基于后向差分Delta算子的卡尔曼滤波算法及其仿真

摘要

In the high-speed sampling, the parameters of the discrete model based on delta operator tend to the original continuous-time model, and the system has a better digital characteristic when delta operator achieves, which can improve the problem of filtering divergence of discrete Kalman filters based on traditional shift operator. This article uses orthogonal projection approach to derive the Kalman filter equation of stochastic linear discrete systems based on delta operator. The recursive Kalman filter algorithm based on delta operator is given. The simulation results show that in the high-speed sampling, the convergence performance of the derived Kalman filter based on backward differentiation formula of delta operator is better than the traditional Kalman filters.%在高速采样时，Delta算子离散化模型的参数趋于原来的连续时间模型，且Delta算子实现时系统具有较好的数字特性，使其能够改善基于传统移位算子的离散卡尔曼滤波中存在的滤波发散问题。该文采用正交投影法，推导了基于Delta算子的随机线性离散系统的卡尔曼滤波方程，最终给出了基于后向差分Delta算子的卡尔曼滤波递推算法，并进行了仿真研究。实验结果和性能分析表明，在高频采样情形下基于后向差分Delta算子的递推卡尔曼滤波的收敛性能优于常规卡尔曼滤波。