Fisher suggested in 1930s algebraically structured pivot functions (PFs) whose distribution does not depend on unknown parameters.
In this paper we investigate when a parameterized controller, designed for a plant depending on unknown parameters, admits a realization which is independent of these parameters.
A composite detection problem is considered to have a uniformly LMP detector, when both the metric and the threshold for a given PFA do not depend on unknown parameters (in this case the variances).
Motivated by constant parameter estimation in nonlinear models, as well as state observation in dynamical systems, an adaptive observer is proposed for a class of nonlinear systems linearly depending on unknown parameters.
The design is based on three steps, (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters, (2) representation of the delay as a transport PDE, (3) design of the adaptive controller by using the backstepping boundary control technique for PDEs.
The nonlinearities depend linearly on unknown parameters with known basis functions.
The model depends on unknown fecundity and mortality parameters.
The approach of G ianola and van K aam (2008) and our approach are different in that we maximize the full likelihood whereas they drop the summand log(c) in Equation 3. Note that c depends on the unknown parameters, i.e., the variance components and the parameters of the Matérn covariance function.
It is proved that, if the noise variance is larger than a threshold, which depends on the unknown parameters and on the extended design matrix, then the proposed estimator of the original parameters dominates the least-squares estimator, in the sense of the mean square error.
