System Identification Using Laguerre Basis Functions

This document describes how to use discrete time Laguerre basis functions, and their associated z-transforms, to construct a system identification process using experimentally determined Laguerre expansion coefficients of the input and output sequences. The process is derived using a new Product Propert} for the discrete time Laguerre basis functions. The system identification process is "linear in the parameters"; it does not require assumptions/knowledge of the poles locations of the system under test. An example is presented using data generated by a system that has appeared in the recent literature. The procedure naturally produces equations that can be used to determine if the chosen model order is correct or if its order needs to be increased. Constraints can easily be incorporated.