初值偏差对线性系统状态向量Kalman滤波的影响

发布时间：2018-09-01 09:49

【摘要】：Kalman滤波在系统控制、信号处理和飞行器导航等领域有广泛应用.众所周知,Kalman滤波是建立在一组递推计算的滤波算法.不准确的初始值设置是否影响状态滤波结果,这是实际应用Kalman滤波时必须关注和解决的问题.本文在推导滤波初始值与系统真实初态之间偏差对滤波结果影响的基础上,建立了初始值偏差对后续滤波影响的传递关系,以及滤波结果收敛的充分条件;通过设置多组不同初始值偏差,分别对某三阶可观测系统和不可观测系统进行了仿真计算及结果分析,验证了滤波初始值偏差会导致滤波结果发生明显偏离.研究结果揭示,即使是可观测的线性系统,采用Kalman滤波时也必须尽可能选取准确的初始值.
[Abstract]:Kalman filter is widely used in system control, signal processing and aircraft navigation. It is well known that Kalman filtering is a filtering algorithm based on a set of recursive calculations. Whether the inaccurate initial value will affect the state filtering results is a problem that must be paid attention to and solved in the practical application of Kalman filtering. Based on the derivation of the effect of the deviation between the initial value of the filter and the real initial state of the system on the filtering results, the transfer relation of the effect of the initial value deviation on the subsequent filtering and the sufficient conditions for the convergence of the filtering results are established. By setting several sets of different initial value deviations, the simulation and analysis of a third order observable system and a non-observable system are carried out, respectively. It is verified that the deviation of the initial value of the filter will cause the obvious deviation of the filtering result. The results show that even for observable linear systems, the accurate initial values must be chosen as far as possible when using Kalman filtering.
【作者单位】：西安理工大学;航天器故障诊断与维护重点实验室;
【基金】：国家自然科学基金(61473222,91646108)资助~~
【分类号】：TN713

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