Some aspects of Kalman filtering
Abstract
In hydrography and surveying the use of kinematic positioning techniques is nowadays very common. An optimal estimate of position of the kinematic user is usually obtained by means of the Kalman filter algorithm. Dynamic and measurement models are established for a discrete time, time varying system. Some problems in establishing such a model are addressed. Based on this model and the derived Kalman filter several aspects of Kalman filtering that are important for kinematic positioning applications are discussed.
Computational and numerical considerations indicate that so-called covariance filers are to be used for kinematic positioning, and a specific covariance filter mechanization is described in detail. For some special applications linear smoothing techniques lead to considerable improve estimation results. Possible applications of smoothing techniques are reviewed. To guarantee optimal estimation results the analysis of the performance of Kalman filters is essential. Misspecification in the filter model can be detected and diagnosed. The performance analysis is based on the innovation sequence.
Overall, this report presents a detailed analysis pf some aspects of Kalman filtering.