LFT approach to parameter estimation

In this paper we consider a unified framework for parameter estimation problems which arise in a system identification context. In this framework, the parameters to be estimated appear in a linear fractional transform (LFT) with a known constant matrix M. Through the addition of other nonlinear or time-varying elements in a similar fashion, this framework is capable of treating a wide variety of identification problems, including structured nonlinear systems, linear parameter-varying (LPV) systems, and all of the various parametric linear system model structures. In this paper, we consider both output error and maximum likelihood (ML) cost functions. Using the structure of the problem, we are able to compute the gradient and the Hessian directly, without inefficient finite-difference approximations. Since the LFT structure is general, it allows us to consider issues such as identifiability and persistence of excitation for a large class of model structures, in a single unified framework. Within this framework, there is no distinction between `open-loop' and `closed-loop' identification.