Generalized System Reduced-order State Fusion

Recently, the state estimation problems for descriptor (singular) systems havereceived great attention due to extensive application backgrounds, including circuits,economics, and robotics etc. The information fusion Kalman filtering for theconventional systems has widely been applied in many fields. But the multisensorinformation fusion state estimation problem for descriptor systems is an open problem.For the linear discrete time-invariant stochastic descriptor system withmultisensor ,based on the singular value decomposition, by the linear transformation,the descriptor system can be transformed into two canonical forms, where eachcanonical form consists of two reduced-order non-descriptor subsystems. Using themodern time series analysis method, based on the autoregressive movingaverage(ARMA) innovation model, white noise estimation theory. Three differentweighted fusion approaches are presented for the original state, transformed state, andsubsystems'state, respectively. Each weighted fusion approach is realized three rulesweighted by matrices, diagonal matrices, and scalars, respectively. Then thereduced-order information fusion steady-state descriptor Kalman estimator is presentedfor the descriptor system under the two canonical forms. They can handle the fusedfiltering, smoothing and prediction problems in a unified framework. Gives thecounterpart of information fusion Kalman estimator. Under the optimal fusion rulesweighted by diagonal matrices, a information fusion steady-state decoupled Wiener stateestimator for descriptor is presented, and realizes local estimation for state componentsWiener estimator and two subsystems decoupled fusion estimation. The formulas ofcomputing the variance and cross-covariance matrices among local estimation errors arepresented, which are applied to compute the optimal weights. It is proved that for eachweighted fusion approach, the accuracy of the fuser with matrix weights is higher than that of the fuser with scalar weights, and the accuracy of the fuser with diagonal matrixweights is between both of them, and the accuracy of each fuser is higher than that oflocal estimators. Many Monte Carlo simulation examples show their effectiveness, andshow that the accuracy distinction for three kinds of fused filters is not obvious, so thatthe fused filter weighed by scalars and by diagonal matrix can obviously reduce theon-line computational burden, and is suitable for real time applications.