高斯渐进贝叶斯滤波器

渐进贝叶斯方法将先验分布到后验分布的演化描述为一阶动态系统,通过在伪时间上连续地引入观测信息实现后验状态估计.该方法的一般形式解,即动态系统的时间导数,是难以得到的.本文提出一种高斯型渐进贝叶斯滤波器.首先在线性高斯条件下推导了时间导数的解析解;然后证明了在该条件下,由该解析解确定的一阶动态系统与常量状态估计的Kalman-Bucy滤波器是一致的,且由此导出的高斯渐进贝叶斯滤波器与卡尔曼滤波器是一致的.最后利用一阶Taylor展开推导了滤波器在非线性高斯条件下的近似解表达式,并采用Monte Carlo方法给出了具体实现方法.通过若干仿真算例表明,新滤波器具有较高的精度,且在一定精度条件下的时间复杂度低于一般粒子滤波器.     

非线性动态滤波的迭代算法

阐述了标称状态的线性化方法和扩展的卡尔曼滤波公式及迭代卡尔曼滤波,探讨了非线性动态滤波的近似处理方法,围绕标称状态将非线性模型进行线性化,将标准的卡尔曼滤波扩展到非线性模型,得到扩展的卡尔曼滤波公式,研究了迭代滤波计算方法。扩展的卡尔曼滤波方法已经有效地用于非线性模型。     

磁偶极子跟踪的渐进贝叶斯滤波方法

提出一种新的非线性滤波器应用于磁偶极子目标跟踪问题.建立了跟踪问题的状态空间模型, 在此基础上, 从高斯矩近似误差的角度分析了现有卡尔曼滤波更新在磁偶极子跟踪中的问题.对此, 将贝叶斯更新过程等效为求解连续时间上的渐进贝叶斯问题, 在线性高斯条件下推导了其解析解, 表明渐进贝叶斯更新可等效为定常系统的Kalman-Bucy滤波器; 进一步采用一阶Taylor展开得到非线性近似解表达式, 导出一种渐进贝叶斯滤波器, 从理论上分析了与现有方法的异同.仿真与实测磁目标跟踪试验结果表明, 渐进贝叶斯滤波器具有良好的精度和收敛性, 能够有效抑制磁目标跟踪中由于大初始误差导致的性能下降和滤波发散, 且计算效率与扩展卡尔曼滤波器相当, 适于实际应用.     

On-line Support Vector Regression of the transition model for the Kalman filter

Recursive Bayesian Estimation (RBE) is a widespread solution for visual tracking as well as for applications in other domains where a hidden state is estimated recursively from noisy measurements. From a practical point of view, deployment of RBE filters is limited by the assumption of complete knowledge on the process and measurement statistics. These missing tokens of information lead to an approximate or even uninformed assignment of filter parameters. Unfortunately, the use of the wrong transition or measurement model may lead to large estimation errors or to divergence, even when the otherwise optimal filter is deployed. In this paper on-line learning of the transition model via Support Vector Regression is proposed. The specialization of this general framework for linear/Gaussian filters, which we dub Support Vector Kalman (SVK), is then introduced and shown to outperform a standard, non adaptive Kalman filter as well as a widespread solution to cope with unknown transition models such as the Interacting Multiple Models (IMM) filter.     

CDKF在车载捷联惯导自对准中的应用

研究了车载捷联惯导在大方位失准角下的静基座自对准。采用Sigma点卡尔曼滤波,根据均值与协方差信息按非线性映射传播的特点,直接利用非线性模型,可以消除EKF存在的需要解析Jacobi矩阵以及将非线性系统线性化后的系统模型误差问题不易调整的弊端,其中的中心差分卡尔曼滤波(CDKF)精度高,且对状态协方差阵不敏感。仿真结果表明,在大方位失准角下采用CDKF进行初始对准,比用传统的EKF更精确且收敛速度更快。     

Adaptive Gaussian filters for nonlinear state estimation with one-step randomly delayed measurements

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one-step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off-line harmonics estimation problem with real data.     

Turning point identification and Bayesian forecasting of a volatile time series

Volatile time series are part of the industrial engineering forecasting and planning environment. An example of a volatile time series is the daily closing price of a stock, such as IBM, which is adaptively forecasted in this paper. Volatile series are beset with random shocks, from day-to-day, which may be characterized as 1) no charge in the series, 2) a step change, 3) a ramp change, or 4) a transient change. These random shocks are referred to as states of the time series. Probabilities for the various states are determined (computationally and subjectively) and are combined with the Bayesian results of Kaiman (3, 6) to update adaptively a forecasting equation. The method, therefore, is a multi-state procedure which embeds the Bayesian estimation method of Kalman. To illustrate the technique, a linear forecasting equation is used to predict the daily closing prices of IBM stock for 79 trading days starting on September 8 and extending to December 29, 1987; a period which includes the “crash” of October 19, 1987. In general seasonality may be added, if desired. It is assumed that the reader is familiar with Kalman's results.     

基于Huber的鲁棒广义高阶容积卡尔曼滤波算法

为提高随机变量非高斯分布时广义高阶容积卡尔曼滤波(GHCKF)的鲁棒性,提出一种基于Huber的鲁棒GHCKF算法.从近似贝叶斯估计角度,解释Huber方法作用于卡尔曼滤波的本质是对新息进行截断平均.采用Huber方法处理观测量,进行标准的GHCKF量测更新,从而实现算法的鲁棒化.所提出算法充分利用容积变换的优势,无需通过统计线性回归模型对系统的非线性量测模型进行近似.仿真结果表明,所提出算法具有鲁棒性强和估计精度高的特点.     

一种新的车辆辅助驾驶动态障碍物检测与分类方法

车前动态障碍物的检测与识别在智能车辆辅助驾驶中具有重要意义。为了解决道路视频中的运动障碍物检测和分类准确率低的问题,提出了一种基于卡尔曼滤波和朴素贝叶斯网络结合的检测与分类方法。首先采用卡尔曼滤波算法检测视频中的障碍物,并将检测到的障碍物进行特征提取。采用障碍物对称性与边缘直线水平度等特征,建立朴素贝叶斯网络对车辆前方的障碍物进行分类。实验结果表明,障碍物检测的准确率达到95％,对摩托车或自行车、汽车正面、汽车侧面和行人等障碍物识别准确率达到98.75%。     

基于异常值识别卡尔曼滤波器的短期交通流预测

针对智慧交通的需求提出了一种新颖有效的短时交通流预测方法,通过异常值识别扩展了卡尔曼滤波,使其能对噪声进行识别和过滤——异常值识别卡尔曼滤波器。利用卡尔曼滤波能有效地过滤导致系统不确定性的交通流波动,但这可能会使指示交通流突变的细微线索丢失,为了提升预测精度,应用离散小波变换对原始信号进行识别处理,在去掉异常值的同时保留原有对预测有效的信号源信息,此外还使用了历史参考值对预测值进行修正。在四个基准数据集上的大量实验表明,与常用及最新的预测模型相比,其结果MAPE平均降低了2.919%,RMSE平均降低了79.582。     

Forecasting based on time series with correlated errors by information preserving filter Demand forecasting from information theory

An optimal forecasting technique has been developed by us from the viewpoint of mutual information. Generalization of this process is considered for the time series with correlated errors. The recommended technique is also compared with the prevailing method based on the Kalman filter in the optimality. The results indicate that the former may improve the latter in the effectiveness of forecasting.     

基于自适应卡尔曼滤波在气象影响下负荷预测

如今电网系统中所构成电力负荷的电器越来越多,其中像空调等受气象影响的负荷所占比例持续升高,那么气象因素（温度、湿度、降雨量等）对电网的影响自然越来越突出,因此短期负荷预测将气象因素考虑进去,能够大大提升预测精度。根据某地区六年的电力负荷数据,构建卡尔曼滤波模型,可以给出高效准确的预测结果。然后将气象因素考虑到自适应卡尔曼滤波模型,通过不断对状态估计进行修正,得到计及气象因素影响的负荷预测结果精度更高。通过MATLAB 仿真,说明这种算法比较传统的卡尔曼滤波具有更高的预测精度,而且这种改进后的算法对实现短期负荷预测提供了一条新的途径。     

Bayesian robust linear dynamic system approach for dynamic process monitoring

In this paper, a Bayesian robust linear dynamic system approach is proposed for process modeling. Traditional linear dynamic system (LDS) constructed with Kalman filter is designed by Gaussian assumption which can be easily violated in non-Gaussian modeling situations, especially those with outliers. To deal with this issue, the conventional Gaussian-based Kalman filter is modified with heavy tailed Student's t-distribution so as to deal with the non-Gaussian noise and modeling outliers. Then, a variational Bayesian expectation maximization (VBEM) algorithm is developed for learning parameters of the robust linear dynamic system. For process monitoring, traditional monitoring scheme are discussed and the residual space monitoring mechanism has been improved. To explore the feasibility and effectiveness, the proposed method is applied for fault detection, with detailed comparative studies with several other methods through the Tennessee Eastman benchmark.     

基于图像序列的人体跟踪

由于人体的非刚体性和人体之间会经常发生遮挡,使得人体跟踪是一个很有挑战性的课题.针对这一特点,提出了用结合卡尔曼滤波和贝叶斯的方法来完成多个人体的跟踪,先建立简单的背景模型,然后用背景差分法得到前景区域,提取运动人体,并用EM(期望-最大化)算法建立相应的人体模型.在人体间没有发生遮挡时,用卡尔曼滤波方法来跟踪各个人体;人体间出现遮挡时,用贝叶斯方法来判别和跟踪相应人体.实验表明,该方法既能保证跟踪的快速性,又能很好地处理人体间相互遮挡的情况,该算法鲁棒性好,跟踪结果令人满意.     

Distributed adaptive Kalman filter based on variational Bayesian technique

In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distributed adaptive Kalman filter is proposed with the help of variational Bayesian, where the posterior distribution of joint state and noise variance is approximated by a free-form distribution. The convergence of the proposed algorithm is proved in two main steps: noise statistics is estimated, where each agent only use its local information in variational Bayesian expectation (VB-E) step, and state is estimated by a consensus algorithm in variational Bayesian maximum (VB-M) step. Finally, a distributed target tracking problem is investigated with simulations for illustration.     

采用概率密度分布和粒子滤波的室内跟踪算法

提出了一种新的室内定位跟踪算法,采用了直方图法和核函数法估计参考点处的接收信号强度的概率分布,并将其作为该参考点的位置指纹,描述了该参考点处无线信道的特性;利用粒子滤波解决了非线性状态空间模型下的在线跟踪问题,仿真结果表明基于概率密度分布和粒子滤波的跟踪算法收敛速度快,且对环境变化不敏感,性能优于卡尔曼滤波算法。     

Robust derivative-free Kalman filter based on Huber's M-estimation methodology

In this study, a discrete-time robust nonlinear filtering algorithm is proposed to deal with the contaminated Gaussian noise in the measurement, which is based on a robust modification of the derivative-free Kalman filter. By interpreting the Kalman type filter (KTF) as the recursive Bayesian approximation, the innovation is reformulated capitalizing on the Huber's M-estimation methodology. The proposed algorithm achieves not only the robustness of the M-estimation but also the accuracy and flexibility of the derivative-free Kalman filter for the nonlinear problems. The reliability and accuracy of the proposed algorithm are tested in the Univariate Nonstationary Growth Model.     

Mapping extended Kalman filters onto linear arrays

Techniques for mapping extended Kalman filters onto linear arrays of programmable cells designed for real-time applications are described. First, a general method for mapping a standard (nonsquare root) Kalman filter, where the columns of the covariance matrix are updated in parallel, is introduced. Next, a general method for mapping a factorized (square root) filter, where fast Givens rotations are used to triangularize the prematrix and where rotations of the rows of the prematrix are performed in parallel, is introduced. These mappings are used to implement an extended Kalman filter commonly used in target tracking applications on the Warp computer. The Warp is a commercially available linear array of 10 or more programmable cells connected to an MC68020-based workstation. The Warp implementation of the standard Kalman filter running on 8 Warp cells achieves a measured speedup of 7 over the same filter running on a single cell. The Warp implementation of the factorized filter running on 10 Warp cells achieves a measured speedup of 2     

Approaches to adaptive filtering

The different methods of adaptive filtering are divided into four categories: Bayesian, maximum likelihood (ML), correlation, and covariance matching. The relationship between the methods and the difficulties associated with each method are described. New algorithms for the direct estimation of the optimal gain of a Kalman filter are given.     

基于Huber的鲁棒高阶容积卡尔曼滤波算法

为提高随机变量非高斯分布时高阶容积卡尔曼滤波（High-degree Cubature Kalman Filter,HCKF）算法的鲁棒性,提出了一种基于Huber方法的鲁棒高阶容积卡尔曼滤波算法。从近似贝叶斯估计角度解释了Huber方法作用于卡尔曼滤波算法的本质是对新息进行截断平均,通过在现有滤波框架内利用Huber方法对观测量进行预处理,并将处理后的观测量进行标准的HCKF量测更新,实现了HCKF算法的鲁棒化。所提算法无需通过统计线性回归模型对系统的非线性量测模型进行近似,高阶容积变换的优势得到充分利用,从而在保持鲁棒性的前提下提高了算法的滤波精度。单变量非平稳增长模型和再入飞行器目标跟踪问题验证了该算法在鲁棒性和滤波精度方面的优势。