This paper deals with data (or information) fusionfor the purpose of estimation. Three estimation fusion architecturesare considered: centralized, distributed, and hybrid. A unifiedlinear model and a general framework for these three architecturesare established. Optimal fusion rules based on the best linearunbiased estimation (BLUE), the weighted least squares (WLS), and their generalized versions are presented for cases with complete,incomplete, or no prior information. These rules are moregeneral and flexible, and have wider applicability than previous results.For example, they are in a unified form that is optimal for allof the three fusion architectures with arbitrary correlation of localestimates or observation errors across sensors or across time. Theyare also in explicit forms convenient for implementation. The optimalfusion rules presented are not limited to linear data models.Illustrative numerical results are provided to verify the fusion rulesand demonstrate how these fusion rules can be used in cases withcomplete, incomplete, or no prior information.

In this paper, we present a fusion rule for distributed multihypothesis decision systems where communication patterns among sensors are given and the fusion center may also observe data. It is a specific form of the most general fusion rule, independent of statistical characteristics of bservations and decision criteria, and thus, is called a unified fusion rule of the decision system. To achieve globally optimum performance, only sensor rules need to be optimized under the proposed fusion rule for the given conditional distributions of observations and decision criterion. Following this idea, we present a systematic and efficient scheme for generating optimum sensor rules and ence, optimum fusion rules, which reduce computation tremendously as compared with the commonly used exhaustive search. Numerical examples are given, which support the above results and provide a guideline on how to assign sensors to nodes in a signal detection networks with a given communication pattern. In addition, performance of parallel and tandem networks is compared.

When there exists the limitation of communication bandwidth between sensors and a fusion center, one needs to optimally pre-compress sensor outputs-sensor observations or estimates before sensors' transmission in order to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion; or when an allowed performance loss constraint exists, one needs to design the minimum dimension of sensor data. This paper will answer the above questions by using the matrix decomposition, pseudo-inverse, and eigenvalue techniques.

For single-target multisensor systems, two fusion methods are presented for distributed recursive state estimation of dynamic systems without knowledge of noise covariances. The estimator at every local sensor embeds the dynamics and the forgetting factor into the recursive least squares (RLS) method to remedy the lack of knowledge of noise statistics, developed before as the extended forgetting factor recursive least squares (EFRLS) estimator. It is proved that the two fusion methods are equivalent to the centralized EFRLS that uses all measurements from local sensors directly and their good performance is shown by simulation examples.

This paper shows that a general multisensor unbiased linearly weighted estimationfusion essentially is the linear minimum variance (LMV) estimation with linearequality constraint, and the general estimation fusion formula is developed by extendingthe Gauss-Markov estimation to the random parameter under estimation. First, we formulatethe problem of distributed estimation fusion in the LMV setting. In this setting, thefused estimator is a weighted sum of local estimates with a matrix weight. We show thatthe set of weights is optimal if and only if it is a solution of a matrix quadratic optimizationproblem subject to a convex linear equality constraint. Second, we present a uniquesolution to the above optimization problem, which depends only on the covariance matrixCk. Third, if a priori information, the expectation and covariance, of the estimated quantityis unknown, a necessary and suf[1] cient condition for the above LMV fusion becoming thebest unbiased LMV estimation with known prior information as the above is presented. Wealso discuss the generality and usefulness of the LMV fusion formulas developed. Finally,we provide an off-line recursion of Ck for a class of multisensor linear systems with coupledmeasurement noises.

When there exists the limitation of communication bandwidth between sensors and a fusion center, one needs to optimally pre-compresssensor outputs-sensor observations or estimates before sensors'transmission to obtain a constrained optimal estimation at the fusion center interms of the linear minimum error variance criterion. This paper will give an analytic solution of the optimal linear dimensionality compressionmatrix for the single sensor case and analyze the existence of the optimal linear dimensionality compression matrix for the multisensor case, as well as how to implement a Gauss-Seidel algorithm to search for an optimal solution to linear dimensionality compression matrix.

Optimum-distributed signal detection system design is studied for cases with statistically dependent observations from sensor to sensor. The common parallel architecture is assumed. Here, each sensor sends a decision to a fusion center that determines a final binary decision using a nonrandomized fusion rule. General sensor cases are considered. A discretized iterative algorithm is suggested that can provide approximate solutions to the necessary conditions for optimum distributed sensor decision rules under a fixed fusion rule. The algorithm is shown to converge in a finite number of iterations, and the solutions obtained are shown to approach the solutions to the original problem, without discretization, as the variable step size shrinks to zero. In the formulation, both binary and multiple-bit sensor decisions cases are considered. Illustrative numerical examples are presented for two-L, three-L, and four-sensor cases, in which a common random Gaussian signal is to be detected in Gaussian noise. Some unexpected properties of distributed signal detection systems are also proven to be true. In an L-sensor-distributed detection system, which uses 1 bits in the decisions of the first 1 sensors, the last sensor should use no greater than 21 bits in its decision. Using more than this number of bits cannot improve performance. Further, in these cases, a particular fusion rule, which depends only on the number of bits used in the sensor decisions, can be used without acrificing any performance. This fusion rule can achieve optimum performance with the correct set of sensor decision rules.

In a multisensor target tracking system, observations produced by sensors typically arrive at a central processor out of sequence. There have been some update algorithms for single out-of-sequence measurement (OOSM). In this paper, we consider optimal centralized update algorithms with multiple asynchronous (different lag time) OOSMs. First, we generalize the optimal update algorithm with single one-step-lag OOSM in [Y. Bar-Shalom, "Update With Out-of-Sequence Measurements in Tracking: Exact Solution," IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, vol.38, pp.769-778, July 2002] to optimal centralized update algorithm with multiple one-step-lag OOSMs. Then, based on best linear unbiased estimation, we present an optimal centralized update algorithm with multiple arbitrary-step-lag OOSMs. Finally, two suboptimal centralized update algorithms are proposed to reduce the computational complexity. A numerical example shows that performances of two suboptimal centralized algorithms are close to that of the optimal centralized update algorithm.

In this paper, we consider an asymptotic normality problem for a vector stochastic difference equation of the form Un+1=(I+an(B+En)) Un+an(un+en), where B is a stable matrix, and En→n0, an is a positive real step size sequence with an→n0, Σ∞=1 an=∞, and a-1-a-1→λ≥0, un is an infinite-term moving average process, and en=o(an). Obviously, an here is a quite general step size sequence and includes (log n)β\nα, 1/2<α<1, α=1 with β≥0 as special cases. It is well known that the problem of an asymptotic normality for a vector stochastic approximation algorithm is usually reduced to the above problem. We prove that Un/√an converges in distribution to a zero mean normal random vector with covariance ∞e (B+(182)λI) tRe(Bt+(1/2)λI)t dt, where matrix R depends only on some stochastic properties of un, which implies that the asymptotic distributions for both the vector stochastic difference equation and vector stochastic approximation algorithm do not depend on the specific choices of an directly but on λ, the limit of a-1 a-1.