Orthoregressive estimates for the parameters of systems of linear difference equations

Comparison of methods for estimating the parameters of linear dynamic systems by measurements of short sections of transient processes

“…It is shown that the variational methods [7,9,10] completely use the information on the structure of a linear dynamic object in the form of linear constraints on the set of admissible trajectories and enable us to obtain consistent estimates of the parameters with a lower variance in short sections of the transient processes on account of more intensive calculations.…”

“…This dependence is preset as an implicit function by the system of equalities ∂J(z, χ)/∂χ = 0. The existence and the continuity of the implicit function χ(z) for orthoregressive methods follow directly from the results in [9].…”

“…The estimates under investigation are set up as a result of the minimization of loss functions with constraints (for more details, see [3,5,7,9,10]):…”

“…The conditions of the strong consistency of the estimates θ l (5) were studied in [9,10,12]. Further, without the loss of generality of the presentation, we will set l = 1 and omit the requisite indices in the quantities.…”

“…Let us note that they formally differ by loss functions: the modified estimate (9) includes the matrix C OR with a simpler cellwise-diagonal structure instead of the matrix C with the cellwise-Toeplitz structure in the loss function (8) of the VI method.…”