State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that uses a pair of neural networks to learn the proposal distribution and transition distribution of a particle filter. Both distributions are approximated using multivariate Gaussian mixtures. The component means and covariances of these mixtures are learnt as outputs of learned functions. Our method is trained targeting the log-likelihood, thereby requiring only the observation series, and combines the interpretability of state-space models with the flexibility and approximation power of artificial neural networks. The proposed method significantly improves recovery of the hidden state in comparison with the state-of-the-art, showing greater improvement in highly non-linear scenarios.

翻译：状态空间模型是分析序列数据的常用统计框架。在该框架下，粒子滤波常被用于非线性状态空间模型的推断。本文提出一种新方法StateMixNN，该方法利用一对神经网络学习粒子滤波的提议分布与状态转移分布。两种分布均通过多元高斯混合模型进行近似，其各分量的均值与协方差通过学习得到的函数输出。本方法以对数似然为训练目标，仅需观测序列即可训练，兼具状态空间模型的可解释性与人工神经网络的灵活逼近能力。相较于现有最优方法，所提方法显著提升了隐状态的恢复精度，在高度非线性场景中改进尤为明显。