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Estimation algorithm for system with non‐Gaussian multiplicative/additive noises based on variational Bayesian inference
Author(s) -
Yu Xingkai,
Li Jianxun,
Xu Jian
Publication year - 2019
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2973
Subject(s) - algorithm , multiplicative noise , mathematics , posterior probability , multiplicative function , bayesian inference , noise (video) , gaussian noise , mathematical optimization , computer science , bayesian probability , artificial intelligence , statistics , mathematical analysis , signal transfer function , digital signal processing , analog signal , computer hardware , image (mathematics)
Summary This paper considers estimation algorithms for linear and nonlinear systems contaminated by non‐Gaussian multiplicative and additive noises. Based on the variational idea, in order to derive optimal estimation algorithms, we combine the multiplicative noise with states as the joint parameters to estimate. The application of variational Bayesian inference to joint estimation of the state and the multiplicative noise is established. By treating the states as unknown quantities as well as the multiplicative noise, there are now correlations between the states and multiplicative noise in the posterior distribution. There are two main goals in Bayesian learning. The first is approximating the marginal likelihood (PDF of multiplicative noise) to perform model comparison. The second is approximating the posterior distribution over the states (also called a system model), which can then be used for prediction. The two goals constitute the iterative algorithm. The rules for determining the loop is the Kullback‐Leibler divergence between the true distribution of state and a chosen fixed tractable distribution, which is used to approximate the true one. The iterative algorithm is deduced, which is initialized based on the idea of sampling. Meanwhile, the convergence analysis of the proposed iterative algorithm is presented. The numerical simulation results in a comparison between the proposed method and these existing classic algorithms in the context of nonlinear hidden Markov models, state‐space models, and target‐tracking models with non‐Gaussian multiplicative noise demonstrate the superiorities, not only in speed, precision, and computation load but also in the ability to process non‐Gaussian complex noise.