Adaptive fitting of systematic errors in navigation

To use Kalman filtering for kinematic positioning and navigation, we have to deal with both observational and kinematic models. Both of the functional models may contain global or local systematic errors. The influence functions of the systematic errors on the estimates of kinematic states are derived. An adaptive fitting method for systematic errors of the observations and kinematic model errors is presented. The systematic errors are fitted with a mean or a weighted mean by using the residuals of observations and residuals of predicted states within a chosen time window. The covariance matrices of the modified observations and the predicted states are estimated within the same window. The estimation formulae and calculation strategy, as well as a real example, are given. It is shown by theory and calculations that Kalman filtering based on the adaptive fittings of the systematic errors and covariance matrices can, to some degree, resist the influences of systematic errors on the estimated states of navigation.