A new technique is discussed and developed for correcting atmospherically induced errors in phase data collected by radio astronomy interferometers and synthetic aperture antenna arrays. The main features of this technique are modeling and filtering the information content of the complex visibility data in time sequences. Because the atmospheric phase variations are highly correlated in time, they can be described by stochastic time series models. In conjunction with other radio astronomy data processing algorithms, a time series modeling and parameter estimation technique is developed to obtain noise models and source models from observed phase data. These models can be in the form of stochastic difference equations, autocorrelation, power spectral density, and a state space format ready for further data processing. Once the models are in a state space format, the Kalman filter is used for optimally extracting source information from the noisy data. The synthetic image is then improved by reducing the phase error. The quality of the corrected phase data is quantitatively described by the error covariance matrix of the Kalman filter. One useful application of this technique is for reducing atmospherically induced phase errors of small synthesis arrays that have too few antennas to apply self-calibration. Another application of this technique is for improving the performance of large synthesis arrays when the standard calibration methods are insufficient for correcting very noisy phase data. This technique has been tested using the very large array (VLA) (operated by the National Radio Astronomy Observatory) and the Hat Creek millimeter interferometer.