Latent variable models are widely used to perform unsupervised segmentation of time series in different context such as robotics, speech recognition, and economics. One of the most widely used latent variable model is the Auto-Regressive Hidden Markov Model (ARHMM), which combines a latent mode governed by a Markov chain dynamics with a linear Auto-Regressive dynamics of the observed state. In this work, we propose two generalizations of the ARHMM. First, we propose a more general AR dynamics in Cartesian space, described as a linear combination of non-linear basis functions. Second, we propose a linear dynamics in unit quaternion space, in order to properly describe orientations. These extensions allow to describe more complex dynamics of the observed state. Although this extension is proposed for the ARHMM, it can be easily extended to other latent variable models with AR dynamics in the observed space, such as Auto-Regressive Hidden semi-Markov Models.

翻译：隐变量模型广泛应用于不同场景下时间序列的无监督分割，例如机器人学、语音识别和经济学。其中最常用的隐变量模型之一是自回归隐马尔可夫模型（ARHMM），该模型将由马尔可夫链动力学控制的隐模式与观测状态的线性自回归动力学相结合。本文提出ARHMM的两种推广形式。首先，在笛卡尔空间中提出一种更广义的自回归动力学，将其描述为非线性基函数的线性组合。其次，在单位四元数空间中提出线性动力学机制，以合理描述方向信息。这些扩展使得观测状态的动力学描述更具复杂性。尽管本扩展针对ARHMM提出，但可便捷推广至其他具有观测空间自回归动力学的隐变量模型，例如自回归隐半马尔可夫模型。