A new approach to determination of the attitude of a moving rigid body with a fixed point is suggested. The body (device) is assumed to be equipped with a satellite antenna, GNSS receiver, and a 3-axis gyro. Unlike in the traditional approach, the method does not employ accelerometers and compass. The approach relies on the fact that the body attitude can be determined from gyro readings by solving the Poisson kinematic equation if the initial attitude is known. Using the attitude matrix found and the gyro measurements, one can calculate the linear velocity of the antenna, which will be a function of an unknown initial attitude matrix. The latter is found by minimizing the functional obtained by integrating the quadratic deviation of the calculated antenna velocity from that measured by the GNSS receiver. The discussion is illustrated by numerical examples obtained by processing results of field experiments.