Tolerance-weighted L-optimal experiment design for active sensing

The choice of "where to look next" is a special case of an optimal experiment design. The paper proposes the tolerance-optimal experiment design, which is a special instance of the well-known L-optimal design, that minimises the weighted trace of the covariance matrix of the estimated state under Gaussian assumptions. The weighting matrix is chosen such that the design is invariant to transformations with nonsingular Jacobians, and such that the emerging sensing sequence reflects the information needs of the task. This tolerance-optimal design does not require more calculations than existing optimal experiment designs. Existing optimal experiment designs do not reflect the information needs of the task. In addition, some of them physically do not make sense if the estimated state has inconsistent units. The tolerance-optimal design is illustrated with two examples.