基于严密Helmert方差分量估计的动态Kalman滤波

Variance Component Estimation of Helmert Type-Based Dynamic Kalman Filtering

针对Kalman滤波模型推导了严密的Helmert方差分量估计公式.在此基础上,构建了方差分量估计辅助的Kalamn滤波解,改进的Kalman滤波与标准Kalman滤波的计算过程基本相同.推导了方差分量估计对Kalman滤波解的影响.理论推导和计算结果均表明,Helmert方差分量估计辅助的Kalman滤波能够合理调控动力学模型误差的影响,合理平衡观测信息与动力学模型信息对Kalman滤波解的贡献,提高状态参数估计的精度;严密Helmert方差分量估计与简化Helmert方差分量估计辅助的Kalman滤波解基本等效.

A variance component estimator of Helmert typebased dynamic Kalman filtering is derived in this paper. The corresponding Kalman filtering supported by estimated variance components is given, which is very similar to the standard Kalman filtering in calculation. The influence functions of the variance components or the ratio of the variance components on the state estimates of the Kalman filter are a/so deduced. The theoretic formulae and an actual example show that the error influences of the dynamic model information on the dynamic state estimates can be controlled, the contribution of the measurements and the dynamic model information to the dynamic state estimates can be balanced, and the accuracy of the new Kaman filtering is improved by using the variance component estimation. The results of the modified Kalman filters by using the rigorous and approximate Helmert type estimates of variance components are nearly equal.