Sapegin O. Improvement of methods and algorithms for determining attitude parameters for strapdown inertial navigation system

The thesis describes the development of an information model for determining the orientation parameters of high precision SINS. A detailed substantiation and study of methods for calibration of sensitive elements: accelerometers and gyroscopes. It was created the simulation model, which allows studying different calibration methods. The mathematical model of sensors output signal was increased by adding stands and sensors errors. It was compared the eight-position method for accelerometer calibration with new spatial method. One axis rotation method for gyroscopes calibration was compared with spatial calibration approach as well. Mean values and standard deviation of method's errors according to stand equipment and sensors 24 hardware random errors was studied. The specifications of real navigation accelerometer and ring laser gyroscope were used for testing calibration methods. The high accuracy of the spatial calibration method of the inertial measuring unit in comparison with the wellknown ones is confirmed. The main approaches to synthesis of attitude algorithms presented. It was described the main types of attitude kinematic parameters such as directional cosines matrix, Euler's rotation vector and quaternions. All of these parameters describe the same attitude of body frame about inertial frame. Transformations of some parameters into others were shown as well transformations into Euler–Krylov. Different methods of numerical integration of attitude equations such as low accurate squares and trapeziums, predictor–corrector Runge–Kutta and Picard methods were presented. A simulation model of a strapdown inertial attitude system has been developed. The model contains procedures for modeling an angular motion of the base, numerical integration of kinematic equations and a block for comparing and studying the obtained results. It was tested a several Picard methods for integration of Bortz's equation with different integration steps. This well-known methods was compared with Picard methods for Poisson's kinematic equation. All tests were made for conning motion, which is the most dangerous for all types of inertial systems. In consist of two harmonic angular oscillations around two body axes. It leads to an algorithm drift of the third angle. An empirical dependence the error drift was obtained. It makes possible to assess the accuracy of any integration method. Research shows, the use of the three-step Picard method of the fourth accuracy order for the integration the Poisson's kinematic equation is the best for the synthesis of the attitude system algorithmic software. A method for compensating the algorithmic drift of attitude system due to the conning motion of the base is proposed. This method allowed to compensate the algorithmic drift more than an one order. An information model of a strapdown inertial attitude system is constructed. It was designed to work with real signals of the inertial measuring unit of the navigation system. The software algorithm contains a set of procedures for calibrating the output signals of sensitive elements, calculating the initial value of the directional cosines matrix by conducting an initial exhibition and calculating the kinematic parameters of object attitude by numerical integration the Poisson's kinematic equation by Picard's method. The output signals of accelerometers and ring laser gyroscopes of high-precision SINS were used for testing and studying the model. The information model confirmed its adequacy by working on a fixed base. System was showed the imaginary drift of attitude, according to real local values of Earth's angular rate projections. The integration algorithm was expanded to consider this imaginary drift. Information model of attitude system was tested by constant angular rotation of the stand around each axis. The errors of system were in the accuracy orders of gyroscopes, which showed the great accuracy of software. Final tests were made for conning motion of base. It was several different motions with their own amplitudes and frequencies but the phase was ninety degrees. System showed the great accuracy, but conning frequencies was not big enough to see an algorithm drift.