随机逼近自适应滤波在捷联惯导系统初始对准中的应用

对于测量噪声方差未知的捷联惯导系统(SINS),采用常规Kalman滤波进行初始对准会造成较大状态估计误差,甚至使滤波器发散。为了解决系统测量噪声方差未知或不确切知道时SINS的误差估计问题,提出一种基于随机逼近的自适应滤波方法。该方法将Robbins-Monro算法与Kalman滤波相结合,通过简化求逆运算,解决了系统观测噪声特性未知情况下SINS的误差估计问题,并提高了算法的数值稳定性。仿真结果表明,该方法能在系统测量噪声方差未知情况下有效实现SINS初始对准。     

满意滤波在航迹辨识中的应用

利用线性矩阵不等式(LMI,linear matrix inequalities)方法,首先研究了Kalman滤波的稳态误差方差和滤波增益的解法,并根据满意控制的思想,提出了具有误差方差上界约束的滤波问题,然后研究了误差方差上界约束下对系统测量噪声具有最大容许强度的满意鲁棒滤波.本文的研究成果已被应用于某型C3I系统中的航迹辨识.     

新型联邦最小二乘滤波算法及应用

为克服多传感器信息融合时联邦Kalman滤波在系统噪声和测量噪声的统计信息不准确时所存在的局限性,提出了一种基于最小二乘估计的新型联邦滤波算法,定义为联邦最小二乘滤波.定性讨论了它与联邦Kalman滤波的关系,通过在INS/双星/GPS组合导航系统中的实际应用进一步地比较两种算法.实测数据的仿真结果证明,在系统噪声和测量噪声不准确的情况下,联邦最小二乘滤波的精度要高于联邦Kalman滤波.     

基于自适应Kalman滤波的改进RTQC算法

为对原始雷达数据进行空间配准,对原始的实时质量控制方法(real time quality control,RTQC)进行了研究.在传统的RTQC算法的基础上,加入Kalman滤波,用于对随机误差进行处理,得出雷达测量的固定误差.对Kalman算法进行改进,改进了传统的Kalman滤波算法,通过对量测噪声方差矩阵和模型噪声方差矩阵进行实时估计,减少了Kalman滤波对于方差矩阵先验知识的要求,提高了Kalman滤波的自适应性,并初步分析了算法的有效性.与实际数据的对比实验结果表明了该方法的有效性.     

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。     

激光陀螺漂移数据的自适应Kalman滤波

针对Sage-Husa自适应Kalman滤波算法存在不能同时估计系统过程噪声方差和量测噪声方差的问题,结合激光陀螺漂移数据的特点,设计了2种改进的Sage-Husa自适应Kalman滤波算法:系统过程噪声时变的自适应滤波算法和系统过程噪声与量测噪声统计特性分开估计的并行Sage-Husa自适应滤波算法。仿真结果表明:所述方法改进算法能够有效提高数据精度,且对系统的初值不敏感。     

离散系统的鲁棒约束方差估计及应用--模型噪声强度不确定情形

考虑离散随机系统在模型噪声强度不确定及估计误差方差受约束情形下的一类鲁棒状态估计问题,即希望找到这样的滤波增益,使得当模型噪声强度在一定范围内变动时,每个状态分量的估计误差方差始终不大于预先指定值.文中给出了这种滤波增益的设计方法,并以一类机动目标跟踪问题为例,说明这种设计方法的直接性与有效性.     

离散系统的鲁捧约束方差估计及应用──模型噪声强度不确定情形

考虑离散随机系统在模型噪声强度不确定及估计误差方差受约束情形下的一类鲁棒状态估计问题，即希望找到这样的滤波增益，使得当模型噪声强度在一定范围内变动时，每个状态分量的估计误差方差始终不大于预先指定值。文中给出了这种滤波增益的设计方法，并以一类机动目标跟踪问题为例，说明这种设计方法的直接性与有效性。     

广义随机系统的集值滤波

在具有控制输入和动态噪声与观测噪声相关的情况下,给出线性随机系统的集值滤波方程;利用矩阵分解和系统变换的技巧,得到广义随机系统的集值滤波方程.这种状态估计方法适用于初始状态均值位于一个凸集之中的随机系统.与传统Kalman滤波产生单个条件分布不同,这里的集值滤波给出一个条件分布的凸集.     

迭代集合卡尔曼滤波方法的性能比较研究

针对数据同化过程中模型的非线性问题,通过分析对比得出了一种适合强非线性系统的迭代集合Kalman滤波(IEnKF)。在Lorenz\|63模型的框架内,比较分析集合Kalman滤波(EnKF)、迭代集合Kalman滤波(IEnKF)和迭代扩展卡Kalman滤波(IEKF)在集合数、观测误差方差、放大因子和模型步长不同时同化性能差异,由此探讨这3种方法的优劣。研究结果表明:随着集合数的增加,3种算法的同化性能都得到了一定的改善;放大因子的增大,使其同化性能变差且EnKF呈现出多重波峰波谷的现象;3种方法的均方误差(RMSE）随观测误差方差和模型步长的增大而增大,其同化精度都变差;而IEnKF同化性能最优,更具有鲁棒性。     

有色量测噪声下的HCKF及其应用

针对高阶容积卡尔曼滤波（HCKF）算法在有色量测噪声条件下滤波精度下降的问题,提出了有色量测噪声下的HCKF算法。通过一阶马尔科夫模型将有色量测噪声进行白化,将带有色量测噪声的非线性离散随机系统转化为白噪声下的非线性时滞系统,并给出高斯域内针对非线性时滞系统的贝叶斯滤波框架。利用高阶容积准则对该滤波框架进行近似计算,进而得到有色量测噪声下的HCKF算法。将所提算法应用到机动目标跟踪系统中,仿真实验结果表明,量测噪声为白噪声时,所提算法与标准HCKF算法具有相同的估计性能;在量测噪声为有色噪声时,所提算法相比于标准HCKF具有更优的估计精度和鲁棒性。     

有色量测噪声下的改进求容积卡尔曼滤波器

为解决标准求容积卡尔曼滤波器在有色量测噪声条件下滤波精度退化的问题,提出改进求容积卡尔曼滤波器及其平方根形式.首先利用一阶马尔科夫模型白化非线性离散随机系统中有色量测噪声,将有色量测噪声下非线性离散随机系统转化为白噪声下非线性时滞系统.然后根据所得非线性时滞系统推导其高斯域的贝叶斯滤波框架,最后基于3度Spherical-Radial规则将该滤波框架近似为改进的求容积卡尔曼滤波器和其平方根形式.机动目标跟踪仿真试验结果表明两种改进求容积卡尔曼滤波算法在标准白噪声条件下与标准求容积卡尔曼滤波算法的估计精度相同,而在有色量测噪声背景下滤波精度和鲁棒性更优.     

基于参数估计的传感器故障诊断的改进方法

针对基于参数估计的非线性系统传感器故障诊断方法中存在的滤波稳定性差、估计精度低的缺点,提出了卡尔曼滤波与小波滤波相结合的方法.在将传感器故障参数都等效为偏差型故障参数的基础上,通过增大强跟踪滤波器算法中的量测噪声方差和系统噪声方差,使其大于实际噪声方差,以提高滤波器的稳定性和故障检测的快速性,同时引入小波滤波以提高对故障参数的估计精度.仿真实验表明,该方法较好地兼顾了滤波稳定性、估计精度及速度.     

基于强跟踪滤波的传感器故障诊断的改进方法

针对基于强跟踪卡尔曼滤波的传感器故障诊断方法中存在的滤波稳定性差、估计精度低的缺点,提出了双滤波器的方法。一个滤波器的量测噪声方差和系统噪声方差均大于实际值,它对故障的估计精度较低,但跟踪速度较快;另一个滤波器的算法中的量测噪声方差大于实际值,它对故障的估计精度较高,但跟踪速度较慢,正好与前者形成互补,然后用第一个滤波器实现故障的及时检测,用第二个滤波器实现对故障幅值的精确估计。仿真实验表明,该方法较好地兼顾了滤波稳定性、估计精度及速度。     

Linear filtering with adaptive adjustment of the disturbance covariation matrices in the plant and measurement noise

For filtering a nonstationary linear plant under the unknown intensities of input signals such as plant disturbances and measurement noise, a new algorithm was presented. It is based on selecting the vectors of values of these signals compatible with the observed plant output and minimizing the error variances of the last predicted measurement. The measurement prediction is determined from the Kalman filter where the input signals are assumed to be white noise and the covariance matrix coincides with the empirical covariance matrix of the selected vectors. Numerical modeling demonstrated that the so-calculated filter coefficients are close to the optimal ones constructed from the true covariance matrices of plant disturbances and measurement noise. The approximate Newton method for minimization of the prediction error variance was shown to agree with the solution of the auxiliary optimal control problem, which allows to make one or some few iterations to find the point of minimum.     

Self-tuning weighted measurement fusion Kalman filter and its convergence

For multisensor systems, when the model parameters and the noise variances are unknown, the consistent fused estimators of the model parameters and noise variances are obtained, based on the system identification algorithm, correlation method and least squares fusion criterion. Substituting these consistent estimators into the optimal weighted measurement fusion Kalman filter, a self-tuning weighted measurement fusion Kalman filter is presented. Using the dynamic error system analysis (DESA) method, the convergence of the self-tuning weighted measurement fusion Kalman filter is proved, i.e., the self-tuning Kalman filter converges to the corresponding optimal Kalman filter in a realization. Therefore, the self-tuning weighted measurement fusion Kalman filter has asymptotic global optimality. One simulation example for a 4-sensor target tracking system verifies its effectiveness.     

Kalman Filters for Continuous-time Fractional-order Systems Involving Fractional-order Colored Noises Using Tustin Generating Function

This study presents fractional-order Kalman filers for linear fractional-order systems with colored noises using Tustin generating function. A continuous-time fractional-order system with the fractional-order colored process noise is discretized by Tustin generating function. The augmented vector consists of the state and the colored noise is offered to construct an augmented system based on the discretized state equation of a fractional-order system and the colored process noise. The Tustin fractional-order Kalman filter is designed based on the augmented system to obtain the state estimation, effectively. Besides, the colored noise involved in the measurement of a continuous-time fractional-order system is also discussed, and the corresponding Tustin fractional-order Kalman filter is provided in this study. Two illustrative examples are given to verify the effectiveness of Tustin fractional-order Kalman filters for the colored process and measurement noises.     

Fractional-order Kalman filters for continuous-time linear and nonlinear fractional-order systems using Tustin generating function

This paper presents the fractional-order Kalman filters using Tustin generating function for linear and nonlinear fractional-order systems involving process noise and measurement noise. By using the Tustin generating function, the differential equation model is obtained by discretising the investigated continuous-time fractional-order system. The two kinds of fractional-order Kalman filters are given for the correlated and uncorrelated cases in terms of the process noise and measurement noise for linear fractional-order system, respectively. In addition, based on the first-order Taylor expansion formula, the extended fractional-order Kalman filter using Tustin generating function is proposed to improve the accuracy of state estimation. Finally, three examples are illustrated to verify the effectiveness of the Tustion fractional-order Kalman filters for linear and nonlinear fractional-order systems.