Orientation Information Extraction Using Three Components of Vector Observations

This article proposes methods for orientation information extraction using only three components of observations. In two vector situation, the norm equation and the dot production equation are used to estimate the unavailable components, and then the results are used to estimate the orientation; in one vector situation, all possible orientations are described by a function of one variable, from which the formulas for determining limited ranges of Euler angles are derived. The proposed methods are experimentally verified with real sensor data and simulation data in multiple orientations. It is found that a combination of three vector observation components contains effective orientation information, but the information is incomplete and varies with the situation and orientation; in a two vector situation, the method can get at most four orientation estimations in general and even a unique estimation in a special orientation, the rms error of yaw, pitch, and roll estimations in experiments are, respectively, 2.7°, 1.4°, and 2.2°; in one vector situation, the method can always get two Euler angles with smaller ranges than their full ranges, and the spans of the ranges can even reduce to zero in some orientations.