Designing optimal sampling schemes

Abstract

Abstract-In this work, we propose a method for finding an optimal, non-uniform, sampling scheme for a general class of signals in which the signal measurements may be non-linear functions of the parameters to be estimated. Formulated as a convex optimization problem reminiscent of the sensor selection problem, the method determines an optimal sampling scheme given a suitable estimation bound on the parameters of interest. The formulation also allows for putting emphasis on a particular set of parameters of interest by scaling the optimization problem in such a way that the bound to be minimized becomes more sensitive to these parameters. For the case of imprecise a priori knowledge of these parameters, we present a framework for customizing the sampling scheme to take such uncertainty into account. Numerical examples illustrate the efficiency of the proposed scheme.

Designing sampling schemes for multi-dimensional data

“…For example, for a sum of damped sinusoids, the trace constraint in (4) will clearly be dominated by the CRLB for the amplitudes, as these are orders of magnitude larger than those of the frequencies, and the optimization will therefore put an emphasis on minimizing the CRLB of the amplitude parameter. In order to allow for sampling schemes that put an emphasis on a selection of the parameters of interest, we recently proposed to introduce a weighting matrix, A(θ), acting upon the FIM in [27]. Specifically, instead of minimizing the cost function using the FIM, we proposed to perform the minimization using weighted FIMs…”

Most Effective Sampling Scheme for Prediction of Stationary Stochastic Processes

“…e problem of finding an optimal sampling scheme is an important task of researchers, since in applied sciences often collecting of samples is a laborious and expensive process. We refer the interested readers to the works such as McBratney and Webster [3]; Zio et al [4]; Xiao et al [5]; and Sward et al [6].…”