An innovation based random weighting estimation mechanism for denoising fiber optic gyro drift signal

In Interferometric Fiber Optic Gyroscope (IFOG), the diminution of random noise and drift error is a critical task. These errors degrade the performance of IFOG. In this paper, a modified adaptive Kalman gain correction (AKFG) algorithm is proposed to denoise IFOG signal. The covariance matrix of innovation sequence is estimated using weighted average window method in which the weights are randomly generated in the range [0, 1]. Innovation based random weighted estimation (IRWE)-AKFG is applied to denoise the IFOG drift signal. The Kalman gain is adaptively updated using the covariance matrix of innovation sequence. The proposed algorithm is applied for denoising IFOG signal under static and dynamic environment. Allan variance method is used to analyze and quantify the stochastic errors in IFOG sensor. The performance of the proposed algorithm is compared with Conventional Kalman filter (CKF) and the simulation results reveal that the proposed algorithm is an efficient algorithm for denoising the IFOG signal.     

一种新的卫星钟差Kalman滤波噪声协方差估计方法

采用Kalman滤波方法进行钟差参数计算和预报时, 需确定Kalman滤波噪声协方差矩阵. 针对这一问题, 提出了一种新的卫星钟差Kalman滤波噪声协方差估计方法, 通过建立新息的相关函数序列与未知的噪声参数间的线性函数模型, 采用最小二乘法进行噪声参数估计. 采用精密钟差数据进行钟差参数估计和预报分析, 结果表明, 该方法具有较好的收敛性, 并与顾及随机噪声模型的开窗分类因子自适应抗差估计方法进行对比分析, 验证了新方法的正确性和有效性.     

Signal reconstruction in wireless sensor networks based on a cubature Kalman particle filter

For solving the issues of the signal reconstruction of nonlinear non-Gaussian signals in wireless sensor networks(WSNs), a new signal reconstruction algorithm based on a cubature Kalman particle filter(CKPF) is proposed in this paper.We model the reconstruction signal first and then use the CKPF to estimate the signal. The CKPF uses a cubature Kalman filter(CKF) to generate the importance proposal distribution of the particle filter and integrates the latest observation, which can approximate the true posterior distribution better. It can improve the estimation accuracy. CKPF uses fewer cubature points than the unscented Kalman particle filter(UKPF) and has less computational overheads. Meanwhile, CKPF uses the square root of the error covariance for iterating and is more stable and accurate than the UKPF counterpart. Simulation results show that the algorithm can reconstruct the observed signals quickly and effectively, at the same time consuming less computational time and with more accuracy than the method based on UKPF.     

一种破译混沌直接序列扩频保密通信的方法

提出了一种新型的混沌保密通信破译方法,并破译了混沌直接序列扩频保密通信(简称混沌直扩).针对混沌直扩信号中只有一个混沌吸引子的特点,基于混沌系统广义同步的思想,提出了混沌拟合方法;针对混沌直扩中混沌实值序列和数字信号相乘的特点,充分利用混沌直扩的基本原理和信息码是慢变信号的特性,提出了用无先导卡尔曼滤波混沌拟合的方法估计信息码的破译方法;进一步针对无先导卡尔曼滤波的过程噪声和混沌拟合的拟合误差共同导致的跟踪误差,提出了跟踪误差控制因子的方法,从而将跟踪误差转变成有利因素并加以利用,根据跟踪误差的值域范围破     

一种无线传感器网络中的混沌信号重构算法

将无线传感器网络节点观测区域中的一个混沌信号发送到融合中心,进行信号重构.由于节点的通信带宽受限,信号传输之前需要进行量化,给信号带来量化噪声,使得信号重构工作变得更为棘手.本文提出用平方根容积卡尔曼滤波器对融合中心收集的信号进行重构.首先估计观测信号的概率密度函数,使用最优量化器量化观测信号,在有限的量化比特数下,取得最优的信号量化性能.平方根容积卡尔曼滤波器相对无先导卡尔曼算法具有较少的求容积分点,因此具有计算量小的优点,同时迭代过程采用传递误差矩阵的平方根矩阵,保证迭代过程的稳定性和提高数据估计精度.仿真结果表明,该算法能够有效和快速地重构观测信号,并且比基于无先导卡尔曼滤波的算法更快.     

Polarization de-multiplexing using a modified Kalman filter in CO-OFDM transmissions

We propose the modified Kalman filter(MKF) using the received signal for observation and constructing an inverse process of the conventional Kalman filter(CKF) for polarization de-multiplexing in coherent optical(CO) orthogonal frequency-division multiplexing(OFDM) transmissions. The MKF can avoid the convergence error problem in CKF without matrix inverse operation and has a faster converging speed and a much larger tolerance to the process and measurement noise covariance, about two orders of magnitude more than those of CKF. We experimentally demonstrate the 12 Gbaud OFDM signal transmission over 480 km standard singlemode fiber. The performance of MKF and CKF outperforms pilot-aided polarization de-multiplexing with better accuracy and nonlinearity tolerance.     

基于时频差的正交容积卡尔曼滤波跟踪算法

针对基于时频差测量的无源跟踪中面临的非线性估计问题, 提出一种正交容积卡尔曼滤波跟踪算法. 该算法在容积卡尔曼滤波算法的基础上, 通过引入特定正交矩阵改进容积采样方法, 在高维状态估计下减小因采样产生的误差, 在没有增加计算量的前提下, 有效提高收敛速度及跟踪精度. 仿真结果表明, 在基于到达时差和到达频差的联合无源跟踪问题中, 与扩展卡尔曼滤波及容积卡尔曼滤波算法相比, 本文所提算法在跟踪性能上有明显提升.     

Flexible polarization demultiplexing method based on an adaptive process noise covariance Kalman filter

A flexible polarization demultiplexing method based on an adaptive Kalman filter(AKF) is proposed in which the process noise covariance has been estimated adaptively. The proposed method may significantly improve the adaptive capability of an extended Kalman filter(EKF) by adaptively estimating the unknown process noise covariance. Compared to the conventional EKF, the proposed method can avoid the tedious and time consuming parameter-by-parameter tuning operations. The effectiveness of this method is confirmed experimentally in 128 Gb/s 16 QAM polarization-division-multiplexing(PDM) coherent optical transmission systems. The results illustrate that our proposed AKF has a better tracking accuracy and a faster convergence(about 4 times quicker)compared to a conventional algorithm with optimal process noise covariance.     

基于UKF的多用户混沌通信

为克服信道噪声、系统参数误配及多用户干扰对混沌通信系统的影响,本文组合不同的状态空间模型并结合盲提取算法,提出了一种双无先导卡尔曼滤波器 (dual unscented Kalman filter, DUKF),以实现多用户的混沌通信.仿真结果表明,在多输入多输出信道的多用户通信环境下,该算法有较快的收敛速度,并能有效地实现多用户的混沌通信. 关键词： 混沌通信 多输入多输出 双无先导卡尔曼滤波器 盲提取     

视觉技术辅助的无人机自主着陆组合导航研究

为提高无人机自主着陆过程中导航系统的自主性与精确性,设计了一种视觉辅助惯导组合导航方法。该方法以惯导误差方程为过程方程,以着陆过程中单目摄像机2个时刻所得地面特征点投影之间的双视图几何约束为量测方程,构建了非线性滤波器;利用SR-UKF方法实现了惯导误差估计,提高算法效率的同时有效地避免了UKF中由于矩阵开方运算导致的滤波失效;最后根据估计结果校正了惯导导航数据。仿真结果表明:该方法能够提高导航系统精度,使误差降低到惯导系统的8%左右。     

扩展卡尔曼滤波和不敏卡尔曼滤波在实时雷达回波反演大气波导中的应用

为了改善雷达回波反演大气波导(RFC)方面存在的单时次、单方位角反演的问题,提出利用扩展卡尔曼滤波和不敏卡尔曼滤波的反演算法对大气波导结构的多方位角实时跟踪反演. 在卡尔曼滤波方法中分别给出大气波导结构的参数化方程、观测方程、滤波算法的状态转移方程,最后导出滤波反演算法的迭代求解流程. 在大气波导结构不随时间变化和随时间变化的两种条件下,对扩展卡尔曼滤波和不敏卡尔曼滤波算法进行数值实验. 实验结果表明,不敏卡尔曼滤波更适用于RFC这高度非线性反演问题,它可能今后为大气波导结构多方位角实时跟踪反演的业务化运行提供理论基础与技术保证. 关键词： 大气波导 雷达回波 扩展卡尔曼滤波 不敏卡尔曼滤波     

一种混沌映射的相空间去噪方法

对于混沌映射来说,它们的频谱比混沌流的频谱更广阔,与噪声频谱的重叠率更高,所以混沌流的去噪方法对它们并不适用. 在半盲分析法的框架下,混沌系统的参数估计问题终将归结为最小二乘估计问题. 本文从最小二乘拟合的角度出发估计混沌映射的演化参数,进而通过相空间重构以及投影操作,实现对观测信号的噪声抑制. 实验结果表明,该算法的去噪效果优于扩展卡尔曼滤波器（extended Kalman filter,EKF）和无先导卡尔曼滤波器（unscneted Kalman filter,UKF）,并且能够较大程度地将信号源的混沌特征量还原. 关键词： 混沌 噪声抑制 相空间重构 投影     

Estimating parameters in stochastic systems: A variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.     

Scaled unscented transform Gaussian sum filter: Theory and application

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a “complete” solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]).In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel.As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to Lorenz and Emanuel (1998) [27]. We will present the details of implementing the SUT-GSF and examine the effects of filter parameters on the performance of the SUT-GSF.     

逼近积分点数下限的五阶容积卡尔曼滤波定轨算法

为了在保持滤波定轨精度不变的条件下提高定轨计算的实时性,提出一种新的逼近积分点个数下限的五阶容积卡尔曼滤波定轨算法.首先,采用一种数值容积准则对非线性函数的高斯加权积分进行近似,该准则所需的积分点个数仅比五阶代数精度容积准则积分点个数的理论下限多一个积分点,并在贝叶斯滤波算法框架下推导出本文算法的更新步骤.然后,给出实时定轨所需的状态方程和量测方程,在状态方程中考虑了J2项引力摄动和大气阻力摄动,在量测方程中利用坐标系转换推导了轨道状态与测量元素之间的非线性关系.仿真实验结果表明,本文所提算法在定轨精度方面与已有的五阶滤波算法相当,但所需的积分点个数最少,计算实时性最高,从而验证了本文算法的有效性.     

基于预估测量值的EKF在手臂测姿中的应用

针对载体线性加速度以及周围局部磁干扰对姿态测量精度的影响,基于已有的惯性测量单元,设计了一个基于四元数的实时估计手臂姿态的扩展卡尔曼滤波器(EKF)。提出利用四元数引入加速计和磁强计的预估测量值构造自适应测量噪声协方差阵的方法,结合QUEST算法,来判定姿态角解算对陀螺仪、加速计和磁强计输出信息的依赖程度,以此来提高测量精度。文末通过实验仿真对该方法进行了验证,并对实验结果和电磁跟踪系统采集到的数据进行了比较,结果表明,本文提出的方法能显著提高手臂姿态测量精度,可有效满足应用要求。     

基于自适应SRUKF的无人机位姿预测方法

针对无人机自主导航的实时性差、精度低且对时变噪声的鲁棒性弱的问题，建立了机器视觉和惯性导航相融合的组合导航系统，并提出了一种自适应平方根无迹卡尔曼滤波(adaptive square-root unscented kalman filter, ASRUKF)算法。该算法通过观测值与估计值残差的Mahalanobis距离时刻修正系统噪声协方差，再与采用最小偏度采样的SRUKF算法相融合，从而达到时变噪声自适应抑制，滤波快速且对噪声鲁棒性高的效果。仿真结果表明，相比标准SRUKF，ASRUKF计算耗时减少约38.8%，位移、速度和姿态角预测精度分别提高超过4倍和6倍，且对于时变噪声鲁棒性更强。     

一种红外导引头量测误差抑制方法研究

针对自寻的反坦克导弹的红外导引头由于受复杂背景和随机干扰影响测角精度不高的问题,提出了一种惯导信息辅助的无迹卡尔曼滤波方法。利用惯导信息描述导弹自身的运动,基于弹目信息状态变量构建弹目相对运动模型,在此基础上采用无迹卡尔曼滤波方法实现对导引头量测误差的抑制。该方法实现了导引头量测信息与惯导信息的融合,充分利用信息资源,抑制导引头量测误差,提高了导弹的打击精度,仿真实验证明了该方法的有效性。     

小波网络辅助卡尔曼滤波的捷联惯导传递对准

初始对准精度是捷联惯导系统的主要误差来源之一。针对舰载机捷联惯导的传递对准模型准确建模困难,且测量噪声和过程噪声随舰船动态而变化,这样就会降低滤波的精度,卡尔曼滤波有一定的局限性,提出了将小波神经网络辅助卡尔曼滤波器用于惯导系统的传递对准。把能直接影响卡尔曼滤波估计误差的参数作为网络的输入,进过样本训练后,把网络的输出与经过卡尔曼滤波得到的结果相加,实现了捷联惯导的传递对准的滤波功能。这种新算法在实际应用中的非线性情况下优于传统卡尔曼滤波方法。仿真结果表明了其实用性和有效性。     

A generalized polynomial chaos based ensemble Kalman filter with high accuracy

As one of the most adopted sequential data assimilation methods in many areas, especially those involving complex nonlinear dynamics, the ensemble Kalman filter (EnKF) has been under extensive investigation regarding its properties and efficiency. Compared to other variants of the Kalman filter (KF), EnKF is straightforward to implement, as it employs random ensembles to represent solution states. This, however, introduces sampling errors that affect the accuracy of EnKF in a negative manner. Though sampling errors can be easily reduced by using a large number of samples, in practice this is undesirable as each ensemble member is a solution of the system of state equations and can be time consuming to compute for large-scale problems. In this paper we present an efficient EnKF implementation via generalized polynomial chaos (gPC) expansion. The key ingredients of the proposed approach involve (1) solving the system of stochastic state equations via the gPC methodology to gain efficiency; and (2) sampling the gPC approximation of the stochastic solution with an arbitrarily large number of samples, at virtually no additional computational cost, to drastically reduce the sampling errors. The resulting algorithm thus achieves a high accuracy at reduced computational cost, compared to the classical implementations of EnKF. Numerical examples are provided to verify the convergence property and accuracy improvement of the new algorithm. We also prove that for linear systems with Gaussian noise, the first-order gPC Kalman filter method is equivalent to the exact Kalman filter.