Radio frequency interference (RFI) limits radio astronomy observations, while flagging discards contaminated data and reduces sensitivity. This thesis develops TABASCAL (Trajectory-Based RFI Subtraction and Calibration), a Bayesian method for removing post-correlation interference from radio-interferometric measurements. TABASCAL jointly models astronomical visibilities, antenna gains, and signals from multiple moving RFI sources. It combines trajectory and geometric-delay models with Gaussian-process descriptions of unknown, time-varying RFI amplitudes. This structure exploits the spatial signatures of astronomical and interfering sources while accommodating closure errors and using strong interference to constrain phase calibration. Tests on simulations show that TABASCAL can recover astronomical signals and calibration solutions from contaminated observations, producing results comparable to uncontaminated data and outperforming data flagging. The method is computationally demanding and the thesis focuses on simulated observations, but early real-data tests are promising. The work establishes a foundation for scalable RFI subtraction in future radio telescope facilities worldwide, including the Square Kilometre Array.