Decoupled estimation of the parameters and hyperparameters of generalized stochastic constraint TARMA models

Time-dependent ARMA models are a preferred tool the identification of systems with non-stationary characteristics. In order to improve the tracking abilities of the model, the evolution of the time-dependent parameters is defined by either deterministic or stochastic paths. The Generalized linear Stochastic Constraint (GSC) TARMA models define the parameter evolutions by linear difference equations excited by white Gaussian noise. The estimation of these models requires the dual estimation of the time-dependent parameters and the model hyperparameters. The estimation of this models is difficult due to the non-linear coupling between its parameters and hyperparameters. This work features a Maximum A Posteriori decoupled estimation method, where the MAP objective function derived from GSC-TARMA model is sequentially optimized with respect to the parameters and the hyperparameters. The proposed estimation approach is explained and evaluated in the problem of the identification of wind turbine vibration response signals.