Research On Optimal,Robust And Self-tuning Information Fusion Estimation For Multisensor Descriptor Systems

Descriptor system has been widely applied in the large system theory,a singularlyperturbed theory,circuit system control theory,econometrics,decision theory,and otherfields.Multisensor information fusion technology has been a wide range of applications,since it has wider coverage in space and time,stronger system survivability and higher reliability and performance.Combining the estimation problem of the descriptor system and the data fusiontechnique,the accuracy of state estimator algorithms of the multisensor descriptor systemsis improved.In this paper,for the multisensor linear stochastic invariance descriptorsystems,the information fusion estimation problems are researched,when the noise variancesare known or unknown uncertain.The main works include following aspects:(1)For the multisensor linear stochastic descriptor systems with known noise variance,weighted fusion measurement is obtained based on full rank factorization,and thereduced-order subsystems of the fused descriptor system are obtained,according to thethree different standard forms of singular value decomposition(SVD)and the fused measurements.Since the reduced-order subsystems are standard state space systems(nondescriptorsystems),theWMFoptimal Kalman estimators of the subsystems are presented,applying the classical Kalman filtering theory.According to the relationship ofreduced-order subsystems and original descriptor systems,the WMFoptimal Kalmanestimators and estimation error variances of the multisensor descriptor systems are presented.(2)For the multisensor linear stochastic descriptor systems with correlation noises,the fused measurements are obtained applying the weighted measurement fusion method.Combining the obtained fused measurement and the state equation of the multisensor descriptor systems yields new augmented measurements.Then,maximum likelihood estimates of the augmented measurements are obtained,which also are WMFfull-orderfilter and filtering error variance of themultisensor descriptor systems.And the presentedfiltering error variances satisfy the descriptor Riccati equation.The full-ordersmoothing problem of the multisensor descriptor systems are transformed to their filteringproblem of the augmented state,based on augmented state method.(3)For the multisensor descriptor systems with uncertain noises variances,the robustfull-order filtering and smoothing algorithm are presented,applying the max-minrobust design principle,while the uncertain noise variances exist upper variance matrices.The conservative multisensor descriptor systems are defined as the descriptor systemwith upper noise variances and upper initial value of error variances estimation.For theconservative descriptor systems,the conservative WMF and covariance intersection(CI)fusion full-order filters and smoothers are obtained,applying the algorithms in(1)and(2).Substituting the true measurements of original multisensor descriptor systems intothe conservative full-order filters and smoothers yields the robust WMF and CI fusionfull-order filters and smoothers.These estimation error variances of the robust filter andsmoother are called as actual error variances.Applying the Lyapunov equation method,ithas been proved that the actual estimation error variances have upper variance matrices,and presented robust full-order filters and smoothers have robustness.(4)For the multisensor descriptor systems with unknown noise variances,the fusionconsistent estimates of these unknown noise variances are obtained based on thecorrelation function method.Substituting these consistent estimates into the informationfusion reduced-order and full-order estimators with known noise variances yields the selftuninginformation fusion reduced-order and full-order estimators and their estimationerror variances.Applying the dynamic variance error analysis method and the dynamicerror analysis method,the convergence of the self-tuning estimators and the estimationerror variances are proved.