离散系统方差约束鲁棒H2/H∞滤波的新算法

考虑带有稳态误差方差约束的线性受扰系统的鲁棒H2/H∞滤波问题.引入了广义逆矩阵,提出了一个新的算法.通过直接解两个Riccati方程后,获得滤波器,并且同时满足3个性能要求:滤波过程是渐近稳定的;每个状态的稳态估计误差方差不超过规定的上界;从外部噪声输入到误差状态输出的传递函数的H∞范数满足规定的上界.一个数字例子说明了这种设计方法的有效性.     

离散系统方差约束鲁棒H2/H∞滤波的新算法

考虑带有稳态误差方差约束的线性受扰系统的鲁棒H₂/H_∞滤波问题.引入了广义逆矩阵,提出了一个新的算法.通过直接解两个Riccati方程后,获得滤波器,并且同时满足3个性能要求:滤波过程是渐近稳定的;每个状态的稳态估计误差方差不超过规定的上界;从外部噪声输入到误差状态输出的传递函数的H_∞范数满足规定的上界.一个数字例子说明了这种设计方法的有效性.     

航迹辨识系统中约束方差滤波的容许模型噪声

根据Kalman滤波的最小方差特性,分析测量噪声一定时Kalman滤波方差随系统模型噪声强度变化的规律,并在模型噪声和测量噪声一定时,给出求解当前估计型稳态Kalman滤波的LMI方法。针对测噪声一定的系统设计一种滤波器,它在保证滤波误差方差满足指定上界约束下,容许系统有尽可能大强度的模型噪声,并用航迹辨识系统的算例对所给出的结果做了说明。     

区间系统的离散鲁棒Kalman滤波

着重研究区间系统的鲁棒滤波问题.通过等价变换,将区间系统转换为对应的矩阵 范数不确定系统,并据此导出区间系统的鲁棒滤波算法.该算法为一离散验后(a posteriori) 滤波算法,它能保证区间系统的滤波误差有界.理论分析和实际计算结果表明,本算法能达到 比验前(a priori)滤波小得多的滤波误差的方差上界.     

连续时变不确定系统约束方差/H∞鲁棒状态滤波*

基于上限方差配置的混合方差／H∞设计方法可得到满意的设计结果.本文用一个修正的Riccati方程研究了一类时变不确定系统的混合方差／H∞状态滤波器，导出了滤波器的一般公式．对所允许的扰动由该公式所确定的滤波器可使稳态滤波误差方差上限及误差系统的H∞指标均小于指定值，因而具有较好的鲁棒性．     

误差方差约束下Delta算子不确定系统的鲁棒H∞滤波

研究Delta算子不确定系统在稳态估计误差方差约束下的鲁棒H∞滤波问题.目的是设计滤波器,使得系统在状态矩阵和输出矩阵均存在不确定性时,滤波过程是渐近稳定的,每个状态的稳态估计误差的方差不大于事先给定值,且从噪声输入到误差输出的传递函数满足给定的H∞范数约束.基于矩阵不等式方法,提出了滤波器的存在条件和显式表达式.所得结果可将连续和离散系统的有关结论统一到Delta算子框架.     

误差方差约束下Delta算子不确定系统的鲁棒H∞滤波

研究Delta算子不确定系统在稳态估计误差方差约束下的鲁棒H_∞滤波问题. 目的是设计滤波器, 使得系统在状态矩阵和输出矩阵均存在不确定性时, 滤波过程是渐近稳定的, 每个状态的稳态估计误差的方差不大于事先给定值, 且从噪声输入到误差输出的传递函数满足给定的H_∞范数约束. 基于矩阵不等式方法, 提出了滤波器的存在条件和显式表达式. 所得结果可将连续和离散系统的有关结论统一到Delta算子框架.     

一种基于滤波参数在线辨识的鲁棒自适应滤波器

针对一类未建模动态和扰动下的非线性随机系统的状态估计问题,提出了一种基于 滤波参数在线辨识的鲁棒自适应滤波器.该算法通过极小化状态估计误差的方差同时正交化 相邻时刻的滤波残差,在线辨识状态预报误差和滤波残差的协方差,实现了对未建模动态和扰 动的自适应动态补偿,因此对未建模扰动具有很强的鲁棒性.仿真中研究了一个非线性随机时 滞系统,其参数存在缓变和突变,时滞会多次跳变,量测噪声发生了均值漂移和方差突变.算法 对时滞和参数的联合估计效果令人满意.     

光纤陀螺信号误差分析与滤波算法的研究

针对光纤陀螺信号漂移误差和噪声的影响,采用Allan方差法对光纤陀螺的各项随机误差成分进行了分离和计算.然后结合陀螺稳定平台系统研究了滑动滤波、小波变换阈值滤波两种直接对陀螺输出信号进行数字滤波处理的方案.最后对某陀螺惯性稳定跟踪转台中使用的光纤陀螺信号的测试和统计分析结果表明,采用Allan方差法能够有效地分离和辨识陀螺零漂信号中的各项噪声源随机误差系数和误差大小,采用的小波变换阈值滤波的去噪效果明显.     

混合式自适应Kalman滤波算法

采用虚拟噪声补偿模型误差和有偏的噪声方差估值器、滤波器收敛性判据相结合的方法来解决自适应Kalman滤波发散的问题。首先若模型不准确,则引入虚拟噪声对模型误差进行虚拟补偿,然后采用有偏的噪声方差估值器、滤波器收敛性判据对噪声方差估计值进行监控,阻止滤波器发散。采用混合式自适应Kalman滤波算法对Gill公司的风向风速仪实时采集的数据进行处理,实验结果表明,该方法能有效的提高性能、抑制滤波发散,具有较强的实用性、自适应能力。     

Variance-constrained multiobjective filtering for uncertain continuous-time stochastic systems

In this paper, we consider stochastic linear continuous-time systems subject to parameter uncertainties affecting both system dynamics and noise statistics. A linear filter is used to estimate a linear combination of the states of the system. The problem addressed is the design of a perturbation-independent filter such that, for all admissible parameter perturbations, the following three objectives are simultaneously achieved. Firstly the filtering process is D-stable, that is, the eigenvalues of the filtering matrix are located inside a prespecified disc. Secondly the steady-state variance of the estimation error of each state is not more than the individual prespecified value. Thirdly the transfer function from exogenous noise inputs to error state outputs meets the prespecified H norm upper bound constraint. Therefore, the resulting filtering process will be provided with the expected transient property, steady-state error variance constraint and disturbance rejection behaviour, irrespective of the parameter uncertainties. An effective algebraic matrix inequality approach is developed to solve such a multiobjective H₂     

Error variance-constrained ℋ∞ filtering for a class of nonlinear stochastic systems with degraded measurements: the finite horizon case

This article is concerned with the robust ?_∞ filtering problem for a class of time-varying nonlinear stochastic systems with error variance constraint. The stochastic nonlinearities considered are quite general, which contain several well-studied stochastic nonlinear systems as special cases. The purpose of the filtering problem is to design a filter which is capable of achieving the pre-specified ?_∞ performance and meanwhile guaranteeing a minimised upper-bounded on the filtering error variance. By means of the adjoint system method, a necessary and sufficient condition for satisfying the ?_∞ constraint is first given, expressed as a forward Riccati-like difference equation. Then an upper-bound on the variance of filtering error system is given, guaranteeing the error variance is not more than a certain value at each sampling instant. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time, hence is suitable for online computation. A numerical example is presented finally to show the effectiveness and applicability of the proposed method.     

Robust filtering for a class of nonlinear stochastic systems with probability constraints

This paper is concerned with the probability-constrained filtering problem for a class of time-varying nonlinear stochastic systems with estimation error variance constraint. The stochastic nonlinearity considered is quite general that is capable of describing several well-studied stochastic nonlinear systems. The second-order statistics of the noise sequence are unknown but belong to certain known convex set. The purpose of this paper is to design a filter guaranteeing a minimized upper-bound on the estimation error variance. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time. Then, under the probability constraints, a minimax estimation problem is proposed for determining the suboptimal filter structure that minimizes the worst-case performance on the estimation error variance with respect to the uncertain second-order statistics. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed method.     

基于方差配置不确定系统的鲁棒滤波

实际系统普遍存在不确定性,这种不确定性可能导致滤波发散问题.该文对一类时 变不确定系统讨论了一种指定误差方差上限的状态滤波器的设计,该方法采用两个Riccati 方程,其中第一个Riccati方程用以补偿系统的不确定性,第二个Riccati方程用来配置状态 滤波误差的协方差上限.导出了滤波器的存在条件和滤波器的通解,揭示了该滤波器与稳态 Kalman滤波器之间的内在联系.     

基于方差配置不确定系统的鲁棒滤波1)

实际系统普遍存在不确定性,这种不确定性可能导致滤波发散问题.该文对一类时变不确定系统讨论了一种指定误差方差上限的状态滤波器的设计,该方法采用两个Riccati方程,其中第一个Riccati方程用以补偿系统的不确定性,第二个Riccati方程用来配置状态滤波误差的协方差上限.导出了滤波器的存在条件和滤波器的通解,揭示了该滤波器与稳态Kalman滤波器之间的内在联系.     

不确定离散系统的最优鲁棒滤波

本文对一类含有范数有界参数不确定的离散线性系统的滤波问题进行了研究,了有限时域时变以及无限时域时不变两种情形,给出了一个对所有可容许参数不确定都能满足的估计误差方差上界,得到了使得该上界达到最小的最优鲁棒滤波器形式及其存在的充要条件,数值结果表明：当系统存在参数不确定时,本文所得到的滤波器优于标准的Ｋａｌｍａｎ滤波器以及文（４）中的鲁棒滤波器。     

Optimal filtering for linear state delay systems

In this note, the optimal filtering problem for linear systems with state delay over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the optimal estimate equation similar to the traditional Kalman-Bucy one is derived; however, it is impossible to obtain a system of the filtering equations, that is closed with respect to the only two variables, the optimal estimate and the error variance, as in the Kalman-Bucy filter. The resulting system of equations for determining the error variance consists of a set of equations, whose number is specified by the ratio between the current filtering horizon and the delay value in the state equation and increases as the filtering horizon tends to infinity. In the example, performance of the designed optimal filter for linear systems with state delay is verified against the best Kalman-Bucy filter available for linear systems without delays and two versions of the extended Kalman-Bucy filter for time-delay systems.