Open Access
A marginalised particle filter with variational inference for non‐linear state‐space models with Gaussian mixture noise
Author(s) -
Cheng Cheng,
Tourneret JeanYves,
Lu Xiaodong
Publication year - 2022
Publication title -
iet radar, sonar and navigation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.489
H-Index - 82
eISSN - 1751-8792
pISSN - 1751-8784
DOI - 10.1049/rsn2.12179
Subject(s) - gaussian noise , gaussian , context (archaeology) , particle filter , noise (video) , mathematics , state space , posterior probability , bayesian inference , state variable , latent variable , filter (signal processing) , algorithm , control theory (sociology) , computer science , bayesian probability , kalman filter , artificial intelligence , statistics , physics , computer vision , geography , archaeology , image (mathematics) , thermodynamics , control (management) , quantum mechanics
Abstract This work proposes a marginalised particle filter with variational inference for non‐linear state‐space models (SSMs) with Gaussian mixture noise. A latent variable indicating the component of the Gaussian mixture considered at each time instant is introduced to specify the measurement mode of the SSM. The resulting joint posterior distribution of the state vector, the mode variable and the parameters of the Gaussian mixture noise is marginalised with respect to the noise variables. The marginalised posterior distribution of the state and mode is then approximated by using an appropriate marginalised particle filter. The noise parameters conditionally on each particle system of the state and mode variable are finally updated by using variational Bayesian inference. A simulation study is conducted to compare the proposed method with state‐of‐the‐art approaches in the context of positioning in urban canyons using global navigation satellite systems.