APPENDIX
KALMAN FILTER IN THE GPS TECHNOLOGY
The use of Kalman filters for GPS data processing is a growing trend. The standard Least
Squares estimation technique is usually used when the estimation problem is overdetermined
(more observations than required to estimate the position parameters).
In kinematic applications Least Squares techniques can be applied to data on an epochby-epoch
basis. However, the parameters of interest such as the position, and/or dominant
system error parameters, are time-varying quantities. Therefore, the utilization of
techniques based on the extension of the Least Square for the data processing is the most
suitable, efficient, and optimal, thus can be considered as the most appropriate for such
applications which encompasses the concepts of prediction, filtering and smoothing.
The three concepts of prediction, filtering and smoothing are closely related can be
illustrated as following:
• The filtering concept can be defined as the process of computing the vehicle's
position in real-time, in other words when observations are made at time k t , then
the position results are computed at k t .
• The prediction concept can be defined as the computation of the expected position
of the vehicle at some consequent time k t , based on the last measurements at k−1 t
is properly termed prediction.
• The smoothing concept is when the estimation of where the vehicle was at time k t ,
once all the measurements are post-processed to time k+1 t .
Although the three procedures differ, however they can be used not only separately, but
also they can used sequentially:
• The prediction step: based on past positioning information together with a kinematic
model, the expected position and its precision at the next epoch of measurement are
computed. The kinematic model is composed, as is the measurement model, of functional