Generalized System Optimal And Self-calibration Of Distributed Information Fusion Estimators

The descriptor systems extensively exist in some practical applications such asrobot, electronic network and economic systems, and so on. The state estimationproblem for descriptor systems has very important significance in systems design andcontrol. In this paper, we investigate the distributed information fusion state estimationalgorithms for descriptor systems, including the design of reduced-order informationfusion estimators, full-order information fusion estimators and self-tuning reduced-orderfilter and full-order filter for descriptor systems with unknown noises statistics and/orunknown model parameters.For descriptor discrete-time stochastic linear systems with multiple sensors andcorrelated noises, by some non-singular transformations, the descriptor system istransferred to four reduced-order subsystems canonical forms. Based on the optimalfusion estimation algorithm in the linear minimum variance sense and projection theory,distributed reduced-order information fusion Kalman estimators and Wiener estimators,including filter, predictor and smoother, are presented for different canonical forms,respectively. The computation formulas for error covariance matrices between any twolocal estimation errors and two reduced-order subsystems are derived. Convergences ofsolutions of equations that cross-covariance matrices between any local estimationerrors satisfy are proven when steady-state Kalman filter exists for each sensor system,i.e., the solution can be computed by the iteration with an arbitrary initial value. Thedistributed steady-state reduced-order information fusion Kalman estimators are given.Furthermore, the reduced-order information fusion steady-state Kalman estimators canbe obtained by fusing once after all local subsystems reach the steady state. Comparingwith non-steady-state information fusion estimators, computations of fusion weights areavoided at each time step, so the online computational burden can be reduced obviously. A descriptor system with correlated noises at the same time is transferred to theequivalent non-descriptor system with correlated noises at the same and neighboringtime. The local full-order Kalman filter and smoother are presented for thisnon-descriptor system. Further, based on the optimal weighted fusion estimationalgorithms in the linear minimum variance sense, the distributed optimal weightedfusion full-order Kalman estimators are presented for the descriptor system withmultiple sensors. The estimation error cross-covariance matrices between any two localestimation errors are derived. Under the condition that the system is detectable andstabilizable, convergence of solution of Riccati equation that variance matrix of localestimation error satisfies is proved. Further, convergences of solutions of equations thatcross-covariance matrices between any local estimation errors satisfy are proven for thesystem with multiple sensors. Also, the full-order information fusion steady-stateestimators are given.When system has unknown noise statistics, a distributed identification approach fornoise statistic information is presented based on correlation functions and self-tuningreduced- and full-order information fusion filters are given. When the system model isunknown, information fusion estimators for model parameters and self-tuning reduced-and full-order information fusion filters are given by identifying ARMA innovationmodel parameter. When the system model parameters and noise statistics are unknown,the self-tuning reduced- and full-order information fusion filters with the three-stagefusion structures are given.