We discuss the application of Kalman filtering techniques to the analysis of very long baseline interferometry (VLBI) data. The VLBI observables are geometrically related to the geodetic and astrometric parameters which can be determined from them. However, contributions to the observables from the clocks at, and the atmospheres above, the VLBI sites must be accounted for if reliable estimates of geodetic and astrometric parameters are to be obtained. Here an implementation of a Kalman filter to account for stochastic behavior on those parameters which vary during the course of a VLBI experiment is discussed. Both the nature of the stochastic processes which should be used in the model for the VLBI data and the implementation of the Kalman filter estimator are considered. From the results obtained, we conclude that the Kalman filter is appropriate for analyzing VLBI data. The choice of stochastic model does not unduly affect the estimates of the geodetic parameters and the quality of these esimates is higher than that for conventional weight least squares estimators. ¿ American Geophysical Union 1990