In this article, we introduce parallel-in-time methods for state and parameter estimation in general nonlinear non-Gaussian state-space models using the statistical linear regression and the iterated statistical posterior linearization paradigms. We also reformulate the proposed methods in a square-root form, resulting in improved numerical stability while preserving the parallelization capabilities. We then leverage the fixed-point structure of our methods to perform likelihood-based parameter estimation in logarithmic time with respect to the number of observations. Finally, we demonstrate the practical performance of the methodology with numerical experiments run on a graphics processing unit (GPU).
翻译:在本文中,我们介绍了使用统计线性回归和迭代统计后验线性化模型进行状态和参数估计的时域并行方法,用于一般的非线性非高斯状态空间模型。我们还将所提出的方法重新表述为平方根形式,从而提高了数值稳定性,同时保持了并行化能力。然后,我们利用所提出方法的固定点结构,用对数时间相对于观测次数的方式进行基于似然的参数估计。最后,我们借助在图形处理单元(GPU)上运行的数值实验,展示了该方法的实际性能。