Keywords: 
• active optics /
• pose control /
• ridge regression /
• sparse aperture

Abstract: The influence of the position of the sparse aperture mirror hard spot and the layout of the edge sensor on the precision of the relative pose control was studied. Using the geometry characteristic of sparse aperture, a primary mirror model composed of seven circular apertures was established and the control matrix of relative pose among apertures was derived. The generalized least squares method was used to solve this problem, considering the large condition number of control matrix, ridge regression was introduced and the intrinsic bound on the error function of the control matrix was also given. The possible 128 location strategies between edge sensors and hard spots and the effect of geometric distance on the condition number of control matrix were analyzed. The results show that the layout of the hard points and edge sensors is intrinsically linked to the coefficient matrix, the sparse aperture is serious Multi-Collinearity with respect to the coefficient matrix of pose control, and the normal matrix appears seriously ill-conditioned. The condition number of normal matrix are reduced significantly when the distances between the adjacent two edge sensors while the layout is fixed. For the ill-conditioned problem of the normal matrix, the ridge regression is used to effectively suppress the ill-conditioned characteristic by choosing appropriate ridge parameters. Using this method, the redundant edge sensor structure can be effectively used to realize data fusion and ensure the stability and reliability of the measurement system.