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.     

Robust Kalman filter for linear discrete-time system with gaussian sum noises

This paper considers the filtering problem for discrete-time linear systems where the distributions of the process and observation noises are of gaussian sum distributions. Since the gaussian sum noise can be considered to be a sample from one of the gaussian distributions forming the gaussian sum, we define the distribution selection parameters that specify sample noises from the gaussian sum distribution. By using the maximum a posteriori (MAP) estimates of the selection parameters, a robust state estimation algorithm combined with the Kalman filter is developed. Simulation studies are also included to show the effectiveness of the present algorithm.     

基于高斯马尔可夫随机场的MAP估计在高斯噪声滤波中的应用

提出了基于高斯马尔可夫随机场(GMRF)的最大后验概率(MAP)估计在图像高斯噪声滤波中的应用方法。根据高斯噪声的先验特点,建立基于高斯马尔可夫随机场的退化图像恢复模型,从而将图像高斯噪声滤波问题转化为求解最大后验概率问题。先验概率可以根据马尔可夫随机场(MRF)和吉布斯分布(GD)的等效性, 用GD的概率估计。为了求解最大后验概率,第一,通过期望最大化(EM）算法对GMRF模型进行参数估计。第二,用共轭梯度法将目标函数最小化。实验结果表明,与其他滤波器（如高斯滤波、维纳滤波等）相比,本文所阐述的方法在滤除高斯噪声、保持图像原有结构方面效果更好。     

Delta sum state estimation for discrete-time dynamical models

Optimal recursive estimates are derived for a class of non-Gaussian nonlinear systems using a discrete approximation of the probability density function of the measurement noise.     

含有迟滞Hammerstein系统的非光滑卡尔曼状态估计

迟滞特性具有非光滑、多值映射等复杂特性.如果迟滞环节的末端还存在一个线性子系统,导致迟滞的输出信号不可测,使得整个系统的状态估计工作成为很大的难题,常规的估计方法无法直接应用到这类系统中.本文提出一种新的非光滑卡尔曼滤波器,描述了Hammerstein系统的状态空间方程.据此构造了能够随系统工作区间变化而自动切换的非光滑滤波器.最后通过仿真和实验,比较了非光滑卡尔曼滤波器和传统的卡尔曼滤波器的状态估计效果,比较结果表明非光滑卡尔曼滤波器对于带迟滞的Hammerstein系统状态变量的估计的准确性要优于传统的卡尔曼滤波器.     

基于UKF的CDMA系统信道参数估计

CDMA系统信道时间延迟估计是一个非线性的迭代过程。UKF算法能够避免EKF由于线性化非线性系统而带来的误差过大等问题,比EKF估计的更加精确。利用UKF算法对CDMA系统信道的幅度衰减参数与延时参数进行了估计。在研究中考虑到了多址干扰和远近效应对信道参数的影响,仿真结果表明UKF算法能有效地抑制远近效应及多址干扰,估计出无线信道参数。     

Constructing an analogue of the Kalman filter for a guaranteed state estimation of a dynamic system

A filter similar to the known Kalman filter is constructed to obtain the external guaranteed ellipsoidal estimate of the state of a dynamic system using measurements. Information on uncertain factors acting upon the system and observation errors is supposed to be restricted to knowing the boundaries of possible values of these variables. A numeric example of how the obtained relations can be used is given.     

基于UKF的自适应野值剔除算法

在基于RSSI信号的无线定位系统中,由于外界环境中各种存在随机干扰噪声,使得采样到的RSSI信号往往具有非线性、不稳定等特点,很大程度上偏离了其真实值,它直接影响了定位系统的定位精度。为了提取RSSI信号的真实值,提出一种基于UKF的自适应野值剔除算法,它根据信息来修正其预测值和增益,可以实时对动态观测数据中的野值进行检测和剔除。并通过与UKF算法对比仿真实验,matlab仿真结果表明,使用改进算法对RSSI信号进行滤波处理,提取的RSSI信号值更接近其真实值,收敛速度更快,误差更小,稳定性更好, 可以有效地剔除野值信号,并抑制了野值信号对滤波的影响。     

Fuzzy filter for state estimation of a glucoregulatory system

A filter based on fuzzy logic for state estimation of a glucoregulatory system is presented. A published non-linear model for the dynamics of glucose and its hormonal control including a single glucose compartment, five insulin compartments and a glucagon compartment was used for simulation. The simulated data were corrupted by an additive white noise with zero mean and a coefficient of variation (CV) of between 2 and 20% and then submitted to the state estimation procedure using a fuzzy filter (FF). The performance of the FF was compared with an extended Kalman filter (EKF) for state estimation. Both the FF and the EKF were evaluated in the following cases: (a) five state variables are measurable; three plasma variables are measurable; only plasma glucose is measurable; (b) for different measurement noise levels (CV of 2–20%); and (c) a mismatch between the glucoregulatory system and the given mathematical model (uncertain or approximate model). In contrast to the FF, in the case of approximate model of the glucose system, the EKF failed to achieve useful state estimation. Moreover, the performance of the FF was independent of the noise level. In conclusion, the FF approach is a viable alternative for state estimation in a noisy environment and with an uncertain mathematical model of the glucoregulatory system.     

不确定噪声下基于轴对称盒空间滤波的非线性系统状态估计

针对不确定噪声下的非线性系统状态估计问题, 本文提出了一种基于轴对称盒空间滤波的状态估计方法. 首先, 利用轴对称盒空间包裹线性化过程带来的误差项, 将状态函数线性化误差轴对称盒空间与噪声轴对称盒空间求取闵可夫斯基和, 得到干扰误差轴对称盒空间; 随后, 利用状态量、线性误差和测量噪声的轴对称盒空间的闵可夫斯基和, 得到系统状态预测集; 进而, 利用轴对称盒空间边界正交的性质, 将盒空间拆分为多组超平面, 构造测量更新的约束条件并得到集员包裹. 本文所提方法相比传统的椭球滤波方法而言, 降低了算法的复杂度, 减少了包裹状态可行集和线性化过程带来的余, 获得了更加紧致精确的系统状态集. 最后, 采用非线性弹簧–质量–阻尼器系统验证了本文所提算法的有效性.     

Simplex filter: A novel heuristic filter for nonlinear systems state estimation

This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on simplex technique to find and track the best estimation. The vertices of the simplex search the state space dynamically in a similar scheme to the optimization algorithm, known as Nelder-Mead simplex. The parameters of the proposed filter are tuned, using an information visualization technique to identify the optimal region of the parameters space. The visualization is performed using the concept of parallel coordinates. The proposed filter is applied to estimate the state of some nonlinear dynamic systems with noisy measurement and its performance is compared with other filters.     

Applying the unscented Kalman filter for nonlinear state estimation

Based on presentation of the principles of the EKF and UKF for state estimation, we discuss the differences of the two approaches. Four rather different simulation cases are considered to compare the performance. A simple procedure to include state constraints in the UKF is proposed and tested. The overall impression is that the performance of the UKF is better than the EKF in terms of robustness and speed of convergence. The computational load in applying the UKF is comparable to the EKF.     

基于UKF和优化组合策略的改进粒子滤波算法

针对标准粒子滤波算法存在的粒子退化与贫化问题,提出了一种新的改进粒子滤波算法。该算法采用无迹卡尔曼滤波、优化组合策略和标准粒子滤波相结合的方法,运用UKF产生重要性密度函数,解决标准PF算法中以先验概率密度函数作为建议分布所引发的退化问题;运用优化组合重采样策略保证所有粒子的信息以一定概率得到继承,维持粒子集中粒子的多样性。理论分析与仿真结果均表明,改进算法能有效地解决标准粒子滤波存在的粒子退化问题并避免粒子贫化现象的出现,具有更高的状态估计精度。     

Multi-pitch estimation based on multi-scale product analysis,improved comb filter and dynamic programming

There are many multi-pitch estimation methods, but most of them can’t perform perfectly for intrusion pitch detection. For this reason, a new multi-pitch detection approach is proposed. This method consists on the autocorrelation function of the Multi-scale product calculation of the mixture signal, its filtered version by a rectangular improved comb filter and the dynamic programming of the residual signal spectral density. First, we analyze the composite speech. Then, we apply the autocorrelation on the multi-scale product (AMP). We find the first pitch which represents the dominant one. Then, we apply the rectangular comb filter which has adaptive amplitude to remove the resulting signal from the original one. We operate AMP on the residue to obtain a pitch estimation of the intrusion. To improve the residue pitch estimation, we apply the dynamic programming to the spectral density of the residual signal to get optimum pitches corresponding also to intrusion signal. After that, we compare the two resulting pitch residue series to choose the most appropriate. Finally, this method is evaluated using the Cooke database and is compared to other well-known techniques. Experimental results confirm the strength and the performance of the proposed approach.     

动态系统运动状态最优化估计研究

动态系统运动状态最优化估计是运动分析领域的一个重要研究内容.以卡尔曼滤波器为研究基点,进一步研究分析了动态系统运动状态最优化估计方法.工作主要从两个方面展开.首先建立动态系统运动状态相适应的数学模型,通过数学推导分析研究了卡尔曼滤波器、H-滤波器和扩展卡尔曼滤波器的设计原理和应用范围.然后就车辆导航系统和永磁同步电机系统作了仿真实验.仿真结果表明了理论分析的正确性.     

DOA estimation based on the difference and sum coarray for coprime arrays

In this paper, we construct a novel coarray named as the difference and sum (diff–sum) coarray by exploiting an improved Conjugate Augmented MUSIC (CAM) estimator, which utilizes both the temporal information and the spatial information. The diff–sum coarray is the union of the difference coarray and the sum coarray. When taking the coprime array as the array model, we find that the elements of the sum coarray can fill up all the holes in the difference coarray. Besides, the sum coarray contains bonus uniform linear array (ULA) segments which extend the consecutive range of the difference coarray. As a result, the consecutive lags of the diff–sum coarray are much more than those of the difference coarray. For analysis, we derive the hole locations and consecutive ranges of the difference set and the sum set, discuss the complementarity of the two sets, and provide the analytical expression of the diff–sum virtual aperture. Simulations verify the effectivity of the improved method and show the high DOF of the diff–sum coarray.     

An alternative FIR filter for state estimation in discrete-time systems

To overcome the resulting problems of existing finite impulse response (FIR) structure filters, this paper proposes an alternative FIR filter for state estimation in discrete-time systems, which is derived from the well-known Kalman filter with recursive infinite impulse response (IIR) structure. The proposed FIR filter obtains a posteriori knowledge about the window initial condition from the most recent finite observations, while existing FIR filters handle this task arbitrarily or heuristically. The gain matrix for the proposed FIR filter incorporates a posteriori knowledge about the window initial condition during its design and is shown to be time-invariant. The proposed FIR filter is shown to have good inherent properties such as unbiasedness and deadbeat. Through extensive computer simulations, the proposed FIR filter can be shown to be comparable with the Kalman filter for the nominal system and better than that for the temporarily uncertain system.     

Posterior representation with a multi‐modal likelihood using the gaussian sum filter for localization in a known map

A Gaussian sum filter (GSF) with component extended Kalman filters (EKF) is proposed as an approach to localizing an autonomous vehicle in an urban environment with limited GPS availability. The GSF uses vehicle‐relative vision‐based measurements of known map features coupled with inertial navigation solutions to accomplish localization in the absence of GPS. The vision‐based measurements have multimodal measurement likelihood functions that are well represented as weighted sums of Gaussian densities. The GSF is used because of its ability to represent the posterior distribution of the vehicle pose with better efficiency (fewer terms, less computational complexity) than a corresponding bootstrap particle filter with various numbers of particles because of the interaction with measurement hypothesis tests. The expectation‐maximization algorithm is used off line to determine the representational efficiency of the particle filter in terms of an effective number of Gaussian densities. In comparison, the GSF, which uses an iterative condensation procedure after each iteration of the filter to maintain real‐time capabilities, is shown through a series of in‐depth empirical studies to more accurately maintain a representation of the posterior distribution than the particle filter using 37 min of recorded data from Cornell University's autonomous vehicle driven in an urban environment, including a 32 min GPS blackout. © 2012 Wiley Periodicals, Inc.     

基于粒子滤波的非线性系统静态参数估计方法*

针对基于滤波方法的最大似然参数估计步长序列过于单一,算法收敛缓慢并很容易收敛于局部最优解的问题,提出了基于似然权值的在线EM参数估计算法(LWOEM)。通过粒子滤波方法实时估计系统的状态值变化,结合最大似然方法计算静态参数的点估计,然后通过计算更新参数的似然值来动态更新步长序列.与在线EM参数估计算法(OEM)的实验结果比较,表明该算法具有更好的适应性和收敛效果。