Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities

Necessary and sufficient conditions are derived for the existence of a solution to the continuous-time and discrete-time reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering problems. These conditions are expressed in terms of linear matrix inequalities (LMIs) and a coupling nonconvex matrix rank constraint. Convex LMI problems are obtained for the full-order and the zeroth-order filtering. An explicit parametrization of all reduced-order filters that correspond to a feasible solution is derived in terms of a contractive matrix, and iterative algorithms are proposed to solve the reduced-order filtering problems using alternating projections.     

LMI approach to the mixed H2/H∞filtering design for discrete-time uncertain systems

The problem of full-order robust filtering design for discrete-time uncertain linear systems is addressed. The uncertain parameters are assumed to belong to convex bounded domains (polytope type uncertainty). The main purpose is to design a stable linear filter such that the filtering error output signal remains bounded. For that, the parameterization of all linear filters assuring quadratic stability with an H_∞ attenuation constraint to the filtering error system is provided in terms of linear matrix inequalities (LMIs). Then, through the definition of an auxiliary cost, an upper bound to the filtering error variance is minimized, providing a mixed H₂/H _∞ guaranteed cost filtering design. Standard optimization procedures with global convergence assured can be used to solve the problem, as illustrated by an example     

Mixed H/sub 2//H/sub /spl infin// filtering for uncertain systems with regional pole assignment

The mixed H/sub 2//H/sub /spl infin// filtering problem for uncertain linear continuous-time systems with regional pole assignment is considered. The purpose of the problem is to design an uncertainty-independent filter such that, for all admissible parameter uncertainties, the following filtering requirements are simultaneously satisfied: 1) the filtering process is asymptotically stable; 2) the poles of the filtering matrix are located inside a prescribed region that compasses the vertical strips, horizontal strips, disks, or conic sectors; 3) both the H/sub 2/ norm and the H/sub /spl infin// norm on the respective transfer functions are not more than the specified upper bound constraints. We establish a general framework to solve the addressed multiobjective filtering problem completely. In particular, we derive necessary and sufficient conditions for the solvability of the problem in terms of a set of feasible linear matrix inequalities (LMIs). An illustrative example is given to illustrate the design procedures and performances of the proposed method.     

涡扇发动机变参数鲁棒H_∞滤波器设计

针对存在建模误差及测量噪声干扰条件下的涡扇发动机性能参数估计问题,标准卡尔曼滤波及其改进算法滤波估计误差收敛速度慢,滤波估计精度低,对不确定测量噪声及建模误差较为敏感,为此本文提出了一种变参数鲁棒H_∞滤波器设计方法。该方法采用仿射参数依赖Lyapunov函数设计满足H_∞性能指标要求的鲁棒滤波器,通过引入凸多胞技术,将参数依赖线性矩阵不等式(Linear Matrix Inequality,LMI)中变参数Lyapunov矩阵与系统系数矩阵之间耦合乘积导致的非凸优化问题,转化为常规LMI约束下的凸优化问题进行求解,降低了线性变参数(Linear Parameter Varying,LPV)鲁棒滤波器设计的保守性,得到了全局解。针对涡扇发动机的仿真结果表明:与扩展卡尔曼滤波器对比,采用该方法设计的滤波器具有较快的动态跟踪速度和较高的滤波精度,ΔFn的稳态估计误差不大于0.1%,ΔFn的相对估计误差不大于2.5%,同时对建模误差和测量噪声干扰具有较强的抑制能力。     

自适应滤波算法在SINS/GPS组合导航系统中的应用研究

以SINS/GPS组合导航系统为应用背景,对具有代表性的Sage自适应滤波和渐消卡尔曼滤波进行了研究,分析了这些方法在SINS/GPS组合导航应用中存在的问题,提出了适合工程应用的改进方法。改进的Sage自适应滤波主要对系统状态噪声协方差阵利用状态误差进行估计,更符合SINS/GPS组合导航系统的实际情况,提高了滤波稳定性。改进的渐消卡尔曼滤波采用矩阵因子的形式直接对状态预测协方差阵各分量进行不同程度的调节,使调节更趋合理。此外,改进算法增加了对观测粗差的处理,降低了观测粗差对滤波结果的影响。最后,用实际跑车试验验证了改进方法的有效性。     

传统组合导航中的实用Kalman滤波技术评述

在随机线性系统建模准确的情况下,Kalman滤波是线性最小方差无偏估计。针对传统惯导/卫导组合导航的实际应用,难以精确建模,给出了常用的建模方法、状态量选取原则、离散化方法及滤波快速计算方法。讨论了平方根滤波、自适应滤波、联邦滤波和非线性滤波等技术的适用场合,并给出了使用建议。针对前人研究可观测度中未考虑随机系统噪声的缺陷,提出了更加合理的以初始状态均方误差阵为参考的可观测度定义和分析方法。提出了均方误差阵边界限制方法,可有效抑制滤波器的过度收敛和滤波发散。该讨论可为工程技术人员提供一些有实用价值的参考。     

基于广义系统表达式的模糊系统稳定性分析

研究不确定T-S模糊系统的稳定性问题,并基于模糊广义系统表达式,给出了系统稳定的充分条件。在此基础上,转化为求解线性矩阵不等式的问题。与以往结果相比,减少了求解过程的计算量。同时,为了得到更为松弛的线性矩阵不等式条件,提出一种新的模糊控制器设计及模糊Lyapunov函数。算例说明所提方法有效和可行。     

一种混合的扩展目标跟踪方法

与传统的目标跟踪不同,扩展目标跟踪（EOT）不忽略目标的轮廓特征,同时对目标的质心运动学状态和轮廓特征进行估计。基于随机矩阵的扩展目标跟踪方法用随机正定矩阵来描述目标的轮廓特征,并且建立了适合扩展目标跟踪的量测模型。为了改善目标机动时的跟踪性能,根据椭圆（体）与正定矩阵的关系,提出基于椭圆（体）拟合的扩展目标跟踪方法。进一步地,为了综合上述两类方法的优点,提出一种混合的扩展目标跟踪方法,能够根据目标机动与否在两类方法中进行选择。仿真结果表明,该混合方法的轮廓特征估计误差低于前述两类方法,质心运动学状态的估计性能也更好。     

优化抗差自适应滤波器在深组合导航中的应用

为了提高惯性/卫星深组合导航系统的滤波性能,在抗差自适应滤波算法的 基础上,研究了一种优化抗差自适应滤波算法。该算法通过比较实际预测残差协方差矩 阵和理论协方差阵的差值来生成自适应因子,从而优化抗差自适应滤波。将所研究的算 法应用于惯性/卫星深组合导航系统, 在高动态环境下进行仿真验证, 并与常规卡尔曼 滤波、抗差自适应滤波进行比较。结果表明,优化算法能有效地控制观测异常和动态模 型异常对状态参数估值的影响,所得组合导航位置误差和速度误差明显减小,提高了组 合导航系统的滤波精度。     

Robust adaptive filtering method for SINS/SAR integrated navigation system

This paper presents a new robust adaptive filtering method for SINS/SAR (Strap-down Inertial Navigation System/Synthetic Aperture Radar) integrated navigation system. This method adopts the principle of robust estimation to adaptive filtering of observational data. A robust adaptive filter is developed to adaptively determine the covariance matrix of observation noise, and adaptively adjust the covariance matrix of system state noise according to the adaptive factor constructed based on predicted residuals. Experimental results and comparison analysis demonstrate that the proposed method cannot only effectively resist disturbances due to system state noise and observation noise, but it can also achieve higher accuracy than the adaptive Kalman filtering method.     

基于改进强跟踪ASCKF算法的SINS/GNSS组合对准方法

大方位失准角下的SINS/GNSS组合对准系统呈非线性,采用传统的卡尔曼滤波方法进行初始对准易导致对准精度下降甚至滤波发散。基于此,提出了一种基于改进强跟踪自适应平方根容积卡尔曼滤波算法的组合对准方法。该方法采用QR分解求取协方差的分解因子,并在状态预测方差阵的平方根更新中引入多重渐消因子调整滤波增益;同时,基于Sage-Husa自适应滤波,引入改进的时变噪声估计器实时估计噪声的统计特性。仿真结果表明,采用改进的滤波算法进行大方位失准角下的组合对准,对准精度明显提高。     

抗差自适应分步滤波算法在PPP/INS组合导航中的应用

针对常规抗差自适应滤波算法在PPP/INS组合导航应用中存在难以准确识别和分离观测粗差及运动异常对定位结果影响的问题，基于分类因子自适应滤波原理,提出了一种抗差自适应分步滤波算法。该算法首先执行第一步滤波,对状态模型异常信息进行隔离，仅对观测粗差进行诊断和抗差处理；然后在第一步滤波的基础上，执行第二步滤波，对状态模型异常进行诊断和自适应处理。算法分析表明，抗差自适应分步滤波算法可以准确地识别和分离观测粗差和运动异常扰动。实验结果表明，抗差自适应分步滤波算法能够进一步增强滤波算法抵抗观测粗差和运动异常扰动对滤波结果的影响，提高PPP/INS组合导航系统定位结果的稳定性和可靠性。     

Application of nonlinear filtering to navigation system designusing passive sensors

The problem of navigation system design for autonomous aircraft landing is addressed. New nonlinear filter structures are introduced to estimate the position and velocity of an aircraft with respect to a possibly moving landing site, such as a naval vessel, based on measurements provided by airborne vision and inertial sensors. By exploring the geometry of the navigation problem, the navigation filter dynamics are cast in the framework of linear parametrically varying systems (LPVs). Using this set-up, filter performance and stability are studied in an H_∞ setting by resorting to the theory of linear matrix inequalities (LMIs). The design of nonlinear, regionally stable filters to meet adequate H_∞ performance measures is thus converted into that of determining the feasibility of a related set of LMIs and finding a solution to them, if it exists. This is done by using-widely available numerical tools that borrow from convex optimization techniques. The mathematical framework that is required for integrated vision/inertial navigation system design is developed and a design example for an air vehicle landing on an aircraft carrier is detailed     

Filtering of moving targets using SBIR sequential frames

In this paper three-dimensional (3-D) finite-impulse response (FIR) filters are proposed for moving target detection and tracking from multiframe space-based infrared (SBIR) data. An optimal, in the l_p sense, 3-D FIR filter design technique is proposed which is suitable for the above application. This technique is the first 3-D FIR design of its kind presented in the open literature. Directional, matched, and adaptive 3-D filtering techniques are proposed. Prior to the filtering, clutter mean estimation and mean subtraction are required. Real time implementation of directional and/or matched filters for processing maneuvering targets is discussed and filter design methods are proposed. Finally, performance comparisons of the proposed and other available 3-D FIR and infinite-impulse response (IIR) filters, on real SBIR data, are presented in which the advantages of the proposed 3-D filters are shown     

Navigation system design using time-varying complementary filters

A new methodology for the design of navigation systems for autonomous vehicles is introduced. Using simple kinematic relationships, the problem of estimating the velocity and position of an autonomous vehicle is solved by resorting to special bilinear time-varying filters. These are the natural generalization of linear time-invariant complementary filters that are commonly used to properly merge sensor information available at low frequency with that available in the complementary region. Complementary filters lend themselves to frequency domain interpretations that provide valuable insight into the filtering design process. This work extends these properties to the time-varying setting by resorting to the theory of linear differential inclusions and by converting the problem of weighted filter performance analysis into that of determining the feasibility of a related set of linear matrix inequalities (LMIs). Using this set-up, the stability of the resulting filters as well as their "frequency-like" performance can be assessed using efficient numerical analysis tools that borrow from convex optimization techniques. The mathematical background that is required for complementary time-varying filter analysis and design is introduced. Its application to the design of a navigation system that estimates position and velocity of an autonomous vehicle by complementing position information available from GPS with the velocity information provided by a Doppler sonar system is described.     

一种非线性滤波器的误差分析及应用

针对一类具有未建模误差和扰动的非线性系统的状态估计问题,提出一种在线估计并补偿模型误差的非线性滤波算法,该算法利用非线性预测滤波(NPF)基于预测输出残差的方差最小的基本原则估计模型误差,冉利用扩展卡尔曼滤波(EKF)的思想对补偿后的模型进行状态估计;详细推导了状态估计误差及其方差阵的传播模型.以卫星姿态确定系统为例,...     

关于n阶矩阵的三角分解

本文研究了关于n阶矩阵的LU分解及n阶正定矩阵的乔累斯基分解。这几种分解方法在解决问题的过程中不仅简单明了，而且增加了结果的准确性。     

基于多模型预测的再入飞行器制导方法

在具有控制和轨迹约束的再入制导中,提出了一种新的基于多模型预测再入飞行器纵向制导方法。首先对再入飞行器的纵向运动方程沿着标准轨道线性化,基于分段仿射约束系统建模理论逼近原非线性系统,并采用线性矩阵不等式(LMIs)优化技术离线将保证闭环系统稳定的终端二次代价项求出;然后,在每个制导周期内,基于多模型预测在线求解构造好的有限时域优化目标,从而获得控制量的增量,并把第一个控制增量分量与标准轨道的控制量叠加后形成全量控制,用于实际再入轨道的制导,而在下一个制导周期基于新的状态参数重复上面的优化过程。数字仿真结果证实了所提方法的有效性。     

基于LMI的航空发动机鲁棒H_∞控制器设计

 研究了系统矩阵均具有参数不确定性系统的非标准H_∞鲁棒控制问题。基于 LMI的H_∞控制器设计方法,给出了参数不确定性系统用 3个线性矩阵不等式表征的非标准H_∞控制问题可解的充分必要条件,采用“内点法”求解线性矩阵不等式,可得使闭环系统对于所有可能的参数不确定性均二次稳定且传递函数的H∞ 范数 γ有界的鲁棒控制解。该方法应用于非“标准”系统——某型双转子涡喷发动机稳态双变量调节控制器的设计,通过在气动热力学模型上的仿真结果表明,取得了良好的结果。     

离散系统LMI滤波技术

给出了一种离散系统最优滤波器的线性矩阵不等式（ＬＭＩ）设计方法。在系统干扰噪声能量有界情况下,将有约束的滤波问题转换为无约束的最优状态估计问题。利用ＬＭＩ方法给出了最优无偏滤波器存在的充分必要条件,所得滤波器的阶数小于系统状态个数。将ＬＭＩ方法应用于飞机飞行试验数据处理中,分析了实际飞行条件下飞机运动的模型,并对该模型进行扩展线性化处理,得到了一个较易实现的ＬＭＩ滤波算法。仿真结果表明,所提出的算