| We consider the estimation of unknown signals in structured models that are interconnections of known linear dynamic systems and unknown static maps, and contain unmeasured exogenous disturbances. A main motivation for analyzing such an issue is a system identification problem in which such an interconnection exists, and the static maps are to be identified when the inputs and/or outputs of the maps themselves are not available, and instead we must investigate them by interacting with the larger system.; Our technique is to formulate criteria and then search for estimates of the unmeasured signals based on three main types of criteria, these being that they are consistent with the linear dynamic system, that stochastic assumptions for disturbance processes are met, and that input-output pairs of the static maps are consistent with there being a static relationship between them. After revealing the basic approach to estimating signals, some time is spent on each of these three main parts of the estimation problem, presenting alternatives and implementation details.; The “staticness” consideration is a main contribution, and we present various possibilities for enforcing it. These are what make our formulation different from some other common estimation methods such as the Kalman filter or a least squares formulation.; Computational considerations are important, because the entities being estimated are signals, and so the number of decision variables is necessarily large. We focus on solution elements which are compatible with efficient convex programming methods, and what can be done when they are not. We show examples and evaluate performance and usability of the method.; In a later chapter we present an approach to computing bounds on how good estimates can be guaranteed to be, for estimation formulations that meet certain assumptions. Alternatively, something can be learned from the bounding ideas about issues that make an estimation problem harder or easier. |
