Trace Versus Determinant in Ellipsoidal Outer-Bounding, with Application to State Estimation

Abstract Computing minimal-size ellipsoids guaranteed to contain the sum or the intersection of possibly degenerate ellipsoids are the basic tools of a bounded-error counterpart to Kalman filtering. In this paper, two measures of the size of an ellipsoid are considered and compared, namely its volume and the sum of the squares of its semi-axes, which respectively correspond to the determinant and trace criteria. The approach is oriented towards analytic solution, sometimes at the cost of suboptimality. and much attention is paid to recursive algorithms, which are applied to state estimation.