Dempster–Shafer fusion of multisensor signals in nonstationary Markovian context

Abstract

The latest developments in Markov models' theory and their corresponding computational techniques have opened new rooms for image and signal modeling. In particular, the use of Dempster-Shafer theory of evidence within Markov models has brought some keys to several challenging difficulties that the conventional hidden Markov models cannot handle. These difficulties are concerned mainly with two situations: multisensor data, where the use of the Dempster-Shafer fusion is unworkable; and nonstationary data, due to the mismatch between the estimated stationary model and the actual data. For each of the two situations, the Dempster-Shafer combination rule has been applied, thanks to the triplet Markov models' formalism, to overcome the drawbacks of the standard Bayesian models. However, so far, both situations have not been considered in the same time. In this article, we propose an evidential Markov chain that uses the Dempster-Shafer combination rule to bring the effect of contextual information into segmentation of multisensor nonstationary data. We also provide the Expectation-Maximization parameters' estimation and the maximum posterior marginal's restoration procedures. To validate the proposed model, experiments are conducted on some synthetic multisensor data and noised images. The obtained segmentation results are then compared to those obtained with conventional approaches to bring out the efficiency of the present model.

Distributed fault detection based on HMM for Wireless Sensor Networks

“…A hidden Markov model can be considered a generalization of a mixture model where the hidden variables (or latent variables), which control the mixture component to be selected for each observation, are related through a Markov process rather than independent of each other. Recently, hidden Markov models have been generalized to pairwise Markov models and triplet Markov models which allow consideration of more complex data structures [21] [22] and the modeling of non stationary data [23] [24].…”

Filtrage statistique optimal rapide dans des systèmes linéaires à sauts non stationnaires

“…is not necessarily Markovian. This context has already proven very effective in image segmentation for modeling multiple-stationaries (Lanchantin et al, 2011;Boudaren et al, 2012a), in hidden semi-Markov chains (Lapuyade-Lahorgue et Pieczynski, 2011a) or in hidden evidential Markov chains (Pieczynski, 2007 ;Boudaren et al, 2012b ;Ramasso et Denoeux, 2013), but is novel in optimal statistical filtering. Simulations are provided to illustrate the value of the new modeling in the context of non-stationary on-line filtering of time-series.…”

“…peut conduire à une amélioration significative des résultats obtenus (Lanchantin et al, 2011). Au plan plus théorique, les différentes interprétations de N U 1 peuvent mener à différentes modélisations comme les semi-Markov cachés (Lapuyade-Lahorgue et ou les chaînes cachées évidentielles (Pieczynski, 2007 ;Boudaren et al, 2012b ;Ramasso et Denoeux, 2013). Notons également l'utilisation récente du processus auxiliaire pour modéliser, dans le cas multivarié, les états à retard existant entre les canaux observés (Le Cam, 2013).…”

Phasic Triplet Markov Chains

“…Similarly, the Gaussian mixture model (GMM) [22] can also be considered as a particular TMC. Using Dempster-Shafer fusion [23] in Markovian context leads to another class of TMCs with interesting possibilities of integrating different partial pieces of information in conventional HMCs [24], [25], [26], [27], [28], [29]. In addition, different uses of U can be dealt with simultaneously as, for example, in the case of nonstationary hidden semi-Markov model [26].…”