A new approach to determining the attitude of a rigid body is suggested, which does not rely on the use of magnetometers. In the framework of this approach, the problem of determining the attitude reduces to solving a minimization problem for a function of three variables (angles characterizing the initial attitude of the body). The proposed method can be employed in precise geodetic measurements carried out with the use of a geodetic pole with a satellite antenna and an IMU installed on its top when, for some reasons, the surveyor cannot position the pole vertically (e.g., near walls or buildings). The use of the traditional approach, which relies on a compass and accelerometers, in this case does not ensure the desired accuracy of the attitude determination due to magnetic disturbances (both external ones and those induced by the receiver) affecting badly compass readings. The discussion is illustrated by results of field experiments