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A New Linear Programming Algorithm for Optimal Estimation and Correction of an Aircraft Trajectory

Boris Bakhshiyan, Alexander Goryainov
Problems of optimal estimation under uncertainty and scalar optimal design of experiment may be reduced
to a problem of linear programming. Problems of ideal linear ideal trajectory correction and many problems of optimal design of experiment may be solved with the help of multiparametrical (so-called generalized) linear programming. Traditional methods for solving these problems are the simplex method and the the column-generate method
respectively. While using these methods two main difficulties may appear. Current basic matrix often turns out to be be ill
conditioned, and the solution is usually accompanied by a large number of almost degenerate iterations thus accumulating large computational errors. Besides this convergence of the column-generate method is not proved. An new efficient method for solving problems of this class the so-called skeleton algorithm is proposed. This algorithm helps to avoid problems mentioned above. The algorithm is easy
enough because it does not use inversion of matrices.
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