Diffuse Kalman filtering with linear constraints on the state parameters

We give a general proof, based on Piet de Jong’s diffuse Kalman filter, that imposing linear constraints on state smoothing is still feasible under diffuse initialization. We also offer simple derivations of existing identities related to the diffuse Kalman filter and smoother.本文基于皮特·德容（Piet de Jong）提出的扩散卡尔曼滤波器（diffuse Kalman filter），给出了一般性证明：在扩散初始化条件下，对状态平滑施加线性约束仍然具有可行性。此外，本文还针对与扩散卡尔曼滤波器及平滑器相关的现有恒等式，提供了简洁的推导过程。