Title: Alpha-Beta HMM: Hidden Markov Model Filtering with Equal Exit Probabilities and a Step-Size Parameter Show Chinese title

Title: α-β隐马尔可夫模型：具有相等退出概率和步长参数的隐马尔可夫模型滤波器

Abstract: The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we propose the $\alpha\beta$-HMM algorithm, which simplifies the state transition model to a Markov chain with equal exit probabilities and introduces a step-size parameter to balance the influence of observational data and the model. By analyzing the algorithm's dynamics in stationary environments, we uncover a fundamental trade-off between inference accuracy and adaptation capability, highlighting how key parameters and observation quality impact performance. A comprehensive theoretical analysis of the nonlinear dynamical system governing the evolution of the log-belief ratio, along with supporting numerical experiments, demonstrates that the proposed approach effectively balances adaptability and inference performance in dynamic environments. Show Chinese abstract

Abstract: 隐马尔可夫模型（HMM）为随时间变化的环境中提供了强大的推理框架，在这种环境中，潜在状态根据马尔可夫链演化。 为了处理一般动态环境下的最优滤波问题，我们提出了$\alpha\beta$-HMM 算法，该算法将状态转移模型简化为具有相等退出概率的马尔可夫链，并引入了一个步长参数以平衡观测数据和模型的影响。 通过分析算法在平稳环境中的动态特性，我们揭示了推理准确性与适应能力之间的一种基本权衡关系，强调了关键参数和观测质量对性能的影响。 对控制对数信念比演化的非线性动力系统进行全面理论分析，辅以支持性的数值实验，表明所提出的方法在动态环境中有效地平衡了适应性和推理性能。