da6ea77475918a3d83c7e49223d453cc-Supplemental.pdf

Intuitively, if thei-th measurement yi is an inlier (i.e., r2 c2β2i), then θi = +1 and the corresponding term in(A1) reduces to least squares; ifyi is an outlier (i.e., r2 > c2β2i), then θi = 1andthecorrespondingtermin(A1)becomesaconstant c2,whencetheoutlierisirrelevant to the optimization. Directly developing the residual function r2(x,yi) = kbi sΠRBik 2 leads to a quartic polynomial (degree 4) ins and R, which is not suitable for moment relaxation because itwouldincrease theminimum relaxation orderκ[14]. T2 for t (the translation is bounded byaknownvalueT). Towards this goal, we introduce the notion of moments, moment matricesandlocalizingmatrices. Given a probability measureµ supported onP R n, its moment of orderα Z n+ is the scalarzα .