未知状态模型下基于高阶容积卡尔曼滤波和神经网络的状态估计算法

针对非线性系统状态模型未知的情形,提出一种基于高阶容积卡尔曼滤波和神经网络的状态估计算法,解决了未知非线性系统模型的状态估计问题。在算法的实现过程中,首先利用神经网络对非线性系统建立状态空间模型,然后把神经网络的权重和系统的状态变量组合在一起作为新的状态变量,并采用高阶容积卡尔曼滤波对新的状态进行实时更新,从而达到神经网络对非线性系统模型的真实逼近以及对状态值的精确估计。最后的目标跟踪仿真表明,该算法具有更高的估计精度。     

一种改进型残差约束渐消采样滤波器

非线性系统的状态方程和观测方程不准确时,非线性自适应采样滤波器的滤波精度将偏离真实值:严重时将引起滤波器的发散,得到完全虚假的滤波值,失去了滤波原本的意义.为减小线性化误差对非线性系统状态估计的影响,本文采用采样滤波器中的UKF(Unscented Kalman Filter)方法对非线性系统进行高精度滤波.同时深入研究UKF的自适应渐消记忆策略,以增强对建模误差的鲁棒性和对突变状态的跟踪能力,提高状态估计的精度和快速性.本文针对上述滤波方法进行改进,并通过一个非线性系统滤波仿真试验.证明其有效性.     

飞行器自适应神经网络时滞控制

在飞行器稳定性控制问题的研究中,针对含有外部扰动、参数不确定性、状态和控制时滞的非线性飞行器系统,提出了一种时滞状态反馈控制与神经网络自适应估计相结合的方法.对非线性系统线性化处理得到飞行器线性模型,并由线性矩阵不等式(LMI)设计反馈控制律;采用径向基函数(RBF)神经网络自适应在线估计策略,对反馈控制律进行补偿以消除未知非线性影响;采用Lyapunov稳定性理论证明了在所设计控制律作用下,闭环系统渐近稳定同时满足H∞性能指标.仿真结果验证了上述方法的可行性及有效性.     

基于极大似然准则和最大期望算法的自适应UKF 算法

针对噪声先验统计特性未知情况下的非线性系统状态估计问题,提出了基于极大似然准则和 最大期望算法的自适应无迹卡尔曼滤波(Unscented Kalman filter, UKF) 算法.利用极大似然准则构造含有噪声统计特性的对数似然函数,通 过最大期望算法将噪声估计问题转化为对数似然函数数学期望极大化问题,最终得到带次优递 推噪声统计估计器的自适应UKF算法.仿真分析表明,与传统UKF算法相比,提出的自适应UKF算法 有效克服了传统UKF算法在系统噪声统计特性未知情况下滤波精度下降的问题,并实现了系统噪 声统计特性的在线估计.     

基于RBF神经网络的非线性系统故障诊断

针对一类模型未知的非线性动态系统,提出了一种基于神经网络在线估计结构的鲁棒故障诊断检测方法.系统中,仅输入输出可测,且包含输出不确定性项.该方法通过构造神经网络在线逼近结构来拟合该非线性系统模型和系统的非线性故障特性,建立系统的状态观测器.神经网络的权重调整规律由李亚普诺夫稳定性方法获得,系统的输出不确定性部分被用于获得诊断算法的阈值.最后,用Matlab/SIMULINK对的算法予以验证,结果表明本算法的合理性.     

一类非线性系统的神经网络自适应区间观测器设计

本文研究了一类单输入单输出非线性系统的神经网络自适应区间观测器设计问题. 针对由状态和输入所描述的未知非线性函数的界不可测, 现有的区间观测器方法并未有效地处理系统含有参数不确定性的未知非线性函数. 首先, 本文构造两个径向基函数神经网络来逼近未知非线性部分, 进而分别估计系统状态的上下界; 然后, 选择合适的Lyapunov函数, 采用网络权值校正和网络误差选择机制确保所设计的误差动态系统有界和非负性, 并证明了神经网络自适应区间观测器的稳定性; 最后, 通过仿真实例验证了所提出的神经网络自适应区间观测器的有效性.     

基于高阶滑模观测器的状态和未知输入同时估计方法

对一类含有未知输入的仿射非线性系统,讨论了一种能同时估计系统状态和末知输入的未知输入观测器设计方法.首先利用李导数对仿射非线性系统进行线性化,将其转化为可控标准型.其次,针对变化后的等价系统,提出了一种高阶、高增益滑模观测器,由此不仅能得到系统状态的估计,同时还得到状态微分的估计.再次,基于状态及其微分的估计,对未知输入提出了一种重构方法.该方法能对强时变未知输入重构,而且重构中没有用到系统微分的信息.最后,通过对两个实际模型的仿真,表明了方法的可行性.     

基于UKF的惯导/被动导引头组合位置修正方法

在导弹末制导阶段,结合自适应UKF滤波方法和直接滤波模型实现惯导/被动导引头组合导航,以提高惯导系统定位精度.首先采用惯导参数和导引头视线信息建立非线性模型,然后结合模型特点对UKF滤波流程进行简化,并针对系统状态变化较快和量测噪声不稳定的特点给出改进的自适应UKF滤波方法,能实现视线信息辅助修正惯导系统位置误差.仿真结果表明,该滤波方法具有较高的估计精度和较快的收敛速度,7s时惯导/被动导引头组合定位误差不高于30m.     

基于极大后验估计和指数加权的自适应UKF滤波算法

针对传统Unscented卡尔曼滤波器(Unscented Kalman filter, UKF)在噪声先验统计未知时变情况下非线性滤波精度下降甚至发散的问题, 设计了一种带噪声统计估计器的自适应UKF滤波算法. 首先根据极大后验(Maximum a posterior, MAP)估计原理, 推导出一种次优无偏MAP常值噪声统计估计器; 接着在此基础之上, 采用指数加权的方法, 给出了时变噪声统计估计器的递推公式; 最后对自适应UKF算法进行了性能分析. 相比于传统UKF, 该自适应UKF算法在噪声统计未知时变情况下不仅滤波依然收敛, 滤波精度及稳定性显著提高, 而且其具有应对噪声变化的自适应能力. 仿真实例验证了其有效性.     

含有有色噪声的非线性分数阶系统自适应扩展卡尔曼滤波器

研究了含有未知参数的情况下，分别含有分数阶有色过程噪声和有色测量噪声的连续时间非线性分数阶系统状态估计问题.采用Grünwald-Letnikov （G-L）差分方法和1阶泰勒展开公式，对描述连续时间非线性分数阶系统的状态方程进行离散化和线性化.构造由状态量、未知参数和分数阶有色噪声的增广向量，设计自适应分数阶扩展卡尔曼滤波算法实现对有色噪声情况下的连续时间非线性分数阶系统的状态和参数的估计.最后，通过分析两个仿真实例，验证了提出算法的有效性.     

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

Unscented Kalman filter (UKF) has been extensively used for state estimation of nonlinear stochastic systems, which suffers from performance degradation and even divergence when the noise distribution used in the UKF and the truth in a real system are mismatched. For state estimation of nonlinear stochastic systems with non-Gaussian measurement noise, the Masreliez–Martin extended Kalman filter (EKF) gives better state estimates in relation to the standard EKF. However, the process noise and the measurement noise covariance matrices should be known, which is impractical in applications. This paper presents a robust Masreliez–Martin UKF which can provide reliable state estimates in the presence of both unknown process noise and measurement noise covariance matrices. Two numerical examples involving relative navigation of spacecrafts demonstrate that the proposed filter can provide improved state estimation performance over existing robust filtering approaches. Vision-aided robot arm tracking experiments are also provided to show the effectiveness of the proposed approach.     

基于多渐消因子强跟踪UKF 和约束AR模型的故障估计与预测

针对非线性系统中不可观测故障参数估计和预测问题, 提出一种基于多重渐消因子强跟踪无迹卡尔曼滤波(MSTUKF) 的状态和参数联合估计法, 通过引入多重渐消因子增强了对变化函数未知的故障参数的跟踪能力. 对于得到的故障参数估计值, 利用递推最小二乘法更新约束AR预测模型, 从而实现故障参数的在线估计与预测. 仿真结果表明, MSTUKF方法在故障参数估计精度上优于UKF 和单渐消因子强跟踪UKF, 约束AR模型的预测精度高于无约束条件下的预测精度.

     

Adaptive observers for unknown general nonlinear systems

Several neural network (NN) models have been applied successfully for modeling complex nonlinear dynamical systems. However, the stable adaptive state estimation of an unknown general nonlinear system from its input and output measurements is an unresolved problem. This paper addresses the nonlinear adaptive observer design for unknown general nonlinear systems. Only mild assumptions on the system are imposed: output equation is at least C(1) and existence and uniqueness of solution for the state equation. The proposed observer uses linearly parameterized neural networks (LPNNs) whose weights are adaptively adjusted, and Lyapunov theory is used in order to guarantee stability for state estimation and NN weight errors. No strictly positive real (SPR) assumption on the output error equation is required for the construction of the proposed observer.     

基于最小均方误差估计的噪声相关UKF设计

传统Unscented卡尔曼滤波器(UKf)要求系统噪声和量测噪声必须是互不相关的.针对此局限性,研究了一类带相关噪声的非线性离散系统UKF设计方法.基于最小均方误差估计和正交变换,给出了噪声相关UKF滤波递推公式,并采用Unscented变换(UT)来计算系统状态的后验分布.所设计的UKF有效解决了传统UKF在噪声相关条件下非线性滤波失效的问题,拓展了UKF的应用范围.最后,仿真实例表明了所设计UKF的有效性.     

Fault Detection for Nonlinear Systems with Unknown Input

This paper extends the problem of fault detection for linear discrete‐time systems with unknown input to the nonlinear system. A nonlinear recursive filter is developed where the estimation of the state and the input are interconnected. Unknown input which can be any type of signal was obtained by least‐squares unbiased estimation and the state estimation problem is transformed into a standard unscented Kalman filter (UKF) problem. By testing the mean of the innovation process, a real‐time fault detection approach is proposed. Simulations are provided to demonstrate the effectiveness of the theoretical results.     

A novel neural internal model control for multi-input multi-output nonlinear discrete-time processes

An internal model-based neural network control is proposed for unknown non-affine discrete-time multi-input multi-output (MIMO) processes in nonlinear state space form under model mismatch and disturbances. Based on the neural state-space model built for an unknown nonlinear MIMO state space process, an approximate internal model and approximate decoupling controllers are derived simultaneously. Thus, the learning of the inverse process dynamics is not required. A neural network model-based extended Kalman observer is used to estimate the states of a nonlinear process as not all states are accessible. The proposed neural internal model control can work for open-loop unstable processes with its closed-loop stability derived analytically. The application to a distributed thermal process shows the effectiveness of the proposed approach for suppressing nonlinear coupling and external disturbances and its feasibility for the control of unknown non-affine nonlinear discrete-time MIMO state space processes.     

Critical evaluation of non-linear filter configurations for the state estimation of Continuous Stirred Tank Reactor

A systematic approach has been attempted to design a non-linear observer to estimate the states of a non-linear system. The neural network based state filtering algorithm proposed by A.G. Parlos et al. has been used to estimate the state variables, concentration and temperature in the Continuous Stirred Tank Reactor (CSTR) process. (CSTR) is a typical chemical reactor system with complex nonlinear dynamics characteristics. The variables which characterize the quality of the final product in CSTR are often difficult to measure in real-time and cannot be directly measured using the feedback configuration. In this work, the comparison of the performances of an extended Kalman filter (EKF), unscented Kalman filter (UKF) and neural network (NN) based state filter for CSTR that rely solely on concentration estimation of CSTR via measured reactor temperature has been done. The performances of these three filters are analyzed in simulation with Gaussian noise source under various operating conditions and model uncertainties.     

传感器故障条件下的自适应UKF 算法

针对目标跟踪中传感器故障导致滤波发散或者滤波精度不高的问题, 提出一种自适应无迹卡尔曼滤波(UKF) 算法. 该算法在滤波过程中, 根据自适应估计原理引入自适应矩阵因子, 实时调整系统状态向量和量测新息向量的协方差, 以满足无迹卡尔曼滤波算法的最优性条件, 并采取措施对滤波发散的情况进行判断和抑制. 与传统UKF和已有自适应UKF算法相比, 该自适应UKF算法显著提高了滤波精度和数值稳定性, 且具有应对传感器故障的自适应能力. 仿真实验结果表明了所提出算法的有效性.

     

Interacting multiple model estimation-based adaptive robust unscented Kalman filter

The unscented Kalman filter (UKF) is a promising approach for the state estimation of nonlinear dynamic systems due to its simple calculation process and superior performance in highly nonlinear systems. However, its solution will be degraded or even divergent when the system model involves uncertainty. This paper presents an interacting multiple model (IMM) estimation-based adaptive robust UKF to address this problem. This method combines the merits of the adaptive fading UKF and robust UKF and discards their demerits to inhibit the disturbance of system model uncertainty on the filtering solution. An adaptive fading UKF for the case of process model uncertainty and a robust UKF for the case of measurement model uncertainty are established based on the principle of innovation orthogonality. Subsequently, an IMM estimation is developed to fuse the adaptive fading UKF and robust UKF as sub-filters according to the mode probability. The system state estimation is achieved as a probabilistic weighted sum of the estimation results from the two sub-filters. Simulations, experiments and comparison analysis validate the efficacy of the proposed method.     

基于容积卡尔曼滤波的神经网络训练算法

针对现有的利用非线性滤波算法对神经网络进行训练中存在滤波精度受限和效率不高的缺陷, 提出一种基于容积卡尔曼滤波(CKF) 的神经网络训练算法. 在算法实现过程中, 首先构建神经网络的状态空间模型; 然后将网络连接权值作为系统的状态参量, 并采用三阶Spherical-Radial 准则生成的容积点实现神经网络中节点连接权值的训练. 理论分析和仿真结果验证了所提出算法的可行性和有效性.