Adaptively robust filtering for kinematic geodetic positioning

The Kalman filter has been applied extensively in the area of kinematic geodetic positioning. The reliability of the linear filtering results, however, is reduced when the kinematic model noise is not accurately modeled in filtering or the measurement noises at any measurement epoch are not normally distributed. A new adaptively robust filtering is proposed based on the robust M (maximum-likelihood-type) estimation. It consists in weighting the influence of the updated parameters in accordance with the magnitude of discrepancy between the updated parameters and the robust estimates obtained from the kinematic measurements and in weighting individual measurements at each discrete epoch. The new procedure is different from functional model-error compensation; it changes the covariance matrix or equivalently changes the weight matrix of the predicted parameters to cover the model errors. A general estimator for an adaptively robust filter is developed, which includes the estimators of the classical Kalman filter, adaptive Kalman filter, robust filter, sequential least-squares adjustment and robust sequential adjustment. The procedure can not only resist the influence of outlying kinematic model errors, but also controls the effects of measurement outliers. In addition to the robustness, the feasibility of implementing the new filter is achieved by using the equivalent weights of the measurements and the predicted state parameters. A numerical example is given to demonstrate the ideas involved.