The problem of optimal robust Kalman state estimation via limited capacity digital communication channels

This paper considers a state estimation problem for a continuous-time uncertain system via a digital communication channel with bit-rate constraints. The estimated state must be quantized, coded and transmitted via a limited capacity digital communication channel. Optimal and suboptimal recursive coder–decoder state estimation schemes are proposed and investigated.     

Corner-based estimation of tire forces and vehicle velocities robust to road conditions

Recent developments in vehicle stability control and active safety systems have led to an interest in reliable vehicle state estimation on various road conditions. This paper presents a novel method for tire force and velocity estimation at each corner to monitor tire capacities individually. This is entailed for more demanding advanced vehicle stability systems and especially in full autonomous driving in harsh maneuvers. By integrating the lumped LuGre tire model and the vehicle kinematics, it is shown that the proposed corner-based estimator does not require knowledge of the road friction and is robust to model uncertainties. The stability of the time-varying longitudinal and lateral velocity estimators is explored. The proposed method is experimentally validated in several maneuvers on different road surface frictions. The experimental results confirm the accuracy and robustness of the state estimators.     

Robust state estimation for a class of uncertain time-delay systems

This paper considers a robust state estimation problem for a class of uncertain time-delay systems. In this problem, the noise and uncertainty are modelled deterministically via an integral quadratic constraint. The robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint. This set is found to be an ellipsoid which is constructed via a linear state estimator.     

Joint state and parameter robust estimation of stochastic nonlinear systems

Successful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez–Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non‐Gaussian distributions is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

A novel phase performance evaluation method for particle swarm optimization algorithms using velocity-based state estimation

The searching process of particle swarm optimizations (PSO) includes four states: exploration, exploitation, convergence and jump-out. Performance information of each state is essential to learn the characteristics of different algorithms as well as to improve their performances. To this end, this paper discusses a novel performance evaluation method of each phase in PSOs. Firstly, we propose a velocity-based state estimation (VSE) method, which can estimate the real-time state of PSO variants with less computation. Subsequently, we provide a phase performance evaluation based on VSE, which includes phase identification, two kinds of phase performance indicators and ranking method. Finally, we design hybrid algorithm experiments, to compare phase performance of six main PSO algorithms, and the phase replacement experiments is used to verify the experimental results.     

Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter

The performance of Bayesian state estimators, such as the extended Kalman filter (EKF), is dependent on the accurate characterisation of the uncertainties in the state dynamics and in the measurements. The parameters of the noise densities associated with these uncertainties are, however, often treated as ‘tuning parameters’ and adjusted in an ad hoc manner while carrying out state and parameter estimation. In this work, two approaches are developed for constructing the maximum likelihood estimates (MLE) of the state and measurement noise covariance matrices from operating input-output data when the states and/or parameters are estimated using the EKF. The unmeasured disturbances affecting the process are either modelled as unstructured noise affecting all the states or as structured noise entering the process predominantly through known, but unmeasured inputs. The first approach is based on direct optimisation of the ML objective function constructed by using the innovation sequence generated from the EKF. The second approach - the extended EM algorithm - is a derivative-free method, that uses the joint likelihood function of the complete data, i.e. states and measurements, to compute the next iterate of the decision variables for the optimisation problem. The efficacy of the proposed approaches is demonstrated on a benchmark continuous fermenter system. The simulation results reveal that both the proposed approaches generate fairly accurate estimates of the noise covariances. Experimental studies on a benchmark laboratory scale heater-mixer setup demonstrate a marked improvement in the predictions of the EKF that uses the covariance estimates obtained from the proposed approaches.     

Design of optimal interval observers using set‐theoretic methods for robust state estimation

This article aims to design an optimal interval observer for discrete linear time‐invariant systems. Particularly, the proposed design method first transforms the interval observer into a zonotopic set‐valued observer by establishing an explicit mathematical relationship between the interval observer and the zonoptopic set‐valued observer. Then, based on the established mathematical relationship, a locally optimal observer gain is designed for the interval observer via the equivalent zonotopic set‐valued observer structure and the Frobenious norm‐based size of zonotopes. Third, considering that the dynamics of the optimal interval observer becomes a discrete linear time‐varying system due to the designed time‐varying optimal gain, an optimization problem to obtain a coordinate transformation matrix and the locally optimal observer gain for the interval observer is formulated and handled. Finally, a theoretic comparison on the conservatism of the interval observer and the zonotopic set‐valued observer is made. At the end of this article, a microbial growth bioprocess is used to illustrate the effectiveness of the proposed method.     

Using the fuzzy-ellipsoid method for robust estimation of the state of a grid system node

Constructing a workload model for a node of a Grid system is considered in terms of control theory. A node is represented as a linear dynamic object acted upon by perturbations with unknown statistical properties. Fuzzy set estimates are used to evaluate the state of the object. They ensure the robustness of the algorithm proposed and its usability under the lack of a priori information on the unknown vector and the inaccuracy of current measurements. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 67–74, November–December 2008.     

A quick method for estimation of parameters of individual pulses in a multipath signal

Consider a multipath signal whose individual signals are deterministic known increasing or decreasing pulses. The problem is to estimate the amplitudes and delay times of individual signals. Several methods have been devoted to the solution of these unknown parameters. The maximum likelihood (ML) estimation and the estimate maximize (EM) algorithm are commonly used, but they are computationally intensive and still insufficient to obtain accurate estimations. The method can provide a quick and accurate estimate of the amplitudes and arrival (delay) times, even in the closely spaced multipaths and heavy noise.     

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.     

A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets

In this article, a computational method based on Haar wavelet in time-domain for solving the problem of optimal control of the linear time invariant systems for any finite time interval is proposed. Haar wavelet integral operational matrix and the properties of Kronecker product are utilized to find the approximated optimal trajectory and optimal control law of the linear systems with respect to a quadratic cost function by solving only the linear algebraic equations. It is shown that parameter estimation of linear system can be done easily using the idea proposed. On the basis of Haar function properties, the results of the article, which include the time information, are illustrated in two examples.     

On the choice of importance distributions for unconstrained and constrained state estimation using particle filter

Recursive state estimation of constrained nonlinear dynamical system has attracted the attention of many researchers in recent years. For nonlinear/non-Gaussian state estimation problems, particle filters have been widely used (Arulampalam et al. [1]). As pointed out by Daum [2], particle filters require a proposal distribution and the choice of proposal distribution is the key design issue. In this paper, a novel approach for generating the proposal distribution based on a constrained Extended Kalman filter (C-EKF), Constrained Unscented Kalman filter (C-UKF) and constrained Ensemble Kalman filter (C-EnkF) has been proposed. The efficacy of the proposed state estimation algorithms using a particle filter is illustrated via a successful implementation on a simulated gas-phase reactor, involving constraints on estimated state variables and another example problem, which involves constraints on the process noise (Rao et al. [10]). We also propose a state estimation scheme for estimating state variables in an autonomous hybrid system using particle filter with Unscented Kalman filter as a proposal and unconstrained Ensemble Kalman filter (EnKF) as a proposal. The efficacy of the proposed state estimation scheme for an autonomous hybrid system is demonstrated by conducting simulation studies on a three-tank hybrid system. The simulation studies underline the crucial role played by the choice of proposal distribution in formulation of particle filters.     

基于IGG抗差最小二乘法的三相配电网谐波状态估计

针对传统最小二乘法在谐波状态估计量测数据中混有粗差时的处理能力不足,提出了一种基于IGG法的抗差最小二乘法。抗差估计是统计学里面常用的一种针对数据中含有粗差的处理方法,而抗差最小二乘法就是将抗差估计和最小二乘法相结合的一种新的估计方法。该方法对量测数据进行降权、保权和淘汰,改善量测数据的权重,从而抵御了粗差对估计结果带来的恶劣影响。同时,目前大多数的配电网谐波状态估计模型采用简化的单相模型,并未考虑配电网三相不平衡的特点,本文建立了配电网的三相数学模型,并采用IEEE33节点系统进行仿真分析,在量测数据中混有粗差时分别运用抗差最小二乘法和传统最小二乘法求解并对估计结果进行误差对比,算例结果表明了抗差最小二乘法具有较强的抗差能力且估计精度优于传统最小二乘法。     

A survey on cyber attacks against nonlinear state estimation in power systems of ubiquitous cities

It is well-known that critical infrastructures would be targets for cyber attacks. In this paper, we focus on the power systems (i.e. smart grids) in ubiquitous cities, where every meter is linked to an information network through wireless networking. In a smart grid system, information from smart meters would be used to perform a state estimation in real time to maintain the stability of the system. A wrong estimation may lead to disastrous consequences (e.g. suspension of electricity supply or a big financial loss). Unfortunately, quite a number of recent results showed that attacks on this estimation process are feasible by manipulating readings of only a few meters. In this paper, we focus on nonlinear state estimation which is a more realistic model and widely employed in a real power grid environment. We category cyber attacks against nonlinear state estimation, and review the mechanisms behind. State-of-the-art security measures to detect these attacks are discussed via sensor protection. Hope that the community would be able to come up with a secure system architecture for ubiquitous cities.     

A model of cerebellar computations for dynamical state estimation

The cerebellum is a neural structure that is essential for agility in vertebrate movements. Its contribution to motor control appears to be due to a fundamental role in dynamical state estimation, which also underlies its role in various non-motor tasks. Single spikes in vestibular sensory neurons carry information about head state. We show how computations for optimal dynamical state estimation may be accomplished when signals are encoded in spikes. This provides a novel way to design dynamical state estimators, and a novel way to interpret the structure and function of the cerebellum.     

Exponential synchronization and state estimation of inertial quaternion‐valued Cohen‐Grossberg neural networks: Lexicographical order method

This paper addresses the problems of synchronization and state estimation for a class of inertial quaternion‐valued Cohen‐Grossberg neural networks. By means of proper control strategy, sufficient conditions are derived for ascertaining exponential synchronization of quaternion‐valued Cohen‐Grossberg neural networks. Subsequently, the state estimation problem has also been augmented to achieve robust stable performance of the estimation error system. What should be mentioned is that, the system states considered in this paper are taking values in an interval, which implies that the states are varying between two different quaternions, thus, an optimal algorithm (lexicographical order method) is employed, which can be used to determine the “magnitude" of two different quaternions. In this case, the interval proposed by the quaternion‐valued is meaningful. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.