基于迭代平方根容积粒子滤波目标跟踪算法

针对粒子滤波目标跟踪算法粒子退化及跟踪精度问题,提出了一种基于马尔可夫链-蒙特卡罗(MCMC,Markov Chain Monte Carlo)的迭代平方根容积粒子滤波(ISRCPF,iterated square root cubature Kalman particle filter)算法(ISRCPF-MCMC).在该滤波算法中,利用容积数值积分原则计算非线性随机函数的均值和方差,通过正交矩阵分解代替矩阵开方,在生成的粒子滤波建议分布中融入当前量测值,提高对系统后验概率的逼近程度.然后在此基础上融合MCMC抽样算法(MH,Metropolis Hasting)对所选建议分布进行优化,增加粒子多样性,以提高跟踪精度.仿真试验结果表明,ISRCPF-MCMC算法的估计误差与其他算法相比降低至0.403％.     

Collaborative target tracking in WSNs using the combination of maximum likelihood estimation and Kalman filtering

Target tracking using wireless sensor networks requires efficient collaboration among sensors to tradeoff between energy consumption and tracking accuracy. This paper presents a collaborative target tracking approach in wireless sensor networks using the combination of maximum likelihood estimation and the Kalman filter. The cluster leader converts the received nonlinear distance measurements into linear observation model and approximates the covariance of the converted measurement noise using maximum likelihood estimation, then applies Kalman filter to recursively update the target state estimate using the converted measurements. Finally, a measure based on the Fisher information matrix of maximum likelihood estimation is used by the leader to select the most informative sensors as a new tracking cluster for further tracking. The advantages of the proposed collaborative tracking approach are demonstrated via simulation results.     

基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法

在机动目标跟踪中,用于模型辨识和状态估计的非线性滤波器的合理选择和优化是提升滤波精度的关键.融合量测迭代更新集合卡尔曼滤波和交互式多模型(interacting multiple models,IMM)方法,本文提出了基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法.通过迭代更新思想的引入构建了一种量测迭代更新下集合卡尔曼滤波的实现结构,并将其作为IMM的模型滤波器实现对于目标运动模式和状态的辨识与估计.针对算法结合过程中滤波精度和计算量的平衡,设计了用于输入交互环节的状态估计样本,同时简化输入交互环节和输出交互环节中滤波误差协方差矩阵的交互过程.理论分析和仿真结果验证了算法的可行性和有效性.     

基于扩展PASTd跟踪算法的谐波检测方法

子空间分解类算法在理论上具有任意的高分辨率,非常适合于电力系统各类谐波的分析,但需要对高维矩阵进行特征值分解,这不仅费时而且不易于工程实现。将投影近似子空间跟踪算法引入电力系统谐波分析领域,详细分析评估PASTd算法的性能。仿真结果表明,紧缩投影近似子空间跟踪算法即PASTd算法不仅保留了子空间分解类算法的超分辨率特性,而且收敛速度较快,稳定性好,可推广用于电力系统谐波检测领域。     

确定采样型强跟踪滤波飞机舵面故障诊断与隔离

为了克服扩展多模型自适应估计中扩展卡尔曼滤波的理论局限性,多重渐消因子强跟踪改进引起的滤波发散现象以及多维高斯故障概率计算量大等问题,本文将一类基于确定解析采样近似方法的非线性次优高斯滤波与多模型自适应估计相结合,提出了改进的多重渐消因子强跟踪非线性滤波快速故障诊断方法.确定采样型滤波克服了扩展卡尔曼滤波的理论局限性;推导了等效多重渐消因子计算方法,避免了非线性系统雅克比矩阵的计算,提高了故障突变时的跟踪性能;提出了基于平方根分解的改进的一步预测协方差更新方程,保证了滤波稳定性;提出了基于欧几里得范数简化的故障概率计算方法,降低了计算量.通过对比仿真验证了3种不同非线性滤波算法及其强跟踪改进算法的有效性,故障诊断方法跟踪性强、速度快、精度高,具有较好的鲁棒性和稳定性.     

Adaptive parameter estimation for a general dynamical system with unknown states

This paper is concerned with the design of a state filter for a time‐delay state‐space system with unknown parameters from noisy observation information. The key is to investigate new identification algorithms for interactive state and parameter estimation of the considered system. Firstly, an observability canonical state‐space model is derived from the original model by linear transformation for the purpose of simplifying the model structure. Secondly, a direct state filter is formulated by minimizing the state estimation error covariance matrix on the basis of the Kalman filtering principle. Thirdly, once the unknown states are estimated, a state filter–based recursive least squares algorithm is proposed for parameter estimation using the least squares principle. Then, a state filter–based hierarchical least squares algorithm is derived by decomposing the original system into several subsystems for improving the computational efficiency. Finally, the numerical examples illustrate the effectiveness and robustness of the proposed algorithms.     

An enhanced adaptive Kalman filtering for linear systems with inaccurate noise statistics

This paper investigates the simultaneous state and noise covariance estimation for linear systems with inaccurate noise statistics. An enhanced adaptive Kalman filtering (EAKF) based on dynamic recursive nominal covariance estimation (DNRCE) and modified variational Bayesian (VB) inference is presented. The EAKF realizes the concurrently estimation of state and noise covariance matrices by introducing a nominal parameter in the traditional recursive covariance estimation and designing a new adaptive forgotten factor for the dynamic model of the estimated information propagation. The simulation of a target tracking example shows that, compared with the existing filters, the proposed filter has good adaptive performance for inaccurate and time-varying noise covariance matrices.     

平方根体积积分卡尔曼滤波

体积积分是一种新的具有较高代数精度的积分方法。为了提高非线性滤波算法的精度和数值稳定性,将体积积分规则和平方根分解引入卡尔曼滤波框架中,提出了平方根体积积分卡尔曼滤波算法（SRCQKF）。新算法采用球半径体积规则和高斯-拉盖尔积分规则计算积分点,利用矩阵的QR分解得到协方差矩阵的平方根并传播平方根。两个典型的非线性系统的实验结果表明,与体积卡尔曼滤波相比,新算法提高了非线性状态的估计精度,具有较高的数值稳定性。     

Closed-loop subspace identification: an orthogonal projection approach

In this paper, a closed-loop subspace identification approach through an orthogonal projection and subsequent singular value decomposition is proposed. As a by-product of this development, it explains why some existing subspace methods may deliver a bias in the presence of the feedback control and suggests a remedy to eliminate the bias. Furthermore, as the proposed method is a projection based method, it can simultaneously provide extended observability matrix, lower triangular block-Toeplitz matrix, and Kalman filtered state sequences. Therefore, using this method, the system state space matrices can be recovered either from the extended observability matrix/the block-Toeplitz matrix or from the Kalman filter state sequences.     

基于系统误差和状态联合估计的目标跟踪算法

针对线性系统中系统误差对状态估计精度造成的不利影响,在卡尔曼滤波算法框架下提出一种基于系统误差和状态联合估计的目标跟踪算法。在算法实现过程中,首先定量分析了系统误差对目标状态估计及其估计误差协方差矩阵的影响,进而结合状态扩维技术构建系统误差配准的实现过程,最终依据标准卡尔曼滤波迭代流程设计了算法实现步骤。仿真实验结果表明: 在系统误差恒定和时变两种情况下,新算法在系统误差配准和状态估计上具有可行性和有效性。     

Performance analysis of general tracking algorithms

A general family of tracking algorithms for linear regression models is studied. It includes the familiar least mean square gradient approach, recursive least squares, and Kalman filter based estimators. The exact expressions for the quality of the obtained estimates are complicated. Approximate, and easy-to-use, expressions for the covariance matrix of the parameter tracking error are developed. These are applicable over the whole time interval, including the transient, and the approximation error can be explicitly calculated     

Adaptive Gaussian filters for nonlinear state estimation with one-step randomly delayed measurements

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one-step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off-line harmonics estimation problem with real data.     

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.     

自适应渐消有偏扩展卡尔曼滤波在目标跟踪中的应用

针对机动目标跟踪过程观测矩阵病态导致扩展卡尔曼滤波算法跟踪效果不佳的问题,提出一种自适应渐消有偏扩展卡尔曼滤波算法。该算法以扩展卡尔曼滤波为基本框架,并借鉴Gauss-Markov模型的思想以解决观测矩阵病态问题。算法根据状态估计均方误差最小条件求得有偏因子,以降低病态观测矩阵对滤波估计的影响;根据滤波发散判据提出一种新的渐消因子估计方法,以实时调整预测协方差矩阵,从而改善滤波增益并有效提高目标跟踪精度。仿真结果表明,改进算法比传统扩展卡尔曼滤波对目标跟踪的精度有较大提高,同时稳定性更好。     

Hyperbolic‐singular‐value‐decomposition‐based square‐root accurate continuous‐discrete extended‐unscented Kalman filters for estimating continuous‐time stochastic models with discrete measurements

This paper presents novel square‐root accurate continuous‐discrete extended‐unscented Kalman filtering (ACD‐EUKF) algorithms for treating continuous‐time stochastic systems with discrete measurements. The time updates in such methods are fulfilled as those in the extended Kalman filter whereas their measurement updates are copied from the unscented Kalman filter. All this allows accurate predictions of the state mean and covariance to be combined with accurate measurement updates. The main weakness of this technique is the need for the Cholesky decomposition of predicted covariances derived in time‐update steps. Such a factorization is highly sensitive to numerical integration and round‐off errors committed, which may result in losing the covariance's positivity and, hence, failing the Cholesky decomposition. The latter problem is usually solved in the form of square‐root filtering implementations, which propagate not the covariance matrix but its square root instead. Here, we devise square‐root ACD‐EUKF methods grounded in the singular value decomposition (SVD). The SVD rooted in orthogonal transforms is applicable to any ACD‐EUKF with nonnegative weights, whereas the remaining ones, which can enjoy negative weights as well, are treated by means of the hyperbolic SVD based on J‐orthogonal transforms. The filters constructed are presented in a concise algorithmic form, which is convenient for practical use. Their two particular versions grounded in the classical and cubature unscented Kalman filtering parameterizations are examined in severe conditions of tackling a radar tracking problem, where an aircraft executes a coordinated turn. These are also compared to their non‐square‐root predecessor and other methods within the target tracking scenario with ill‐conditioned measurements.     

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of the noise variances, the five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.     

改进的自适应Kalman滤波在SINS/GPS组合导航中的应用

全球定位系统（GPS）因信号受到遮挡和干扰而产生观测量突然失准,使捷联式惯性导航系统（SINS）/GPS组合导航的卡尔曼滤波器性能急剧下降。针对上述问题,提出了一种改进的自适应卡尔曼滤波的方法,通过失准时的新息对先验状态均方误差阵进行自适应调节,解决了新息协方差与实际严重不符的问题。仿真实验中,对比了传统的卡尔曼滤波、自适应卡尔曼滤波、自适应抗差卡尔曼滤波和改进的自适应卡尔曼滤波的估计性能,证明了所提出算法的有效性。     

Active fault tolerant control using state-space self-tuning control approach

This paper presents a new fault tolerant control scheme for unknown multivariable stochastic systems by modifying the conventional state-space self-tuning control approach. For the detection of faults, a quantitative criterion is developed by comparing the innovation process errors occurring in the Kalman filter estimation algorithm, which, for faulty system recovery, a weighting matrix resetting technique is developed by adjusting and resetting the covariance matrices of the parameter estimate obtained in the Kalman filter estimation algorithm to improve the parameter estimation of the faulty systems. The proposed method can effectively cope with partially abrupt and/or gradual system faults and/or input failures with fault detection. The modified state-space self-tuning control scheme can be applied to the multivariable stochastic faulty system without requiring prior knowledge of system parameters and noise properties.     

基于Kalman滤波的神经网络学习算法及其应用

针对传统神经网络学习算法速度慢、容易陷入局部最优解的缺点,将卡尔曼滤波应用于人工神经网络的训练算法中。同时,在卡尔曼滤波计算中,将奇异值分解应用于卡尔曼滤波的递推公式中,提高了协方差阵计算的数值稳定性。最后,本文通过将神经网络的卡尔曼滤波算法应用于电力系统短期负荷预测中,验证了该方法不仅具有理论意义,同时也有实用价值。     

基于指纹库更新补偿的波束跟踪算法研究

针对拒止、复杂电磁环境下,高动态无人节点定向通信面临的坐标信息不精确、飞行姿态和轨迹变化剧烈等问题,为保持可靠的波束对准与跟踪,提出了一种基于卡尔曼滤波的指纹库更新补偿算法。首先,利用卡尔曼滤波算法对自身姿态进行预测更新,建立新的载体坐标系;利用改进的算法对波束指向进行预测更新,并利用指纹库对状态向量均值和协方差矩阵进行更新补偿,调节采样比例,并将新的数据存入指纹库对指纹库数据更新,然后进行二次状态信息预测,完成最终波束指向。整体设计的波束跟踪算法流程更加符合实际应用场景,满足无人机自组网的需求。仿真结果表明,在半波束宽度为3°,100个通信时隙中,维持正常通信的成功率有92%以上,相比传统跟踪算法提高了8%,具有更加稳定的通信质量。