Frequency domain system identification when assuming unknown but bounded errors

When performing parameter estimation of dynamical systems, one must evaluate unknown variables given uncertain measurements. Often the problem is approached using a probabilistic description of the uncertainty and statistical estimation theory is applied. Another approach is to make the so-called “set-membership” or “unknown-but-bounded error” (UBBE) assumption. Here it is assumed that the measurements contain errors that are within known bounds. This paper discusses the frequency domain system identification problem under the UBBE assumption. It demonstrates that the set of all possible identifications is a finite union of polyhedra. The paper also shows how the problem of finding one valid identification reduces to finding a feasible solution to a nonlinear system of equations under box constraints. An example of applying the resulting algorithm to actual measurements is given