Estimation Performance for the Cubature Particle Filter under Nonlinear/Non-Gaussian Environments

This paper evaluates the state estimation performance for processing nonlinear/non-Gaussian systems using the cubature particle filter (CPF), which is an estimation algorithm that combines the cubature Kalman filter (CKF) and the particle filter (PF). The CPF is essentially a realization of PF where the third-degree cubature rule based on numerical integration method is adopted to approximate the proposal distribution. It is beneficial where the CKF is used to generate the importance density function in the PF framework for effectively resolving the nonlinear/non-Gaussian problems. Based on the spherical-radial transformation to generate an even number of equally weighted cubature points, the CKF uses cubature points with the same weights through the spherical-radial integration rule and employs an analytical probability density function (pdf) to capture the mean and covariance of the posterior distribution using the total probability theorem and subsequently uses the measurement to update with Bayes’ rule. It is capable of acquiring a maximum a posteriori probability estimate of the nonlinear system, and thus the importance density function can be used to approximate the true posterior density distribution. In Bayesian filtering, the nonlinear filter performs well when all conditional densities are assumed Gaussian. When applied to the nonlinear/non-Gaussian distribution systems, the CPF algorithm can remarkably improve the estimation accuracy as compared to the other particle filter-based approaches, such as the extended particle filter (EPF), and unscented particle filter (UPF), and also the Kalman filter (KF)-type approaches, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF) and CKF. Two illustrative examples are presented showing that the CPF achieves better performance as compared to the other approaches.     

光电跟踪的非线性卡尔曼滤波算法

为得到最小方差意义下的光电跟踪目标的最优状态估计,提出将部分状态卡尔曼滤波和非线性系统的一阶线性化思想相结合,构成一种适用于非线性光电跟踪目标的卡尔曼滤波算法,并总结出详细算法结构.同时将此方法应用到非线性测量光电跟踪系统中,并与扩展卡尔曼滤波和U卡尔曼滤波进行性能对比.仿真实验结果证明,将部分状态卡尔曼滤波和非线性系统的一阶线性化思想相结合是有效可行的,而且其性能明显优于扩展卡尔曼滤波和U卡尔曼滤波.     

A semi-analytical particle filter for identification of nonlinear oscillators

Particle filters find important applications in the problems of state and parameter estimations of dynamical systems of engineering interest. Since a typical filtering algorithm involves Monte Carlo simulations of the process equations, sample variance of the estimator is inversely proportional to the number of particles. The sample variance may be reduced if one uses a Rao–Blackwell marginalization of states and performs analytical computations as much as possible. In this work, we propose a semi-analytical particle filter, requiring no Rao–Blackwell marginalization, for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito–Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. This information is further exploited within the particle filter algorithm for obtaining samples from the optimal posterior density of the states. The potential of the method in state/parameter estimations is demonstrated through numerical illustrations for a few nonlinear oscillators. The proposed filter is found to yield estimates with reduced sample variance and improved accuracy vis-à-vis results from a form of sequential importance sampling filter.     

基于RFF及GWO-PF的锂电池SOC估计

为了提高锂电池剩余电量估计的准确性,提出一种在线参数辨识与改进粒子滤波算法相结合的锂电池SOC估计方法。针对粒子滤波中的粒子退化问题,引入灰狼算法,利用灰狼算法较强的全局寻优能力优化粒子分布,保证粒子多样性,有效抑制粒子退化现象,提高滤波精度。采用带遗忘因子的递推最小二乘法实时更新模型参数,并与改进粒子滤波算法交替运行,进一步提高SOC的估计精度。实验结果表明,改进算法的平均估计误差始终保持在±0.15%以内,相比扩展卡尔曼滤波与无迹卡尔曼滤波算法,在电池SOC估计上有更高的估计精度与稳定性。     

基于卡尔曼滤波和粒子滤波融合的UWB室内定位算法

基于超宽带(ultra-wideband,UWB)室内定位技术得到了广泛的发展,然而,在LOS(line-of-sight)和NLOS(non-line-of-sight)环境下的UWB的测距信息均存在不同程度的误差,因此,提出了一种改进的卡尔曼滤波算法对UWB原始数据进行平滑处理;之后提出卡尔曼滤波(Kalman filters and particle filters,KPF)和粒子滤波融合的算法。通过卡尔曼滤波得到的状态量和误差协方差进行粒子采样,克服了传统粒子滤波进行粒子采样时的运动学模型与实际运动不相符的缺点,大幅减少了粒子退化的现象。经过实验,该算法在LOS和NLOS环境中的定位精度分别提升了20.6%和15.6%。     

结构物理参数识别的多尺度参数卡尔曼滤波方法

经过正交小波变换后,低尺度上测量信号的信噪比提高。应用小波变换将结构的激励信号和响应信号分解到不同尺度上,得到不同尺度上结构的状态方程和测量方程,结合动力学系统辨识的参数卡尔曼滤波方法,提出了结构物理参数的多尺度参数卡尔曼滤波辨识方法。理论分析和数值算例表明:在多尺度上对结构参数进行辨识比在单一尺度上辨识能获得更高的精度。     

一种新的自适应非线性卡尔曼滤波算法

为避免由于系统噪声统计特性不准确所导致的滤波性能下降问题,改进了一种基于新息的系统噪声方差调整方法,并将其与扩展卡尔曼滤波、Unscented 卡尔曼滤波和差分滤波相结合,形成自适应非线性卡尔曼滤波.将此方法应用到非线性测量光电跟踪系统中,并与采用基本非线性卡尔曼滤波进行性能对比.仿真实验结果证明该方法可以实时调整系统噪声方差,有效地避免由于系统噪声统计特性不准确所带来的滤波性能下降的问题,而且其性能明显优于基本非线性卡尔曼滤波.     

Adaptive exponential smoothing versus conventional approaches for lumpy demand forecasting: case of production planning for a manufacturing line

Production planning in a lumpy demand environment can be tenuous, with potentially costly forecasting errors. This paper addresses the issue of selecting the smoothing factor used in lumpy demand forecasting models. We propose a simple adaptive smoothing approach to replace the conventional industrial practice of choosing a smoothing factor largely based on the analyst or engineer's experience and subjective judgment. The Kalman filter approach developed in this study processes measurements to estimate the state of a linear system and utilises knowledge from states of measurements and system dynamics. Performances of an array of forecasting models that have been shown to work well in lumpy demand environments are compared with respect to the proposed adaptive smoothing factor and the conventional smoothing constant across a spectrum of lumpy demand scenarios. All models using the adaptive smoothing factor based on Kalman filter weighting function generate smaller errors than their conventional counterparts, especially under high lumpiness demand environments. Our proposed approach is particularly useful when production management is concerned about simplicity and transferability of knowledge due to constant personnel turnaround and low retention rate of expertise.     

Sequential Monte Carlo filters for abruptly changing state estimation

Sequential Monte Carlo techniques are evaluated for the nonlinear Bayesian filtering problem applied to systems exhibiting rapid state transitions. When systems show a large disparity between states (long periods of random diffusion about states interspersed with relatively rapid transitions), sequential Monte Carlo methods suffer from the problem known as sample impoverishment. In this paper, we introduce the maximum entropy particle filter, a new technique for avoiding this problem. We demonstrate the effectiveness of the proposed technique by applying it to highly nonlinear dynamical systems in geosciences and econometrics and comparing its performance with that of standard particle-based filters such as the sequential importance resampling method and the ensemble Kalman filter.     

光电跟踪系统非线性新息自适应卡尔曼滤波算法

为解决非线性部分状态卡尔曼滤波算法中由于线性化误差所导致的滤波精度下降问题,提出采用UT变换方法计算系统状态误差方差,及基于新息自适应调整系统噪声方差,进而构成一种新的非线性自适应部分状态卡尔曼滤波算法,并总结出详细算法结构.同时,将此方法应用到非线性测量光电跟踪系统中,并与U卡尔曼滤波和非线性部分状态卡尔曼滤波进行性...