Augmented robust three-stage extended Kalman filter for Mars entry-phase autonomous navigation

High-precision entry navigation capability is essential for future Mars pinpoint landing missions. An augmented robust three-stage extended Kalman filter (ARThSEKF) for integrated navigation algorithm of Mars atmospheric entry with models containing parameter uncertainties and measurement errors is presented in this paper. The derivation is conducted, and the character of stability has also been analysed, in which it has been proved to be uniformly asymptotically stable. In the further simulation of Mars entry-phase navigation, ARThSEKF showed a good performance to compare with the standard extended Kalman filter. As the atmosphere density uncertainties and unknown measurement errors have been estimated precisely, the state estimation errors were controlled to a low level, of which the position and velocity were less than 100 m and 5 m/s, respectively. Therefore, ARThSEKF is suitable for dealing with non-linear systems in the presence of parameter uncertainties and unknown measurement errors, which can fulfil the requirement of future pinpoint Mars landing mission.     

扩展Kalman滤波框架下的地平线检测算法

针对基于视觉的无人机姿态测量中的地平线检测问题, 提出一种结合图像处理和扩展Kalman滤波的地平线检测算法. 图像处理部分先从图像边缘中提取直线来获取候选地平线, 再根据图像暗原色先验来选取地平线. 扩展Kalman滤波部分将地平线观测模型与机身旋转模型结合起来, 获得观测值和残差协方差的先验信息, 用于判别检测到的地平线是否正确, 并在检测到错误地平线时进行修正. 实验结果表明, 该算法能够有效地检测地平线, 对复杂场景具有鲁棒性.     

Limit behaviors of extended Kalman filter as a parameter estimator for a sinusoidal signal

In this note, the basic limit behaviors of the solution to Riccati equation in the extended Kalman filter as a parameter estimator for a sinusoidal signal are analytically investigated by using lim sup and lim inf in advanced calculus. We show that if the covariance matrix has a limit, then it must be a zero matrix.     

Online tuning fuzzy PID controller using robust extended Kalman filter

Fuzzy PID controllers have been developed and applied to many fields for over a period of 30 years. However, there is no systematic method to design membership functions (MFs) for inputs and outputs of a fuzzy system. Then optimizing the MFs is considered as a system identification problem for a nonlinear dynamic system which makes control challenges. This paper presents a novel online method using a robust extended Kalman filter to optimize a Mamdani fuzzy PID controller. The robust extended Kalman filter (REKF) is used to adjust the controller parameters automatically during the operation process of any system applying the controller to minimize the control error. The fuzzy PID controller is tuned about the shape of MFs and rules to adapt with the working conditions and the control performance is improved significantly. The proposed method in this research is verified by its application to the force control problem of an electro-hydraulic actuator. Simulations and experimental results show that proposed method is effective for the online optimization of the fuzzy PID controller.     

基于M估计的非线性鲁棒检测卡尔曼滤波算法

针对传统鲁棒非线性滤波在观测噪声为非高斯强干扰噪声情况下,滤波性能下降的问题,提出一种利用卡方检测法预判断的非线性鲁棒检测滤波算法。该算法通过卡方检测设置门限,剔除突变野值,利用M估计修正量测更新。仿真实验对比了几种典型非线性滤波方法在不同观测噪声环境下的性能。所提算法在非高斯强干扰噪声情况下,比传统鲁棒滤波算法估计精度平均提高了25.5%;估计方差平均减少了18.3%。实验结果表明:所提算法可以抑制观测量非高斯强干扰噪声的影响,提高滤波精度及稳定性。     

基于抗差扩展卡尔曼滤波器的永磁同步电机转速估计策略

通过分析粗差对扩展卡尔曼滤波器(extended Kalman filte,EKF)状态估计的影响,对无速度传感器矢量控制的永磁同步电机的转速,提出了一种基于抗差扩展卡尔曼滤波器(robust extended Kalman filter,REKF)的估计方法.建立了永磁同步电机的REKF模型,探讨了永磁同步电机在粗差干扰下引入REKF能否获得优于EKF的估计性能这一问题,比较了REKF与EKF在遇到外部粗差干扰或内部估算粗差干扰时转速和磁链的变化.仿真和实验结果表明REKF较EKF而言具有更好的抗粗差性能,使系统遇到干扰时能更快收敛.     

多传感器系统中基于扩展卡尔曼滤波器的在线故障检测

随着多传感器系统的广泛应用,在线故障对于系统性能影响严重,如何使得多传感器系统具有自主故障检测与诊断能力成为首要问题。根据非线性多传感器系统的输入信号、输出信号和故障阵列,建立一种具有多输入多输出处理和自调节加强功能的扩展卡尔曼滤波器（ EKF）的故障分析模型,在此基础上,提出了一种适用于多传感器系统的在线故障检测算法及其在传感器节点上的实施架构。实验结果表明：所提算法在低并发故障和高并发故障环境下均具有高准确度故障报告能力。此外,在温度传感器上实施所提算法,温度监测值的对比结果验证了所提算法比传统算法具有更好的系统性能保证能力。     

Decomposition of the extended Kalman filter

The use of the extended Kalman filter as an approximate estimator for the states and parameters of nonlinear systems is well known. A decomposition is pointed out in this letter, which is possible with the usual augumentations of the state space by parameters, and which may lead to a more efficient computing algorithm.     

改进扩展卡尔曼滤波的四旋翼姿态估计算法

为了提高标准扩展卡尔曼姿态估计算法的精确度和快速性,将运动加速度抑制的动态步长梯度下降算法融入扩展卡尔曼中,提出一种改进扩展卡尔曼的四旋翼姿态估计算法。该算法在卡尔曼测量更新中采用梯度下降法进行非线性观测,消除标准扩展卡尔曼算法在线性化时带来的线性化误差,提高算法的准确性和快速性;对梯度下降法的梯度步长进行动态处理,使算法步长与四旋翼飞行器的运动合角速度成正比,增强微型四旋翼飞行器姿态解算的动态性能;对强机动运动过程中机体产生的运动加速度进行抑制处理,消除运动加速度对姿态解算的不利影响,提高了微型四旋翼飞行器姿态解算的跟踪精度。为了验证所设计算法的可行性和有效性,基于STM32单片机搭建四旋翼实验平台系统进行实时在线性能验证。结果表明,所设计算法能提高四旋翼飞行器在强机动、高速运动情况下的姿态跟踪精度、动态性能,增强姿态融合算法的抗干扰性,保证微型四旋翼飞行器的稳定飞行。     

Tracking of multiple target types with a single neural extended Kalman filter

The neural extended Kalman filter is an adaptive state estimation routine that can be used in target‐tracking systems to aid in the tracking through maneuvers without prior knowledge of the targets' dynamics. Within the neural extended Kalman filter, a neural network is trained using a Kalman filter training paradigm that is driven by the same residual as the state estimator. The difference between the a priori model used in the prediction steps of the estimator and the actual target dynamics is approximated. An important benefit of the technique is its versatility because little if any a priori knowledge of the target dynamics is needed. This allows the technique to be used in a generic tracking system that will encounter various classes of targets. In this paper, the neural extended Kalman filter is applied simultaneously to three separate classes of targets, each with different maneuver capabilities. The results show that the approach is well suited for use within a tracking system with multiple possible or unknown target characteristics. © 2010 Wiley Periodicals, Inc.     

EKF和互补滤波器在飞行姿态确定中的应用

设计了一种旋翼飞行姿态参考系统,采用基于加速度计和陀螺仪的惯性测量组合(IMU)测量飞行姿态数据。采集实测数据并运用Allan方差分析法分析其噪声特性,建立传感器模型;针对旋翼飞行器分别应用经典扩展Kalman滤波(EKF)算法和互补滤波算法进行姿态解算。在详细阐述2种算法的原理与实现的基础上,进行飞行器平台实验验证。研究结果表明2种算法均有效,且互补滤波器相对经典Kal-man滤波器更为简单、有效。     

An iterated fuzzy extended Kalman filter for nonlinear systems

The fuzzy extended Kalman filter (FEKF) for state estimation can be used to deal with fuzzy uncertainty effectively. However, the linearisation processing of the FEKF introduces truncation error, which degrades the estimation precision. In order to reduce the error, a new iterated fuzzy extended Kalman filter (IFEKF), based on the FEKF and the maximum a posteriori estimation, is proposed in this article. Compared with the FEKF, the proposed algorithm can be used not only to deal with the fuzzy uncertainty, but also to reduce the truncation error and to estimate the states more accurately. With an algebraic example and a passive location simulation, it is shown that the IFEKF has better estimation precision than that of the FEKF.     

A modified extended Kalman filter for linear discrete-time systems with unknown parameters

This technical communique presents a modified extended Kalman filter for estimating the states and unknown parameters in discrete-time, multi-input multi-output linear systems. The hyperstability of the filter is guaranteed by introducing a compensator into the estimation mechanism. It is proved that the estimates for the states and unknown parameters converge to the exact values if some conditions are assumed to the estimation mechanism. A numerical example shows that the proposed filter is much more effective than the extended Kalman filter in the estimation of unknown parameters.     

Stochastic stability of the discrete-time extended Kalman filter

The authors analyze the error behavior for the discrete-time extended Kalman filter for general nonlinear systems in a stochastic framework. In particular, it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough. This result is verified by numerical simulations for an example system     

基于扩展卡尔曼滤波的主动视觉跟踪技术

提出一种基于主动视觉的物体跟踪系统.该系统利用基于扩展卡尔曼滤波的物体锁定(Object Locked Based on Extended Kalman Filter,OLBEKF)技术,根据物体的运动预测摄像头的运动,并通过控制摄像头的两个关节实现主动跟踪.实际运用表明,在复杂的环境下,能够实时地获得高准确率的跟踪结果,并且显著提高摄像头拍摄图像的质量.     

Application of the extended Kalman filter to a lysine hydrochlorination process

This paper reports on the practical application of the extended Kalman filter to design a non-linear observer to estimate the state of a lysine hydrochlorination process at AECI Bioproducts in Umbogintwini, South Africa.     

Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems

The extended Kalman filter is an approximate filter for nonlinear systems, based on first-order linearization. Its use for the joint parameter and state estimation problem for linear systems with unknown parameters is well known and widely spread. Here a convergence analysis of this method is given. It is shown that in general, the estimates may be biased or divergent and the causes for this are displayed. Some common special cases where convergence is guaranteed are also given. The analysis gives insight into the convergence mechanisms and it is shown that with a modification of the algorithm, global convergence results can be obtained for a general case. The scheme can then be interpreted as maximization of the likelihood function for the estimation problem, or as a recursive prediction error algorithm.     

基于多新息理论的 EKF 改进算法

针对标准的扩展卡尔曼滤波算法（EKF）在强非线性系统中估计精度较低的问题,提出了一种改进的扩展卡尔曼滤波算法（MI-EKF）,使得滤波精度得到很大的提高。MI-EKF 是在标准 EKF 基础上,结合多新息理论,不仅考虑了系统当前的测量值,而且也充分考虑了之前时刻的有用信息,从而使得 MI-EKF 的滤波精度和稳定性得到改善。最后,讨论了新息数量对改进算法精度的影响,仿真结果表明包含两个新息的 MI-EKF 算法滤波效果最佳。     

A Zakai equation derivation of the extended Kalman filter

A discrete time filter is considered where both the observation and signal process have non-linear dynamics with additive Gaussian noise. Using the reference probability framework a convolution type Zakai equation is obtained which updates the unnormalized conditional density. Using first order approximations this equation can be solved recursively and the extended Kalman filter can be derived.