Cross Covariance Information Fusion Filter

Multisensor information fusion Kalman filtering is the combination of informationfusion and filtering theory, the main purpose is to correlation, estimation and fusionlocal information and data to get a more accurate fusion estimation than single sourceestimate. Now the commonly used method of information fusion filtering is centralizedfusion Kalman filtering and distributed fusion Kalman filtering.Distributed fusion Kalman filtering based on linear minimum variance rules hasthree information fusion algorithm according to the matrix weighted, scalar weightedand diagonal matrix weighted. Compared with the centralized fuser, the distributed fusercan reduce the calculation burden and are more flexible and reliable. The distributedfusion estimation needs to calculate the cross-covariance of local estimate. However, inmany theoretical and application problems, the cross-covariance is unknown, or thecomputing of the cross-covariance is very difficult, or may not calculate thecross-covariance. If the cross-covariance is neglected, they are assumed to be zero,which can lead to the increase of the variance of the local filtering error, even thedivergence of the filtering.In this paper, the covariance intersection fusion Kalman filtering algorithm ispresented, which can avoid identification and computing local cross-covariance and cansolve the fused filtering problems for multisensor systems with unknowncross-covariance. Covariance intersection fusion algorithm give an upper bound ofactual filtering error variances, and the upper bound is irrelevant of the unknowncross-covariance, so the consistency and robustness are ensured, and CI fusionalgorithm can reduce the computing burden and avoid the divergence of Kalmanfiltering. Further, the proof of consistency is given.For the two-sensor stochastic system with uncorrelated observation noises, correlated observation noises and colored observation noises, and with unknowncross-covariance, the CI fusion Kalman filtering is presented.For the multisensor stochastic system that the number of sensor is equal or greaterthan three, the sequential CI fusion Kalman filtering and batch CI fusion Kalmanfiltering are presented, and their consistency is proved.Applying the proposed results to the signal processing, based on the transformationof the ARMA model to the state space model, the signal estimation problems cantranslate into the state estimation problems. The two-sensor multi-channel ARMA signalCI fusion filtering is presented.For the two-sensor stochastic system with time-delayed measurements, using themeasurement transformation method, the time-delayed system with measurement delayscan be transformed into the standard system without measurement delays directly. TheCI fusion Kalman filtering for two-sensor system with time-delayed is presented.In this paper, the accuracy relations among the CI fuser, local Kalman fusers,centralized fuser and fusers weighted by matrix,scalar or diagonal are proved. Theaccuracy of the CI fuser is higher than each local fusers and close to the accuracy of thefuser weighted by matrix, the accuracy of fuser weighted by matrix is higher than that ofthe fuser weighted by scalar and the accuracy of the fuser weighted by diagonal isbetween them. The geometric interpretations of these accuracy relations are given basedon the covariance ellipses, Monte-Carlo simulation results show the accuracy of therelations.Many simulation examples show the effectiveness and correctness of thetheoretical results.