Very long baseline interferometry (VLBI) is one of the fundamental space geodetic techniques. Important goals for the next generation of VLBI technology are continuous operations as well as automated data processing. For this reason, it is necessary to introduce real time capable parameter estimation algorithms, such as Kalman filters, to VLBI data analysis. In this study, such a filter was implemented in the VLBI software VieVS@GFZ, and several aspects related to VLBI data processing were investigated. Within the corresponding module VIE_KAL it is possible, for example, to estimate all parameters important in VLBI analysis, adapt their stochastic models, flexibly define the datum, integrate external data, as well as extract datum free normal equations. The foci of the investigations were on the effects of the troposphere, the most important error source in VLBI analysis, and on the determination of station positions, which are of great importance in geodesy. For the stochastic model of the tropospheric delays, station- and time-dependent differences were considered. In comparisons with tropospheric parameters from GNSS, water vapor radiometers and numerical weather models, the Kalman filter solution yielded 5 to 15% smaller differences than a least squares solution based on the same models and VLBI data. Also in the case of estimated station coordinates, the Kalman filter solution exhibited better baseline length and station coordinate repeatabilities. The application of station-based process noise led to additional improvements. Furthermore, the Kalman filter was used to estimate subdaily station coordinate variations caused by tidal and loading effects. Finally, the findings were used to determine Kalman-filter-based global terrestrial reference frames (TRFs). For the stochastic model of the coordinate variations of particular stations, loading deformation time series were utilized. The non-deterministic approach of the Kalman filter allowed the consideration of non-linear station movement, for example, due to irregular seasonal effects or post-seismic deformations. In comparisons with a VLBI TRF solution from a classical adjustment and ITRF2008, a good agreement in terms of transformation parameters and station velocities was achieved. The findings from testing different options related to the parameterization and to the stochastic model will help to improve future reference frames.