Finite-dimensional filters with nonlinear drift. III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for the linear filtering system and the Benes filtering system

We consider the Duncan-Mortensen-Zakai (DMZ) equation for the Kalman-Bucy filtering system and Benes filtering system. We show that this equation can be solved explicitly with an arbitrary initial condition by solving a system of ordinary differential equations and a Kolmogorov-type equation, Let n be the dimension of state space. We show that we need only n sufficient statistics in order to solve the DMZ equation.     

Nonlinear filtering and time varying Schrodinger equation

Based on our previous work we have successfully reduced the nonlinear filtering problem for Yau filtering system to the time-varying Schrodinger equation. In order to solve the nonlinear filtering problem, one needs to solve the time-varying Schrodinger equation with an arbitrary initial condition. We then solve the time-varying Schrodinger equation by constructing the fundamental solution explicitly via a system of nonlinear ODES in case the potential is quadratic in state variables. This system of nonlinear ODES is solved explicitly by the power series method.     

多传感器组合导航系统的多尺度异步信息融合算法

首先,将状态方程采用数据块变换的方式得到新的状态块方程,并将量测方程表达为数据块的形式;然后,将量测向量进行多层小波变换以得到新的量测向量,结合状态块方程进行卡尔曼滤波;最后,利用异步贯序滤波的方法,建立了基于全局的最优估计值。将上述算法应用于GPS/SST/高度表/SINS多组合导航系统,仿真结果表明:相对于单一尺度的异步滤波算法,该算法可明显地提高系统的滤波精度。     

Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.     

应用卡尔曼滤波的机载雷达跟踪系统

本文论述将滤波理论应用于机载雷达中对单个目标进行距离、速度、方位角和高低角跟踪的多环反馈系统。首先根据目标和天线的相对运动建立控制四坐标跟踪环所需的状态矢量微分方程,然后推导相应的非线性滤波算法。最后给出计算机的模拟结果。计算机模拟的结果清晰地说明采用最佳滤波的系统性能比通常的有很大改善,并且这种瞄准轴坐标系的最佳系统对目标的随机机动是不灵敏的。 本文所讨论的方法和得出的结论可以延用到地面雷达、舰载雷达以及其他有源和无源的跟踪系统。     

一种改进的GPS动态定位滤波方法

针对GPS接收机能够测量卫星信号的多普勒频率的特性,亦即能够测量三维速度的特性,引入了一种改进的GPS定位系统滤波算法。首先,根据机动载体的"当前"统计模型建立了系统状态方程;然后,根据GPS接收机实际能够输出位置与速度信息的特点建立了系统的量测方程;最后,给出了标准的卡尔曼滤波算法模型并详细描述了算法的推导过程。仿真结果表明,改进算法相对于以前的算法无论是在精度和跟踪速度方面都有较大的提高。     

舰载导弹飞行中传递对准技术

舰载导弹初始发射条件恶劣,利用外部参考信息辅助弹上捷联惯性导航系统初始对准,在导弹飞行中进行传递对准是一条有效的研究路线。本文给出了三种飞行中传递对准方案,其中对卫星组合与弹上捷联惯性导航系统进行飞行中传递对准方案,还给出了详细的卫星组合与捷联惯性导航系统速度、位置反馈修正下的卡尔曼滤波方程。并且讨论了随滤波技术发展飞行中传递对准算法的导弹失准角修正方案。     

Wavelet filtering of measurement information in unmanned aerial vehicle control system

The problems of filtering the measurement signals in the unmanned aerial vehicle control system are considered. We propose that the methods of filtering based on the wavelet transformation be used.     

一种鲁棒Sigma-point滤波算法及其在相对导航中的应用

研究了一种鲁棒Sigma-point滤波方法在无人机编队相对导航问题上的应用。该方法采用Huber估计方法,将Sigma-point滤波量测更新转化为求解线性回归问题,新的Sigma-point滤波方法是一种混合L1、L2范数最小估计,当量测噪声为受污染的高斯白噪声时,该方法具有一定的鲁棒性。给出了编队无人机相对惯导方程和相对视线矢量测量原理,应用鲁棒Sigma-point滤波方法融合相对惯导信息和相对视线矢量信息,估计出无人机之间的相对姿态、相对速度和相对位置。仿真结果表明,与扩展卡尔曼滤波和常规Sigma-point滤波相比,鲁棒Sigma-point滤波可以获得更高的估计精度。     

A second-order numerical method for elliptic equations with singular sources using local flter

The presence of Dirac delta function in differential equation can lead to a discontinuity,which may degrade the accuracy of related numerical methods.To improve the accuracy,a secondorder numerical method for elliptic equations with singular sources is introduced by employing a local kernel flter.In this method,the discontinuous equation is convoluted with the kernel function to obtain a more regular one.Then the original equation is replaced by this fltered equation around the singular points,to obtain discrete numerical form.The unchanged equations at the other points are discretized by using a central difference scheme.1D and 2D examples are carried out to validate the correctness and accuracy of the present method.The results show that a second-order of accuracy can be obtained in the fltering framework with an appropriate integration rule.Furthermore,the present method does not need any jump condition,and also has extremely simple form that can be easily extended to high dimensional cases and complex geometry.     

基于可观测度分析的稳定姿态滤波器

提出一种适用于惯性/天文组合航天飞行器的稳定姿态滤波器,可以在不降低系统可观测度的前提下解决滤波计算中的奇异问题。对于奇异问题的传统解决方案是删除观测方程的一行,通过对比删除前后系统可观测度的变化,证明此解决方案会导致系统可观测度下降,并指出如何选择最优删除方案以使系统可观测度下降最小。根据对传统解决方案的分析结果,提出了不降低系统可观测度的投影算法。理论分析和仿真试验证明,应用了投影算法的姿态滤波器更为稳定,估计效率更高。     

Closed-form posterior Cramer-Rao bounds for bearings-only tracking

We address the classical bearings-only tracking problem (BOT) for a single object, which belongs to the general class of nonlinear filtering problems. Recently, algorithms based on sequential Monte-Carlo methods (particle filtering) have been proposed. As far as performance analysis is concerned, the posterior Cramer-Rao bound (PCRB) provides a lower bound on the mean square error. Classically, under a technical assumption named "asymptotic unbiasedness assumption", the PCRB is given by the inverse Fisher information matrix (FIM). The latter is computed using Tichavsky's recursive formula via Monte-Carlo methods. Two major problems are studied here. First, we show that the asymptotic unbiasedness assumption can be replaced by an assumption which is more meaningful. Second, an exact algorithm to compute the PCRB is derived via Tichavsky's recursive formula without using Monte-Carlo methods. This result is based on a new coordinate system named logarithmic polar coordinate (LPC) system. Simulation results illustrate that PCRB can now be computed accurately and quickly, making it suitable for sensor management applications     

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。     

无人机地面站图像预处理系统的设计与应用

为了实现无人机侦察图像的图形字符叠加和预处理,设计了与系统主计算机松耦合的图像处理系统,系统基于DSP技术,通过串行接口控制叠加信息的内容和位置以及滤波增强算法切换,系统封装于独立外置的IU机箱中,有效减小了其与主控制计算机间的相互干扰。对系统组成原理和软硬件实现进行了详细介绍,实验结果表明,系统实现满足性能指标要求,滤波增强功能高效实时,其设计思想对同类型系统具有一定借鉴意义。     

H_∞滤波算法及其在GPS/SINS组合导航系统中的应用

 在对 H∞ 估计问题进行数学描述的基础上,建立了一种 H∞ 次优滤波算法的迭代方程。定性讨论了H∞滤波算法与传统 Kalman滤波器的关系,通过在 GPS/SINS组合系统中的实际应用进一步从精度、鲁棒性等性能指标方面对 H∞ 滤波和 Kalman滤波算法进行了比较。仿真结果表明,在理想条件下,Kalman滤波方法具有较高的精度;但是,当系统模型和外部干扰统计特性发生变化时,H∞ 滤波算法明显具有良好的鲁棒性能,同时,估计精度也较高,有效地克服了 Kalman滤波器存在的局限性。     

利用压电传感器/驱动器的柔性结构主动振动控制研究

 以粘贴有压电传感器/驱动器的柔性梁主动振动控制为例，论述了进行柔性结构传感器/驱动器及控制系统一体化研究的方法。给出了压电传感器的检测方程和驱动器的的驱动方程，以玻璃钢材料的柔性梁为实验对象，并采用自适应滤波技术来实现主动振动控制，控制系统有TMS320C25及486计算机组成的主从机系统来实现，实验结果表明此种控制方法是有效的。     

连续最小阶奇异滤波器

 本文讨论了当动态噪声统计特性未知时,奇异线性定常连续随机系统最小阶滤波器的设计问题。在系统部分观测量能精确测量的情况下,利用广义逆阵方法选择L矩阵,以消除动态噪声对降阶系统的影响,从而推导出缺动态噪声统计特性时的降阶奇异最优滤波器,其阶数为n-m+r。当量测方程奇异假设条件成立及引理有解时,本文证明了最小阶奇异滤波器必定存在。文中举例说明了这一降阶滤波方法的可行性。     

A new adaptive Kalman filter for navigation systems of carrier-based aircraft

The features of carrier-based aircraft’s navigation systems during the approach and landing phases are investigated. A new adaptive Kalman filter with unknown state noise statistics is proposed to improve the accuracy of the INS/GNSS integrated navigation system. The adaptive filtering algorithm aims to estimate and adapt the unknown state noise covariance Q in high dynamic conditions, when the measurement noise covariance R is assumed to be known empirically in advance. The new adaptive Kalman ...     

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。     

双轴连续旋转调制捷联惯导系统大失准角初始对准技术

由于可以补偿惯性器件在三个轴向上的输出误差,双轴旋转调制技术被广泛应用于捷联惯导系统(SINS)。选择了一种合理且实用的十六次序双轴转位方案,并对其调制原理和误差进行了分析。初始对准技术是捷联惯导系统的一项重要技术,其对准精度直接决定了后续导航的精度。在粗对准完成后,当姿态误差角较大时,后续的精对准误差模型呈非线性特性,故选择了滤波精度高、稳定性强的平方根容积Kalman滤波算法(SCKF)来解决这一问题。考虑到在实际对准过程中,量测噪声的统计特性易发生变化,将SCKF算法与Sage-Husa算法相结合,在传统Sage-Husa SCKF算法的基础上提出了一种改进的自适应滤波算法(ASCKF)。该算法采用QR分解来完成对噪声协方差的平方根矩阵估计,从而避免了传统Sage-Husa SCKF算法中所估噪声协方差矩阵不正定的问题。最后,通过仿真证实了ASCKF算法可被很好地应用于量测噪声统计特性发生变化的初始对准中。