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 upon prior assumptions about the noise and the unmodelled 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. Here we show 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. We illustrate the usefulness of the method with a number of simulation examples. The paper concludes by showing how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and undermodelling. Another simulation study compares our method to Akaike's well known FPE and AIC criteria