In several industrial processes, measurements are limited due to time or cost constraints. Hence, scheduling of these measurements to obtain maximally informative and accurate estimates of the states becomes important. The focus of this contribution is to determine a schedule of measurements that maximizes the quality of the estimates at the end of a finite time horizon. This work finds applications in batch chemical processes. The estimate covariance matrix as obtained by applying standard Kalman filtering theory is approximated and the original problem is relaxed and reformulated as a cone program. For a certain class of systems, the approximated covariance matrix is parameterized in terms of a point belonging to a moment space induced by a Tchebycheff system. The theory of Tchebycheff systems is used to determine an improved upper bound on the guaranteed minimum number of measurements. A tractable solution methodology to obtain the optimal cost and a parsimonious discrete schedule using the theory of cone programming, generalized barrier functions and Tchebycheff systems is described.