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. We exclusively consider parameter estimation in a maximum likelihood (ML) context. A key advantage of our LFT problem formulation is that it allows us to efficiently compute gradients, Hessians, and Gauss-Newton (G-N) directions for general parameter estimation problems without resorting to 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.