Passive tracking from the combined set of bearings and frequency measurements by single satellite

In this paper,a new passive modified iterated extended Kalman filter(MIEKF) using the combined set of bearings and frequency measurements in Earth Centered Inertial(ECI) coordinate is proposed.A new measurement update equation of MIEKF is derived by modifying the objective function of the Gauss-Newton iteration.A new gain equation and iteration termination criteria are acquired by applying the property of the maximum likelihood estimate. The approximated second order linearized state propagation equation,Jacobian matrix of state transfer and measurement equations are derived in satellite two-body movement.The tracking performances of MIEKF,iterated extended Kalman filter(IEKF) and extended Kalman filter(EKF) are compared via Monte Carlo simulations through simulated data from STK8.1.Simulation results indicate that the proposed MIEKF is possible to passively track low earth circular orbit satellite by a high earth orbit satellite,and has higher tracking precision than the IEKF and EKF.     

基于MIEKF的移动机器人同时定位与地图构建研究*

由于移动机器人处在未知并且不确定的环境中,主要采用基于概率的方法对同时定位与地图构建(SLAM)进行描述。本文建立了SLAM问题的概率表示模型,并对在解决SLAM问题中用最常用的扩展卡尔曼滤波(EKF)算法以及迭代扩展卡尔曼滤波(IEKF)算法进行描述。本文针对两种算法的缺陷和不足,将应用于跟踪领域的修正迭代扩展卡尔曼滤波算法(MIEKF)与SLAM思想结合,提出了一种新的基于MIEKF的SLAM算法。通过基于点特征的SLAM实验验证了该算法的有效性。     

一种迭代离差差分滤波算法及其应用研究

针对扩展卡尔曼滤波（EKF）和迭代EKF量测更新过程采用线性化误差传递,导致状态估计精度偏低的问题,将迭代方法、统计线性化误差传递和离差差分滤波器相结合,建立了一种新型迭代离差差分滤波方法．将该方法应用于再入弹道目标状态估计,仿真实验结果显示,此方法降低了测量方程的非线性对滤波的影响,有效提高了目标的状态估计精度．     

Discrete‐time invariant extended Kalman filter on matrix Lie groups

In this article, we derive symmetry preserving discrete‐time invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters offer an advantage over classical extended Kalman filters as the error dynamics for such filters are independent of the group configuration which, in turn, provides a uniform estimate of the region of convergence. In contrast to existing techniques in the literature, the discrete‐time IEKF is derived using minimal tools from differential geometry which simplifies the derivation and the representation of IEKF. In our technique, the linearized error dynamics is defined on the Lie algebra directly using variational approaches, unlike conventional approaches where the error dynamics is translated to an Euclidean space using the logarithm map before its linearization. Moreover, the Kalman gains and its associated difference Riccati equations are derived in operator spaces by setting a discrete‐time optimal control problem and solving it with discrete‐time Pontryagin's maximum principle. The proposed discrete‐time IEKF is implemented for the attitude dynamics of the rigid body, which is a benchmark problem in control. It is observed from the numerical studies that the IEKF is computationally less intensive and provides better performance than the classical extended Kalman filter.     

Adaptive Iterated Extended KALMAN Filter for Relative Spacecraft Attitude and Position Estimation

This paper presents a novel adaptive iterated extended Kalman filter (AIEKF) for relative position and attitude estimation, taking into account the influence of model uncertainty. Considering a nonlinear stochastic discrete‐time system with unknown disturbance, the AIEKF algorithm adopts the Gauss‐Newton iterative optimization steps to implement a maximum a posteriori (MAP) estimation, and the switch‐mode combination technique is used to achieve the adaptive capability. The mean‐square estimation error (MSE) of the state estimate is derived. It is proved that the AIEKF can yield a smaller MSE than that of the traditional extended Kalman filter (EKF) or iterated extended Kalman filter (IEKF). The performance advantage of the AIEKF is illustrated via Monte Carlo simulations on a typical relative position and attitude estimation application. Through comparisons in different scenarios, the presented algorithm is shown to improve adaptability and ensure estimation accuracy.     

一种多传感器实时误差配准算法研究

针对多传感器的系统误差配准问题,研究了系统误差时变的情况,提出了一种基于迭代扩展卡尔曼滤波(IEKF)的配准算法。该算法将目标的运动状态和传感器系统误差组合在同一状态方程中,构建扩维状态的系统动态方程,采用IEKF的方法对目标状态和系统误差进行联合估计。仿真结果表明,与采用EKF和UKF的方法相比,该算法能取得和UKF相近估计精度,并且时间效率和EKF相当。     

基于快速不变卡尔曼滤波的视觉惯性里程计

针对相机定位问题,设计基于深度相机和惯性传感器的视觉惯性里程计,里程计包含定位部分和重定位部分.定位部分使用不变卡尔曼滤波融合多层迭代最近点(ICP)的估计值和惯性传感器的测量值来获得精确的相机位姿,其中ICP的估计误差使用费舍尔信息矩阵进行量化.由于需要使用海量的点云作为输入,采用GPU并行计算以快速实现ICP估计和误差量化的过程. 当视觉惯性里程计出现定位失败时,结合惯性传感器数据建立恒速模型,并基于此模型改进随机蕨定位方法,实现视觉惯性里程计的重定位.实验结果表明,所设计的视觉惯性里程计可以获得准确追踪相机且可以进行有效的重定位.     

Closed-Loop Behavior of a Class of Nonlinear Systems Under EKF-Based Control

We study the closed-loop behavior of the extended Kalman filter (EKF) for a class of deterministic nonlinear systems that are transformable to the special normal form with linear internal dynamics. We argue that the closed-loop system is asymptotically stable and the estimation error exponentially converges to zero. We compare the performance of the EKF to a high-gain observer through simulation     

非线性随机离散系统推广卡尔曼滤波方法收敛性分析

讨论了非线性随机离散系统的推广卡尔曼滤波算法的收敛性 .基于BoutayebM的一阶线性化技巧 ,得到了确保局部渐近收敛的充分条件     

基于深度信息的移动机器人室内环境三维地图创建

针对使用扩展卡尔曼滤波(EKF）进行环境地图的创建对线性系统效果较好而对非线性系统的线性化受误差影响较大的问题,提出一种基于对Kinect采集到的环境数据和迭代扩展卡尔曼滤波(IEKF）算法的室内环境三维地图创建。该方法使用成本较低的Kinect传感器获取深度数据然后结合IEKF实现摄像头轨迹预测,最后利用最近点迭代(ICP）算法对深度图像进行配准得到室内环境三维点云图。实验结果表明,IEKF算法与传统的EKF算法相比,得到的轨迹更平滑、误差更小,同时所得到的三维点云图更加光滑。该方法实现了三维地图构建,较为实用,效果较好。     

Passive location of the nonlinear systems with fuzzy uncertainty

With the merits such as hiding receiving, easy-deploying and high security, passive location has attracted more and more attention and plays an important role in fields as diverse as navigation, location, and tracking, etc. However, the current filters models for passive location methods are most under the framework of the probability theory, thus they can not estimate the state in some passive location with fuzzy uncertainty accurately. Although the fuzzy extended Kalman filter (FEKF) can deal with the fuzzy uncertainty, it unavoidably introduces truncation error. In this paper, based on the FEKF and the iterated extended Kalman filter (IEKF) principle, a new fuzzy passive location model is built, and moreover, an iterated fuzzy extended Kalman filter (IFEKF) is proposed for estimating the target state. Compared to the FEKF and the IEKF, the proposed algorithm can not only reduce the truncation error, but also deal with fuzzy uncertainty. Moreover, it is proved that the IFEKF update is an application of the Gauss–Newton method. Then, a fuzzy passive location algorithm is proposed. Simulation results demonstrate that the proposed approach has better estimation precision than the traditional fuzzy extended Kalman filter.     

Convergence analysis of the extended Kalman filter used as anobserver for nonlinear deterministic discrete-time systems

In this paper, convergence analysis of the extended Kalman filter (EKF), when used as an observer for nonlinear deterministic discrete-time systems, is presented. Based on a new formulation of the first-order linearization technique, sufficient conditions to ensure local asymptotic convergence are established. Furthermore, it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified EKF significantly. The efficiency of this approach, compared to the classical version of the EKF, is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete-time systems     

On the parametrization and design of an extended Kalman filterfrequency tracker

The problem of estimating the frequency of a harmonic signal embedded in broad-band noise is considered. The paper focuses on the extended Kalman filter frequency tracker, which is the application of the extended Kalman filter (EKF) framework to the frequency estimation problem. The EKF frequency tracker recently proposed in the literature is characterized by a vector of three design parameters {q,r,ε}, whose role and tuning is still a controversial and unclear issue. In this paper it is shown that a wise parametrization of the extended Kalman frequency tracker is characterized by just one parameter: the ε must be set to zero to achieve the basic property of unbiasedness in a noise-free setting; the performances of the tracker are not influenced independently by q and r; and what really matters is the ratio λ=r/q only. The proposed simplification of the extended Kalman filter frequency tracker allows an easier and more transparent tuning of its tracking behavior     

基于IMM-PF的分布式估计融合算法

针对基于扩展卡尔曼滤波的估计融合算法存在线性化误差,且受高斯噪声假设限制的问题,提出一种基于交互式多模型粒子滤波(IMM-PF)的分布式多传感器估计融合算法.各传感器节点采用IMM-PF算法,以便在非线性、非高斯条件下稳健地跟踪机动目标;融合中心则采用基于粒子滤波(PF)的分布式融合方法进行全局估计融合.该算法适用于非线性、非高斯条件下的多传感器状态估计.仿真结果表明,该算法能够提高多传感器系统状态估计的精度.     

A new method for the nonlinear transformation of means andcovariances in filters and estimators

This paper describes a new approach for generalizing the Kalman filter to nonlinear systems. A set of samples are used to parametrize the mean and covariance of a (not necessarily Gaussian) probability distribution. The method yields a filter that is more accurate than an extended Kalman filter (EKF) and easier to implement than an EKF or a Gauss second-order filter. Its effectiveness is demonstrated using an example     

Critical evaluation of non-linear filter configurations for the state estimation of Continuous Stirred Tank Reactor

A systematic approach has been attempted to design a non-linear observer to estimate the states of a non-linear system. The neural network based state filtering algorithm proposed by A.G. Parlos et al. has been used to estimate the state variables, concentration and temperature in the Continuous Stirred Tank Reactor (CSTR) process. (CSTR) is a typical chemical reactor system with complex nonlinear dynamics characteristics. The variables which characterize the quality of the final product in CSTR are often difficult to measure in real-time and cannot be directly measured using the feedback configuration. In this work, the comparison of the performances of an extended Kalman filter (EKF), unscented Kalman filter (UKF) and neural network (NN) based state filter for CSTR that rely solely on concentration estimation of CSTR via measured reactor temperature has been done. The performances of these three filters are analyzed in simulation with Gaussian noise source under various operating conditions and model uncertainties.     

纯方位目标定位观测器轨迹的 快速优化算法

在移动传感器网络中,观测器与目标的相对位置对目标的定位性能有重要的影响.为了提高目标的定位精度,提出了一种观测器运动轨迹的优化算法.算法把目标均方位置误差作为优化对象,使用扩展卡尔曼滤波器估计目标的位置.算法以目标和观测器的方位分布关系为基础,减小了观测器最优位置的搜索范围.仿真结果表明,使用多个观测器进行目标定位,滤波收敛速度快,定位误差小.最后给出了单个和多个观测器的"最优"运动规则.     

Conditions for stability of the extended Kalman filter and their application to the frequency tracking problem

The error dynamics of the extended Kalman filter (EKF), employed as an observer for a general nonlinear, stochastic discrete time system, are analyzed. Sufficient conditions for the boundedness of the errors of the EKF are determined. An expression for the bound on the errors is given in terms of the size of the nonlinearities of the system and the error covariance matrices used in the design of the EKF. The results are applied to the design of a stable EKF frequency tracker for a signal with time-varying frequency.This research was supported by the Co-operative Research Centre for Robust and Adaptive Systems ((CR)² ASys). The authors wish to acknowledge the funding of the activities of (CR)² ASys by the Australian Commonwealth Government under the Co-operative Research Centre Program.     

基于降阶EKF的永磁同步电机转速和磁链观测器

在永磁同步电机(PMSM)无速度传感器直接转矩控制中,针对扩展卡尔曼滤波(EKF)算法复杂、实时性较差等问题,提出了一种基于降阶扩展卡尔曼滤波器(REKF)的预估永磁同步电机磁链和转速的新算法。仿真结果证明该算法不仅延续了传统扩展卡尔曼滤波算法的优势,且算法更加简单,更易于数字化实现,鲁棒性好。     

Developing practical filters for non-linear systems using a new approach

Practical filters for non-linear system, in the sense of having- finite dimensional equations, are treated through a new approach which combines the model simplification and filtering aspects of the problem. Three filters are derived, the first extended filter (E1F), the second extended filter (E2F), and the second extended non-linear filter (E2NF). The EIF enjoys the accuracy of the extended Kalman filter (EKF) and the computational simplicity of the Kalman filter (KF). The E2F and the E2NF have structures similar to the KF and the EKF respectively, with with new formulae for the filter gain. The gain formula for the E2F and the E2NF provide an explanation as to the effect of the system non-linearities. Numerical results comparing the performance of the developed filters to those of other known filters like KF, EKF, and the modified second order filter (M2F) using the van der Pol equations are given.