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Based on various approaches, several different solutions to the smoothing problem have been given. The relationships between these solutions are not immediate, although they solve the same problem. Making use of a certain framework from scattering theory, we derive two families of solutions, with equations evolving forwards and backwards in time, respectively. Within these families three major pre
The possibility of estimating process parameters using input-output data collected when the system operates in closed loop is discussed in this paper. Concepts that are useful for a systematic treatment of the problem are introduced. The results refer to the case where the regulator is a linear feedback law or alternates between several such laws. It is shown that a straightforwardly applied ident
The ever-increasing consumption of natural resources required for the production of consumer electronics, and the growing amount of electronic waste, underline the importance and urgency of extending the lifespan and use of such products. Information and Communication Technology (ICT) remanufacturing is a growing industry, which nonetheless faces several barriers. Consumers often have a perception
A recursive algorithm for parametric identification of discrete-time systems known as Panuska's method, the approximate maximum likelihood method or the extended matrix method, is analyzed. Making use of recently developed theory for asymptotic analysis of recursive stochastic algorithms, dynamic systems, and autoregressive moving average (ARMA) processes are constructed for which this algorithm d
The convergence of a proposed method for state estimation in power systems is analysed for a case with constant state vector. In particular, a set into which estimates obtained by two versions of the SCI method converge is determined.
The Riccati equation plays as important a role in scattering theory as it does in linear least squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. This framework is shown to be appropriate for estimation problems and makes possible simple derivations of known results as well as leading to several new
A certain "star-product" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g., the distinctions between time and measurement updates, predicted and filtered estima
The results stated in the above paper1 concerning an approved stochastic approximation method are considered. Formulas for the variances of the estimates are derived, and it is found that, in fact, the new algorithm is inferior to previously suggested ones.
At the same time as our dependence on IT systems increases, the number of reports of problems caused by failures of critical IT systems has also increased. Today, almost every societal system or service, e.g., water supply, power supply, transportation, depends on IT systems, and failures of these systems have serious and negative effects on society. In general, public organizations are responsibl
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