A New Coning Attitude Algorithm for a Low Cost INS-GPS Integration

Navin G. Mathur

Abstract:	It is required for a tightly-coupled GPS-INS integration utilizing a low-cost inertial measurement unit to use a high accuracy attitude algorithm. With moderate performance of the gyro, lack of a good attitude algorithm may cause the INS solution to drift rapidly. Conventional attitude algorithms (Direction Cosine Matrix (DCM) update and conventional Quaternion update) suffer from so called coning errors, which are due to the noncommutativity of small rotations. To avoid the coning problem, John E. Bortz (1971)[1] derived an algorithm formulating the noncommutativity rate vector, which results in an attitude update algorithm free from coning errors. The basis for the algorithm is the Euler Theorem stating that “Any general rotation of a rigid body can be visualized as a single rotation about an imaginary axis through the body”. Bortz derived a real time differential equation for the imaginary axis taht is mentioned in Eulers Theorem. Since the evolution of the mathematical definition of the noncommutativity rate vector, research scientists have been involved in solving the differential equation to be more suitably implementable in the digital environment. The mathematical derivation for the solution of the coning attitude update algorithm is suggested by several different authors. While some authors derive the algorithm using geometrical means others have used the minimization of the estimation error in the reconstruction of the rotation vector step). Among the research done in this field, a great deal of attention has been given to the minimization of reconstruction error of the rotation vector while neglecting the attention to the performance of the attitude algorithm attitude algorithms along with different (single step and new single step algorithm is also propose in the paper that minimizes the reconstruction error in the rotation vector for single step algorithm. It is observed that the new algorithm produces an equivalent or better error performance than several multi step algorithms. The improvement is not only computational burden on the processor. with a predetermined structure (single step and multiple with limitation on data rate. This paper defines, evaluates and compares the performance of several conventional multi step) coning algorithms that are presently popular. A in the error performance of the algorithm but also is in theestimation error in the reconstruction of the rotation vector step). Among the research done in this field, a great deal of attention has been given to the minimization of reconstruction error of the rotation vector while neglecting the attention to the performance of the attitude algorithm attitude algorithms along with different (single step and new single step algorithm is also propose in the paper that minimizes the reconstruction error in the rotation vector for single step algorithm. It is observed that the new algorithm produces an equivalent or better error performance than several multi step algorithms. The improvement is not only computational burden on the processor. with a predetermined structure (single step and multiple with limitation on data rate. This paper defines, evaluates and compares the performance of several conventional multi step) coning algorithms that are presently popular. A in the error performance of the algorithm but also is in theestimation error in the reconstruction of the rotation vector step). Among the research done in this field, a great deal of attention has been given to the minimization of reconstruction error of the rotation vector while neglecting the attention to the performance of the attitude algorithm attitude algorithms along with different (single step and new single step algorithm is also propose in the paper that minimizes the reconstruction error in the rotation vector for single step algorithm. It is observed that the new algorithm produces an equivalent or better error performance than several multi step algorithms. The improvement is not only computational burden on the processor. with a predetermined structure (single step and multiple with limitation on data rate. This paper defines, evaluates and compares the performance of several conventional multi step) coning algorithms that are presently popular. A in the error performance of the algorithm but also is in theestimation error in the reconstruction of the rotation vector step). Among the research done in this field, a great deal of attention has been given to the minimization of reconstruction error of the rotation vector while neglecting the attention to the performance of the attitude algorithm attitude algorithms along with different (single step and new single step algorithm is also propose in the paper that minimizes the reconstruction error in the rotation vector for single step algorithm. It is observed that the new algorithm produces an equivalent or better error performance than several multi step algorithms. The improvement is not only computational burden on the processor. with a predetermined structure (single step and multiple with limitation on data rate. This paper defines, evaluates and compares the performance of several conventional multi step) coning algorithms that are presently popular. A in the error performance of the algorithm but also is in theestimation error in the reconstruction of the rotation vector step). Among the research done in this field, a great deal of attention has been given to the minimization of reconstruction error of the rotation vector while neglecting the attention to the performance of the attitude algorithm attitude algorithms along with different (single step and new single step algorithm is also propose in the paper that minimizes the reconstruction error in the rotation vector for single step algorithm. It is observed that the new algorithm produces an equivalent or better error performance than several multi step algorithms. The improvement is not only computational burden on the processor. with a predetermined structure (single step and multiple with limitation on data rate. This paper defines, evaluates and compares the performance of several conventional multi step) coning algorithms that are presently popular. A in the error performance of the algorithm but also is in theestimation error in the reconstruction of the rotation vector step). Among the research done in this field, a great deal of attention has been given to the minimization of reconstruction error of the rotation vector while neglecting the attention to the performance of the attitude algorithm attitude algorithms along with different (single step and new single step algorithm is also propose in the paper that minimizes the reconstruction error in the rotation vector for single step algorithm. It is observed that the new algorithm produces an equivalent or better error performance than several multi step algorithms. The improvement is not only computational burden on the processor. with a predetermined structure (single step and multiple with limitation on data rate. This paper defines, evaluates and compares the performance of several conventional multi step) coning algorithms that are presently popular. A in the error performance of the algorithm but also is in the
Published in:	Proceedings of the 10th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1997) September 16 - 19, 1997 Kansas City, MO
Pages:	807 - 813
Cite this article:	Mathur, Navin G., "A New Coning Attitude Algorithm for a Low Cost INS-GPS Integration," Proceedings of the 10th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1997), Kansas City, MO, September 1997, pp. 807-813.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In