Questions related to description and algorithms for device (platform) used to identify space orientation and vertex angle of right circular cone are considered. The main measuring facility - rate gyro attached rigidly to measuring platform is used. Reference frame of platform coincides with gyro frame. For getting solution of the task pointed out above it is suggested to organize three stage process. First-measuring the Earth angular rate; second - carrying the measuring platform by operator from one initial position served as a reference to another desired one (cone surface) and third-performing measurements by relocating the platform on cone surface without loss of contact. The most important stage - performing the measurements. To try out the third stage it was worked out an environmental simple software-based simulator. To delete disturbances from operator activity it is suggested to measure the vertical axis angular direction of reference platform frame in current platform position. So properties of dot and cross products for platform different angular positions (for vertical axis only) are used together with procedure of kinematic equation integration. Mathematical description and processing algorithms are given to perform on-line treatment of current measurement data and get the estimates of orientation and vertex angle. Experiments were performed on software-based simulator which showed good results. It is turned out the suggested approach may be extended to more wider area of application as estimation of mutual orthogonality of separate construction elements and so on.