This paper treats the problem of quadratically constrained least squares with positive semidefinite weight matrices. A new method of solution is presented that searches directly over the constraint set, and does not require the determination of Lagrange multipliers. Global convergence of the algorithm is rigorously proven. In addition, a covariance analysis is performed for the constrained optimal solution. Two aerospace applications are presented: 1) quadratically constrained Kalman filtering similar in form to the norm-constrained Kalman filter from the literature—it is shown that the optimal quadratically constrained update is simply an orthogonal projection of the optimal unconstrained update onto the constraint set, and 2) a new quadratically constrained Kalman filter using the covariance expression developed in this paper, yielding a statistically more consistent constrained filter. The new filter is demonstrated numerically with a spacecraft attitude estimation example.
Quadratically Constrained Least Squares with Aerospace Applications
Journal of Guidance, Control, and Dynamics ; 39 , 3 ; 487-497
2016-01-08
11 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Quadratically Constrained Least Squares with Aerospace Applications
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