Determination of Volterra kernels from input-output data

Abstract

In this paper a class of system identification problems of non-parametric type is considered. Specifically, given an unknown deterministic system whose input-output relation can be expressed by a Volterra expansion, some basic structural aspects related to the problem of determining Volterra kernels from input-output records are discussed from a coordinate-free point of view. The model adopted for the system input—output relation is general enough to cover a number of situations ranging from problems of identification where the kernels are time-varying to those where the kernels must be constrained in Hilbert spaces of well-behaved functions. The emphasis is on establishing what, in principle, can be recovered of the system kernels through a noiseless identification process, and the ultimate limitations imposed by the presence of observation or measurement noise. An application of the steepest descent iteration to the ill-posed estimation problem resulting from the presence of observation noise is considered.