Suboptimal input signals for linear system identification

Abstract

It is well known that inputs for identification experiments can be synthesized on the basis of optimizing a certain performance criterion, such as variances of parameters, estimates of weighting functions and probabilities of transmission error. Such signals give the best possible performance for given constraints of input energy, observation time and nature of noise. The question arises whether one can choose signals on the basis of other possibly more intuitive or physical criteria and see what kind of performance they give w.r.t. optimal inputs and common signals, as unit step inputs. These signals, which fit between the two extremes are here referred to as suboptimal. The measure of performance is here taken to be the sum of parameter variances. It is shown that suboptimal inputs on the basis of maximizing the output signal/noise ratio, matching the system bandwidth and of pseudo-random binary noise nature can be selected for a given system. It is, however, also indicated that this is not a general me...