| When approximating systems with Laguerre Basis Functions it's important to tune the Laguerre pole such that the expansion is parsimonious and accurate. The sum of squared errors has multiple minima with respect to the Laguerre pole, ruling out numerical optimization. Currently there are two alternate methods: an asymptotical method, and the enforced convergence criterion (ECC). A generalization of the ECC will be investigated such that minimizing this generalized ECC and computing the asymptotically optimal Laguerre pole lead to equivalent solutions. It will be proved that the ECC is quasiconvex (it can be solved using numerical optimization techniques). Currently the methods of finding the optimal Laguerre pole are only appropriate in a system modeling framework since they depend on knowledge of the system's poles. It will be shown that the ECC can be formulated in a system identification framework and an algorithm will be proposed to find the minimizing Laguerre pole. |
