A Generalized Decomposed State Estimation Approach for Uncertain Constrained Stochastic Nonlinear Systems

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.