极限学习(ELM)的电力系统状态估计方法。针对量测量之间的强相关性问题,采用偏最小二乘(PLS)对各量测量进行重要信息提取和变量选择,将得到的最优变量输入ELM模型,从而建立了状态量的PLS-ELM模型,然后,采用IEEE14节点系统数据样本和实际电网历史数据对所提方法进行了验证,并将该方法与其他方法进行对比。结果表明,所提状态估计方法降低了模型的复杂程度,能够有效地抵抗量测量中的不良数据,具有较高的估计精度和较强的鲁棒性。     

Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems

This paper is concerned with the joint estimation of states and parameters of a special class of nonlinear systems, ie, bilinear systems. The key is to investigate new estimation methods for interactive state and parameter estimation of the considered system based on the interactive estimation theory. Because the system states are unknown, a bilinear state observer is established based on the Kalman filtering principle. Then, the unavailable states are updated by the state observer outputs recursively. Once the state estimates are obtained, the bilinear state observer–based hierarchical stochastic gradient algorithm is developed by using the gradient search. For the purpose of improving the convergence rate and the parameter estimation accuracy, a bilinear state observer–based hierarchical multi‐innovation stochastic gradient algorithm is proposed by expanding a scalar innovation to an innovation vector. The convergence analysis indicates that the parameter estimates can converge to their true values. The numerical example illustrates the effectiveness of the proposed algorithms.     

Observer-enhanced distributed moving horizon state estimation subject to communication delays

In this work, we focus on distributed moving horizon estimation (DMHE) of nonlinear systems subject to time-varying communication delays. In particular, a class of nonlinear systems composed of subsystems interacting with each other via their states is considered. In the proposed design, an observer-enhanced moving horizon state estimator (MHE) is designed for each subsystem. The distributed MHEs exchange information via a shared communication network. To handle communication delays, an open-loop state predictor is designed for each subsystem to provide predictions of unavailable subsystem states (due to delays). Based on the predictions, an auxiliary nonlinear observer is used to generate a reference subsystem state estimate for each subsystem. The reference subsystem state estimate is used to formulate a confidence region for the actual subsystem state. The MHE of a subsystem is only allowed to optimize its subsystem state estimate within the corresponding confidence region. Under the assumption that there is an upper bound on the time-varying delays, the proposed DMHE is proved to give decreasing and ultimately bounded estimation error. The theoretical results are illustrated via the application to a reactor–separator chemical process.