Particle filters (PFs) are recursive Monte Carlo algorithms for Bayesian tracking and prediction in state space models. This paper addresses continuous-discrete filtering problems, where the hidden state evolves as an Itô stochastic differential equation (SDE) and observations arrive at discrete times. We propose a novel class of constrained PFs that enforce compact support on the state at each observation instant, thereby limiting exploration to plausible regions of the state space. Unlike earlier approaches that truncate the likelihood, the proposed method constrains the dynamics directly, yielding improved numerical stability. Under standard regularity assumptions, we prove convergence of the constrained filter, derive uniform-in-time error estimates, and extend the analysis to account for discretisation errors arising from numerical SDE solvers. A numerical study on a stochastic Lorenz-96 system demonstrates the practical application of the methodology when the constraint is implemented via barrier functions.

翻译：粒子滤波器（PFs）是用于状态空间模型中贝叶斯跟踪与预测的递归蒙特卡洛算法。本文针对连续-离散滤波问题展开研究，其中隐状态由伊藤随机微分方程（SDE）演化，而观测值在离散时刻获取。我们提出了一类新型约束粒子滤波器，该滤波器在每个观测时刻对状态施加紧支撑约束，从而将探索限制在状态空间的合理区域。与早期截断似然函数的方法不同，所提方法直接约束动力学过程，从而提升了数值稳定性。在标准正则性假设下，我们证明了约束滤波器的收敛性，推导了时域一致误差估计，并将分析扩展至数值SDE求解器离散误差的考量。基于随机Lorenz-96系统的数值研究展示了该方法的实际应用场景——通过势函数实现约束。