Adaptive Methods of Kalman Filtering for Personal Positioning Systems

Kalman filtering is very efficient for data fusion, in which the definition of the process and measurement noises (i.e. the matrices Q and R, respectively) greatly influences the filter performance. In recent years several studies reported that adjustments of Q and R can be helpful to reduce the errors of the estimations. In this paper, various methods for making adjustments to the matrices Q and R are introduced for the particular case of Personal Positioning Systems (PPS). The aim is to observe the improvements achieved in an extended Kalman filter when adaptive methods are applied, in other words to observe their influence on the user's path obtained. These adjustments are considered to be needed because environmental conditions in such systems are often not fixed. The methods to be analyzed are: (1) the weighted Kalman filter; (2) scaling matrix Q (3) adjustments of Q and R based on sequence-innovation; and (4) a combination of the method (2) and (3), i.e. Q is estimated by applying a scale factor and adjustments to R are realized in accordance with the method (3). Given that the filter may diverge, we use the 2 χ test to evaluate validity of the estimations, which is based on the analysis of the innovations. Individual components of the innovation vector are evaluated in order to correct or eliminate wrong information for data fusion. The PPS is based on the Dead Reckoning (DR) algorithm. The errors of the DR parameters are estimated with an Extended Kalman Filter (EKF), which combines the measurements of a GPS and an inertial measurement unit (IMU). The results show that each method allows us to obtain consistent Kalman filtering and they help to obtain better user’s trajectories, but additional techniques and/or technologies should be used.