基于最优定界椭球的扩展集员滤波算法研究

针对噪声未知但有界的非线性系统,提出了一种基于最优定界椭球的扩展集员滤波算法.首先,对非线性状态方程和量测方程进行泰勒级数展开,采用区间分析方法对线性化误差进行外包定界,并通过椭球近似将其整合到系统噪声中;在此基础上通过预测步和滤波步两步过程来计算与量测和噪声边界近似相一致的待估计状态的可行集.以Duffing方程为例,与扩展卡尔曼滤波方法的仿真比较表明了该算法的精确性和鲁棒性.     

非线性系统中心差分集员估计方法

用于非线性椭球估计的扩展集员算法在实际应用中存在着实现性差、边界估计相对保守等缺陷.本文提出了一种用于非线性系统状态估计的中心差分集员估计方法,以改善传统非线性集员滤波算法的估计性能.为克服泰勒展开的固有缺陷,采用低阶多维Stirling内插多项式代替泰勒展开实现非线性模型的线性化处理;利用半定规划方法对线性化误差进行外包定界并将其融入过程噪声和量测噪声中,以降低误差定界的保守性;量测更新中,为提高算法的实时性,将量测椭球松弛为多个带的交,依次参与状态椭球的更新,从而实现状态定界椭球的次优估计;同时,对椭球—带交集迭代过程中椭球中心到超平面的归一化距离的计算方法进行了改进,使当前时刻每次迭代的椭球均参与计算并选取最优值,以减小累计误差.仿真结果表明了本文所提出算法的有效性和改进性能.     

基于超平行空间集员滤波的非线性系统状态估计方法

针对噪声有界但未知条件下的非线性系统状态估计问题,提出基于超平行空间集员滤波算法.利用Stirling矩阵将模型进行一阶展开,基于凸差规划完成线性化误差定界,采用超平行空间表示误差边界和状态可行集,求解下一时刻预测状态可行集超平行体.在更新步将观测值分解为多个带,融入观测值的线性化误差并将带依次与超平行体相交,得到该时刻超平行空间描述下的状态可行集更新情况.所提出算法能够避免在求解线性化误差过程中外包误差集合带来的体积扩充,降低非线性集员滤波算法的保守性,仿真示例验证了所提出算法的可行性和有效性.     

基于MIT规则的自适应扩展集员估计方法

用于非线性椭球估计的自适应扩展集员(Adaptive extended set-membership filter, AESMF)算法在实际应用中存在着过程噪声设定椭球与真实噪声椭球失配的问题, 导致滤波器的估计出现偏差甚至发散. 本文提出了一种基于MIT规则过程噪声椭球最优化的自适应扩展集员估计算法(MIT-AESMF), 用于解决非线性系统时变状态和参数的联合估计和定界中过程噪声无法精确建模问题的新算法. 本算法通过MIT优化规则,在线计算使一步预测偏差包络椭球最小化的过程噪声包络椭球, 以此保证滤波器健康指标满足有效条件; 最后, 采用地面移动机器人状态和动力学参数联合估计验证了所提出方法的有效性.     

基于改进集员滤波的港口自动跨运车状态估计方法

针对自动跨运车状态估计问题,设计改进的集员滤波算法,在未知有界噪声环境下,获取自动跨运车实时运动状态的估计信息.首先,将自动跨运车运动学模型进行线性化处理,同时考虑其转向因素和侧倾因素,得到车辆的动力学线性模型;其次,将可能存在的内外部扰动建模为未知有界噪声,进而设计改进的集员滤波器,通过获取状态椭球域实现对自动跨运车运动参数的状态估计,同时给出改进的集员滤波算法;最后,通过仿真实验验证所提出算法的可行性和有效性.实验结果表明,所提出的改进集员滤波算法具有良好的状态估计性能.     

不确定噪声下基于轴对称盒空间滤波的非线性系统状态估计

针对不确定噪声下的非线性系统状态估计问题, 本文提出了一种基于轴对称盒空间滤波的状态估计方法. 首先, 利用轴对称盒空间包裹线性化过程带来的误差项, 将状态函数线性化误差轴对称盒空间与噪声轴对称盒空间求取闵可夫斯基和, 得到干扰误差轴对称盒空间; 随后, 利用状态量、线性误差和测量噪声的轴对称盒空间的闵可夫斯基和, 得到系统状态预测集; 进而, 利用轴对称盒空间边界正交的性质, 将盒空间拆分为多组超平面, 构造测量更新的约束条件并得到集员包裹. 本文所提方法相比传统的椭球滤波方法而言, 降低了算法的复杂度, 减少了包裹状态可行集和线性化过程带来的余, 获得了更加紧致精确的系统状态集. 最后, 采用非线性弹簧–质量–阻尼器系统验证了本文所提算法的有效性.     

基于UD分解的自适应扩展集员估计方法

用于非线性椭球估计的扩展集员算法在实际应用中存在着数值稳定性差、计算复杂度高以及滤波器参数难以选择等问题. 本文提出了一种基于 UD 分解的自适应扩展集员估计算法, 用于解决非线性系统时变状态和参数的联合估计和定界问题. 新算法将 UD 分解与序列更新和选择更新策略结合起来, 改进了传统扩展集员算法的数值稳定性和实时性能; 同时, 对滤波器参数进行自适应选择以进一步降低计算复杂度并达到次优估计结果. 仿真实验表明了该算法的有效性和鲁棒性.     

模型参数失配有界下的扩展集员估计方法

在非线性模型参数失配下,直接采用滤波算法很难获到理想的估计状态.本文基于扩展集员估计方法,在状态估计中引入参数的不确定信息,提出一种参数失配有界下的状态估计方法.该方法应用区间或集合运算的法则,计算由参数失配引起的偏差范围,并将其用椭球集外包.在状态估计的预测步,通过该偏差椭球集与先验椭球区间的并运算,得到预测椭球区间;在状态估计的更新步,利用观测椭球集对预测椭球区间进行更新,从而得到后验椭球集合以及状态估计值.最后,在数值仿真和发酵模型中的仿真应用验证了算法的有效性.     

自适应噪声定界的改进集员辨识算法

集员辨识所需的系统噪声边界在现实应用中往往难于精确确定, 通常采取的过估边界将导致算法性能的退化. 本文针对缺乏足够先验噪声边界知识下的集员辨识问题进行了相应的研究, 通过对输入干扰和测量误差的有界假设, 将系统噪声边界建模为一个依赖于模型参数的时变量, 由此提出了一种根据估计参数自适应调定噪声边界的改进最优定界椭球辨识算法, 避免了过估噪声边界假设引起的保守性增大的缺陷, 提高了算法的收敛速度. 仿真中将本文提出的改进算法和带固定过估噪声边界的原始算法进行了比较, 表明了该方法的有效性.     

跳变约束下马尔可夫切换非线性系统滤波

针对系统状态演化多模不确定性和状态约束多样性,本文提出了跳变约束下马尔可夫切换非线性系统的交互式多假设估计方法.定义了包含跳变马尔可夫参数可能取值的假设集,根据最优贝叶斯滤波,推导出状态与假设的后验概率递推更新.基于统计线性回归线性化非线性函数,利用伪量测法,将线性化的约束扩维到真实量测中,给出了非线性系统滤波的近似解析最优解.最终给出所提算法的稀疏网格积分近似最优估计实现.在交叉道路机动目标跟踪仿真场景中,所提算法的滤波精度优于基于泰勒展开的交互式多模型算法,基于统计线性回归的交互式多模型算法,以及基于泰勒展开的非线性系统约束滤波算法.     

基于ESMF 算法的GPS 信号多普勒频率估计

针对GPS 接收机对载波信号的跟踪性能受到不同类型噪声的影响, 且这些噪声的统计特性很难得到的问题, 提出一种基于扩展集员滤波(ESMF) 的解决方法. 该方法根据载波信号中噪声统计特性未知但有界(UBB) 的特点, 设定合理的噪声边界, 将UBB噪声包含在椭球集合内; 利用集员的思想实现载波信号多普勒频率的在线非线性估 计, 且估计过程中同时能够检测系统坏值的发生时刻. 仿真中, 模型选取三维空间运动的载体. 仿真结果表明, ESMF在处理该模型时是一种有效的鲁棒估计算法.

     

A nonlinear set‐membership filter for on‐line applications

A guaranteed estimator for a general class of nonlinear systems and on‐line usage is developed and analysed. This filter bounds the linearization error, then applies a linear set‐membership filter such that stability guarantees hold for nonlinear systems. A tight bound on the linearization error is found using interval analysis. This filter recursively estimates an ellipsoidal set in which the true state lies. General assumptions include the use of bounded noises and twice continuously differentiable dynamics. When the system is uniformly observable, it is proven that the nonlinear set‐membership filter is stable. In addition, if no noise is present and the initial error is small, the error between the centre of the estimated set and the true value converges to zero. The result is an estimator which is computationally attractive and can be implemented robustly in real‐time. The proposed method is applied to a two‐state example to demonstrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

A UD factorization‐based nonlinear adaptive set‐membership filter for ellipsoidal estimation

The extended set‐membership filter (ESMF) for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity as well as the difficulty in filter parameter selection. In this paper, a UD factorization‐based adaptive set‐membership filter is developed and applied to nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed UD factorization, combined with a new sequential and selective measurement update strategy, the numerical stability and real‐time applicability of conventional ESMF are substantially improved. Furthermore, an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub‐optimal estimation. Simulation results have shown the efficiency and robustness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Set membership filtering for discrete saturated time-varying networked systems with incomplete measurements under round-robin protocol

In this paper, the set membership filtering problem is investigated for a class of discrete networked systems with time delay and state saturation under the round-robin (RR) protocol, where the system noise is unknown but bounded. In order to reduce the communication burden, the RR protocol is used to schedule the measurement information of the system. In addition, the incompleteness of the measurement information is considered. A set membership filter is established based on incomplete measurements. The objective is to give a criterion that the filtering error is confined to the ellipsoidal set by using the recursive linear matrix inequality (RLMI) method. Moreover, a convex optimization method is proposed to minimize the obtained ellipsoids. Finally, a numerical simulation illustrates that the designed set membership filtering scheme is effective.     

Sequential approximation of feasible parameter sets foridentification with set membership uncertainty

In this paper the problem of approximating the feasible parameter set for identification of a system in a set membership setting is considered. The system model is linear in the unknown parameters. A recursive procedure providing an approximation of the parameter set of interest through parallelotopes is presented, and an efficient algorithm is proposed. Its computational complexity is similar to that of the commonly used ellipsoidal approximation schemes. Numerical results are also reported on some simulation experiments conducted to assess the performance of the proposed algorithm     

The detection mechanism for false data injection attack via the ellipsoidal set-membership approach

The false data injection (FDI) attack detection problem in cyber-physical systems (CPSs) is investigated in this paper. A novel attack detection algorithm is proposed based on the ellipsoidal set-membership approach. In comparison to the existing FDI attack detection methods, the developed attack detection approach in this paper neither requires predefined thresholds nor specific statistical characteristics of the attacks. In order to guarantee that the estimation ellipsoid contains normal states despite the unknown but bounded (UBB) process and measurement noises, the one-step ellipsoidal set-membership estimation method is put forward. In addition, a convex optimization algorithm is introduced to calculate the gain matrix of the observer recursively. Moreover, with the help of the state estimation ellipsoid, the residual ellipsoid can be obtained for attack detection. Whether a detector can detect the FDI attack depends on the relationship between the residual value and residual ellipsoidal set. Finally, the effectiveness of the proposed method is demonstrated by a numerical simulation example.     

一种改进的自适应模糊卡尔曼滤波算法

针对常规卡尔曼滤波（KF）处理小噪声和变化噪声不足,提出了一种改进的自适应模糊卡尔曼滤波[1]（IAF-KF）算法。该算法根据模糊推理输入量的变化特点建立一个新的非线性隶属度函数,取代了常用的三角形线形隶属度函数;然后利用模糊化后的等级和隶属度构造了补偿调节函数（CAF）,用于调节卡尔曼滤波算法中的误差,提高实际测量误差与理论测量误差间的匹配程度。仿真实验表明,较之传统的卡尔曼滤波,该方法在小噪声和变化的噪声情形下有效的克服了稳态误差,同时降低了模糊卡尔曼滤波算法的复杂程度。     

Modified UBB-based input estimation method for nonlinear manoeuvring target tracking problem

The input detection and estimation methods in the manoeuvring target tracking (MTT) application need algorithms for manoeuvring detection and covariance resetting. This algorithm causes an improper delay in target states tracking. In this paper, for solving this problem, unknown but bounded approach for uncertainties modelling is used and a different state space model is developed. In this model, target acceleration is treated as an augmented state in the corresponding state equation. By using interval mathematics, the linearisation error is bounded by an ellipsoidal set and considered in the model development. In augmented state equations, the MTT problem converted to non-manoeuvring target tracking problem. Therefore, the set membership filter is rearranged and used for simultaneous target state and manoeuvre estimation. Furthermore, estimated convex set boundedness is analysed and an upper bound for the estimation error is calculated. The theoretical development of the proposed method is verified with numerical simulations, which contain examples of tracking various manoeuvring targets. The simulation result of the proposed method is compared with traditional input estimation methods. The comparison shows the acceptable performance of the proposed method in the simultaneous estimation of the target acceleration and state vector for the manoeuvring and non-manoeuvring scenarios.