Abstract
Introduction. Calculative algorithms of Strapdown inertial navigation systems (SINS) can be divided on navigation algorithms, which transform accelerometers output signals into local coordinates and attitude algorithms, which transform gyroscopes output signals into vehicle angular attitude [1]. Wherein, navigation task solution requires double integration of acceleration and attitude task – integration of kinematic attitude equation, related measured object angular velocity with attitude parameters.Paper considered of autonomous position determination methods based on vehicle angular velocity information without acceleration measurement. Thus, attitude algorithms are considered only.Paper researched the errors of algorithm based on quaternion attitude equation, moreover algorithm error drifts were accepted as a main accuracy characteristicThe main part. Algorithm researched by imitation modeling of vehicle’s computer with SINS attitude algorithm. The main task of modeling is defining depends between algorithm drift and sensor’s call step in cases of different frequencies and amplitudes of base angular oscillations. It was researched four one-step algorithms: reverse, based on modified Euler method; Picard method with two successive approximations and the new author’s algorithm which combines formulas of first two algorithms. It was studied depends of algorithm drift and faze shift between two orthogonal axes oscillations. It was shown, the biggest drift values are obtained in case of base conning movement. It was made the modeling researches of algorithm drift amplitudes relatively to sensor sample steps and oscillation frequencies in dimensionless form. It was shown, substantial increase new algorithm accuracy compared to other researched.Conclusions. The algorithm drift accuracy of new algorithm in 2600 times exceeds the revers algorithm. Small modification of one-step algorithm allowed increase accuracy in few orders, almost without computing increase. Received results allows to expend attitude algorithms application area and prognose their accuracy with different base movement.
Highlights
Calculative algorithms of Strapdown inertial navigation systems (SINS) can be divided on navigation algorithms, which transform accelerometers output signals into local coordinates and attitude algorithms, which transform gyroscopes output signals into vehicle angular attitude [1]
Paper considered of autonomous position determination methods based on vehicle angular velocity information without acceleration measurement
Paper researched the errors of algorithm based on quaternion attitude equation, algorithm error drifts were accepted as a main accuracy characteristic
Summary
There are known six types of kinematic parameters [2]: − Euler-Krylov rotation angles; − directional cosines between navigation and base frames; − Euler orientation vector; − Gibbs and Rodrigo rotation vectors which are variants of orientation vector; − quaternions of rotation [3]. The final result of computer simulation is defining the dependence between attitude integration algorithm errors and sensors polling rate with different base angular oscillation amplitudes and frequencies. One-step revers algorithm One-step revers algorithm is commonly used in practice currently It calculates quaternion values on n-th step by known value on (n-1)-th step and measured angular rate at the same times by formulas: λn 0. One-step Runge-Kutta integration method of second-order accuracy was applied to Matlab in algorithm RK21: function [tout,yout]=RK21(Zpfun,h,t,y) k1=feval(Zpfun,t,y); k2=feval(Zpfun,t+h,y+h*k1); F=(k1+k2)/2; yout=y+h*F; tout=t+h; If RK21 applies to quaternion attitude equation, Zpfun parameter need to assign a name of right part quaternion attitude equation calculating function, for example ZPfun ='KwUrAtt'.
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