基于自适应插值扩展卡尔曼滤波的永磁同步电机状态估计

PMSM无传感控制的转速与转子位置估计对系统至关重要,扩展EKF算法作为无传感控制技术被广泛应用在工业领域。但是EKF算法在系统线性化过程中产生截断误差,对于高度非线性模型无法得到精确估计值。为减小EKF算法因非线性问题而造成的误差,文中提出了一种基于AIEKF状态估计法。该方法以量化状态方程的非线性程度为依据,通过添加伪状态值减小EKF算法线性化中产生的误差对估值精度的影响,从而降低系统在线性化过程引起的误差。仿真计算结果表明,AIEKF较EKF的截断误差平均降低了55.6%。     

基于UKF的星载GNSS地球静止卫星定轨算法

针对星载GNSS接收机的采样间隔较长以及EKF处理非线性问题会引入线性化误差的问题,提出了利用UKF进行GEO星定轨计算的方法。依照GEO轨道动力学特性建立了状态模型,并对星载接收机进行了可见性分析,将UKF算法应用于接收机输出信息的处理。仿真结果表明该算法比EKF更适用于定轨计算,尤其当因采样间隔较长而使得系统非线性较强时,仍可保证定轨结果拥有较高的精度。     

哈默斯坦非线性时变系统的加权学习辨识方法

针对有限区间哈默斯坦(Hammerstein)非线性时变系统,该文提出一种加权迭代学习算法用以估计系统时变参数。首先将Hammerstein系统输入非线性部分进行多项式展开,采用迭代学习最小二乘算法辨识系统的时变参数。为了防止数据饱和,采用带遗忘因子的迭代学习最小二乘算法,进而引入权矩阵,采用加权迭代学习最小二乘算法改进系统跟踪误差,以提高辨识精度。该文分别给出3种算法的推导过程并进行仿真验证。结果表明,与迭代学习最小二乘算法和带遗忘因子迭代学习最小二乘算法相比,加权迭代学习最小二乘算法具有辨识精度高、跟踪误差小以及迭代次数少等优点。     

稳健的单站无源目标跟踪算法研究

无源定位与跟踪系统中面临着可观测性弱、初始误差大的问题,因此寻找一种稳健快速的跟踪算法显得尤为关键。本文在对现有跟踪算法进行分析和比较的基础上,提出一种IUKF(Improved Unscented Kalman Filter)算法,它通过对传统的UKF算法进行修正,改善了对状态滤波值和协方差的估计。与现有算法(如EKF,UKF)相比,新算法不仅适应能力强、稳定性高,而且收敛速度快、跟踪误差小,是一种稳健的无源目标跟踪算法,数值仿真和试验结果表明了算法的正确性和有效性。     

An EM Algorithm for Nonlinear State Estimation With Model Uncertainties

In most solutions to state estimation problems, e.g., target tracking, it is generally assumed that the state transition and measurement models are known a priori. However, there are situations where the model parameters or the model structure itself are not known a priori or are known only partially. In these scenarios, standard estimation algorithms like the Kalman filter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the nonlinear state estimation problem with possibly non-Gaussian process noise in the presence of a certain class of measurement model uncertainty is considered. It is shown that the problem can be considered as a special case of maximum-likelihood estimation with incomplete data. Thus, in this paper, we propose an EM-type algorithm that casts the problem in a joint state estimation and model parameter identification framework. The expectation (E) step is implemented by a particle filter that is initialized by a Monte Carlo Markov chain algorithm. Within this step, the posterior distribution of the states given the measurements, as well as the state vector itself, are estimated. Consequently, in the maximization (M) step, we approximate the nonlinear observation equation as a mixture of Gaussians (MoG) model. During the M-step, the MoG model is fit to the observed data by estimating a set of MoG parameters. The proposed procedure, called EM-PF (expectation-maximization particle filter) algorithm, is used to solve a highly nonlinear bearing-only tracking problem, where the model structure is assumed unknown a priori. It is shown that the algorithm is capable of modeling the observations and accurately tracking the state vector. In addition, the algorithm is also applied to the sensor registration problem in a multi-sensor fusion scenario. It is again shown that the algorithm is successful in accommodating an unknown nonlinear model for a target tracking scenario.     

Finite dimensional smoothers for MAP state estimation of bilinearsystems

In this paper, we present two finite-dimensional iterative algorithms for maximum a posteriori (MAP) state sequence estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. Our iterative algorithms for state estimation are based on the expectation-maximization (EM) algorithm and outperform the widely used extended Kalman smoother (EKS). Unlike the EKS, these EM algorithms are optimal (in the MAP sense) finite-dimensional solutions to the state sequence estimation problem for bilinear models. We also present recursive (on-line) versions of the two algorithms and show that they outperform the extended Kalman filter (EKF). Our main conclusion is that the EM-based algorithms presented in this paper are novel nonlinear filtering methods that perform better than traditional methods such as the EKF     

A general class of nonlinear normalized adaptive filteringalgorithms

The normalized least mean square (NLMS) algorithm is an important variant of the classical LMS algorithm for adaptive linear filtering. It possesses many advantages over the LMS algorithm, including having a faster convergence and providing for an automatic time-varying choice of the LMS stepsize parameter that affects the stability, steady-state mean square error (MSE), and convergence speed of the algorithm. An auxiliary fixed step-size that is often introduced in the NLMS algorithm has the advantage that its stability region (step-size range for algorithm stability) is independent of the signal statistics. In this paper, we generalize the NLMS algorithm by deriving a class of nonlinear normalized LMS-type (NLMS-type) algorithms that are applicable to a wide variety of nonlinear filter structures. We obtain a general nonlinear NLMS-type algorithm by choosing an optimal time-varying step-size that minimizes the next-step MSE at each iteration of the general nonlinear LMS-type algorithm. As in the linear case, we introduce a dimensionless auxiliary step-size whose stability range is independent of the signal statistics. The stability region could therefore be determined empirically for any given nonlinear filter type. We present computer simulations of these algorithms for two specific nonlinear filter structures: Volterra filters and the previously proposed class of Myriad filters. These simulations indicate that the NLMS-type algorithms, in general, converge faster than their LMS-type counterparts     

基于Kalman的滤波目标精确跟踪技术研究

阐述了基本kalman滤波方法,讨论了针对非线性系统应用的kalman滤波方法的改进形式EKF、UKF。为了增进UKF运算效能,提出了引入衰减系数的滤波形式DCUKF。针对二维平面非匀速运动的目标的精确跟踪定位系统,仿真对比分析了EKF、UKF及DCUKF的滤波计算效果。结果表明DCUKF有更好的滤波效果。     

光电经纬仪的粒子-卡尔曼联合目标跟踪算法及仿真

针对系统状态方程是线性,观测方程是非线性的被动光电测量问题,分析了常用的EKF法（扩展卡尔曼滤波法）、PF法（粒子滤波法）、UKF法（无迹卡尔曼滤波法）的优缺点,提出了以PF法与EKF法相结合的方法作为光电经纬仪的目标跟踪算法．为解决单台光电经纬仪的不可观测性问题,采用2台交汇的观测数据作为观测量进行计算．通过蒙特卡洛仿真计算,比较了上述各种方法对同一运动模型的跟踪结果,证明PF-EKF法在交汇光电经纬仪的目标跟踪中精度较高,而EKF算法的实时性较高．     

基于辅助变量粒子滤波的空对海BO-TMA的研究

论文探讨了TMA(目标运动分析)中基本的非线性估计问题;介绍了粒子滤波(PF)的基本思想和辅助变量PF(AVPF)的基本算法,特别针对空对海单站只测方位TMA(BO-TMA)问题应用AVPF和EKF(扩展卡尔曼滤波)进行了对照研究;建立了问题的离散非线性滤波估计模型;设计了典型的应用场景;给出了Monte Carlo仿真运行结果;表明AVPF具有更高的估计精度、更好的收敛特性和滤波一致性。     

粒子滤波器及其在目标跟踪中的应用

为了在物理条件下对目标进行精确建模，有时需要运用非线性、非高斯系统。而常规的卡尔曼滤波算法要求系统是线性高斯型的，因而不能直接用来解决非线性、非高斯问题。为了解决这一问题，人们开发出各种非线性滤波算法。一种是扩展卡尔曼算法(EKF)，它对非线性系统进行局部线性化，从而间接利用卡尔曼算法进行滤波与估算；另一种是序列蒙特卡罗算法，亦即粒子滤波器(PF)，它是最近出现的解决非线性问题的有效算法。本文简要介绍非线性跟踪的最优与次优贝叶斯算法，重点关注粒子滤波器，通过再入大气层弹道目标的例子，说明PF在目标跟踪中的应用。     

Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions

We present an efficient particle filtering method to perform optimal estimation in jump Markov (nonlinear) systems (JMSs). Such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure. We take advantage of these specificities in order to develop a generic filtering methodology for these models. The method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature, namely, the auxiliary particle filter and the unscented transform. This algorithm is applied to the complex problem of time-varying autoregressive estimation with an unknown time-varying model order. More precisely, we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations. We show that this problem can be formulated as a JMS and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper. Simulations demonstrate the performance of our method compared to standard particle filtering techniques.     

多站无源跟踪边缘化卡尔曼滤波算法

多站无源跟踪量测方程非线性强,对跟踪算法的稳定性及精度提出了更高的要求。为实现稳定高精度跟踪,提出了新的基于边缘化卡尔曼滤波（MKF）的多机无源跟踪算法。该算法将非线性的量测方程表示为p阶Hermite多项式的加权和,将加权矩阵的先验分布建模为高斯过程,求得其后验分布后对其进行积分来消除加权矩阵的影响,最终可得对状态及其协方差矩阵估计的闭式解。以只测角跟踪为例对所提算法性能进行验证,仿真结果表明,相对于扩展卡尔曼滤波（EKF）算法、不敏卡尔曼滤波（UKF）算法及容积卡尔曼滤波（CKF）算法,所提算法具有更好的跟踪性能。      

基于WLS-KF的GPS非线性动态滤波研究

为了提高动态定位精度,将卡尔曼（KF）算法应用到GPS非线性动态定位解算中,提出加权最小二乘-卡尔曼滤波（WLS-KF）算法。通过加权最小二乘（WLS）算法得到近似的线性化模型,再将KF算法应用到这个线性化模型进行校正。因此既保持了KF算法能够对系统状态进行最优估算的优点,同时对各个测量值进行了联系制约,具有更高的精度。结果表明,这种方法精度介于EKF和UKF之间,且实现容易,预测可靠,具有实际应用价值。     

一类 Wiener 非线性时变系统的迭代学习辨识

针对Wiener非线性时变系统的参数辨识问题,该文提出一种基于重复轴的迭代学习算法来实现对时变甚至突变参数的估计。文中将维纳系统输出非线性部分的反函数进行多项式展开,进而构造了回归模型,未知参数及中间变量用其估计替代,分别给出了采用迭代学习梯度算法和迭代学习最小二乘算法实现时变参数辨识的方法。仿真结果表明,与带遗忘因子的递推算法和迭代学习梯度算法相比,迭代学习最小二乘算法更具有参数估计收敛速度快,辨识精度高,系统输出误差小等优势,验证了所提学习算法的有效性。     

基于扩展Kalman滤波的单领航者自主水下航行器协同导航判别式训练方法研究

单领航者自主水下航行器(AUV)协同导航算法中,系统模型是非线性的,扩展Kalman滤波(EKF)是针对非线性系统的很有影响力的滤波算法,但是,EKF算法的性能严格依赖于一系列模型参数,而这些参数往往需要花费很大的代价来捕获,并且常需要人工调整。该文应用一种能自动学习Kalman滤波噪声协方差参数的方法,通过仿真分析,证明了该学习算法可以完全自主并且高效、准确地输出Kalman滤波噪声参数,进一步提高了单领航者AUV协同导航系统的导航精度。     

变遗忘因子递推最小二乘Hammerstein系统辨识算法

摘.要:本论文研究了单输入单输出非线性Hammerstein系统的辨识问题,提出了一种具有变遗忘因子的递推最小二乘算法.由于Hammerstein系统模型的非线性特征,传统的递推最小二乘算法无法直接用来解决该系统的辨识问题.为此,论文将Hammerstein系统参数进行了映射变换,使得变换后的系统参数与Hammerst...     

基于UKF的单站无源定位与跟踪算法

单站无源定位与跟踪系统观测方程的非线性性决定了定位与跟踪中必须采用非线性滤波技术.MGEKF等非线性滤波方法本质上都属于扩展卡尔曼滤波算法,都存在由于线性化误差而导致滤波器稳定性差等问题.基于unscented变换的UKF算法不存在线性化误差,具有更好的稳定性,但由于协方差估计不足,导致收敛速度较慢.该文基于UKF算法提出了一种迭代UKF(IUKF)算法,通过对状态和协方差的迭代估计,改善了UKF协方差估计不足的问题.仿真结果表明在不同的参数测量精度条件下,IUKF算法既保持了较好的稳定性又提高了算法的跟踪精度和收敛速度.     

Extended Kalman Filter-based localization algorithm by edge computing in Wireless Sensor Networks

The Extended Kalman Filter (EKF) has received abundant attention with the growing demands for robotic localization. The EKF algorithm is more realistic in non-linear systems, which has an autonomous white noise in both the system and the estimation model. Also, in the field of engineering, most systems are non-linear. Therefore, the EKF attracts more attention than the Kalman Filter (KF). In this paper, we propose an EKF-based localization algorithm by edge computing, and a mobile robot is used to update its location concerning the landmark. This localization algorithm aims to achieve a high level of accuracy and wider coverage. The proposed algorithm is helpful for the research related to the use of EKF localization algorithms. Simulation results demonstrate that, under the situations presented in the paper, the proposed localization algorithm is more accurate compared with the current state-of-the-art localization algorithms.     

Joint angular and spectral estimation technique using nonlinear Kalman filters for cognitive radio

The joint estimation of direction of arrivals (DOA) and carrier frequencies of band-limited source signals is considered in this paper. A novel technique based on nonlinear Kalman filters is proposed for this joint angular and spectral estimation problem for cognitive radio (CR). Since sampling a wideband spectrum at Nyquist rate increases the analog-to-digital converter (ADC) requirements, we propose executing Kalman filter algorithm over a spatial state space model. Thus, one time sample is required and hardware complexity is reduced. Two types of nonlinear Kalman filters, extended Kalman filter (EKF) and unscented Kalman filter (UKF), are proposed. We consider their sub-optimal performance and show how to control their convergence. However, the proposed algorithms can detect a number of source signals limited to the number of elements in employing arrays.