条件线性状态空间模型Rao-Blackwellized卷积滤波算法

针对条件线性高斯状态空间模型，提出一种新的状态滤波方法，称为Rao-Blackwellized卷积滤波（Rao-Blackwellized convolution filtering, RBCF）算法，算法用卷积滤波器（convolution filter, CF）估计模型中的非线性状态，用卡尔曼滤波器 （Kalman filter, KF）估计线性状态；与Rao-Blackwellized粒子滤波器（Rao-Blackwellized particle filter， RBPF）相比，算法使用了基于核函数的CF，提高了在小噪声条件下的估计精度。RBCF滤波算法应用于机动目标跟踪的仿真结果表明：在小噪声条件下,RBCF的估计精度明显高于RBPF，其对位置和速度估计的均方根误差比RBPF低一个数量级以上。而且随着噪声进一步的减小，这种优势将更加明显。

Rao-Blackwellized convolution filtering algorithm for conditionally linear Gaussian state space models

A new filtering method, called as the Rao-Blackwellized convolution filtering (RBCF) algorithm, is presented for conditional linear Gaussian state space models. The method uses a convolution filter (CF) to estimate the nonlinear states of the model while its linear states are estimated by the Kalman filter (KF). The new algorithm, which uses CF based on the kernel function, improves the precision of estimation compared with the Rao Blackwellized particle filter (RBPF) when the noise is low. The simulation results of the proposed method applying to tracking the maneuver target show that the estimate precision of the RBCF is obviously higher than the RBPF,  and the root mean square error (RMSE) of position and velocity is lower by more than an order of magnitude comparing with RBPF, when the noise is low. The tendency is more obvious as the noise become lower.