Local parametric modeling based on rational approximation

The local polynomial method (LPM) for nonparametric noise and frequency response matrix estimation was introduced in [1]. Essentially it is a signal processing technique that approximates transfer function and transients in a narrow band around each line in the frequency domain with low-degree polynomials by solving a least squares problem. The idea of local parametric modeling was taken further in 2] where a rational instead of polynomial approximation was suggested. The resulting estimation method is called the local rational method (LRM). It holds the potential for superior performance when the system exhibits very sharp resonance peaks. In [3] we investigated this behaviour in a case-study of an eight inputs, six outputs active vibration isolation system. This contribution gives a theoretical motivation for the improvement that was observed in particular circumstances. More specifically we focus on the approximation error, the phenomenon of pole-zero cancellation, and the effect of local approximation on the noise covariance matrix estimate.