Optimal adaptive estimation: Structure and parameter adaptation

Abstract

Optimal structure and parameter adaptive estimators have been obtained for continuous a s well a s d i s c r e t e data gaussian process models with linear dynamlcs. Specifically, the essentially nonlinear adaptive estimators are shown to be decomposable (partition theorem) into two parts, a linear nonadaptive part consisting of a bank of Kalman-Bucy filters, and a nonlinear part that incorporates the learning or adaptive nature of the estimator. The conditional-error-covariance matrix of the estimator is also obtained in a form suitable for ou-line performance evaluation. The adaptive estimators are applied to the problem of state-estimation with nongaussian initial state and also to estimation under measurement uncertainty (joint detection-estimation) . Examples are given of the application of the proposed adaptive estimators to structure and parameter adaptation indicating their applicability to practical engineering problems.I.

Identifying the radiation belt source region by data assimilation

“…[23] We use a so-called ''augmented state vector'' approach [Lainiotis, 1971;Ljung, 1979] where the state vector is extended by parameters of the physics model. We added the phase space density of the outer boundary f b to the state vector which then reads (0) and an estimation of its error in P f (0), the first step is to compute the Kalman gain matrix K .…”

State estimation for hybrid systems: applications to aircraft tracking

“…These conditions are valid for the hybrid estimation of a specific class of systems, in which a constant parameter vector is unknown and the continuous dynamics in each mode has a single output. Lainiotis et al [10,11,12] extended these results to systems with multiple outputs, and derived the recursive form of the optimal adaptive estimator as well as its exact error covariance. Hawkes et al [8] examined the asymptotic behavior of the adaptive weights which determine the performance of hybrid estimation algorithms.…”

Application and Comparison of Evolutionary Techniques for Forecasting the Hellenic Grid Electricity Load

“…The first method is based on a hybrid model that combines the adaptive MMPF [18][19][20], known for its stability, with SVM. The idea of using this method for electric load forecasting came from the fact that it was applied for wind speed prediction with very good results [21].…”

“…Some of the proposed techniques make use of time series analysis using ARMA [1][2][3][4][5] or ARIMA models [6][7][8][9][10]. Other algorithms achieve load forecasting by adopting evolutionary techniques such as ANN's [11-12], SVM's [13][14] either alone or combined with other methods for the same purpose [15][16][17].The purpose of this study is not to introduce one more load forecasting criterion, but it focuses on applying three different methods to real electric load data and evaluating their performance.The first method is based on a hybrid model that combines the adaptive MMPF [18][19][20], known for its stability, with SVM. The idea of using this method for electric load forecasting came from the fact that it was applied for wind speed prediction with very good results [21].…”