Exact Fast Computation of Optimal Filter in Gaussian Switching Linear Systems

IEEE Trans. Automat. Contr.

et al. 2015

Self Cite

Abstract-We consider a general triplet Markov Gaussian linear system (X, R, Y), where X is an hidden continuous random sequence, R is an hidden discrete Markov chain, Y is an observed continuous random sequence. When the triplet (X, R, Y) is a classical "Conditionally Gaussian Linear State-Space Model" (CGLSSM), the mean square error optimal filter is not workable with a reasonable complexity and different approximate methods, e.g. based on particle filters, are used. We propose two contributions. The first one is to extend the CGLSSM to a new, more general model, called the "Conditionally Gaussian Pairwise Markov Switching Model" (CGPMSM), in which X is not necessarily Markov given R. The second contribution is to consider a particular case of CGPMSM in which (R, Y) is Markov and in which an exact filter, optimal in the sense of mean square error, can be performed with linear-time complexity. Some experiments show that the proposed method and the suited particle filter have comparable efficiency, while the second one is much faster.Index Terms-Conditionally Gaussian linear state-space model, conditionally Gaussian pairwise markov switching model, exact optimal filtering, Gaussian switching system, hidden Markov models.

Section: Discussionmentioning

confidence: 99%

Optimal Filter Approximations in Conditionally Gaussian Pairwise Markov Switching Models

Abbassi

Benboudjema

IEEE Trans. Automat. Contr.

et al. 2015

Self Cite

“…More precisely, any stationary CGLSSM is given by p(r 2 1 ), p(x 2 1 |r 2 1 ) and p(y 1 |r 1 ). If these distributions are the only information about some physical system, then a Model 2 can capture them as well [23]. Specifically, p(r 2 1 ), p(x 2 1 |r 2 1 ) and p(y 2 1 |r 2 1 ) would be the same in CGLSSM and Model 2, and only p(x 2 , y 1 |r 2 1 ) would differ.…”

Section: Stationnary Conditionnaly Gaussian Observed Markov Switchingmentioning

confidence: 99%

Fast smoothing in switching approximations of non-linear and non-Gaussian models

Gorynin

Computational Statistics & Data Analysis

Monfrini

et al. 2017

Statistical smoothing in general non-linear non-Gaussian systems is a challenging problem. A new smoothing method based on approximating the original system by a recent switching model has been introduced. Such switching model allows fast and optimal smoothing. The new algorithm is validated through an application on stochastic volatility and dynamic beta models. Simulation experiments indicate its remarkable performances and low processing cost. In practice, the proposed approach can overcome the limitations of particle smoothing methods and may apply where their usage is discarded.

“…Let us remember that SCGOMSMs can be very close to the classic "conditionally Gaussian linear state-space model" (CGLSSM) [11,12], which does not offer the possibility of fast smoothing [5].…”

Section: Stationary Conditionally Gaussian Observed Markov Switching mentioning

confidence: 99%

Exact fast smoothing in switching models with application to stochastic volatility

Gorynin

2015 23rd European Signal Processing Conference (EUSIPCO)

Monfrini

et al. 2015