Noise modeling concepts in nonlinear state estimation

It is quite common to assume that uncertainty enters through additive white noise sources when using recursive state estimation algorithms. Also unknown and time-varying parameters are often modeled similarly by augmenting the states with a parameter vector. Further, it is common to reflect initial model uncertainty through the choice of the initial covariance matrices for the states and parameters.In this paper we study noise modeling based on a hypothesis that it is important to model noise correctly. In practice this implies a critical view on the dominating ‘additive noise paradigm’ as a means to model uncertainty. Alternative concepts of modeling the noise are investigated, and it is shown that modeling noise by introducing it in the system auxiliary variables and control inputs may have a positive impact on estimation performance.     

Ellipsoidal parameter or state estimation under model uncertainty

Ellipsoidal outer-bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown-but-bounded state perturbations and measurement noise. The technique described in this paper applies to linear discrete-time dynamic systems; it can also be applied to weakly non-linear systems if non-linearity is replaced by uncertainty. Many difficulties arise because of the non-convexity of feasible sets. Combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis. Analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented, which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids. The results obtained for combined quadratic constraints are extended to other types of model uncertainty.     

离散系统的鲁棒约束方差估计及应用——模型噪声强度不确定情形

考虑离散随机系统在模型噪声强度不确定及估计误差方差受约束情形下的一类鲁棒状态 估计问题,即希望找到这样的滤波增益,使得当模型噪声强度在一定范围内变动时,每个状态 分量的估计误差方差始终不大于预先指定值.文中给出了这种滤波增益的设计方法,并以一 类机动目标跟踪问题为例,说明这种设计方法的直接性与有效性.     

离散系统的鲁捧约束方差估计及应用──模型噪声强度不确定情形

考虑离散随机系统在模型噪声强度不确定及估计误差方差受约束情形下的一类鲁棒状态估计问题，即希望找到这样的滤波增益，使得当模型噪声强度在一定范围内变动时，每个状态分量的估计误差方差始终不大于预先指定值。文中给出了这种滤波增益的设计方法，并以一类机动目标跟踪问题为例，说明这种设计方法的直接性与有效性。     

噪声强度不确定的连续系统的鲁棒采样估计

基于内采产特性讨论噪声强度不确定的连续系统的鲁棒采样估计问题,主要目的是为这类不确定系统设计离散滤波器,使每个状态的估计误差方差不大于预先指定值,从而获得满意的稳态滤波特性,文中首先研究了仅有模型噪声强度不确定时的情形,随后说明当测量噪声强度不确定时可用同样方法进行研究,最后用数值例子说明了本文设计方法的有用性和有效性。     

Interval observer versus set‐membership approaches for fault detection in uncertain systems using zonotopes

This paper presents both analysis and comparison of the interval observer–based and set‐membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both state disturbance and measurement noise are modeled in a deterministic context following the unknown but bounded approach. The propagation of uncertainty in the state estimation is bounded through a zonotopic set representation. Both approaches have been mathematically related and compared when used for state estimation and FD. A case study based on a two‐tanks system is employed for showing the relationship between both approaches while comparing their performance.     

State estimation and nonlinear predictive control of autonomous hybrid system using derivative free state estimators

In this work, we develop a state estimation scheme for nonlinear autonomous hybrid systems, which are subjected to stochastic state disturbances and measurement noise, using derivative free state estimators. In particular, we propose the use of ensemble Kalman filters (EnKF), which belong to the class of particle filters, and unscented Kalman filters (UKF) to carry out estimation of state variables of autonomous hybrid system. We then proceed to develop novel nonlinear model predictive control (NMPC) schemes using these derivative free estimators for better control of autonomous hybrid systems. A salient feature of the proposed NMPC schemes is that the future trajectory predictions are based on stochastic simulations, which explicitly account for the uncertainty in predictions arising from the uncertainties in the initial state and the unmeasured disturbances. The efficacy of the proposed state estimation based control scheme is demonstrated by conducting simulation studies on a benchmark three-tank hybrid system. Analysis of the simulation results reveals that EnKF and UKF based NMPC strategies is well suited for effective control of nonlinear autonomous three-tank hybrid system.     

离散时间线性时变系统的传感器故障估计滤波器设计

针对一类离散时间线性时变系统提出了一种传感器故障诊断方法.本文首先通过状态增广的方式将被研究的系统转化为描述系统的形式,并且基于该描述系统模型,采用方差最小化原则设计了一种能够同时估计系统状态和传感器故障的故障估计滤波器,然后利用一组故障估计滤波器提出了一种故障诊断方法.本文的主要贡献在于针对离散线性时变系统提出了一种不需要对故障动态进行假设的传感器故障诊断方法.所提出方法的另一个优点是该方法能够在存在过程和测量噪声的情况下实现故障检测、分离与估计.仿真结果说明了所提出方法的有效性.     

High-gain observers in the presence of measurement noise: A switched-gain approach

This paper considers output feedback control using high-gain observers in the presence of measurement noise for a class of nonlinear systems. We study stability in the presence of measurement noise and illustrate the tradeoff when selecting the observer gain between state reconstruction speed and robustness to model uncertainty on the one hand versus amplification of noise on the other. Based on this tradeoff we propose a high-gain observer that switches between two gain values. This scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error. We argue boundedness and ultimate boundedness of the closed-loop system under switched-gain output feedback.     

Robust moving horizon estimation based output feedback economic model predictive control

In this work, we develop an economic model predictive control scheme for a class of nonlinear systems with bounded process and measurement noise. In order to achieve fast convergence of the state estimates to the actual system state as well as the robustness of the observer to measurement and process noise, a deterministic (high-gain) observer is first applied for a small time period with continuous output measurements to drive the estimation error to a small value; after this initial small time period, a robust moving horizon estimation scheme is used on-line to provide more accurate and smoother state estimates. In the design of the robust moving horizon estimation scheme, the deterministic observer is used to calculate reference estimates and confidence regions that contain the actual system state. Within the confidence regions, the moving horizon estimation scheme is allowed to optimize its estimates. The output feedback economic model predictive controller is designed via Lyapunov techniques based on state estimates provided by the deterministic observer and the moving horizon estimation scheme. The stability of the closed-loop system is analyzed rigorously and conditions that ensure the closed-loop stability are derived. Extensive simulations based on a chemical process example illustrate the effectiveness of the proposed approach.     

自适应SVD–UKF算法及在穿刺状态估计中的应用

柔性针在实际穿刺过程中会产生不规则形变, 导致柔性针模型存在参数不确定性问题, 影响穿刺精度. 本文针对柔性针穿刺过程存在的不确定性问题以及超声成像等设备存在的量测噪声统计特征不准确性问题, 提出了一种带有噪声估计器的自适应奇异值分解无迹卡尔曼滤波算法. 该算法采用自适应因子实时修正动力学模型误差, 通过奇异值分解抑制系统状态协方差矩阵的负定性, 利用Sage-Husa估计器在线估计噪声的统计特性, 减小了系统状态估计误差. 将新算法应用于带有曲率不定性的柔性针穿刺模型进行计算仿真, 仿真结果显示, 新的算法较现有的UKF算法相比, 估计误差减小了0.28 mm(82.7%), 与AUKF算法相比, 估计误差减小0.06 mm(52%). 因此, 新算法可有效改善滤波性能, 提高穿刺状态的估计精度.     

具有噪声信息与状态模型不确定系统的IMM自适应滤波

卡尔曼滤波器广泛用于解决线性高斯系统的状态估计问题.然而,在实际应用中过程噪声和系统模型参数先验信息未知,且量测受到异常值干扰,给准确估计系统状态带来极大困难.针对具有噪声信息和状态模型不确定的动态系统,提出一种广义交互式多模型自适应滤波算法.该算法设计多个模型并行的方式对系统不确定进行处理,对于每个模型,建立Skew-T分布非对称重尾噪声表示模型,为了解决过程噪声与系统协方差相互耦合难以求解的问题,利用逆威沙特分布对系统预测协方差矩阵进行描述,并通过变分贝叶斯推理递归计算系统状态的后验分布.仿真结果和实验验证表明,在噪声信息和状态模型不确定条件下,所提出算法具有较高的估计精度.     

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.     

Mission-based online generation of probabilistic monitoring models for mobile robot navigation using Petri nets

This paper presents a generic hybrid monitoring approach, which allows the detection of inconsistencies in the navigation of autonomous mobile robots using online-generated models. A mission on the context of the navigation corresponds to an autonomous navigation from a start to an end mission point. The operator defines this mission by selecting a final goal point. Based on this selection the monitoring models for the current mission must be generated online. The originalities of this work are (i) the association of classic state estimation based on a particle filter with a special class of Petri net in order to deliver an estimation of the next robot state (position) as well as the environment state (graph nodes) and to use both pieces of information to distinguish between external noise influences, internal component faults and global behaviour inconsistency (ii) the integration of the geometrical and the logical environment representation into the monitor model (iii) the online generation of the corresponding monitoring model for the present mission trajectory while the system is running. The model takes simultaneously into account the uncertainty of the robot and of the environment through a unified modelling of both. To show the feasibility of the approach we apply it to an intelligent wheelchair (IWC) as a special type of autonomous mobile robot.     

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 uncertainty and 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 shall demonstrate 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 compare estimators designed using various techniques.     

State estimation for nonlinear systems under model uncertainties: a class of sliding-mode observers

This paper deals with the classical problem of state estimation, considering partially unknown, nonlinear systems with noise measurements. Estimation of both, state variables and unstructured uncertain term, are performed simultaneously. In order to transform the measured disturbance into system disturbance, an alternative system representation is proposed, which lead a more advantageous observer structure. The observer proposed contains a proportional-type contribution and a sliding term for the measurement of error, which provides robustness against noisy measurements and model uncertainties. Convergence analysis of the estimation methodology proposed is performed, analysing the equation of the dynamics of the estimation error; it is shown that the observer exhibits asymptotic convergence. Estimation of monomer concentration, average molecular weight, polydispersity and filtering of temperature in a batch stirred polymerization reactor illustrates the good performance of the observer proposed.     

基于凸空间收缩滤波的噪声不确定时滞系统状态估计

针对受未知但有界噪声干扰的噪声不确定时滞系统, 提出了一种基于凸空间收缩滤波的系统状态估计方法. 首先, 利用凸空间定义包裹系统真实状态的可行集, 求解下一时刻的凸空间体形状矩阵; 随后从凸空间收缩角度, 利用当前时刻噪声和扰动构造带空间, 得到满足状态预测和量测更新条件的凸空间结构; 进而, 依据时滞系统约束条件构造线性规划不等式方程组, 利用线性规划求解该凸空间, 得到包裹状态可行集的最紧致凸空间体; 最后, 通过数值仿真与电池化成工艺变换器案例仿真, 验证了本文所提方法解决不确定时滞系统状态估计问题的有效性和准确性.     

Stochastic tube MPC with state estimation

An output feedback Model Predictive Control (MPC) strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed. Given the probability distributions of the disturbance input, the measurement noise and the initial state estimation error, the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator. From these distributions, a set of deterministic constraints is computed for the predictions of a nominal model. The constraints are incorporated in a receding horizon optimization of an expected quadratic cost, which is formulated as a quadratic program. The constraints are constructed so as to provide a guarantee of recursive feasibility, and the closed loop system is stable in a mean-square sense. All uncertainties in this paper are taken to be bounded—in most control applications this gives a more realistic representation of process and measurement noise than the more traditional Gaussian assumption.     

基于自适应卡尔曼滤波的机动目标跟踪算法

在机动目标跟踪过程中,由于目标运动的不确定性,雷达系统接收的数据存在噪声,使预置目标运动模型通常很难得到较高的跟踪精度。为此,以自适应卡尔曼滤波为基础,将直角坐标系和球坐标系相结合,提出了一种混合坐标系下的自适应卡尔曼滤波算法。算法避免了两个坐标系变换引起的噪声统计规律变化问题,并针对目标发生大机动运动的情况,自适应的调整动态模型中机动目标运动参数。蒙特卡洛仿真结果表明,改进算法的收敛速度和对状态的估计精度均得到优化,并对机动目标具有较好的跟踪性能。