|Abstract:||In this paper, we propose an approach to solution of the attitude determination problem using multiple GNSS antennas. In general, the least squares approach to the attitude determination leads to the non-convex optimization problem. Standard approach proposed by G.Wahba, (see [1,2]) consists in minimizing the sum of the squares of the residuals between the baseline vectors measured in the local horizon frame and the same vectors, but determined by a rotation from the body frame to the local horizon. The advantage of the Wahba method is its ease of implementation. The expression to be minimized does not contain terms quadratically dependent on the rotation matrix entries. Thus, the least squares problem reduces to maximizing the linear form of the matrix to be found over the set of orthogonal matrices. This problem is then solved via SVD decomposition (see ). To take into account the correlation between the coordinates of the baselines, the Wahba problem can be formulated in terms of the generalized least-squares problem by introducing a weight matrix. However, the main advantage of the Wahba method disappears, because now the term that depends quadratically on the orthogonal matrix does not vanish. We show how this problem can be reduced to the convex semidefinite programming problem (SDP) (see [4,5]) and, therefore, efficiently solved. The method of semidefinite relaxation has been widely used to solve nonconvex quadratic programming problems. Using this method, the original nonconvex problem is immersed in a wider class of convex optimization problems that can be efficiently solved. Thus, instead of the original computationally complex problem, a convex problem is solved that gives an approximate solution to the original problem. Based on this approximation, the exact solution is then found.|
Proceedings of the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2018)
September 24 - 28, 2018
Hyatt Regency Miami
|Pages:||3859 - 3867|
|Cite this article:||
Rapoport, Lev, Tormagov, Timofey, "Attitude Determination with Multiple Antennas Using SDP Relaxation," Proceedings of the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2018), Miami, Florida, September 2018, pp. 3859-3867.
ION Members/Non-Members: 1 Download Credit