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。     

带未知有色观测噪声的自校正融合Kalman滤波器

对于带未知有色观测噪声的多传感器线性离散定常随机系统, 未知模型参数和噪声方差的一致的融合估值器用递推增广最小二乘法(RELS)和求解相关函数方程得到. 将这些估值器代入到最优解耦融合Kalman滤波器中, 得出了自校正解耦融合Kalman滤波器, 并用动态方差误差系统分析(DVESA)和动态误差分析(DESA)方法证明了它收敛于最优解耦融合Kalman滤波器, 因而具有渐近最优性. 一个带3传感器跟踪系统的仿真例子说明了其有效 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.     

Critical Issues on Kalman Filter with Colored and Correlated System Noises

The Kalman filtering (KF) is optimal under the assumption that both process and observation noises are independent white Gaussian noise. However, this assumption is not always satisfied in real‐world navigation campaigns. In this paper, two types of KF methods are investigated, i.e. augmented KF (AKF) and the second moment information based KF (SMIKF) with colored system noises, including process and observation noises. As a popular noise‐whitening method, the principle of AKF is briefly reviewed for dealing with the colored system noises. The SMIKF method is developed for the colored and correlated system noises, which directly compensates for the covariance through stochastic model in the sense of minimum mean square error. To accurately implement the SMIKF, a refined SMIKF is further derived regarding the continuous‐time dynamic model rather than the discrete one. The computational burdens of the proposed SMIKF along with representative methods are analyzed and compared. The simulation results demonstrate the performances of proposed methods.     

Estimation of wiener nonlinear systems with measurement noises utilizing correlation analysis and Kalman filter

This paper is concerned with parameter estimation of Wiener systems with measurement noises employing correlation analysis method and adaptive Kalman filter. The presented Wiener system consists of two series blocks, that is, a dynamic block represented by auto-regressive moving average (ARMA) model, and static nonlinear block established by neural fuzzy model. Aim at estimating separately the two blocks, the separable signals are introduced. First, applying the separable signals to decouple the identification of linear dynamic block from that of static nonlinear block, then ARMA model parameters are estimated employing correlation function-based least squares principle. Moreover, aiming at handle with error caused by colored measurement noise, adaptive Kalman filter technique and cluster method are introduced to estimate parameter of the nonlinear block and noises model, enhancing parameter estimation precision. The accuracy and applicability of estimated scheme presented are verified through numerical simulation and nonlinear process, the results demonstrate that it is feasible for estimating the Wiener systems in the presence of colored measurement noises.     

含有分数阶有色关联噪声的分数阶系统的卡尔曼滤波器设计

提出基于Tustin生成函数的分数阶卡尔曼滤波器设计方法,以解决含有相互关联的分数阶有色过程噪声和分数阶有色测量噪声的连续时间线性分数阶系统的状态估计问题.通过Tustin生成函数方法,对连续时间线性分数阶系统进行离散化,将分数阶系统的微分方程转化为差分方程.利用增广向量法,将分数阶状态方程和分数阶有色噪声作为新的增广状态向量,从而将分数阶有色噪声转化为高斯白噪声.然后,提出一种基于Tustin生成函数的分数阶卡尔曼滤波算法,有效地实现对含有相互关联的分数阶有色过程噪声和分数阶有色测量噪声的连续时间线性分数阶系统的状态估计.与基于Grddotunwald-Letnikov差分的离散化方法相比,所提出的基于Tustin生成函数的卡尔曼滤波算法得到的状态估计精度更高,状态估计效果更好.最后,通过仿真结果验证所提出算法的有效性.     

含未知参数的自校正融合Kalman滤波器及其收敛性

对于带未知模型参数和噪声方差的多传感器系统,基于分量按标量加权最优融合准则,提出了自校正解耦融合Kalman滤波器,并应用动态误差系统分析(Dynamic error system analysis,DESA)方法证明了它的收敛性.作为在信号处理中的应用,对带有色和白色观测噪声的多传感器多维自回归(Autoregressive,AR)信号,分别提出了AR信号模型参数估计的多维和多重偏差补偿递推最小二乘(Bias compensated recursive least-squares,BCRLS)算法,证明了两种算法的等价性,并且用DESA方法证明了它们的收敛性.在此基础上提出了AR信号的自校正融合Kalman滤波器,它具有渐近最优性.仿真例子说明了其有效性.     

Convergence of self-tuning Riccati equation with correlated noises

For the linear discrete time-invariant stochastic system with correlated noises,and with unknown model parameters and noise statistics,substituting the online consistent estimators of the model paramet...     

基于卡尔曼滤波的轨迹规划高度修正仿真实现

综合地形跟随/地形回避（TF/TA）是新一代低空突防技术,其中的轨迹规划技术是飞行器低空突防飞行控制律设计的重要依据.针对飞行器实时飞行过程中存在各种误差因素影响规划轨迹性能的情况,设计卡尔曼滤波器在实时轨迹规划中对所获取的飞行器高度值进行修正,可以获得比较精确的离地高度信息提供给飞行器,从而增加飞行器的安全系数.建立系统的状态与观测数学模型,在给定初始值和噪声方差阵的情况下进行了仿真.仿真结果显示所设计的卡尔曼滤波器可行,大大减小了组合导航系统误差模型的作用效果.     

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.     

有色量测噪声下带广义未知扰动的递推上限滤波

针对博弈对抗环境下利用快速采样雷达进行非合作目标跟踪带来的有色噪声和未知干扰共存问题, 本文提出有色量测噪声下带广义未知扰动的随机动态系统递推上限滤波. 这里, 有色量测噪声用于描述由于快速采样或持续干扰带来的噪声相关性, 广义未知扰动用于建模博弈对抗对雷达观测带来的异常影响(先验信息缺失). 针对所考虑系统, 通过参数优化实现状态估计误差协方差上限(而不是理论值)的在线递推, 提出有色噪声下上限滤波(CU-BF), 给出状态估计误差协方差最小上限的近似实现, 讨论了所提CUBF的存在性条件. 在具有时变未知扰动和有色量测噪声的目标跟踪仿真中验证了所提方法的有效性.     

色噪声下卡尔曼滤波焊缝跟踪算法与试验研究

精确控制激光束使其始终对中并跟踪焊缝是保证激光焊接质量的前提．以大功率光纤激光焊接Type304不锈钢为试验对象,研究一种有色噪声环境下应用卡尔曼滤波最优状态估计预测激光束与焊缝路径偏差的方法．使用高速红外视觉传感器摄取焊接区红外热像,提取焊缝位置参数并构成状态向量,建立基于焊缝位置参数的系统状态方程和焊缝位置测量方程．针对系统动态噪声为有色噪声,通过扩展状态变量的方法建立有色噪声环境下的卡尔曼滤波算法,对焊缝位置进行最优状态估计并得到最小均方差条件下的焊缝偏差最优预测值,消除系统噪声对焊缝偏差测量的影响．焊接试验结果表明新方法可有效抑制有色噪声干扰并提高焊缝跟踪精度．     

Gaussian approximate filter for stochastic dynamic systems with randomly delayed measurements and colored measurement noises带随机延迟量测和有色量测噪声随机动态系统的高斯近似滤波器

In this paper, a new Gaussian approximate (GA) filter for stochastic dynamic systems with both one-step randomly delayed measurements and colored measurement noises is presented. For linear systems, a Kalman filter can be obtained to include one-step randomly delayed measurements and colored measurement noises. On the other hand, for nonlinear stochastic dynamic systems, different GA filters can be developed which exploit numerical methods to compute Gaussian weighted integrals involved in the proposed Bayesian solution. Existing GA filter with one-step randomly delayed measurements and existing GA filter with colored measurement noises are special cases of the proposed GA filter. The efficiency and superiority of the proposed method are illustrated in a numerical example concerning a target tracking problem.     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.     

加速度计信号处理的建模与仿真

研究车载公路路面平整度动态测量系统的优化设计问题,加速度计输出信号的二次积分用于修正路面高程数值,由于目前处理一维加速度计信号的方法中均不能滤除混入的标度因数误差。为解决上述问题,提出根据卡尔曼滤波原理建立标定车载道路路面平整度检测单元中一维加速度计混入的零偏差和标度因数误差的卡尔曼滤波模型,并使用MATLAB软件上进行仿真,仿真结果表明建立的卡尔曼滤波模型可以有效估计和滤除加速度计输出信号中混入的固有零偏差、标度因数误差和随机白噪声,为优化设计提供了依据。     

Non-linear smoothing algorithm for multi-dimensional dynamic systems

A new sub-optimum smoothing algorithm is presented for multi-dimensional dynamic systems. This algorithm is based upon quantization, multiple hypothesis testing, and the Viterbi decoding algorithm. The estimation of state vectors is carried out sequentially, component-by-component, and in parallel. A considerable memory reduction is achieved for state estimation implementation with the proposed algorithm. Simulation results, some of which are presented, show that the sub-optimum algorithm performs better than the extended Kalman filter algorithm for some non-linear multi-dimensional models with white gaussian disturbance and observation noises. In addition, the performance of the sub-optimum algorithm is almost as good as the Kalman filter algorithm for linear multi-dimensional models with white gaussian noise.     

Application of Kalman filters to the regulation of dead time processes

A single-input single-output control algorithm for a process with dead time and dead time uncertainty is described. The process dynamics consist of first-order mixing and pure delay with the pure delay being dominant. The process is disturbed at the upstream end by a disturbance sequence consisting of white noise passed through a first-order shaping filter. The process output is subject to white measurement noise. A discrete Kalman filter is used to produce state estimates for the disturbance mixing and dead time states which are updated from the process output residual error. In order to handle dead time uncertainty of up to a priori established limits, the residual error is passed through a dynamic dead band whose magnitude is a function of the dead time states of a separate process dynamic model driven by the process input. The dead band eliminates dead time error components from the residual. Control is achieved by state feedback from the upstream Kalman filter state estimate. The algorithm is in use on paper machine and bleach plant control applications and gives near minimum variance performance when properly tuned.     

The Cramér-Rao estimation error lower bound computation for deterministic nonlinear systems

For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive Ganssian white noise, the extended Kalman filter (EKF) convariance propagation equations linearized about the true unknown trajectory provide the Cramér-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.     

A new information fusion white noise deconvolution estimator

The white noise deconvolution or input white noise estimation problem has important applications in oil seismic exploration, communication and signal processing. By the modern time series analysis method, based on the autoregressive moving average （ARMA） innovation model, a new information fusion white noise deconvolution estimator is presented for the general multisensor systems with different local dynamic models and correlated noises. It can handle the input white noise fused filtering, prediction and smoothing problems, and it is applicable to systems with colored measurement noises. It is locally optimal, and is globally suboptimal. The accuracy of the fuser is higher than that of each local white noise estimator. In order to compute the optimal weights, the formula computing the local estimation error cross-covariances is given. A Monte Carlo simulation example for the system with Bernoulli-Gaussian input white noise shows the effectiveness and performances.     

广义系统Kalman融合器的研究

研究带自回归滑动平均(ARMA)有色观测噪声的多传感器广义离散随机线性系统,根据Kalman滤波方法和白噪声估计理论,在线性最小方差信息融合准则下,应用奇异值分解和增广状态空间模型,为了提高融合器的精度,提出了按矩阵加权降阶稳态广义Kalman融合器,可统一处理稳态滤波、平滑和预报问题,可减少计算负担和改善局部估计精度。并提出最优加权系数的局部估计误差方差和协方差阵的计算公式。用一个Monte Carlo数值仿真实例说明了所提方法的有效性。