In this article, we derive an optimal transportation particle filter for linear time-varying systems with correlated noises. This method can be regarded as the extension of the feedback particle filter with an optimal transportation structure. However, the particles in our method are evolved in a deterministic way, while we need to generate random particles in a feedback particle filter. Consequently, we only need a very few particles to obtain the satisfying results, and this property is especially significant for high-dimensional problems. The error analysis of our method and the feedback particle filter has been carried out when the system is time invariant. Compared with the feedback particle filter and the ensemble Kalman filter, our method shows great efficiency in numerical experiments, including both the scalar and high-dimensional cases.

在这篇文章中，我们为具有相关噪声的线性时变系统推导了一个最优传输粒子滤波器。该方法可以看作是具有最优传输结构的反馈粒子滤波器的扩展。然而，我们方法中的粒子是以确定性方式进化的，而我们需要在反馈粒子滤波器中生成随机粒子。因此，我们只需要很少的粒子就可以获得令人满意的结果，这一性质对于高维问题尤为重要。我们的方法和反馈粒子滤波器的误差分析是在系统时不变的情况下进行的。与反馈粒子滤波器和集合卡尔曼滤波器相比，我们的方法在数值实验中表现出很高的效率，包括标量和高维情况。