This paper describes the development of a gyroless attitude determination system that can rely on magnetometer and sun sensor measurements and achieve good accuracy. Vectors coming from the selected sensor data and developed models can be placed in Wahba's problem. The system uses Singular Value Decomposition (SVD) method to minimize the Wahba's loss function and determine the attitude of the satellite. In order to obtain the attitude of the satellite with desired accuracy an extended Kalman filter (EKF) for satellite's angular motion parameter estimation is designed. The EKF uses this attitude information as the measurements for providing more accurate attitude estimates even when the satellite is in eclipse. The "attitude angle error covariance matrix" calculated for the estimations of the SVD method is regarded as the measurement noise covariance for the EKF.