基于小波神经网络的滤波器设计方法

利用卡尔曼滤波器进行状态估计时,要求系统具有已知的数学模型和噪声统计特性等先验知识,而实际系统往往不能满足这一要求;针对这种情况,提出了一种小波神经网络滤波器设计的方法,它结合了神经网络的函数逼进能力和小波变换的良好局部特性及多分辨率特性,使网络能根据数据的分布情况以不同的分辨率进行学习,从而使网络具有更灵活有效的函数逼近能力,提高了估计精度;仿真结果表明,用该滤波器对系统状态进行估计,其精度高于卡尔曼滤波器的估计精度.     

一种复杂场景下的运动目标跟踪算法

提出了一种基于跟踪窗口自适应和抗遮挡的目标跟踪算法。采用Mean Shift算法确定当前帧的目标位置,最优选取核函数带宽,使跟踪窗口能够根据目标尺寸大小作出自适应调整。利用Bhattacharyya系数作为遮挡的判断依据,当目标遮挡时引入卡尔曼滤波器估计目标的运动信息,进行后续状态预测。实验表明,该算法能有效跟踪复杂场景下的运动目标。     

单被动传感器BOT鲁棒跟踪算法研究

对系统建立了仅有角度测量信息的单传感器跟踪(BOT)模型和算法,从机动目标鲁棒跟踪的角度给出了单传感器仅有角测量信息时的状态估计方法.BOT的状态估计采用修正增益扩展卡尔曼滤波器(MGEKF),目标加速度采用周期递推估计.该算法的模型简单、无噪声假定、无模型切换,并对目标机动具有良好的自适应能力.仿真结果验证了该方法的有效性.     

基于混合卡尔曼粒子滤波算法的期权定价方法

针对金融领域的期权定价问题,为提高粒子滤波算法对期权价格的估计精度,提出使用混合卡尔曼粒子滤波算法(MKPF)进行期权价格预测,该算法使用Unscented 卡尔曼滤波器和扩展卡尔曼滤波器作为混合建议分布产生重要采样密度.在某一时刻,每一个粒子首先经过Unscented卡尔曼滤波器更新得到一个状态估计值,然后以该估计值作为扩展卡尔曼滤波器的先验估计再次更新粒子,得到该时刻最终的估计值.实验中针对经典的Black-Scholes期权定价公式,使用包括MKPF算法在内的4种算法对期权价格进行预测,结果表明MKPF算法预测的期权价格与真实期权价格的误差最小,证明了MKPF算法在期权定价问题中的有效性.     

用于弹道目标跟踪的新的非线性滤波算法

针对再入阶段弹道目标的跟踪问题,提出一种新的自适应滤波算法,即强跟踪有限差分扩展卡尔曼滤波（STFDEKF）算法,用于非线性系统的目标跟踪。该方法使用Sterling内插公式进行多项式的近似,从而实现对非线性函数的近似,避免了非线性函数的求导运算;并且算法中引入强跟踪的因子来修正先验的协方差矩阵。新算法改进了跟踪精度,扩大了应用范围,增强了滤波收敛性。仿真实验将新算法与扩展卡尔曼滤波器（EKF）、有限差分扩展卡尔曼滤波器（FDEKF）进行了比较,结果表明,STFDEKF在跟踪精度和滤波可靠性上均优于EKF和FDEKF,但其计算复杂性更大。得出结论,STFDEKF是个很有效的非线性滤波算法。     

动载体环境视觉惯性自适应融合物体姿态测量算法

针对动载体环境下视觉惯性组合姿态测量的过程中,惯性器件噪声时变和突变干扰会使卡尔曼滤波器估计不准确的问题,研究了一种Sage-Husa自适应强跟踪扩展卡尔曼算法。算法采用Sage-Husa自适应滤波来实时估计惯性器件的噪声协方差,引入多重渐消因子来抑制突变干扰,增强融合算法的鲁棒性。实验证明,当存在系统噪声变化和突变干扰时,所提算法优于Sage-Husa自适应扩展卡尔曼算法与强跟踪扩展卡尔曼算法,具有良好的鲁棒性。     

改进粒子群算法优化扩展卡尔曼滤波器电机转速估计

针对感应电机扩展卡尔曼滤波器转速估计中难以取得卡尔曼滤波器系统噪声矩阵和测量噪声矩阵最优值的问题, 提出了一种基于改进粒子群算法优化的扩展卡尔曼滤波器转速估计方法。算法通过融合遗传算法和粒子群算法的优点, 采用可调整的算法模型对粒子群算法进行改进, 将改进的粒子群算法对扩展卡尔曼滤波器中的系统噪声矩阵和测量噪声矩阵进行优化处理, 将优化后的卡尔曼滤波器应用于感应电机转速估计。仿真实验表明, 与试探法、标准粒子群算法及遗传算法比较, 改进粒子群算法优化的扩展卡尔曼滤波器能够有效提高转速估计的精度, 从而提高无速度传感器矢量控制系统的控制性能。     

一种高精度APNCKF算法在谐波检测中的应用

为了进一步提高含噪环境下谐波检测的精确度,提高卡尔曼滤波器的稳定性,对系统噪声协方差进行了分析,通过不断的在线辨识出过程噪声协方差,提出了一种自适应过程噪声协方差卡尔曼滤波算法。该算法利用序贯最大化可信度更新先验信息来辨识过程噪声,然后通过卡尔曼滤波器进行迭代运算,估计出相应的幅值和相位。该算法最大的特点就是辨识出的过程噪声Q的骤然增大匹配的即是谐波幅值暂降的出现。通过在MATLAB环境下进行谐波仿真验证,结果表明该算法在准稳态条件下较好地跟踪电力系统谐波状态,且与常规卡尔曼、基于最大似然准则的卡尔曼、小波/小波包变换相比,该自适应算法的收敛速度较快、滤波精度高、实时性以及稳定性较好,具有重要的工程实际意义。     

无人机自适应姿态角度估计仿真

针对复杂环境下传感器噪声未知且不断变化,会导致姿态融合结果不准确的问题,设计了一种基于单新息自适应算法的卡尔曼滤波器,对加速度计和陀螺仪噪声协方差进行在线估计。首先,介绍了能够结合各个传感器优势的无人机姿态融合算法。然后,设计了采用基于单新息自适应算法的卡尔曼滤波器,给出了能够在线估计加速度噪声协方差R和陀螺仪噪声协方差Q的自适应算法。MATLAB仿真表明单新息自适应卡尔曼滤波器在环境噪声变化时,能够更准确地获得无人机的姿态信息,提高了姿态融合精确度,提高了滤波器的鲁棒性。     

基于强跟踪平方根容积卡尔曼滤波的纯方位目标运动分析方法

针对纯方位目标跟踪系统中模型状态简化、系统噪声统计特性未知、目标初始距离信息不准确导致的滤波收敛时间长和滤波精度不高的问题,以自主水下机器人(Autonomous Underwater Vehicle, AUV)跟踪水下动态目标为例,提出了一种基于强跟踪平方根容积卡尔曼滤波器(Strong Tracking Square Root Cubature Kalman Filter, STFSRCKF)的纯方位目标运动分析算法。该算法在滤波过程中,利用平方根容积卡尔曼滤波器(Square Root Cubature Kalman Filter, SRCKF)完成预测更新,对于SRCKF中的每个容积点采用强跟踪滤波器(Strong Tracking Filter, STF)进行更新,设计滤波增益以抑制噪声对系统状态估计的影响,有效提高了滤波的数值稳定性,减小了状态估计误差。通过仿真分析,比较了扩展卡尔曼滤波器(Extended Kalman Filter, EKF)、无迹卡尔曼滤波器(Unscented Kalman Filter, UKF)、平方根容积卡尔曼滤波器(Square-Root Cubature Kalman Filter, SRCKF)、STFSRCKF的算法性能,实验表明所提算法具有跟踪速度快,精度高等优点。     

自适应快速弱敏无迹Kalman滤波算法

针对现有弱敏无迹Kalman滤波需要代数求解增益矩阵耗时长和不能实时调节敏感性权重的问题,提出一种自适应快速弱敏无迹Kalman滤波算法.该算法在弱敏控制技术的基础上,重新定义弱敏无迹Kalman滤波的敏感性权重矩阵,将状态估计误差对不确定参数的敏感性加入滤波的代价函数,并通过最小化该代价函数得到滤波增益矩阵的解析解,...     

衰减因子自适应估计卡尔曼滤波比较研究

针对卡尔曼滤波算法发散的问题,从卡尔曼滤波技术的稳定性出发,分析了卡尔曼滤波发散的原因,提出了新的衰减记忆卡尔曼滤波中衰减因子的自适应估计方法。该方法利用滤波残差序列在最优估计时为零均值白噪声的性质,分别检验滤波残差每一个分量得出衰减因子值,并与强跟踪滤波器进行了对比研究。仿真结果表明,新算法在系统噪声特性不准确的情况下,能自适应地估计出衰减因子的大小,抑制卡尔曼滤波估计的发散,滤波精度要高于强跟踪滤波器;且其推导形式简单、计算量小、适合于在线运算。     

基于转换量测容积卡尔曼滤波器带多普勒量测的目标跟踪算法

针对带多普勒量测的目标跟踪问题,提出一种基于转换量测容积卡尔曼滤波器的序贯滤波目标跟踪算法.对具有量测误差相关性的距离和多普勒量测进行解相关处理,构造出新的解相关量测方程,进而基于贝叶斯方法提出带多普勒量测的序贯处理算法的统一理论框架,实现对位置量测和多普勒量测的序贯滤波.在该理论框架下,提出基于转换量测容积卡尔曼滤波器的序贯滤波目标跟踪算法.该算法先采用转换量测容积卡尔曼滤波器和位置量测对目标状态进行估计,再利用经典容积卡尔曼滤波器对新构造的伪多普勒量测进行量测更新以实现目标跟踪.通过对所提算法的性能分析验证该算法的一致性和收敛性.仿真结果表明,该算法与其他跟踪算法相比,具有更高的跟踪精度.     

Constrained Kalman filtering via density function truncation for turbofan engine health estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This article develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the probability density function (PDF) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but also improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. It is also shown that the truncated Kalman filter may provide a more accurate way of incorporating inequality constraints than other constrained filters (e.g. the projection approach to constrained filtering).     

Hierarchical bayesian models for regularisation in sequential learning

We show that a hierarchical Bayesian modeling approach allows us to perform regularization in sequential learning. We identify three inference levels within this hierarchy: model selection, parameter estimation, and noise estimation. In environments where data arrive sequentially, techniques such as cross validation to achieve regularization or model selection are not possible. The Bayesian approach, with extended Kalman filtering at the parameter estimation level, allows for regularization within a minimum variance framework. A multilayer perceptron is used to generate the extended Kalman filter nonlinear measurements mapping. We describe several algorithms at the noise estimation level that allow us to implement on-line regularization. We also show the theoretical links between adaptive noise estimation in extended Kalman filtering, multiple adaptive learning rates, and multiple smoothing regularization coefficients.     

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.      

Unscented卡尔曼滤波在状态估计中的应用

针对非线形系统的滤波问题，无法使用卡尔曼滤波器（KF），扩展卡尔曼滤波（EKF）方法虽能应用于非线形系统，但给出的是状态的有偏估计，并且对模型误差的鲁棒性较差。为了给出更好的状态估计值，该文介绍了Unscented卡尔曼滤波（UKF）的基本原理。其思想是：基于unscented变换，UKF滤波算法能够给出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Mackey—Glass模型时间序列的状态估计仿真实侧说明：同EKF相比，UKF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，是一种良好的非线性滤波方法。     

A mixture-of-experts framework for adaptive Kalman filtering

This paper proposes a modular and flexible approach to adaptive Kalman filtering using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters such as process and measurement noise. The gating network performs on-line adaptation of the weights given to individual filter estimates based on performance. This scheme compares very favorably with the classical Magill filter bank, which is based on a Bayesian technique, in terms of: estimation accuracy; quicker response to changing environments; and numerical stability and computational demands. The proposed filter bank is further enhanced by periodically using a search algorithm in a feedback loop. Two search algorithms are considered. The first algorithm uses a recursive quadratic programming approach which extremizes a modified maximum likelihood function to update the parameters of the best performing filter in the bank. This particular approach to parameter adaptation allows a real-time implementation. The second algorithm uses a genetic algorithm to search for the parameter vector and is suited for post-processed data type applications. The workings and power of the overall filter bank and the suggested adaptation schemes are illustrated by a number of examples.     

Invariant Kalman Filter for Correlated Wide Band Noises

Kalman filtering is a powerful estimation method. One of its weaknesses is related to the white or coloured nature of the disturbing noises in the Kalman filtering model. At the same time, real noises are rarely white or coloured. They are mostly wide band. In this regard, white or coloured noise Kalman filtering makes concessions on adequacy. This pushes system scientists to develop mathematical methods of estimation for systems corrupted by wide band noises. In applications, wide band noises are detected by their autocovariance and cross‐covariance functions, which do not allow to model them uniquely. Therefore, it becomes important to develop estimation methods which are independent of a class of wide band noises, but dependent on the unique autocovariance and cross‐covariance functions. Such results are called invariant results. In this paper, we prove a complete set of invariant equations for Kalman type filter for a linear signal‐observation system corrupted by correlated wide band noises. This filter has a ready form to be used in applications, just respective numerical methods must be developed.     

Robust two-stage Kalman filters for systems with unknown inputs

A method is developed for the state estimation of linear time-varying discrete systems with unknown inputs. By making use of the two-stage Kalman filtering technique and a proposed unknown inputs filtering technique, a robust two-stage Kalman filter which is unaffected by the unknown inputs can be readily derived and serves as an alternative to the Kitanidis' (1987) unbiased minimum-variance filter. The application of this new filter is illustrated by optimal filtering for systems with unknown inputs