State estimation formulations are developed in discrete time using an extended Kalman filter (EKF) and an unscented Kalman filter (UKF).
This one-level approach is consistent with user equilibrium conditions, and improves previous one-level relaxed OD estimation formulations in the literature by 'equilibrating' path flows using external path cost parameters.
Specifically, two parameter estimation formulations are proposed with objective functions that depend on model prediction errors of metabolite concentrations and of concentration time-slopes.
The proposed computational method is based on shape estimation and state estimation formulation of the EIT problem.
In addition, a problem of binary integer linear programming is solved to obtain and optimally place the minimum number of μPMUs necessary to provide a unique solution for the proposed state estimation formulation.
The methods for calculating LPCs include covariance method, autocorrelation (Durbin) method, lattice method, inverse filter formulation, spectral estimation formulation, maximum likelihood method, and inner product method [ 6].
Twenty methods are reviewed for their goal and scope, developer, target application, required data, considered aspects and parameters, exposure assessment, hazard extent estimation, index formulation, and output data.
The input estimation filtering formulation facilitates the considerations of input data uncertainty, and the Kalman filtering principles are adopted to achieve optimal estimation of the myocardial kinematics over corrected input forces.
While for single frame estimation this formulation fuses the measurements (of head pose and body direction) with prior beliefs, when analysing video data we can further impose smoothness constraints to encode temporal coherence: the joint prior at time is in this case taken to be, where we use the assumption that the current direction is independent of previous gaze.
Further details on the formulation, estimation methods, features of the model, and properties of the estimators have been published elsewhere [ 18- 20].
As heteroscedasticity is common incross-sectional data and small sample data, alternative estimations, mainlyheteroscedasticity consistent formulations, were employed in addition to OLSestimation.
