线性动态系统基于块采样的卡尔曼平滑推理算法

Block Sampling Inference Algorithm of Kalman Smoothing for Linear Dynamic System

针对线性动态系统在复杂噪声环境中的不确定性的传递问题,提出了用块采样推理方法逼近状态和噪声的后验分布.该方法在时序采样中,样本在基于条件独立性准则下可一次性更新,这通常比单独更新来得简单和有效.通过引入Dirichlet过程混合模型(Dirichlet Process Mixture,DPM),能够较方便地获得马尔科夫链式样本.结合卡尔曼平滑技术,使块采样算法能够在分布空间逼近基础上取得较高的精度.仿真结果显示,块采样平滑算法具有较好的效果.

Aiming at exploring the propagation property of uncertainty for dynamic system under complex noisy environments, a scheme using block sampling method was presented to approximate the posterior distribution of the states and the noise. The most prominent advantage of the method lies in its simplicity and efficiency, by which the samples can be updated once on conditional independence, other than one by one. With an introduction of the model of Dirichlet process mixture （DPM）, the samples of Markov chain can be conveniently obtained. Incorporating Kalman smoothing technique, the sampling algorithm approximately in the space of distribution has a high precision. Various simulations prove that the approach is effective.