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：本文介绍了一种利用统计线性回归和迭代统计后验线性化范式，对一般非线性非高斯状态空间模型进行状态和参数估计的并行时域方法。我们还以平方根形式重新表述了所提方法，从而在保持并行化能力的同时提高了数值稳定性。接着，我们利用方法的定点结构，以观测量数量的对数时间进行基于似然的参数估计。最后，通过图形处理器（GPU）上运行的数值实验，展示了该方法在实际中的性能表现。