Optimal And Self-tuning Multisensor Weighted Measurement Fusion Kalman Filter

With the rapid development of science and technology, multi-sensor information fu-sion technology has been widely applied to modern military, industry, traffic and financialetc. Combining the multi-sensor information fusion technology with the state estimationtechnology yields the multi-sensor information fusion state estimation theory, where theoptimal and self-tuning multisensor state or signal estimation problems are researched.The purpose of the information fusion estimation is to smooth the past state, filter thecurrent state and predict the further state by applying the measurement data of the mul-tisensor. The accuracy of the fused estimation is higher than that of the single sensorestimation. For the multisensor linear discrete stochastic systems, an in-depth study ofthe optimal and self-tuning weighted measurement fusion Kalman filtering problems ispresented, applying the Kalman filtering method. The main works include:Firstly, for the multisensor linear stochastic system with exactly known systemmodel, based on the Kalman filtering method, several globally optimal weighted mea-surement fusion Kalman estimation methods are presented. Compared with the tradi-tional Kalman estimation method, they can reduce the computational burden and have theglobal optimality. Especially for the multisensor systems with correlated measurementnoises, applying the inversion of the partitioned matrix, the recursive inversion algorithmof a high-dimension matrix is presented. And for the measurements of the multisensorsystems with a common disturbance noise, extending the inversion of the Pei-Radmanmatrix yields a fast inversion of high dimension matrix. Applying the fast inversion al-gorithm into the fused measurement and fused measurement noise variance, their simpleforms are obtained. Applying the Kalman filter based on the information matrix, it isproved that the presented weighted measurement fusion algorithms are completely func- tionally equivalent to the centralized fusion algorithm, i.e. the estimators based on thesealgorithms are globally optimal.Secondly, when the multisensor systems contain the unknown model parametersand noise variances, applying the system identification method, the correlation methodand Gevers-Wouters algorithm with a dead band, the fused and local estimates of theunknown parameters and noise variances are obtained. Substituting these fused estimatesinto optimal weighted measurement fusion Kalman estimators yields self-tuning weightedmeasurement fusion Kalman estimators. This part mainly focuses on two kinds of sys-tems. One is the multisensor system with unknown noise variances and with uncorrelatedmeasurement noises. Another is the multisensor system with unknown model parametersand noise variances and with correlated measurement noises.Thirdly, the convergence and the asymptotical global optimality of the proposedself-tuning multisensor measurement fusion Kalman estimator is proved. The key prob-lem of the convergence analysis is the convergence of the self-tuning Riccati equation.The dynamic variance error system analysis(DVESA) method is presented, where theconvergence problem of the self-tuning Riccati equation is transformed into the stabilityproblem of a dynamic Laypunov equation. Based on the convergence of the self-tuningRiccati equation, applying the dynamic error system analysis (DESA) method, the con-vergence of the proposed self-tuning measurement fusion Kalman estimator is proved, i.e.its asymptotical global optimality is proved.Finally, these presented optimal and self-tuning weighted measurement fusionKalman estimation algorithms are applied to the multisensor single channel autoregressive(AR) signal and the multisensor multichannel autoregressive moving average (ARMA)signal with sensor bias and a common disturbance noise. The AR signal or the ARMAsignal can be transformed into the equivalent state space model, where AR signal or theARMA signal is the partial components of the state. Hence the signal estimation prob- lem is transformed into the state estimation problem. The multi-stage information fusionidentification methods are presented to solve the unknown parameters and noise statis-tics identification problem of the single channel AR signal and the multichannel ARMAsignal. Based on these, the self-tuning measurement fusion Kalman signal estimators arepresented.The simulation examples in the target tracking and signal processing verify the ef-fectiveness of the proposed results and methods.