Результаты поиска по 'hidden Markov models':
Найдено статей: 2
  1. Tsyganova J.V., Tsyganov A.V.
    LD filter for the state estimation of pairwise Markov models
    Computer Research and Modeling, 2026, v. 18, no. 4, pp. 747-764

    The paper addresses the state estimation problem for pairwise Markov models with Gaussian noises. The class of pairwise Markov models generalizes the classical hidden Markov models. The key difference lies in the assumption that the Markov property holds not for the hidden process alone, but for the pair consisting of the state and the observation. This allows modeling more complex dependencies and, in particular, eliminates the requirement of Markovianity for the hidden process. For linear Gaussian pairwise models, Kalman filtering methods remain applicable, leading to the concept of the pairwise Kalman filter.

    This work proposes a new modification of the pairwise Kalman filter based on the application of modified weighted Gram – Schmidt orthogonalization and the LD decomposition of covariance matrices. The main results are as follows: a novel LD modification of the pairwise Kalman filter (Theorem 1); a new LD-PKF algorithm for state estimation of pairwise Markov models, based on a direct procedure of modified weighted Gram–Schmidt orthogonalization and LD decomposition of covariance matrices (algorithm 2); results of comparative analysis on the numerical properties of pairwise discrete filtering algorithms.

    The obtained theoretical results complement the theory of pairwise filtering in the class of linear discrete pairwise Markov models with Gaussian noises.

    The developed algorithm is implemented in MATLAB. A series of numerical experiments are conducted, and the results demonstrate its effectiveness and numerical advantages over other existing modifications of the pairwise Kalman filter.

    The presented results can be further used to develop new methods for parameter identification of pairwise Markov models.

    Keywords: pairwise Markov model, pairwise Kalman filter, MWGS orthogonalization, LD factorization, discrete-time filtering algorithm.
  2. Kondratyev M.A.
    Forecasting methods and models of disease spread
    Computer Research and Modeling, 2013, v. 5, no. 5, pp. 863-882

    The number of papers addressing the forecasting of the infectious disease morbidity is rapidly growing due to accumulation of available statistical data. This article surveys the major approaches for the shortterm and the long-term morbidity forecasting. Their limitations and the practical application possibilities are pointed out. The paper presents the conventional time series analysis methods — regression and autoregressive models; machine learning-based approaches — Bayesian networks and artificial neural networks; case-based reasoning; filtration-based techniques. The most known mathematical models of infectious diseases are mentioned: classical equation-based models (deterministic and stochastic), modern simulation models (network and agent-based).

    Keywords: morbidity forecasting, point-to-point estimates, regression models, ARIMA, hidden Markov models, method of analogues, exponential smoothing, SIR, Rvachev–Baroyan model, cellular automata, populationbased models, agent-based models.
    Views (last year): 71. Citations: 19 (RSCI).

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