Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian trend and seasonal components, many real-world systems require more expressive representations. GP-SSMs address this need by learning transition functions directly from data, while particle filtering enables Bayesian state estimation even when posterior distributions deviate from Gaussianity. This paper develops a particle-filtering framework for GP-SSM inference and compares its performance with the Kalman filter in trend extraction and seasonal adjustment. We further evaluate nonlinear signal-extraction tasks, demonstrating that GP-SSMs can recover latent states under sharp or asymmetric dynamics. The results highlight the utility of combining GP modeling with sequential Monte Carlo methods for complex time-series analysis.

翻译：高斯过程状态空间模型（GP-SSMs）为建模非线性或难以参数化描述的时间序列动态提供了一种灵活的非参数化替代方案。尽管卡尔曼滤波器在线性高斯趋势与季节成分处理中表现优异，但许多实际系统需要更具表达能力的表示方法。GP-SSMs通过直接从数据中学习转移函数来满足这一需求，而粒子滤波则能在后验分布偏离高斯分布时仍实现贝叶斯状态估计。本文开发了用于GP-SSM推断的粒子滤波框架，并在趋势提取与季节调整任务中将其性能与卡尔曼滤波器进行比较。我们进一步评估了非线性信号提取任务，证明GP-SSMs能够在剧烈或非对称动态下恢复潜在状态。研究结果凸显了将高斯过程建模与序贯蒙特卡洛方法相结合在复杂时间序列分析中的实用价值。