Pole structure estimation from laguerre representations using hyperbolic metrics on the unit disc

This paper proposes a new approach to identification of the poles in a linear system from frequency domain data. The discrete rational transfer function is represented in a rational Laguerre-basis, where the basis elements can be expressed by powers of the Blaschke-function. This function can be interpreted as a congruence transform on the Poincaré unit disc model of the hyperbolic geometry, leading to a nice geometric interpretation of the identification algorithm. Convergence results in hyperbolic metrics will be given. The full procedure is illustrated by simulation examples.