Hidden Markov Models (HMMs) provide a rigorous framework for inference in dynamic environments. In this work, we study the alpha-HMM algorithm motivated by the optimal online filtering formulation in settings where the true state evolves as a Markov chain with equal exit probabilities. We quantify the dynamics of the algorithm in stationary environments, revealing a trade-off between inference and adaptation, showing how key parameters and the quality of observations affect performance. Comprehensive theoretical analysis on the nonlinear dynamical system that governs the evolution of the log-belief ratio over time and numerical experiments demonstrate that the proposed approach effectively balances adaptation and inference performance.

翻译：隐马尔可夫模型为动态环境中的推理提供了一个严谨的框架。在本工作中，我们研究了由最优在线滤波公式所激发的alpha-HMM算法，该公式适用于真实状态以具有等退出概率的马尔可夫链演化的场景。我们量化了算法在平稳环境中的动态特性，揭示了推理与适应之间的权衡，并展示了关键参数和观测质量如何影响性能。对控制对数置信比随时间演化的非线性动力系统的全面理论分析以及数值实验表明，所提出的方法有效地平衡了适应性与推理性能。