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IssuesArchive of Issues2002-1pp.13-25

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Yu. A. Litmanovich, "Determination of parameters of angular and linear motions of a rigid body according to the inertial information in the form of increments of multiple integrals of the parameters to be measured," Mech. Solids. 37 (1), 13-25 (2002)
Year 2002 Volume 37 Number 1 Pages 13-25
Title Determination of parameters of angular and linear motions of a rigid body according to the inertial information in the form of increments of multiple integrals of the parameters to be measured
Author(s) Yu. A. Litmanovich (St. Petersburg)
Abstract We consider the problems of determining the parameters of the angular and linear motions of a rigid body by means of integration of the kinematic and navigational equations. We assume that the inertial information is given by increments of multiple integrals of the angular velocity and apparent acceleration of the body represented in the body-fixed reference frame. Two approaches-smoothing and invariant-are proposed for the synthesis of numerical algorithms solving these problems. For each of these approaches, we present a technique for synthesizing the algorithms, give examples of such algorithms, and obtain expressions for their errors. Separately, we consider the problem of the integration of the velocity in an inertial basis. A precise discrete-time algorithm has been obtained which can be implemented for the inertial information represented in the form indicated above. The results of the numerical simulation of the conventional and new algorithms are presented. During the simulation we take into account high-frequency harmonic components in the readings of the inertial meters which cause systematic errors.
References
1.  D. V. Lebedev and A. I. Tkachenko, Inertial Control Systems: Algorithmic Aspects [in Russian], Naukova Dumka, Kiev, 1991.
2.  A. P. Panov, Mathematical Fundamentals of the Theory of Inertial Orientation [in Russian], Naukova Dumka, Kiev, 1995.
3.  V. N. Branets and I. P. Shmyglevskii, Introduction to the Theory of Strapdown Inertial Navigation Systems [in Russian], Nauka, Moscow, 1992.
4.  P. G. Savage, "Strapdown inertial navigation algorithm design. Pt. 1. Attitude algorithms," Guidance, Control, and Dynamics, Vol. 21, No. 1, pp. 19-28, 1998.
5.  P. G. Savage, "Strapdown inertial navigation algorithm design. Pt. 2. Velocity and position algorithms," Guidance, Control, and Dynamics, Vol. 21, No. 2, pp. 208-221, 1998.
6.  V. M. Lesyuchevskii and Yu. A. Litmanovich, "New approaches to the development of discrete algorithms for determining the parameters of the linear motion of an object in inertial navigation systems," Giroskopiya i Navigatsiya, No. 2, pp. 39-58, 1994.
7.  Yu. A. Litmanovich, "Use of angular rate multiple integrals as input signals for strapdown attitude algorithms," in Proc. Symp. Gyro Technology, pp. 20.0-20.9, 1997.
8.  M. B. Ignagni, "Duality of optimal strapdown sculling and coning compensation algorithms," Navigation, Vol. 45, No. 2, pp. 85-96, 1998.
9.  R. B. Miller, "A new strapdown attitude algorithm," Guidance, Control, and Dynamics, Vol. 6, No. 4, pp. 287-291, 1983.
10.  V. Z. Gusinskii, V. M. Lesyuchevsky, Yu. A. Litmanovich, H. Musoff, and G. T. Schmidt, "New procedure for deriving strapdown attitude algorithms," Guidance, Control, and Dynamics, Vol. 20, No. 4, pp. 673-680, 1997.
Received 22 December 1999
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