We present a system that processes phase and group delay time series from a network of dual-frequency GPS receivers and produces a dynamic ionospheric model that is consistent with all the input data. The system is intended for monitoring the ionosphere over a fixed geographical area with dimensions of the order of several thousand kilometers. The inversion technique utilized in this system stems from the inversion technique previously developed by our group within the Coordinate Registration Enhancement by Dynamic Optimization (CREDO) project (a software package for inverting the vertical sounding, backscatter sounding, and satellite total electron content (TEC) data for over-the-horizon radar). The core of this technique is Tikhonov's methodology for solving ill-posed problems. We extended the method to multidimensional nonlinear inverse problems and developed techniques for fast numerical solution. The resulting solution for the ionospheric distribution of electron density is guaranteed to be smooth in space and time and to agree with all input data within errors of measurement. The input data consist of time series of absolute TEC and relative TEC (directly calculated from the raw dual-frequency group delays and phase delays, respectively). The system automatically estimates the measurement noise and receiver-transmitter biases. We test the system using archived data from dual-frequency GPS receivers in the southern California Scripps Orbit and Permanent Array Center (SOPAC) network and data from a vertical sounder.