Quantifying the error in estimated transfer functions with application to model order selection

Previous results on estimating errors or error bounds on identified transfer functions have relied on prior assumptions about the noise and the unmodeled dynamics. This prior information took the form of parameterized bounding functions or parameterized probability density functions, in the time or frequency domain with known parameters. It is shown that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique. This significantly reduces the prior information required to estimate transfer function error bounds. The authors illustrate the usefulness of the method with a number of simulation examples. How the obtained error bounds can be used for intelligent model-order selection that takes into account both measurement noise and under-modeling is shown. Another simulation study compares the method to Akaike´s well-known FPE and AIC criteria