Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bi?s is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.     

机动目标拦截末制导状态估计器的误差特性

 针对大机动目标拦截问题,分析了末制导阶段目标机动条件下状态估计器的误差特性。首先将目标机动输入未知时的状态估计器模型表示为一随机线性混合系统,当混合系统的模式跳变事件满足可观测性条件时,模式决策过程可等效为真实模式的延迟;随后推导了模式决策延迟条件下估计误差的动态方程与传递函数,并得到了一定误差要求下模式决策延迟的上界与目标机动模式逗留时间的下界;最后通过空空导弹拦截高速战机的典型实例验证了该理论分析的正确性。研究结果为设计此类线性混合系统估计器提供了理论依据。     

Stochastic optimal control guidance law with bounded acceleration

A novel stochastic optimal control guidance law is presented for a missile with bounded acceleration. The nonlinear optimal guidance law (NOGL) is obtained by numerically solving the stochastic optimization problem. Since the certainty equivalence principle is not valid in the investigated problem, the resulting NOGL depends on the conditional probability density function of the estimated states. It is shown that the NOGL is also nonlinear in the estimated zero effort miss distance, and that the probability density function of the miss distance is non-Gaussian. The dependence of the new guidance law on the acceleration limit is investigated and it is shown that only for an extremely large acceleration limit does the proposed guidance law degenerate to the classical optimal linear one     

一种带随机偏差的分布式信息融合滤波算法

在通信、计算机、信号处理、自动控制中,对于带有未知的干扰和偏差的随机系统的状态估计已经广泛出现。在现实环境中,不同的传感器可能受到不同的干扰影响。研究随机系统的状态估计问题在实际应用中具有重要的意义。对带有随机偏差的线性随机系统,将系统转换为多模型结构的特殊情况。利用最小方差的最优加权融合估计算法,获得了分布式信息融合滤波算法。通过仿真可以看出,分布式信息融合算法要比局部估计算法具有更高的精度,算法具有分布式结构,这使其具有更好的鲁棒性和可靠性。     

Neighboring optimal guidance for aeroassisted orbital transfer

A neighboring optimal guidance scheme for a nonlinear dynamic system is devised with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory is determined. Then, taking modeling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme is devised. Assuming the additive character of the stochastic effects, the optimal trajectory is approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical aeroassisted orbital transfer vehicle     

飞机的随机变结构最优控制方法

 <正> 一、引言 系统的变结构控制(VSC——Variable Structure Control)方法,最初是由苏联学者Utkin等人提出来的,近二十年来发展非常迅速,并越来越多地应用于各个工业领域,其中包括航空部门。变结构系统(VSS——Variable Structure System)的主要特征是存在滑动模态。处于滑动模态时,系统的运动等价于一个低阶系统。研究表明,VSS比传统的控制系统有更好的优点:快速性,对参数变化及外加扰动有强鲁棒性以及实现简单等。然而,VSC的不足之处在于需要获得全部状态变量,这是很难保证的。     

An alternate algorithm for discrete-time filtering

The discrete-time Kalman filter is an optimal estimator for the states of a linear, stochastic system. It assumes that measurements are linear combinations of the states, and all disturbances are Gaussian. The influence diagram, a decision analysis tool that provides an algorithm for discrete-time filtering equivalent to the Kalman filter when the influence diagram represents Gaussian random variables, is discussed. The influence diagram algorithm is a factored form of the Kalman filter, similar to other factored forms such as the U-D filter. Compared with the Kalman filter, it offers improved numerical properties. Compared with other factored forms, it offers a reduced computational load     

广义离散随机线性系统的最优调节器

讨论广义离散随机线性系统在二次型性能指标下的最优控制问题。导出的最优控制律由系统输出和部分状态的线性反馈构成,这不仅降低了滤波的黎卡提方程的阶次,显著地减少了计算量,而且在工程中也是可实现的。     

Optimal measurement scheduling for state estimation

We consider the problem of optimal allocation of measurement resources, when: (1) the total measurement budget and time duration of measurements are fixed, and (2) the cost of an individual measurement varies inversely with the (controllable) measurement accuracy. The objective is to determine the time-distribution of measurement variances that minimizes a measure of error in estimating a discrete-time, vector stochastic process with known auto-correlation matrix using a linear estimator. The metric of estimation error is the trace of weighted sum of estimation error covariance matrices at various time indices. We show that this problem reduces to a nonlinear optimization problem with linear equality and inequality constraints. The solution to this problem is obtained via a variation of the projected Newton method. For the special case when the vector stochastic process is the state of a linear, finite-dimensional stochastic system, the problem reduces to the solution of a nonlinear optimal control problem. In this case, the gradient and Hessian with respect to the measurement costs are obtained via the solution of a two-point boundary value problem and the resulting optimization problem is solved via a variation of the projected Newton method. The proposed method is illustrated using four examples     

应用LQG方法在生产—库存管理系统中的应用研究

给出线性二次型最优输出跟踪问题的系统方程和目标函数,对目标函数中每一项的实际意义做出分析,并讨论了加权矩阵中元素的选取。给出控制规律的最优解,并对最优控制与预期输出的关系做出分析。给出一个生产—库存管理模型,分析了该模型应满足的状态方程,从而说明了它是一个可观测系统,且可以用线性二次型最优输出跟踪问题来解决。最后用具体实例验证了方法的有效性。     

LQG Guidance Law with Bounded Acceleration Command

A novel missile guidance law that is dependent on the conditional probability density function of the estimated states is presented. The guidance law is derived by analyzing an interception scenario in the framework of an linear quadratic Gaussian (LQG) terminal control problem with bounded acceleration command. The nonlinear saturation function is represented by the equivalent random input describing function. Since for the investigated problem the certainty equivalence property is not valid, the resulting controller depends on the measurement noise level and on the saturation limit. In comparison to the classical optimal guidance law (OGL), the maximal value of the effective navigation gain is achieved during the engagement instead of near the terminal time. Thus, the saturation limit is reached earlier so as to have enough time to reduce the guidance errors. Using Monte-Carlo simulations, the superiority of the new guidance law over the classical OGL is shown. This validates the new approach of designing an estimation statistics dependent guidance law by using a random input describing function to approximate the missile's acceleration saturation.     

飞机着陆导引中的随机最优控制问题

论述了应用随机最优控制理论的基本原理和方法，解决飞机在大气紊流中着陆的控制问题。用协方法分析法，推导出可直接计算机飞机着陆精度的线性离散随机系统的误差方差的传播方程，并进一步分析了滤波灵敏度对飞机着陆控制的影响。     

Flutter analysis of an airfoil with bounded random parameters in incompressible flow via Gegenbauer polynomial approximation

The effects of parameter uncertainty on the flutter characteristics of a two-dimensional airfoil in an incompressible flow were investigated through Gegenbauer polynomial approximation. The uncertain parameters, such as the linear and cubic pitch stiffness coefficients are modeled as bounded random variables with λ-PDFs (probability density functions). With the aid of Gegenbauer polynomial approximation, the two-dimensional stochastic airfoil system is transformed at first into its equivalent deterministic one. Then the Hopf-bifurcation point is determined through the equivalent deterministic system, and the onset of the flutter, together with the flutter frequency against the probability density distribution parameter and the intensity of the random variable is explored. In addition, the ranges of the peak pitch and plunge responses against the flight speed and the PDFs of the peak pitch response are obtained. Numerical results show how the probability density distribution parameters and the intensities of random parameters affect the flutter onset speed, flutter angular frequency, the upper and lower boundaries of peak responses, and the PDFs of peak responses.     

齿轮弯曲疲劳强度可靠性分析的新方法

以三参数可靠性分析模型为基础, 结合随机有限元法与齿轮的疲劳强度理论, 提出了一种计算齿根弯曲疲劳强度的新方法。该方法考虑了影响齿轮可靠性的随机因素, 如载荷、材料性能参数和刀具齿顶圆弧半径等, 从而使得全面、合乎实际地对齿轮疲劳强度的可靠性预测成为可能。计算分析表明, 刀具齿轮圆弧半径对齿轮弯曲疲劳强度可靠性的影响不能予以忽略。文中还讨论了其它随机因素以及齿轮的变位系数对齿轮可靠性的影响。      

基于加速度频响函数小波分解的模型修正方法

为提高模型修正效率，满足修正方法对于实测环境噪声的鲁棒性，将Kriging模型和小波分解引入加速度频响函数模型修正。首先，将加速度频响函数进行小波分解，用得到的第1层幅值较大的小波系数来表征原频响函数。其次，采用拉丁超立方抽样对初选待修正参数进行设计，根据设计结果对各参数进行灵敏度分析，从而确定模型修正的待修正参数，以待修正参数作为Kriging模型输入，所对应的小波系数作为Kriging模型输出，通过混合灰狼算法寻得最优Kriging模型相关系数，建立精确有效的Kriging模型。最后，以目标加速度频响函数小波分解的小波系数与Kriging模型输出的小波系数差值最小为目标，通过水循环算法求解模型待修正参数。数值算例表明，所提模型修正方法具有良好的修正效果，即使在加速度频响函数中加入信噪比为5 dB的高斯白噪声时，修正误差也低于4%，证明了该方法对于随机噪声的鲁棒性。     

Optimal and Suboptimal Control Synthesis for Minimum Time VTOL Transition

Optimal open-loop and suboptimal closed-loop controls for a VTOL aircraft in a minimum climb-to-cruise time transition are presented in this paper. The optimal open-loop controls are synthesized by a proposed gradient technique which provides for the selection of desired changes in physically meaningful parameters during each iteration step. The suboptimal closed-loop controls are synthesized as integral mean-square approximations to the optimal open-loop controls over the minimum time-to- climb interval. Piecewiseconstant feedback gains and switching times are synthesized for multidimensional control vectors which are linear combinations of observable states. Several computational results are presented for optimal and suboptimal minimum time controls with constrained and unconstrained terminal flight-path angles.     

Noise covariances estimation for systems with bias states

This paper presents a new approach to noise covariances estimation for a linear, time-invariant, stochastic system with constant but unknown bias states. The system is supposed to satisfy controllable/observable conditions without bias states. Based on a restructured data representation, the covariance of a new variable that consists of measurement vectors is expressed as a linear combination of unknown parameters. Noise covariances are then estimated by employing a recursive least-squares algorithm. The proposed method requires no a priori estimates of noise covariances, provides consistent estimates, and can also be applied when the relationship between bias states and other states is unknown. The method has been applied to strapdown inertial navigation system initial alignment. Simulation results indicate a satisfactory performance of the proposed method     

高阶系统的降阶控制研究

本文根据线性随机系统的最优控制理论较详细地给出了利用优化技术对高阶系统进行降阶控制的理论分析,并对提高整个控制系统的稳定性提出了一种改进方法.最后对飞机机翼的最简模型——自由-自由梁的振动抑制进行了具体的计算,取得了较为满意的结果。     

面向空中目标威胁评估的多传感器管理方法

为了降低在空中目标威胁评估任务中由于威胁评估结果的不准确性和传感器辐射所带来的潜在损失，提出了一种基于风险的多传感器管理方法。首先，基于部分可观马尔可夫决策过程建立了传感器管理模型；然后，给出了基于信息状态的威胁评估风险和传感器辐射风险的预测方法以量化潜在损失；接着，为获得更优的作战收益，以多步风险预测值为决策依据，以两种风险的加权和最小为优化目标建立了长期目标函数；最后，在求解目标函数时，将传感器管理问题转化为决策树搜索，设计了一种基于分支定界的标准代价搜索算法以快速获得高质量的管理方案。仿真实验表明，所提算法能够在搜索到高质量解的同时大幅减少计算时间和内存消耗；所提方法能够对风险进行准确预测，且相比于经典的传感器管理方法，所提方法具有更好的风险控制效果。     

Modeling Nonstationary Random Processes with an Application to Gyro Drift Rate

The problem of estimating the a priori statistics of a nonstationary process is considered using finite-time averages of experimental data. A model of the form of a linear time-invariant difference equation with a stationary independent random sequence driving function is proposed and investigated. Finite-time averages are calculated and then used in a steepest descent method to determine the coefficients of the difference nce equation. Methods are presented for transforming this model to the statespace pace format necessary for Kalman filtering, and an example is given using actual gyro drift-rate data.