基于EM-EKF算法的RBF-AR模型参数估计

为了利用EKF（extended Kalman filter）算法对RBF-AR（radial basis function network-based autoregressive）模型进行参数估计,重构了RBF-AR模型的网络结构,将其变换成一种新型的广义径向基函数（radial basis function,RBF）神经网络.与典型三层RBF网络结构相比,该广义RBF网络增加了线性输出加权层.为了克服基于EKF神经网络学习算法由于噪声统计特性未知导致滤波发散或者滤波精度不高的问题,利用EM（expectation maximization）算法对RBF-AR模型噪声协方差矩阵进行估计.同时,通过EKF滤波实时估计RBF-AR模型参数（系统状态）,EKF平滑过程得到了更加准确的期望估计.仿真结果显示,该方法用在此变形的RBF-AR模型结构中是有效的,特别在信噪比低的情况下,估计效果比SNPOM（structured nonlinear parameter optimization method）方法好,而且还能估计出噪声方差.F检验显示了两方法估计得到的标准偏差有显著性差异.     

Estimation of elliptical basis function parameters by the EMalgorithm with application to speaker verification

This paper proposes to incorporate full covariance matrices into the radial basis function (RBF) networks and to use the expectation-maximization (EM) algorithm to estimate the basis function parameters. The resulting networks, referred to as elliptical basis function (EBF) networks, are evaluated through a series of text-independent speaker verification experiments involving 258 speakers from a phonetically balanced, continuous speech corpus (TIMIT). We propose a verification procedure using RBF and EBF networks as speaker models and show that the networks are readily applicable to verifying speakers using LP-derived cepstral coefficients as features. Experimental results show that small EBF networks with basis function parameters estimated by the EM algorithm outperform the large RBF networks trained in the conventional approach. The results also show that the equal error rate achieved by the EBF networks is about two-third of that achieved by the vector quantization-based speaker models.     

自适应高斯粒子滤波在导航中的应用

针对粒子滤波中重要性密度函数难以选取和粒子退化导致的计算精度下降的问题,提出一种新的自适应高斯粒子滤波算法。通过高斯混合密度函数和UT变换来获取状态均值和协方差阵,选择并计算合适的自适应因子来调节均值和方差,在迭代过程中可动态调节重要性密度函数,并用WEM和EM步骤代替重采样,上述滤波算法考虑了最新量测信息的影响,使滤波性能明显改善,能更好地解决非线性非高斯系统模型的抗干扰问题。将提出的算法应用于SINS/GPS组合导航系统跑车试验中,结果表明上述滤波算法能提高导航解算的精度,其性能明显优于已有滤波,同时验证了当系统出现噪声干扰突然变化时提出算法的有效性。     

一种模糊QR滤波及在组合导航中的仿真研究

总结了常用的自适应滤波的方法，并提出了一种基于模糊逻辑的自适应卡尔曼滤波技术，用模糊逻辑自适应推理器来“在线”修正卡尔曼滤波系统噪声协方差Q和测量噪声协方差R，从而使滤波器不断执行最优估计。仿真结果表明该方法可以提高GPS／INS组合导航系统的精度和可靠性。     

Noise covariance identification for time-varying and nonlinear systems

Kalman-based state estimators assume a priori knowledge of the covariance matrices of the process and observation noise. However, in most practical situations, noise statistics and initial conditions are often unknown and need to be estimated from measurement data. This paper presents an auto-covariance least-squares-based algorithm for noise and initial state error covariance estimation of large-scale linear time-varying (LTV) and nonlinear systems. Compared to existing auto-covariance least-squares based-algorithms, our method does not involve any approximations for LTV systems, has fewer parameters to determine and is more memory/computationally efficient for large-scale systems. For nonlinear systems, our algorithm uses full information estimation/moving horizon estimation instead of the extended Kalman filter, so that the stability and accuracy of noise covariance estimation for nonlinear systems can be guaranteed or improved, respectively.     

Robust estimation of covariance matrices

Data manipulations which increase the robustness and accuracy of estimators of covariance parameters by using the innovations correlation approach are considered. The procedures are especially useful for improving estimates of process-noise covariance parameters for slowly varying systems when measurement noise is large. The innovations correlate covariance estimation technique developed by P.R. Belanger (1974) is extended to the case where process noise is weak in magnitude compared to measurement noise. Belanger's method exploits the linear relationship between the desired noise covariance parameters and the correlations of the innovation sequence of a suboptimal Kalman filter to formulate a least-squares algorithm. The estimates of the process-noise covariance parameters are improved by low-pass prefiltering and downsampling the data before applying the least-squares innovations correlation algorithm. Results for a single-output, linear time-invariant system are stated, and the subsequent analysis treats only this case     

组合导航自适应卡尔曼滤波改进算法研究

针对常规卡尔曼滤波由于噪声的统计特性与实际情况不相符而引起滤波误差增大的问题,提出了一种新的在线估计系统噪声和量测噪声的自适应滤波算法.新算法通过新息序列自适应量测噪声,对Sage-Husa滤波算法进行改进以估计系统噪声,该算法在噪声统计特性未知的情况下能进行滤波计算.最后对改进的新算法与常规卡尔曼滤波算法作了对比试验...     

自适应平方根无迹卡尔曼滤波算法

将高斯过程回归融入平方根无迹卡尔曼滤波(SRUKF)算法,本文提出了一种不确定系统模型协方差自适应调节滤波算法.该算法分为学习和估计两部分:学习阶段用高斯过程对训练数据进行学习,得到系统回归模型及噪声协方差;估计阶段由回归模型代替状态方程和观测方程,相应的噪声协方差实时自适应调整.该方法克服了传统方法容易受系统动态模型不确定性和噪声协方差不准确限制的问题,仿真结果验证了算法的有效性.     

基于信息补偿的自适应联邦滤波算法

针对采用标准卡尔曼滤波器必须知道系统噪声统计特性的局限性,研究了一类系统噪声未知情况下的自适应联邦滤波方法,指出了自适应滤波方法应用于联邦结构时应当注意的问题,提出了一种基于信息补偿的自适应联邦滤波算法。SINS／BDS／GPS组合导航系统的仿真结果表明,该方法可以有效抑制系统噪声未知情况下的滤波发散现象,提高了滤波的稳定性和估计性能。     

Online identification of nonlinear multivariable processes using self‐generating RBF neural networks

This paper addresses the problem of online model identification for multivariable processes with nonlinear and time‐varying dynamic characteristics. For this purpose, two online multivariable identification approaches with self‐organizing neural network model structures will be presented. The two adaptive radial basis function (RBF) neural networks are called as the growing and pruning radial basis function (GAP‐RBF) and minimal resource allocation network (MRAN). The resulting identification algorithms start without a predefined model structure and the dynamic model is generated autonomously using the sequential input‐output data pairs in real‐time applications. The extended Kalman filter (EKF) learning algorithm has been extended for both of the adaptive RBF‐based neural network approaches to estimate the free parameters of the identified multivariable model. The unscented Kalman filter (UKF) has been proposed as an alternative learning algorithm to enhance the accuracy and robustness of nonlinear multivariable processes in both the GAP‐RBF and MRAN based approaches. In addition, this paper intends to study comparatively the general applicability of the particle filter (PF)‐based approaches for the case of non‐Gaussian noisy environments. For this purpose, the Unscented Particle Filter (UPF) is employed to be used as alternative to the EKF and UKF for online parameter estimation of self‐generating RBF neural networks. The performance of the proposed online identification approaches is evaluated on a highly nonlinear time‐varying multivariable non‐isothermal continuous stirred tank reactor (CSTR) benchmark problem. Simulation results demonstrate the good performances of all identification approaches, especially the GAP‐RBF approach incorporated with the UKF and UPF learning algorithms. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive Kalman filter for MEMS IMU data fusion using enhanced covariance scaling

MEMS (micro-electro-mechanical-system) IMU (inertial measurement unit) sensors are characteristically noisy and this presents a serious problem to their effective use. The Kalman filter assumes zero-mean Gaussian process and measurement noise variables, and then recursively computes optimal state estimates. However, establishing the exact noise statistics is a non-trivial task. Additionally, this noise often varies widely in operation. Addressing this challenge is the focus of adaptive Kalman filtering techniques. In the covariance scaling method, the process and measurement noise covariance matrices Q and R are uniformly scaled by a scalar-quantity attenuating window. This study proposes a new approach where individual elements of Q and R are scaled element-wise to ensure more granular adaptation of noise components and hence improve accuracy. In addition, the scaling is performed over a smoothly decreasing window to balance aggressiveness of response and stability in steady state. Experimental results show that the root mean square errors for both pith and roll axes are significantly reduced compared to the conventional noise adaptation method, albeit at a slightly higher computational cost. Specifically, the root mean square pitch errors are 1.1? under acceleration and 2.1? under rotation, which are significantly less than the corresponding errors of the adaptive complementary filter and conventional covariance scaling-based adaptive Kalman filter tested under the same conditions.     

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

Unscented Kalman filter (UKF) has been extensively used for state estimation of nonlinear stochastic systems, which suffers from performance degradation and even divergence when the noise distribution used in the UKF and the truth in a real system are mismatched. For state estimation of nonlinear stochastic systems with non-Gaussian measurement noise, the Masreliez–Martin extended Kalman filter (EKF) gives better state estimates in relation to the standard EKF. However, the process noise and the measurement noise covariance matrices should be known, which is impractical in applications. This paper presents a robust Masreliez–Martin UKF which can provide reliable state estimates in the presence of both unknown process noise and measurement noise covariance matrices. Two numerical examples involving relative navigation of spacecrafts demonstrate that the proposed filter can provide improved state estimation performance over existing robust filtering approaches. Vision-aided robot arm tracking experiments are also provided to show the effectiveness of the proposed approach.     

Multi-sensor information fusion estimators for stochastic uncertain systems with correlated noises

The information fusion estimation problems are investigated for multi-sensor stochastic uncertain systems with correlated noises. The stochastic uncertainties caused by correlated multiplicative noises exist in the state and observation matrices. The process noise and the observation noises are one-step auto-correlated and two-step cross-correlated, respectively. While the observation noises of different sensors are one-step cross-correlated. The optimal centralized fusion filter, predictor and smoother are proposed in the linear minimum variance sense via an innovative analysis approach. To enhance the robustness and flexibility, a distributed fusion filter is put forward, which requires the calculation of filtering error cross-covariance matrices between any two local filters. To avoid the calculation of cross-covariance matrices, another distributed fusion filter is also presented by using the covariance intersection (CI) fusion algorithm, which can reduce the computational cost. A simulation example is given to show the effectiveness of the proposed algorithms.     

An improved adaptive FastSLAM algorithm with time-varying noise estimator

In this study, an adaptive FastSLAM (AFastSLAM) algorithm, which is obtained by estimating the time-varying noise statistics and improving FastSLAM algorithm, is proposed. This improvement was accomplished by using maximum likelihood estimation and expectation maximization criterion and a one-step smoothing algorithm in importance sampling. In addition, innovation covariance estimation (ICE) method was used to prevent loss of positive definiteness of the process and measurement noise covariance matrices. The proposed method was compared with FastSLAM by calculating the root mean square error (RMSE) using different particle numbers at varying initial process and measurement noise values. Simulation studies have shown that AFastSLAM provides much more accurate, consistent, and successful estimates than FastSLAM for both robot and landmark positions.     

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。     

一种用于移动机器人状态和参数估计的自适应UKF算法

为了提高 UKF 的估计精度和收敛性, 提出了一种新的自适应滤波方法. 新息方差阵的测量值和其相应的估计/预测值的差被用于构造指标函数. MIT 规则被用于构造自适应机制以指标函数最小来在线更新过程不确定性的方差值. 更新后的方差反馈给常规 UKF. 这种自适应机制主要用于补偿过程噪声分布的先验信息不足以及提高 UKF 状态和参数的主动估计性能. 讨论了自适应 UKF 的渐进稳定性. 在全方位移动机器人上进行了仿真, 结果表明与常规的 UKF 相比自适应 UKF 更有效更精确.     

一种用于移动机器人状态和参数估计的自适应UKF算法

For improving the estimation accuracy and the convergence speed of the unscented Kalman filter(UKF),a novel adaptive filter method is proposed.The error between the covariance matrices of innovation measurements and their corresponding estimations/predictions is utilized as the cost function.On the basis of the MIT rule,an adaptive algorithm is designed to update the covariance of the process uncertainties online by minimizing the cost function.The updated covariance is fed back into the normal UKF.Such an adaptive mechanism is intended to compensate the lack of a priori knowledge of the process uncertainty distribution and to improve the performance of UKF for the active state and parameter estimations.The asymptotic properties of this adaptive UKF are discussed.Simulations are conducted using an omni-directional mobile robot,and the results are compared with those obtained by normal UKF to demonstrate its effectiveness and advantage over the previous methods.     

椭球径向基模型及其遥感分类方法研究

椭球径向基函数神经网络(EBF)是在径向基函数(RBF)映射理论基础上的改进。在保留RBF三层网络结构基础上,EBF采用了EM算法来估计特征空间的混合密度分布参数,用椭球体集合来分解混合密度分布,从而构造了神经网络的中间层基函数的状态。由于在遥感数据的特征空间中通常表现为混合密度分布,EBF模型能够充分利用EM算法获得的最大似然参数估计得到更合理的特征空间的密度分解模型,从而使得EBF模型能够在保留了RBF非线性复杂映射能力的同时,获得更合理的分类结果。本文提出了基于EBF的遥感分类方法,试验结果表明EBF方法比RBF方法训练速度更快、网络连接更简单、分类精度更高。     

基于改进卡尔曼滤波的陀螺仪误差补偿算法

针对基于卡尔曼滤波的MEMS陀螺仪误差补偿算法中量测噪声方差选取不准确的问题,提出一种基于改进卡尔曼滤波的陀螺仪误差补偿算法.卡尔曼滤波通常采用统计特性估计得到固定的量测噪声方差,无法自适应地估计不同环境下陀螺仪噪声特性.该算法将卡尔曼滤波与神经网络相融合,使用卡尔曼滤波新息矩阵作为神经网络输入,通过神经网络得到新息协方差矩阵,以此自适应地估计卡尔曼滤波量测噪声方差.将该算法应用到陀螺仪信号误差补偿中,使用Allan方差分析法对原始信号以及误差补偿后的陀螺仪信号进行分析,实验结果表明该算法能够有效地抑制陀螺仪随机误差,提高MEMS陀螺仪的精度.     

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。