Abstract
In this paper, a decomposed state estimator is developed for stochastic constrained nonlinear discrete-time dynamical systems with uncertain parameters. The proposed estimator can deal with general nonlinear uncertain stochastic systems without any pre-defined specifications on the system structure and/or the measurement model. Moreover, it can handle estimation problems for nonlinear stochastic systems subject to a set of imposed linear and/or nonlinear equality and/or inequality constraints. The mathematical structure of the proposed estimator is developed using multiple projection approach and its performance is analyzed and compared with the global (un-decomposed) structure. The main features of the proposed estimator are: it reduces the processing time, it can handle estimation problems with bad initial conditions of the estimator, it can be implemented on modern parallel processing facilities to further reduce the processing time, and last but not least, it minimizes the rounding off errors and hence improves the numerical stability of the algorithm. Simulations results on different real applications are presented to show the effectiveness of the developed approach, and its improved performance when compared with other techniques reported in the literature.
Highlights
From the preceding results, the following can be concluded: 1- Based on the results presented in Table 1, it is clear that the IDUCEKF leads to much better results for the average RMSE
It is obvious that the IDUCEKF has better numerical stability which means that the robustness of the estimator is improved
2- As shown in Table 1, the IDUCEKF is implemented sequentially on a single processor, the average CPU time per sample is much less than others used to solve the same problem
Summary
LITERATURE REVIEW Many algorithms were developed in the literature for state estimation of nonlinear systems [1]–[13] These algorithms include various Kalman Filter (KF) variants such as: the extended Kalman filter (EKF) [1]–[4], the unscented Kalman filter (UKF) [5], [6], the ensemble Kalman filter (EnKF) [7], cubature Kalman Filer [8], central difference Kalman Filer [9], etc. Some equality and/or inequality constraints are imposed on the states of the system due to physical or practical considerations. For this class of systems, the state estimator should be capable of handling state estimation problems of constrained systems
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