Accelerating consistency techniques and Prony's method for reliable parameter estimation of exponential sums

In this paper the problem of parameter estimation for exponential sums is considered, i.e., of finding the set of parameters (amplitudes as well as decay constants) such that the exponential sum attains values in specified intervals at prescribed time data points. These intervals represent uncertainties in the measurements. An interval variant of Prony's method is given by which a box can be found containing all the consistent values of the parameters. Subsequently this box is tightened by the use of consistency techniques, which are accelerated by the introduction of redundant constraints. The use of interval arithmetic results in enclosures for the consistent values of the parameters which can be guaranteed also in the presence of rounding errors.