基于极大后验估计和指数加权的自适应UKF滤波算法

针对传统Unscented卡尔曼滤波器(Unscented Kalman filter, UKF)在噪声先验统计未知时变情况下非线性滤波精度下降甚至发散的问题, 设计了一种带噪声统计估计器的自适应UKF滤波算法. 首先根据极大后验(Maximum a posterior, MAP)估计原理, 推导出一种次优无偏MAP常值噪声统计估计器; 接着在此基础之上, 采用指数加权的方法, 给出了时变噪声统计估计器的递推公式; 最后对自适应UKF算法进行了性能分析. 相比于传统UKF, 该自适应UKF算法在噪声统计未知时变情况下不仅滤波依然收敛, 滤波精度及稳定性显著提高, 而且其具有应对噪声变化的自适应能力. 仿真实例验证了其有效性.     

高精度组合导航系统仿真

以车载捷联惯导系统SINS与全球定位系统GPS的组合导航系统为研究对象,为了解决常规卡尔曼滤波器在非线性时变系统中由于线性化误差导致滤波发散的问题,将UKF算法引入到SINS/GPS组合导航系统。UKF同时适用于线性系统和非线性系统,且不需要对噪声的统计特性精确已知。通过建立SINS/GPS组合模型,对其进行了MATLAB仿真。对比常规卡尔曼滤波器与UKF算法的滤波效果可知,UKF算法提高导航解的精度和收敛速度,同时系统的鲁棒性也得到了提高。     

带有色量测噪声的非线性系统 Unscented 卡尔曼滤波器

传统Unscented卡尔曼滤波器(Unscented Kalman filter, UKF)要求噪声必须为高斯白噪声, 无法解 决带有色噪声的非线性系统滤波问题. 为此, 本文提出了一种带有色量测噪声的UKF滤 波新算法. 首先,基于量测信息增广和最小方差估计, 推导出一类带有色量测噪声的非 线性离散系统状态的最优滤波框架, 接着采用Unscented变换(Unscented transformation, UT)来计算最优框架中的 非线性状态后验均值和协方差, 进而得到有色量测噪声下UKF滤波递推公式. 所设 计的UKF新方法能有效地解决传统UKF在量测噪声有色情况下非线性滤波失效的问题, 数 值仿真实例验证了其可行性和有效性.     

加权观测融合非线性无迹卡尔曼滤波算法

针对非线性系统的无迹卡尔曼滤波器(UKF),应用加权最小二乘(WLS)法,提出了加权观测融合UKF滤波算法.证明了加权观测融合UKF滤波算法与集中式观测融合UKF滤波算法在数值上的完全等价性,因而具有全局最优性.一个带两传感器非线性系统的仿真例子说明了两种融合算法的有效性及等价性.     

自适应扩维UKF算法在SINS/GPS组合导航系统中的应用

针对自适应渐消因子卡尔曼滤波无法应用于非线性系统的问题以及自适应渐消因子的局限性,提出了带自适应渐消矩阵的扩维UKF(adaptive fading matrix augmented UKF,AFM-AUKF)算法.该算法针对含有非加性白噪声的非线性系统,引入了一种新的自适应渐消矩阵计算方法,并用Unscented变换逼近系统的后验均值和协方差,有效解决了此类系统的滤波问题.针对SINS/GPS组合导航系统的非线性状态估计问题,分别设计了滤波器容错试验和系统噪声突变试验,试验结果证明了该算法的有效性.     

噪声相关条件下Unscented卡尔曼滤波器设计

针对传统Unscented卡尔曼滤波器(UKF)在噪声相关条件下非线性滤波失效的问题,研究了一类带相关噪声的非线性离散系统UKF设计方法.文中基于最小均方误差估计准则,给出了系统噪声和量测噪声相关时UKF滤波递推公式,并采用Unscented变换(UT)来计算系统状态的后验均值和协方差.所设计的噪声相关条件下UKF有效克服了传统UKF必须假设系统噪声和量测噪声为互不相关高斯白噪声的局限性,拓展了UKF的应用范围.仿真实例验证了其可行性和有效性.     

改进的UKF在惯导平台误差模型辨识中的应用

为减小建模误差,建立了基于直接法进行惯导平台误差模型辨识的非线性模型.Unscented Kalman滤波(UKF)是一种新的非线性滤波算法,为此将其引入惯导平台的误差模型辨识中.针对系统模型的特点,对标准UKF算法进行了简化改进.改进的UKF算法计算量小、结构简单,滤波精度与标准UKF一致.同时应用扩展Kalman滤波(EKF)算法和改进的UKF算法进行了惯导平台误差模型辨识仿真研究.仿真结果表明,与EKF算法相比,改进的UKF算法的滤波精度显著提高.     

基于通用FLAC的模糊自适应UKF算法及其应用

针对量测噪声方差统计值未知的非线性UKF(Unscented Kalman Filter)滤波问题,提出了一种基于通用FLAC(Fussy Logic Adaptive Controller)的模糊自适应UKF算法.在标准的非线性UKF算法基础上,以残差的实际方差与理论方差的比值作为FLAC的输入,使FLAC对滤波模型的依赖性减弱,强化了模糊自适应UKF方法的通用性;在对未知的量测噪声方差阵进行动态调节的过程中设置了指数调节参数,可不同程度地放大或缩小方差阵调节的幅度,使算法的调节速度和精度得到控制.将算法应用于GPS/DR(Dead-Reckoning)组合导航系统中,仿真结果表明了该算法的有效性.     

基于最小均方误差估计的噪声相关UKF设计

传统Unscented卡尔曼滤波器(UKf)要求系统噪声和量测噪声必须是互不相关的.针对此局限性,研究了一类带相关噪声的非线性离散系统UKF设计方法.基于最小均方误差估计和正交变换,给出了噪声相关UKF滤波递推公式,并采用Unscented变换(UT)来计算系统状态的后验分布.所设计的UKF有效解决了传统UKF在噪声相关条件下非线性滤波失效的问题,拓展了UKF的应用范围.最后,仿真实例表明了所设计UKF的有效性.     

UKF算法在星载GPS低轨卫星定轨中的应用

对于扩展卡尔曼滤波在非线性系统中由于线性化过程引入了线性化误差,从而导致滤波器性能下降甚至造成滤波发散的情况,利用Unscented卡尔曼滤波器对非线性系统进行直接滤波,该方法无需对非线性系统进行线性化,避免了线性化误差。并将该算法用于星载GPS低轨卫星定轨中,建立了仿真模型,在初始条件相同的情况下,与EKF算法仿真结果相比较,结果表明在一定观测噪声水平下,UKF定轨结果更准确,定轨精度更高。     

基于UKF的闪烁噪声机动目标跟踪

闪烁噪声下的机动目标跟踪是一个非线性非高斯系统滤波问题,传统的卡尔曼理论很难保证其跟踪精度.文中提出了一种基于UKF的闪烁噪声机动目标跟踪算法,首先对目标系统的状态方程进行无味变换,然后再进行滤波估计,以减小跟踪误差.UKF不需要求导,它能比EKF更好地迫近目标运动模型的非线性特性,具有更高的估计精度,计算量却与EKF同阶.在仿真实验中采用"协同转弯模型"作为机动目标的运动模型,雷达的量测方程也是非线性的,分别应用UKF和EKF跟踪闪烁噪声下的机动目标,结果表明,UKF能够较好地解决闪烁噪声下跟踪机动目标的难题,其跟踪精度要远远高于EKF.     

基于极大似然准则和最大期望算法的自适应UKF 算法

针对噪声先验统计特性未知情况下的非线性系统状态估计问题,提出了基于极大似然准则和 最大期望算法的自适应无迹卡尔曼滤波(Unscented Kalman filter, UKF) 算法.利用极大似然准则构造含有噪声统计特性的对数似然函数,通 过最大期望算法将噪声估计问题转化为对数似然函数数学期望极大化问题,最终得到带次优递 推噪声统计估计器的自适应UKF算法.仿真分析表明,与传统UKF算法相比,提出的自适应UKF算法 有效克服了传统UKF算法在系统噪声统计特性未知情况下滤波精度下降的问题,并实现了系统噪 声统计特性的在线估计.     

A comparison of simultaneous state and parameter estimation schemes for a continuous fermentor reactor

This article proposes a maximum likelihood algorithm for simultaneous estimation of state and parameter values in nonlinear stochastic state-space models. The proposed algorithm uses a combination of expectation maximization, nonlinear filtering and smoothing algorithms. The algorithm is tested with three popular techniques for filtering namely particle filter (PF), unscented Kalman filter (UKF) and extended Kalman filter (EKF). It is shown that the proposed algorithm when used in conjunction with UKF is computationally more efficient and provides better estimates. An online recursive algorithm based on nonlinear filtering theory is also derived and is shown to perform equally well with UKF and ensemble Kalman filter (EnKF) algorithms. A continuous fermentation reactor is used to illustrate the efficacy of batch and online versions of the proposed algorithms.     

带噪声统计估计器的Unscented卡尔曼滤波器设计

针对传统Unscented卡尔曼滤波器(UKF)在噪声先验统计未知或不准确时滤波精度下降甚至发散的问题,基于极大后验(MAP)估计原理,设计了一种带噪声统计估计器的UKF.该UKF滤波算法在进行状态估计的同时,能实时估计和修正噪声均值和协方差.相比于传统UKF,所提出的UKF具有应对噪声统计变化的自适应能力.仿真结果表明了该UKF滤波算法的有效性.

Abstract：

For the problem that the accuray of the conventional UKF declines and further diverges when the prior noise statistic is unknown or inaccurate, an unscented Kalman filter (UKF) with noise statistic estimator is designed.This UKF filtering algorithm based on maximum a posterior (MAP) estimation can estimate and correct the mean and covariance of the noise in real time while it estimates the states.The proposed UKF has the adaptive capability of dealing with variable noise statistic.The simulation results show the effectiveness of the proposed UKF filtering algorithm.     

An evaluation of the nonlinear/non-Gaussian filters for the sequential data assimilation

This paper aims to investigate several new nonlinear/non-Gaussian filters in the context of the sequential data assimilation. The unscented Kalman filter (UKF), the ensemble Kalman filter (EnKF), the sampling importance resampling particle filter (SIR-PF) and the unscented particle filter (UPF) are described in the state-space model framework in the Bayesian filtering background. We first evaluated those methods with a simple highly nonlinear Lorenz model and a scalar nonlinear non-Gaussian model to investigate the filter stability and the error sensitivity, and then their abilities in the one-dimensional estimation of the soil moisture content with the synthetic microwave brightness temperature assimilation experiment in the land surface model VIC-3L. All the results are compared with the EnKF. The advantages and disadvantages of each filter are discussed.The results in the Lorenz model showed that the particle filters are suitable for the large measurement interval assimilation and that the Kalman filters were suitable for the frequent measurement assimilation as well as small measurement uncertainties. The EnKF also showed its feasibility for the non-Gaussian noise. The performance of the SIR-PF was actually not as good as that of the UKF or the EnKF regarding a very small observation noise level compared with the uncertainties in the system. In the one-dimensional brightness temperature assimilation experiment, the UKF, the EnKF and the SIR-PF all proved to be flexible and reliable nonlinear filter algorithms for the low dimensional sequential land data assimilation application. For the high dimensional land surface system that takes the horizontal error correlations into account, the UKF is restricted by its computational demand in the covariance propagation; we must use the EnKF, the SIR-PF and other covariance reduction algorithms. The large computational cost prevents the UPF from being applied in practice.     

A Filtering Approach Based on MMAE for a SINS/CNS Integrated Navigation System

This paper explores multiple model adaptive estimation (MMAE) method, and with it, proposes a novel filtering algorithm. The proposed algorithm is an improved Kalman filter-multiple model adaptive estimation unscented Kalman filter (MMAE-UKF) rather than conventional Kalman filter methods, like the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). UKF is used as a subfilter to obtain the system state estimate in the MMAE method. Single model filter has poor adaptability with uncertain or unknown system parameters, which the improved filtering method can overcome. Meanwhile, this algorithm is used for integrated navigation system of strapdown inertial navigation system (SINS) and celestial navigation system (CNS) by a ballistic missile's motion. The simulation results indicate that the proposed filtering algorithm has better navigation precision, can achieve optimal estimation of system state, and can be more flexible at the cost of increased computational burden.      

一种提高无迹卡尔曼滤波精确度的方法

无迹卡尔曼滤波是通过确定性采样,以无迹变换为基础,用卡尔曼线性滤波框架而建立起来的,对非线性系统有很好的滤波效果,但当噪声的影响较大时,精确度将会减低。为解决上述问题,提出了一种提高无迹卡尔曼滤波(UKF)精确度的方法,它将观测噪声和系统噪声引入到采样点中,对噪声进行对称采样处理,同时改进了算法过程,增加了无迹卡尔曼滤波的抗干扰性,与常规无迹卡尔曼滤波(UKF)相比,不仅保持了系统的稳定性,而且提高了精确度,最后通过仿真进行了验证。