Parameter-bounding identification algorithms for bounded-noise records

In the identification of dynamical models from noisy observations, an adequate stochastic characterisation of the noise is often unavailable, either because there are relatively few observations and little prior information, or because the noise behaviour is complicated, e.g., nonstationary. An alternative approach to identification has been suggested, which uses bounds on the noise instead of a stochastic description. From the noise bounds in a specified model structure, each observation yields a pair of bounds in parameter space. A succession of observations thus identifies a feasible parameter region rather than a point estimate of the parameters. This paper suggests combined use of two standard algorithms for parameter-bounding identification, outer-bounding by linear programming, and ellipsoidal outer-bounding. The former is expensive in computation but may result in a more accurately defined feasible parameter region. The latter is cheap, but often unsatisfactory on its own because it gives only a loose approximation to the parameter region. Various combined uses of the two methods are described and tested.