Invertible particle flow based Gaussian and Gaussian sum particle filters

Abstract

The estimation of the state of dynamic systems using measurements is a frequently arising challenge. State estimation is used in applications like robotics, industrial manufacturing, weather forecasting, target tracking, etc. The hidden state in the dynamic systems can be estimated using the recursive Bayesian filters. These filters estimate the state by tracking the posterior distribution. These filters include two steps, prediction based on solving the equation modeling the state evolution and update of the state using the measurements. Most real-world systems have non-linear dynamic and measurement models. Additionally, both models can be affected by arbitrary noise sources, which have either Gaussian or nonGaussian characteristics. For state estimation in linear Gaussian models, Kalman filters are employed. Extended Kalman filters (EKF) are utilized for state estimation in non-linear Gaussian models. For state estimation in non-linear non-Gaussian models, particle filters are generally employed. Particle filters, however, are ineffective in high-dimensional non-linear non-Gaussian models because they experience weight degeneracy. In this thesis, we propose incorporating the invertible particle flow methods in the Gaussian particle filter (GPF) framework to generate a proposal distribution. These methods are derived under Gaussian assumptions for the flow equation. The resulting particle flow Gaussian particle filter (PFGPF) method preserves the asymptotic characteristics of Gaussian particle filters and has the potential to perform better at state estimation in high-dimensional spaces. Secondly, we construct a particle flow Gaussian sum particle filter (PFGSPF), which roughly approximates the predictive and posterior as Gaussian mixture models, using a bank of PFGPF filters. In complicated estimating issues where a simple Gaussian approximation is insufficient, this approximation is helpful. We compare the performance of the proposed filters with the existing particle flow filters and particle flow particle filters (PFPF) in high dimensional complex numerical simulations.