This report studies the development of a Multiplicative Extended Kalman Filter for orbit and attitude estimation for the 10times10times20 cm CubeSat at the Norwegian University of Science and Technology (NTNU). The filter was developed in a tightly coupled manner with respect to the GPS attitude solution, based on data from differential carrier phase measurements. These measurements are aided by measurements from a three-axis magnetometer, and inertial measurements from a gyroscope. Four antennas are virtually mounted on the satellite to obtain three baselines of 1 m each. The MEKF is complemented by an integer ambiguity resolution method, which makes sure that the solution for a GPS signal is not accepted until the integrity check value for all baselines is below the acceptance threshold. Until the ambiguities are resolved, the Multiplicative EKF is reliant upon the gyro measurements, and the magnetometer. The filter has been simulated with various attitude maneuvers.The MEKF performs orbit estimation based on measurements from GPS position, velocity, and timing data, from which it estimates the Keplerian orbital parameters to determine the orbit of the craft. It operates as an ordinary EKF for this purpose. Simulation shows that the filter is able to determine the attitude and orbit of the spacecraft from the given measurements, and that it is robust to a temporary loss of the GPS measurements. However, the orbit estimator assumes a circular orbit. The quality of orbit estimates are therefore dependent on the eccentricity of the orbit.