Quadratically Constrained Least Squares with Aerospace Applications

作     者：de Ruiter, Anton H. J. 

作者机构：Ryerson Univ Dept Aerosp Engn 350 Victoria St Toronto ON M5B 2K3 Canada 

出 版 物：《JOURNAL OF GUIDANCE CONTROL AND DYNAMICS》 (制导、控制和动力学杂志)

年 卷 期：2016年第39卷第3期

页      面：487-497页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0804[工学-仪器科学与技术] 0825[工学-航空宇航科学与技术] 

主　　题：Unscented Kalman Filter Lagrange Multipliers Spacecraft Attitude Computing Quaternions Earth's Magnetic Field Optimization Algorithm Argument of Latitude Dirac Delta Function Euler Equations 

摘      要：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.