基于MIT规则的自适应扩展集员估计方法

用于非线性椭球估计的自适应扩展集员(Adaptive extended set-membership filter, AESMF)算法在实际应用中存在着过程噪声设定椭球与真实噪声椭球失配的问题, 导致滤波器的估计出现偏差甚至发散. 本文提出了一种基于MIT规则过程噪声椭球最优化的自适应扩展集员估计算法(MIT-AESMF), 用于解决非线性系统时变状态和参数的联合估计和定界中过程噪声无法精确建模问题的新算法. 本算法通过MIT优化规则,在线计算使一步预测偏差包络椭球最小化的过程噪声包络椭球, 以此保证滤波器健康指标满足有效条件; 最后, 采用地面移动机器人状态和动力学参数联合估计验证了所提出方法的有效性.     

基于集员滤波的二阶Volterra自适应归一化最小平均P范数算法

针对Volterra非线性滤波算法计算复杂度呈幂级数增加的问题,提出了一种α稳定分布噪声下的基于集员滤波的二阶Volterra自适应滤波新算法。由于集员滤波的目标函数考虑了所有输入和期望输出的信号对,通过误差幅值的p次方的门限判决,更新Volterra滤波器的权向量,不仅有效降低了算法复杂度,而且提高了自适应算法对输入信号相关性的鲁棒性;并推导给出了权向量的更新公式。仿真结果表明,该算法计算复杂度低、收敛速度快,对噪声及输入信号相关性有较强的鲁棒性。     

一种新的基于保证定界椭球算法的非线性集员滤波器

基于未知但有界噪声假设的集员滤波器为传统的概率化滤波方法提供了一种可行的替代选择, 然而其潜在的计算负担和保守性考虑制约了该方法的实际应用. 本文提出一种新的基于保证定界椭球近似的改进集员滤波方法, 用于解决针对非线性系统的状态估计问题,在保证实时性的前提下降低了算法的保守性. 首先,对非线性模型进行线性化处理,采用DC (Difference of convex)规划方法对线性化误差进行外包定界, 并通过椭球近似将其融合到系统噪声中; 在此基础上提出了一种结合了椭球直和计算和基于迭代外定界椭球算法的椭球--带交集计算 所构成的经典预测--更新步骤来估计得到状态的可行椭球集. 与常规的非线性扩展集员滤波方法的仿真比较表明了本文所提出算法的有效性和改进性能.     

基于集员滤波的选择权更新子带有源噪声控制

通过子带自适应滤波结构,可以提高宽带噪声降噪效果,归一化子带自适应滤波（NSAF）通过在每个子带上使用相同的全带自适应滤波器,消除了传统子带结构会在输出端产生混叠分量的问题,具有较好的收敛性能和稳态均方误差。但由于在每个子带上采用相同的全带自适应滤波器,计算量要高于传统子带结构,集员滤波（SMF）技术具有数据选择更新的特点,可有效降低计算复杂度。基于NSAF结构,建立了前馈ANC无延迟结构,并基于集员滤波技术,通过选择部分权更新来进一步减少计算量,仿真验证了该算法对宽带噪声具有更优的降噪效果。     

基于SRCKF 的自适应高斯和状态滤波算法

针对非线性非高斯离散动态系统中的状态估计问题,基于高斯和递推关系,提出一种高斯和状态估计算法GSSRCKF.首先将状态噪声、观测噪声及滤波初值均表示为高斯和的形式,以平方根容积卡尔曼滤波为子滤波器分别估计各高斯子项对应的系统状态;然后结合各子项对应的权值实现全局估计;最后设计高斯子项对应权值的自适应策略,并采用约简控制法降低计算复杂度.仿真结果验证了所提出的算法在滤波稳定性方面的优越性.     

一种强跟踪有限差分滤波二元估计算法

针对非线性工业过程测量的滞后性和模型不确定性给系统状态估计和模型参数估计造成的困难，在扩展Kalman滤波器（EKF）的基础上，引入有限差分滤波器（FDEKF）和次优渐消因子，提出了一种强跟踪有限差分滤波状态和参数二元估计算法。该二元估计算法将滤波器分解为参数滤波和状态滤波两个过程，分别估计模型参数和系统状态。最后，将该算法应用于一化学反应过程的仿真，结果表明，这种强跟踪有限差分滤波的二元估计算法在原模型或参数存在偏差的情况下，仍能较准确地估计系统状态和模型参数，并具有较强的数值鲁棒性。     

一种新的分割式比例仿射投影算法

针对自适应算法收敛速度和计算复杂度之间的矛盾．提出一种基于集员滤波的分割式比例仿射投影算法（SM-SPAPA）。该算法中只有当参数估计误差大于给定的误差门限时滤波器系数才进行迭代更新,从而能有效地减少滤波器系数的迭代次数。仿真结果表明,由于每次迭代将对误差性能贡献最大的输入信号筛选出来作为输入,从而能加快收敛速度,同时还能够减少算法的运算量。     

基于平方根求积卡尔曼滤波器的弹道目标跟踪

针对再入阶段的弹道目标跟踪问题,提出运用平方根求积卡尔曼滤波器(SRQKF)估计目标的状态.所提出的算法是求积卡尔曼滤波(QKF)算法的平方根实现.该算法传播了目标状态的均值和协方差的平方根,确保了协方差矩阵的对称性和半正定性,改进了数值精度和稳定性,但其计算复杂性稍有增加.仿真实验表明,所提出算法的估计精度优于QKF算法和扩展卡尔曼滤波(EKF)算法,是一种很有效的非线性滤波方法.     

基于融合EKF的航空发动机气路性能健康预测

针对集中式滤波算法存在计算效率不高、容错性差,引入融合滤波的思想,提出采用非线性融合的联邦式扩展卡尔曼滤波器进行发动机气路健康性能预测.子滤波器根据量测参数完成发动机部分健康性能的局部估计,主滤波根据子滤波器估计参数完成融合滤波估计,并将状态估计值和协方差反馈至子滤波器用于下一步健康预测.通过某型涡扇发动机仿真表明:融合EKF滤波器能准确地预测发动机的健康状态,估计稳定收敛时间短、计算时间短、效率高.     

一种改进的集员滤波仿射投影算法

在优化算法的研究中,集员滤波的仿射投影算法具有比传统仿射投影算法迭代次数少、计算量小等优点,但实际应用中,算法的计算复杂度与滤波器长度成正比,当滤波器长度较大时限制了实时实现.为减少误差,实时运行,提出了一种改进算法.算法中当输出误差小于给定误差门限时,滤波器系数不必进行调节;否则将滤波器系数分成多个系数子集,通过仅更新权系数某一子集的方法,减少了原算法每次迭代中需更新的抽头权系数个数.采用一个声回波消除方法进行仿真.仿真验证了改进算法的性能,表明新算法与基于集员滤波的仿射投影算法相比,具有更快的收敛速度,并降低了计算复杂度.     

A UD factorization‐based nonlinear adaptive set‐membership filter for ellipsoidal estimation

The extended set‐membership filter (ESMF) for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity as well as the difficulty in filter parameter selection. In this paper, a UD factorization‐based adaptive set‐membership filter is developed and applied to nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed UD factorization, combined with a new sequential and selective measurement update strategy, the numerical stability and real‐time applicability of conventional ESMF are substantially improved. Furthermore, an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub‐optimal estimation. Simulation results have shown the efficiency and robustness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

一种鲁棒自适应推广Kalman滤波及其在飞行状态估计中的应用

本文在自适应推广Kalman滤波基础上，为了防止滤波发散，改善自适应Kalman滤波的数值稳定性和计算效率，利用U－D分解滤波，并引进滤波发散的判据等，提出一种鲁棒自适应推广Kalman滤波新算法，并把该算法应用于飞行器飞行状态估计问题，仿真及实际计算结果证明了本文方法的有效性。     

基于方差缩减技术的一种自适应粒子滤波器设计

退化现象是粒子滤波(PF)在非线性状态估计应用中存在的主要问题, 重采样过程一定程度上解决了粒子退化现象, 但同时带来了退化现象所导致的样本贫化问题. 本文将方差缩减技术用于PF之中, 通过给所有粒子权重赋予一个指数衰减因子来解决粒子退化现象, 该衰减因子可以根据有效粒子数进行自适应、迭代的选取, 随后通过一个定理来证明了该方法的有效性, 并基于此提出了一种自适应粒子滤波(APF)算法, 给出了算法的具体步骤, 同时对参数选取的原则和算法的局限性进行了详细的讨论. 最后, 通过一个数值例子说明了本文所提出的APF算法在计算负荷不大的条件下较采样-重要性-重采样粒子滤波(PF-SIR)、遗传粒子滤波(GPF)、粒子群优化粒子滤波(PSOPF)具有更高的估计精度.     

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.     

State estimation of nonlinear dynamic systems using weighted variance-based adaptive particle swarm optimization

New heuristic filters are proposed for state estimation of nonlinear dynamic systems based on particle swarm optimization (PSO) and differential evolution (DE). The methodology converts state estimation problem into dynamic optimization to find the best estimate recursively. In the proposed strategy the particle number is adaptively set based on the weighted variance of the particles. To have a filter with minimal parameter settings, PSO with exponential distribution (PSO-E) is selected in conjunction with jDE to self-adapt the other control parameters. The performance of the proposed adaptive evolutionary algorithms i.e. adaptive PSO-E, adaptive DE and adaptive jDE is studied through a comparative study on a suite of well-known uni- and multi-modal benchmark functions. The results indicate an improved performance of the adaptive algorithms relative to original simple versions. Further, the performance of the proposed heuristic filters generally called adaptive particle swarm filters (APSF) or adaptive differential evolution filters (ADEF) are evaluated using different linear (nonlinear)/Gaussian (non-Gaussian) test systems. Comparison of the results to those of the extended Kalman filter, unscented Kalman filter, and particle filter indicate that the adopted strategy fulfills the essential requirements of accuracy for nonlinear state estimation.     

Novel Rao–Blackwellized jump Markov CBMeMBer filter for multi-target tracking

The jump Markov cardinality balanced multi-target multi-Bernoulli (JM–CBMeMBer) filter can estimate both state and number of targets from uncertain measurements. To deal with high computational complexity and imprecise estimations of the existing JM–CBMeMBer filters, we put forward a novel Rao–Blackwellized JM–CBMeMBer filter and its sequential Monte Carlo implementation in this paper. Different from the previous works, we first divide target state space into the nonlinear and linear components based on the Rao–Blackwellized theory, where the linear component is estimated by the Kalman filter (KF) and the results are applied to extract the nonlinear component in lower dimension state space. Moreover, the track management scheme is considered to simplify tracking parameters and distinguish target track. After analysis on computational complexity, the optimised Rao–Blackwellized filtering scheme is presented to reduce the number of the KF recursions. As a result, the computational complexity is reduced and the estimation accuracy is improved owing to small estimation covariance during the whole filtering process. Finally, the numerical simulation results are provided to show the reliability and efficiency of the proposed filter.     

具有双重不确定性系统的联合滤波算法

卡尔曼滤波在高斯白噪声的假设下是一种最优滤波, 基于区间数学理论的集员滤波 (Set-membership filter, SMF)能够有效处理有界噪声假设下的滤波问题. 然而, 随机噪声和有界噪声在许多情况下会同时干扰控制系统. 由于两种滤波算法都受到各自适用范围的限制, 使用单一滤波算法难以得到理想的估计结果. 本文通过建立具有双重不确定性系统的模型, 提出了一种基于贝叶斯估计联合滤波算法. 该算法用卡尔曼滤波处理系统的随机不确定性, 用集员滤波处理系统的有界不确定性, 得出一个易于实现的滤波器. 最后通过对雷达跟踪系统的仿真, 结果表明, 较单一滤波算法, 联合滤波具有更强的噪声适应性和有效性.     

二阶Volterra变记忆长度LMP算法

针对实际应用中非线性系统记忆长度未知致使Volterra自适应滤波器可能无法达到最优性能的问题,提出一种二阶Volterra变记忆长度LMP算法。利用Volterra滤波器二阶权系数矩阵的对称性和对称矩阵可对角化分解性质,推导得到了一阶权系数与二阶权系数个数相同的信号矢量与权系数矢量内积的二阶Volterra滤波器输出信号表达式;提出了基于DCT的二阶Volterra自适应滤波器（CSVF）及其LMP算法（CSVLMP）;采用FIR抽头长度的自适应调整思想,提出了基于DCT的二阶Volterra变记忆长度LMP算法（CSVMLMP）。记忆长度未知的非线性系统辨识的仿真结果表明,在[α]稳定分布噪声背景下,该算法在收敛速度、稳态性能和计算复杂度之间达到了较好的折中。