Observability of a rigid body with a fixed point equipped with laser retroreflectors

A rigid body with fixed point equipped with laser retroreflectors is considered. The body is lighted up with laser beam and distance to the retroreflectors is computed from the time of the beam returning. A possibility of attitude determination from one-shot measurements is examined and a possibility of rotation determination of the body from these measurements is disclosed in the case when the rotation belongs to some certain kind. Solubility of system of equation builded in the attempt of rotation determination is substantiated when the rotation is regular precession or small-amplitude oscillation.