Study On Estimation And Fusion Algorithm For Systems With Correlated Noises

In practical applications, the external disturbances of dynamic systems are notusually to be uncorrelated Gaussian white noises. Therefore, the filter design fordynamic systems with correlated noises is a hot topic of the estimation theory andmany researchers have paid special attention to this area. In recently years, networkhas been intensively used in engineering applications, and this affects thedevelopment of the estimation theory. Usually, the estimation problem fornetworked control systems with network-induced time-delay or pack dropout can beconverted to be the estimation problem for stochastic systems with correlated noises.On the other hand, the development of the sensor technology also affects thedevelopment of the estimation theory, and the data fusion problem for dynamicsystems with correlated noises has already received significant attention. In additionto this, model uncertainty is an important source that makes estimators have poorperformances and it is also an important source that makes estimators unstable.However, errors between the mathematical model and the plant are unavoidable dueto the constrained knowledge and the variation of the system and environment.Therefore, robust filtering for uncertain systems is another hot topic of theestimation theory. Based on the previous work of other researchers, in this paper, westudy the estimation and fusion problem for a class of dynamic systems withuncertainties, correlated noises and network-induced time-delay or packet dropouts.Parts of the newly obtained theory results are applied to the target tracking systems.The main work of this dissertation can be summarized as follows:Aiming at dynamic systems with finite-step autocorrelated process noises,model uncertainties and missing measurements, a recursive robust filter designmethod is proposed and the obtained filter is optimal in the minimum-variance sense.The dynamic system and measurement output are both subject to stochasticuncertainties. Process noises are assumed to be finite-step autocorrelated and themissing measurements phenomenon is described as a binary switching sequence. Inthe minimum-variance sense, we obtained the proposed robust filter. At last, thesimulation results demonstrate the better performances of the proposed robust filter.An optimal non-fragile filter design method is proposed for a class of dynamicsystems with finite-step autocorrelated measurement noises, model uncertainties andmultiple packet dropouts. We do not only consider the uncertainties in the systemmodel, but also consider the uncertainties in the filter parameter. Based on amultiple packet dropouts model and the state augmentation, an auxiliary system withautocorrelated and cross-correlated noises and stochastic uncertainties is obtained. In the minimum-variance sense, the proposed optimal non-fragile filter is obtained.At last, the simulation results demonstrate the effectiveness of the proposed filter.The time-delay and packet dropout phenomenon are extended to descriptorsystems. By using the sigular value decomposition, an innovation analysis approachand the orthogonal projection theorem, recursive filter, predictor and smootherdesign method are proposed. Based on the singular value decomposition and thestate augmentation, the estimation problem for the descriptor system is transformedto the estimation problem for the process noise and two non-descriptor subsystemswith autocorrelated and one-step forward cross-correlated noises. By using aninnovation analysis approach and the orthogonal projection theorem, the recursivefilter, predictor and smoother are first obtained for the subsystem and the processnoise. Then, based on the newly obtained estimators, the recursive filter, predictorand smoother are obtained for the original descriptor system.The problem of the optimal distributed Kalman filter fusion is studied for aclass of dynamic systems with correlated noises. Each measurement noise and theprocess noise are correlated at the same time instant. Based on the newly obtainedmeasurements whose measurement noises are uncorrelated, the optimal distributedKalman filter fusion without feedback is obtained, also based on the newly obtainedmeasurements, the optimal distributed Kalman filter fusion with feed back isproposed. For the proposed fusion algorithm, we give a rigorous performanceanalysis. At last, the proposed fusion algorithm is applied to the nearly constantvelocity and nearly constant acceleration target tracking systems, and the simulationresults demonstrate the effectiveness of the proposed fusion algorithm and theperformance analysis.The distributed weighted filter fusion problem is studied for a class of dynamicsystems with autocorrelated and cross-correlated noises. For each sensor subsystem,a recursive local filter is first derived. Based on the newly obtained local filter, thedistributed weighted filter fusion algorithm is proposed to deal with optimalunbaised fusion problem for dynamic systems with correlated noises. Comparedwith other fusion algorithms, the newly obtained fusion algorithm has strongerfault-tolerance. Simulation results are employed to demonstrate the usefulness of theproposed fusion algorithm.