Some Progress In Information Fusion And Processing

In the area of information science and technology, the multiple source informationfusion is a research topic that has the widespread application backgrounds and impor-tant theory significance. Establishing its "essential mathematics framework" was onceregarded as a research topic of "extreme priority" by the United States military electronresearch strategy report. In the practice, in order to enhance the precision, timeliness,steadiness and survivability in the adverse circumstance of the information processing,the multisensor information fusion technology widely is already used and researched inthe developed country. It has the widespread practical applications in many military andthe civil department, such as in the war environment military intelligence, communi-cations, computer networks, control and command integration systems, the key defenseequipment, like aircraft carrier, early-warning aircraft, ?ight vehicle guidance technology,air traffic management, optics project, robot, economical system forecast and regulationand so on. Although information fusion research has obtained great progress in the worldin the past 20-30 years, their achievements were still required some restrictive conditions.For example in the statistical decision fusion aspect, people need statistical independenceof multiple source information; in the estimate fusion aspect, one requests sensor obser-vations or sensor noises to be mutually independent. However, these may not be satisfiedvery often in practice.Also in the 80's, under the restrictive condition that the sensor noises are mutu-ally independent, a Kalman filtering fusion formula has been already obtained, and hadbeen proven that it is equivalent to the centralized Kalman filtering achieving the bestglobal performance. But when the sensor noises are correlated, there has been no thecorresponding Kalman filtering fusion formula achieving the best global performancefor about 20 years. In this thesis, we present a multisensor Kalman filtering fusion for- mula by ingeniously using the Kalman filtering theory and the generalized matrix inversetechnique when the sensor noises are correlated, and prove that under a mild conditionthe fused state estimate is equivalent to the centralized Kalman filtering using all sen-sor measurements, therefore, it achieves the best global performance. When the sensornoises are correlated and there is a feedback from the fusion center to sensors, a modifiedKalman filtering fusion with feedback is proposed, and prove that the fusion formula withfeedback is, as the fusion without feedback, still exactly equivalent to the correspondingcentralized Kalman filtering fusion formula. Moreover, the feedback does improve thelocal estimated performance at all sensors. Thus, it has provided the theory basis forusing the modified distributed Kalman filtering fusion with feedback. Our above newresults include all previous results of Kalman filtering fusion formula with independentsensor noises and its performance analysis as special cases.In the multisensor estimate fusion networks, obviously, communications would beinevitably greatly increased as the number of sensors becomes large. in order to imple-ment real-time processing, how to reduce communication bandwidth occupation is oneof key questions that can not be avoided. In particular, when there exists the limitation ofcommunication bandwidth between sensors and a fusion center, one needs to optimallypre-compress sensor outputs–sensor observations or estimates before sensors'transmis-sion. Thus, we need to obtain an optimal sensor's compression matrix in terms of thelinear minimum error variance criterion. In the 90's, sensor's observation dimensionalitycompression without loss of system performance had been obtained. For a generalizedcase, optimal dimensionality compression of arbitrarily requested dimension still needsto be solved. In this thesis, for an arbitrarily requested dimension, we firstly present ananalytic solution of the optimal linear dimensionality compression matrix for the singlesensor case and multisensor case with sensor estimation errors mutually independent.When sensor estimation error are mutually across-correlated, Z.Q. Luo has proved thatthere is no analytic solution of the optimal linear dimensionality compression matrix. Weprove its existence and give an effective Gauss-Seidel iteration algorithm to search for asuboptimal solution of linear dimensionality compression matrix, of course, which maybe an optimal.The optimal design of the multisensor decision fusion network is an important prob-lem related to improvement of performance of the network. Since it is extremely compli- cated and difficult, there has been no any analytic result on this issue up to now. For thedesign of communication direction among sensors, the people think that a sensor with asmall noise power should obtain more message from intuitive point of view. Thus, in amultisensor decision fusion network, a sensor with a large noise power should transmitits message, namely bits, to a sensor with a small noise power, and the latter should beclose to the fusion center in the network, or it is the center itself. Although many com-puter simulation results published have not violated this intuition imagination, but it isalways unreliable without support of a rigorous analysis. In a two-sensor tandem binarydecision system with a bit communication from a sensor to another one, when the signaland sensor noises are both Gaussian, under mild conditions, a rigorous analysis showsthat the performance of communication from the sensor with higher noise power to thesensor with lower noise power will not always better than the performance of the reversecommunication direction, which seems somehow counterintuitive and generally signif-icant for optimization design of sensor communication direction. The performance ofcommunication direction in fact depends not only on the specific two sensor noise pow-ers, but also other parameters of the system model. The above result can be extended tomore general two-sensor tandem binary decision system without statistical knowledge ofsensor observations. Computer experiments support our analytic results.The unbiased estimate has been studied extensively in the estimate theory. Withoutrequirement of unbiasness, an estimate can often be remarkably improved in its perfor-mance. Thus, the method of biased estimate has obtained widespread applications, andstarted attracting more and more attention in the past a few years. It is well knownthat the total variance of any biased estimator with a given bias is lower bounded by theCramér-Rao lower bound (CRLB) ([72]), which is an extension of the CRLB for unbiasedestimators. We present an analytic solution of biased gradient matrix of biased estimatewhich make CRLB reaching its minimum when the Fisher information matrix is singularand bias gradient matrix whose norm is upper bounded by a constant. Furthermore, wegive the two biased estimators which attain the minimum bound for two different norm.In the recent two years, the above problems were already solved in [61] thoroughly onlywhen the Fisher information matrix is nonsingular. This paper is an answer to the openquestion proposed there and is an all-sided extension of [61] for general Fisher infor-mation matrix. Unlike the case of nonsingular Fisher information matrix, in addition to derive the results more complicatedly here, we must carefully analyze the problem andremove some special cases which is brought by a singular Fisher information matrix.For example, to guarantee to have a feasible solution of the problem, the bias gradientmatrix may have nonzero lower bound, which implies that unbiased or nearly unbiasedestimators may not exist when the Fisher information matrix is singular.The above four aspect questions have attracted attention for a long-term in the worldand become the hot spot in the research topic nearly two years in the applied mathematicsand the information science overlapping domain, which has the very strong applicationbackgrounds and the remarkable theory significance. The present paper give a relativelythorough answers to the above questions.