Quaternion Method of Calculating Angles while Measuring via Goniometric Precision Instrument System

Abstract

The article is devoted to the topical problem: increasing accuracy and performance of angle measurements necessary in various branches of science and technology. One of the ways of increasing accuracy and performance of angle measurements is using modern algorithmic methods and mathematic devices for processing measurement information. Thus, in order to increase accuracy and speed of angle measurements on the example of the well-known goniometric precision instrument system (GPIS), it was offered quaternion calculation of angle values while performing goniometric measurements in the work. The efficiency of quaternion calculation is unquestioned as quaternions unlike other traditional methods (in particular matrix with the use of Euler angles, direction cosines) are presented only with four parameters describing angle positions of the objects and have only one connection equation unlike six equations for matrix methods, in particular for direction cosines. The suggested quaternion calculation is used in GPDS as general theoretic and information basis of contactless precision goniometric measurements in preliminary setting navigation sensitive elements (NSE), plane angles, pyramid prisms etc. The usage of the developed quaternion calculation enabled to increase accuracy by 0,25'' (in 3 times) and measurement performance in 9 times (up to 6.5 sec.) in comparison with the famous ones. Applying quaternion calculation of angle values implies using a smaller RAM capacity of PC that increases performance of system work. Besides, a smaller amount of mathematic operations performed in quaternion way of calculating angles, except increasing performance, enables to decrease a rounding error in calculation results that is accumulated in multiple measurements and may reach great values. Thus, accuracy and performance of measurements increase.