Optimal Input Design for the Detection of Changes Towards Unknown Hypotheses

Abstract

The effects of auxiliary input signals on detecting changes in ARMAX processes via statistical tests are discussed. Two extensions to the Cumulative Sum Test are considered. The first is applicable when the direction of the change in the parameter space is known but its magnitude is unknown. The second is applicable when neither is known. The performance criteria for the design of stationary stochastic inputs are based on the asymptotic properties of the tests. It is shown that power-constrained optimal inputs have discrete spectra and a suitably chosen input can greatly improve the detection performance.