Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is well known that the posterior state estimates in nonlinear problems may assume non-Gaussian multimodal densities. In the past, Gaussian mixture filters and particle filters were introduced to handle non-Gaussianity and nonlinearity. However, these methods have seen only limited success as most mixture filters attempt to fix the number of mixture modes during estimation process, and the particle filters suffer from the curse of dimensionality. In this paper, we propose a particle based Gaussian mixture filtering approach for the general nonlinear estimation problem that is free of the particle depletion problem inherent to most particle filters. We employ an ensemble of randomly sampled states for the propagation of state probability density. A Gaussian mixture model of the propagated uncertainty is then recovered by clustering the ensemble. The posterior density is obtained subsequently through a Kalman measurement update of the mixture modes. We prove the weak convergence of the PGM density to the true filter density assuming exponential forgetting of initial conditions by the true filter. The estimation performance of the proposed filtering approach is demonstrated through several test cases.
Fixed-structure Gaussian Mixture Filtering with Robust Measurement Updates under Outliers
European Centre of Excellence NTIS, University of West Bohemia in Pilsen（欧洲卓越中心NTIS，比尔森西波希米亚大学）；Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Karlsruhe Institute of Technology（智能传感器执行器系统实验室（ISAS），卡尔斯鲁厄理工学院）
Exact Consistency Tests for Gaussian Mixture Filters using Normalized Deviation Squared Statistics
Smead Aerospace Engineering Sciences, University of Colorado Boulder（科罗拉多大学博尔德分校斯米德航空航天工程科学学院）；Aurora Flight Sciences, a Boeing Company（波音公司旗下极光飞行科学公司）
State Estimation for Piecewise Affine State-Space Models
Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）；Linköping University（林雪平大学）；University of Cambridge（剑桥大学）；Tampere University of Technology (TUT)（坦佩雷理工大学）
A Distributed Particle-PHD Filter with Arithmetic-Average PHD Fusion
School of Automation, Northwestern Polytechnical University（西北工业大学自动化学院）；University of Salamanca（萨拉曼卡大学）；Institute of Telecommunications, TU Wien（维也纳科技大学电信研究所）；Brno University of Technology（布尔诺理工大学）
Intelligent Sensor-Actuator-Systems Laboratory (ISAS)（智能传感器-执行器系统实验室（ISAS））；Institute for Anthropomatics（人体工程学研究所）；Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院（KIT））
