Variance component estimation of Helmert type-based dynamic Kalman filtering

A variance component estimator of Helmert type-based 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 also 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.