  This paper considers black- and grey-box continuous-time transfer function
estimation from frequency response measurements. The first contribution is a
bilinear mapping of the original problem from the imaginary axis onto the
unitdisk. This improves the numerics of the underlying Sanathanan-Koerner
iterations and the more recent instrumental-variable iterations. Orthonormal
rational basis functions on the unit disk are utilized. Each iteration step
necessitates a minimal state-space realization with these basis functions. One
such derivation is the second contribution. System identification with these
basis functions yield zero-pole-gain models. The third contribution is an
efficient method to express transfer function coefficient constraints in terms
of the orthonormal rational basis functions. This allows for estimating
transfer function models with arbitrary relative degrees (including improper
models), along with other fixed and bounded parameter values. The algorithm is
implemented in the tfest function in System Identification Toolbox (Release
2016b, for use with MATLAB) for frequency domain data. Two examples are
presented to demonstrate the algorithm performance.
