Fittings of Systematic Errors and Covariance Matrices in Navigation
YANG Yuan-xi~1, ZHANG Shuang-cheng~2 (1. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China; 2. School of Geological and Surveying Engineering, Chang'an University, Xi'an 710054, China)
Using Kalman filtering for kinematic positioning and navigation we have to deal with an observational model and a dynamic model. Both of the functional models may contain systematic errors or local systematic errors. Adaptive fittings for both the systematic errors and covariance matrices of the model errors by using moving windows are presented. The systematic errors are fitted by using the residuals of observations and residuals of predicted states within chosen window. The covariance matrices of the modified observations and the modified predicted states are estimated within the same window, which are different from those of Sage filtering. The observations and the predicted states are then modified. The estimation formulae and calculation strategy as well as an example are given. It is shown by the theory and calculation that Kalman filtering, based on the adaptive fittings of the systematic errors and covariance matrices, can in some degree resist the influences of the systematic errors on the estimated states of navigation.