Study For Recursive Algorithms In Information Processing And Fusion

There are many optimization problems in modern information processing and fusion, for example, communication, control, signal processing, multi-source information fusion, data mining, artificial intelligence, biological genetic information processing, financial analysis, and decision support systems. The notable characters of these problems are that the amount of information is large, and accuracy, high speed and reliability are required in the processing of information. Therefore, it is necessary to study the algorithms in various optimization problems. Especially, recursive algorithms are used in various engineering and technical problems since they can be implemented easily in the actual computational equipments. It is significant to investigate the recursive computational methods of the optimal solutions of various problems in information processing and fusion.In this thesis, we studied some recursive algorithms with wide and important applications to information processing and fusion.1. We proposed the exactly initialized recursive formulas of the least squares problems.It is well-known that the recursive least squares (LS) have very wide applications in various practical fields. In the past, the recursive LS algorithm must start at approximate initialization since the initial observed matrix does not have full column rank. Although the approximate initialization makes a small impact on the whole recursive process in asymptotic sense, it can not be neglected in some practical applications.Moore-Penrose generalized inverses of matrices are often involved in the optimal solutions of various scientific and engineering problems. Their computationinvolves an increasing number of variables with a corresponding increase in the matrix order. To find a recursive version of such an optimal solution, a key technique is an order-recursive version of the generalized inverse of a matrix.We improved the classical order-recursive algorithm proposed by Greville, and obtained new recursive formulas for three different matrix structures. Not only do the proposed formulas reduce the required memory locations of the Greville formula at each recursion by almost half, but they are also very useful to derive the recursive formulas for the optimal solutions involving the generalized inverses of matrices.By using the new formulas, we studied the recursive computation for the LS estimation when the observed data are linearly correlated, and derived recursive LS procedures which coincide exactly with the batch LS solutions for the unconstrained LS, forgetting factor weighted LS, and LS with linear equality constraints, respectively, including their simple and exact initializations. New findings include that the linear equality constrained LS and the unconstrained LS can have an identical recursion ?their only difference is the initial conditions. In addition, some robustness issues, during the exact initialization of the recursive LS, are studied. See [65, 66].2. We proposed a new formula of the best linear unbiased estimation (BLUE) of the generalized Gauss-Markov model.The generalized Gauss-Markov model is an important linear statistical model, in which the designed matrix can have no full column rank and the error covariance matrix can be singular. The best linear unbiased estimation (BLUE) of this model can be regarded as the linear combination of the observed data. The generalized inverses of high dimensional matrices are involved in the BLUE, therefore, it is necessary to study the computational methods for the BLUE.Although the BLUE is unique with probability 1, the coefficients of combination have infinite choices within a subspace. Based on this viewpoint, we selected an appropriate coefficient for a kind of models in dynamic stochastic systems, and proposed a new formula for the BLUE which can be computed recursively.3. We proposed a simple algorithm for the distributed multi-sensor optimal estimation fusion under the general conditions.Under the assumption of independence cross sensor...