A chaotic communication system of improved performance based on the Derivative-free nonlinear Kalman filter

The Derivative-free nonlinear Kalman Filter is used for developing a communication system that is based on a chaotic modulator such as the Duffing system. In the transmitter’s side, the source of information undergoes modulation (encryption) in which a chaotic signal generated by the Duffing system is the carrier. The modulated signal is transmitted through a communication channel and at the receiver’s side demodulation takes place, after exploiting the estimation provided about the state vector of the chaotic oscillator by the Derivative-free nonlinear Kalman Filter. Evaluation tests confirm that the proposed filtering method has improved performance over the Extended Kalman Filter and reduces significantly the rate of transmission errors. Moreover, it is shown that the proposed Derivative-free nonlinear Kalman Filter can work within a dual Kalman Filtering scheme, for performing simultaneously transmitter–receiver synchronisation and estimation of unknown coefficients of the communication channel.     

A derivative-free distributed filtering approach for sensorless control of nonlinear systems

This article examines the problem of sensorless control for nonlinear dynamical systems with the use of derivative-free Extended Information Filtering (EIF). The system is first subject to a linearisation transformation and next state estimation is performed by applying the standard Kalman Filter to the linearised model. At a second level, the standard Information Filter is used to fuse the state estimates obtained from local derivative-free Kalman filters running at the local information processing nodes. This approach has significant advantages because unlike the EIF (i) is not based on local linearisation of the nonlinear dynamics (ii) does not assume truncation of higher order Taylor expansion terms thus preserving the accuracy and robustness of the performed estimation and (iii) does not require the computation of Jacobian matrices. As a case study a robotic manipulator is considered and a cameras network consisting of multiple vision nodes is assumed to provide the visual information to be used in the control loop. A derivative-free implementation of the EIF is used to produce the aggregate state vector of the robot by processing local state estimates coming from the distributed vision nodes. The performance of the considered sensorless control scheme is evaluated through simulation experiments.     

Extended Kalman and Particle Filtering for sensor fusion in motion control of mobile robots

Motion control of mobile robots and efficient trajectory tracking is usually based on prior estimation of the robots’ state vector. To this end Gaussian and nonparametric filters (state estimators from position measurements) have been developed. In this paper the Extended Kalman Filter which assumes Gaussian measurement noise is compared to the Particle Filter which does not make any assumption on the measurement noise distribution. As a case study the estimation of the state vector of a mobile robot is used, when measurements are available from both odometric and sonar sensors. It is shown that in this kind of sensor fusion problem the Particle Filter has better performance than the Extended Kalman Filter, at the cost of more demanding computations.     

Adaptive exact linearization control of batch polymerization reactors using a Sigma-Point Kalman Filter

The Chylla–Haase polymerization reactor is widely accepted as a benchmark process for the evaluation of control strategies for batch reactors. In this contribution a control concept based on Exact I/O-Linearization is proposed and compared to a conventional cascade control structure. In order to adapt the exact linearization control strategy to various polymerization products and batch conditions, an advanced probabilistic inference algorithm (Sigma-Point Kalman Filter) is applied and investigated. Sigma-Point Kalman Filters have the major improvement of simplified implementation compared to local linearization methods (i.e. Extended Kalman Filter) because no analytical Jacobians are required. Stochastic simulation studies are introduced and show the effectiveness, accuracy and benefit of the control concept. Within several scenarios a satisfying robustness against structural errors in the underlying model equations for the nonlinear control law and the inference algorithm is demonstrated. Furthermore it is pointed out, that with little effort in reassembling the plant design, control performance can be improved significantly.     

一种新的高动态GPS载波跟踪算法

提出了基于无迹粒子滤波（UPF）算法的高动态GPS载波跟踪环路,仿真分析了该方案在高斯噪声和非高斯噪声环境下对高动态GPS信号的跟踪性能,并与分别基于扩展卡尔曼滤波（EKF）、无迹卡尔曼滤波（UKF）、粒子滤波（PF）及扩展卡尔曼粒子滤波（EPF）这四种算法的载波跟踪环路进行了性能对比。仿真结果表明,基于UPF估计器的载波跟踪环路在高动态、弱信号以及非高斯噪声环境下具有优越的跟踪性能,既可以提高跟踪精度,又解决了非高斯噪声干扰问题。通过模拟实验验证了该方案的有效性。     

基于边缘粒子滤波的目标跟踪算法研究

为了提高目标跟踪过程中粒子滤波结果的精度,将边缘粒子滤波算法应用于目标跟踪。首先将目标运动状态向量划分为线性和非线性两个子向量,然后,采用卡尔曼滤波方法处理线性状态子向量,采用粒子滤波方法处理非线性状态子向量。使用边缘粒子滤波算法和标准粒子滤波算法对目标进行跟踪仿真。仿真结果表明：将边缘粒子滤波算法应用在目标跟踪过程中,能够取得更高的跟踪精度;时间复杂度增加仅6%;在粒子数相对较少的条件下,仍能够保持较好的滤波性能。     

The Study of Improving Kalman Filters Family for Nonlinear SLAM

When Extended Kalman Filter is used to solve the SLAM problem of a nonlinear system, the linearization error will lead to severe estimation error or even make the method to be divergent. After analyzing the linearization principle of Kalman filters family, two improved methods are suggested to decrease the linearization error. These two methods improve posterior estimation accuracy by revising the observation-update step. Simulation results indicate that the two methods are feasible. The method named ‘Mean Extended Kalman Filter’ performs much better than EKF and UKF for nonlinear SLAM. And the iterated version of EKF and UKF even falls behind MEKF in estimation accuracy. In addition, MEKF is computationally efficient. With a view to both estimation accuracy and computational complexity, MEKF seems to be the best filter of the Kalman filters family for nonlinear SLAM. Experiments are carried out with ‘Car Park Dataset’ and ‘Victoria Park Dataset’ to evaluate the performance of MEKF based SLAM solutions. And the experimental results validate the effectiveness of MEKF in real SLAM applications.     

面向调控网络参数学习的无迹粒子滤波算法

目前基于微分方程模型学习网络参数的工作普遍基于卡尔曼滤波器,对所分析系统有线性假设前提,而基因调控网络具有强非线性,因此需要更适用于非线性模型的方法。提出了一种基于无迹粒子滤波器学习基因调控网络参数的方法,由于粒子滤波方法不受模型线性假设的约束,因此能够对非线性系统进行更好的拟合。通过对Repressillar模型中隐变量与未知参数的估计并与无迹卡尔曼滤波器所获结果的比较,提出的算法有效减少了估计误差。并对粒子数目对结果的影响进行了分析。相较于卡尔曼滤波器,无迹粒子滤波方法对于调控网络参数学习精度更高。粒子数目太少或太多都会减弱估计精度,因此选择适当的粒子数目非常重要。     

含有有色噪声的非线性分数阶系统自适应扩展卡尔曼滤波器

研究了含有未知参数的情况下，分别含有分数阶有色过程噪声和有色测量噪声的连续时间非线性分数阶系统状态估计问题.采用Grünwald-Letnikov （G-L）差分方法和1阶泰勒展开公式，对描述连续时间非线性分数阶系统的状态方程进行离散化和线性化.构造由状态量、未知参数和分数阶有色噪声的增广向量，设计自适应分数阶扩展卡尔曼滤波算法实现对有色噪声情况下的连续时间非线性分数阶系统的状态和参数的估计.最后，通过分析两个仿真实例，验证了提出算法的有效性.     

UKF、PF与UPF跟踪性能的比较

无迹卡尔曼滤波器(UKF)是用一系列确定样本来逼近状态的后验概率密度,对任何非线性高斯系统都有较好的跟踪性能。粒子滤波器(PF)是用随机样本来近似状态后验概率密度函数,适用于任何非线性非高斯系统,但当似然函数出现在转移概率密度函数的尾部或者在高精度测量的场合,PF的跟踪性能降低。针对强非线性、非高斯系统、高精度测量的环境,文中提出采用UPF算法进行跟踪,并对PF、UKF和UPF三种跟踪算法进行了仿真,结果表明,UPF的跟踪精度要远高于PF、UKF的精度。     

非线性离散随机时变系统比例微分滤波

扩展卡尔曼滤波（EKF）是从极小化状态估计误差的方差得到的，没有考虑状态误差的变化率，因而对非线性时变系统EKF估计方法惯性作用 较大，从而产生估计滞后，提出了非线性离散随机系统比例微分滤波（PDF），PDF联合考虑极小化状态估计误差和状态误差变化率的方差，克服了EKF对非线性时变系统估计滞后的缺点，估计具有适时性，提出了高估计的精度，仿真例子证明了所提出的估计方法的有效性。     

转换坐标卡尔曼滤波算法分析

在非线性系统的目标跟踪中,常用的滤波算法是扩展卡尔曼滤波算法（EKFA）,但这种滤波算法常常会发散,近年来,Bar-Shalom等人在二维平面上提出了转换坐标卡尔曼滤波算法（CMKFA）,并通过仿真实验证明了在非线性系统的目标跟踪中此算法优于扩展卡尔曼滤波算法（EKFA）,文中对转换坐标卡尔曼滤波算法进行了深入的研究,通过理论推导证明了当状态方程和测量方程满足一定条件时,转换坐标卡尔曼滤波算法是去偏转换测量值的线性无偏最小方差估计算法。     

基于电动汽车磷酸铁锂动力电池荷电状态 估计方法研究

近几年,磷酸铁锂动力电池逐渐成为电动汽车动力电池首选.但是由于材料本身特性,使得磷酸铁锂电池的荷电状态难以精确估算.当电动汽车处于复杂工作环境时,荷电状态估计在保证电动汽车电池操作中的安全性和可靠性方面起到了至关重要的作用.文章采用戴维宁等效电路模型,验证无迹卡尔曼滤波和粒子滤波两种方法的估算效果,并分别与扩展卡尔曼滤波方法作对比,结果证明无迹卡尔曼滤波和粒子滤波都具有更好的估算精度.     

Nonlinear speed estimation of a GPS-free UAV

In this article, the problem of robust state observer design for a class of unmanned aerial vehicles (UAVs) is addressed. A prototype four-rotors helicopter robot for indoors and outdoors applications is considered: the drone is not equipped with GPS related devices, so we describe a strategy to estimate its translational velocity vector based on acceleration, angles and angular speeds measurements only. Since the linearised system is non-observable at the equilibrium point, a nonlinear observability verification is performed for persistently exciting trajectories. A global exponential solution to this open problem is provided in the framework of adaptive observation theory when exact measurements are available. A modified observer is presented to enhance velocity estimation robustness in the realistic case of noisy measurements. The results are compared with a classical estimation strategy based on the extended Kalman filter to test the algorithm's performance.     

基于UKF的超视距雷达跟踪算法研究

天波超视距雷达跟踪目标时电磁波是通过电离层的折射传播的,因而导致在地理坐标系下的量测方程中存在强非线性,而采用传统的EKF（Extended Kalman Filter）实现的跟踪算法,在非线性方程的线性化中舍去了含强非线性的二阶以上的高阶项,导致目标的跟踪精度较低;提出采用UKF（Unscented Kalman Filter）方法处理超视距雷达系统在跟踪算法中的强非线性问题.UKF算法有效降低了非线性方程中的舍入误差,可确保三阶以上的精度.仿真结果表明UKF滤波算法较EKF算法提高估计精度.     

Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation

The quality of process data in a chemical plant significantly affects the performance and benefits gained from activities like performance monitoring, online optimization and control. Since many chemical processes often exhibit nonlinear dynamics, techniques like Extended Kalman Filter (EKF) and Nonlinear Dynamic Data Reconciliation (NDDR) have been developed to improve the data quality. There are various issues that arise with the use of either of these techniques: EKF cannot handle inequality or equality constraints, while the NDDR has high computational cost. Recently a recursive estimation technique for nonlinear dynamic processes has been proposed which combines the merits of EKF and NDDR techniques. This technique, named as Recursive Nonlinear Dynamic Data Reconciliation (RNDDR), provides state and parameter estimates that satisfy bounds and other constraints imposed on them. However, the estimate error covariance matrix in RNDDR is computed in the same manner as in EKF, that is, the effects of both nonlinearity and constraints are neglected in the computation of the estimate error covariance matrix.

A relatively new method known as the Unscented Kalman Filter has been developed for nonlinear processes, in which the statistical properties of the estimates are computed without resorting to linearization of the nonlinear equations. This leads to improved accuracy of the estimates. In this paper, we combine the merits of the Unscented Kalman Filter and the RNDDR to obtain the Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) technique. This technique addresses all concerns arising due to the presence of nonlinearity and constraints within a recursive estimation framework, resulting in an efficient, accurate and stable method for real-time state and parameter estimation for nonlinear dynamic processes.     

基于Sigma点Kalman滤波的车载导航系统状态估计

针对扩展卡尔曼滤波(EKF)在车载组合导航系统状态估计问题中的缺陷,本文介绍了一种新的方法——Sigma点卡尔曼滤波(SPKF)用于车载组合导航系统的非线性状态估计。其思想是基于非线性函数的加权统计线形化,SPKF滤波算法能够给出随机变量非线性变换以后更精确的均值和协方差的估计,从而带来更高的精度。最后通过GPS/DR组合导航模型时间序列的状态估计仿真实例说明:同EKF相比,SPKF的滤波精度和稳定性都显著提高了,还可避免计算烦琐的Jacobi矩阵,是一种良好的非线形滤波方法。     

基于RBPF和数据关联的多目标跟踪

粒子滤波用一组带有权值的随机采样点近似后验概率密度函数,实现对任意状态模型的精确估计。把Rao-Blackwellized粒子滤波与多假设跟踪算法相结合,将多目标跟踪问题分为2个部分,即数据关联中后验概率分布的估计和基于数据关联的单个目标跟踪估计。前者通过序列重要性重采样实现,后者使用卡尔曼滤波进行最小均方误差估计。实验结果表明,采用最优重要性分布可以减少计算所需粒子数和计算量。     

基于无极卡尔曼滤波算法的雅可比矩阵估计

在基于图像的机器人视觉伺服中,采用在线估计图像雅可比的方法,不需事先知道系统的精确模型,可以避免复杂的系统标定过程。为了有效改善图像雅可比矩阵的在线估计精度,进而提高机器人的跟踪精度,针对机器人跟踪运动目标的应用背景,提出了利用无极卡尔曼滤波算法在线估计总雅可比矩阵。在二自由度的机器人视觉伺服仿真平台上,分别用卡尔曼滤波器（KF）、粒子滤波器（PF）和无极卡尔曼滤波器（UKF）三种算法进行总雅可比矩阵的在线估计。实验结果证明,使用UKF算法的跟踪精度优于其他两种算法,时间耗费仅次于KF算法。     

Sparse-grid quadrature nonlinear filtering

In this paper, a novel nonlinear filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The filter utilizes weighted sparse-grid quadrature points to approximate the multi-dimensional integrals in the nonlinear Bayesian estimation algorithm. The locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method. Then the univariate quadrature point sets are extended to form a multi-dimensional grid using the sparse-grid theory. Compared with the conventional point-based methods, the estimation accuracy level of the SGQF can be flexibly controlled and the number of sparse-grid quadrature points for the SGQF is a polynomial of the dimension of the system, which alleviates the curse of dimensionality for high dimensional problems. The Unscented Kalman Filter (UKF) is proven to be a subset of the SGQF at the level-2 accuracy. The performance of this filter is demonstrated by an orbit estimation problem. The simulation results show that the SGQF achieves higher accuracy than the Extended Kalman Filter (EKF), the UKF, and the Cubature Kalman Filter (CKF). In addition, the SGQF is computationally much more efficient than the multi-dimensional Gauss–Hermite Quadrature Filter (GHQF) with the same performance.