This paper discusses the equivalence of the performance between the optimal distributed and centralized fusion based on best linear unbiased estimation (BLUE). A necessary and sufficient condition for the optimal distributed BLUE fusion to have identical performance as their centralized counterparts is obtained by setting the difference of two optimal estimates based on the two fusion rules be zero. Furthermore, under some very mild conditions on estimatee and observation error, we provide two theorems when the observations are linear in the estimatee. Specifically, the optimal distributed BLUE fusion is identical to the centralized BLUE fusion if observation errors are uncorrelated across sensors or the observation matrix of each sensor is full row rank. Numerical examples corroborate our analysis.

The distributed detection fusion is investigated for conditionally dependent sensor networks with channel errors. When the joint probability density functions of the sensor observations are dependent and high dimensional, it is known to be a challenging problem. This paper deals with this problem under Monte Carlo framework. The Bayesian cost function is approximated by Monte Carlo importance sampling. Necessary conditions for optimal sensor rules and optimal fusion rule are derived in the sense of minimizing the approximated Bayesian cost function, respectively. A Gauss-Seidel/person-by-person optimization algorithm is developed to search the optimal sensor rules. It is proved that the discretized algorithm is finitely convergent. Since the error rate of Monte Carlo integration is regardless of dimensionality, the complexity of the new algorithm is much less than that of the previous algorithm based on Riemann sum approximation. The proposed method allows us to design the sensor networks with a higher dimensional joint probability density function of the sensor observations. The typical examples with dependent observations and channel errors are examined. The results of numerical examples demonstrate the effectiveness of the new algorithm.

Multiple-source localization problem based on acoustic energy measurements is investigated by set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurement is a complicated nonlinear function of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. The main contribution of this paper is as follows. Firstly, to deal with the nonlinear function, it is linearized by the first-order Taylor expansion with a remainder error. The point is that the bounding box of the remainder is derived in each iteration based on the convex bounding set of the state. Especially, when the state can be bounded in a cylinder, the remainder bound can be achieved analytically. Secondly, based on the separate property of the nonlinear observation function, an efficient estimation procedure is developed to deal with the high-dimensional state estimation problem by using an alternately optimization iterative algorithm. In the process of iteration, the remainder bound requires to be known on-line. Finally, a typical numerical example in multiple-source localization demonstrates the effectiveness of the set-membership localization algorithms. In particular, it shows that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the maximum likelihood localization algorithm.

This paper explores a novel model to describe linear dynamic system with random delays. Compared with the existing research, the probabilities of random delays in the novel model are calculated by conditional probabilities. Therefore, the process noises and measurements noises in the new model for random delay problems are infinitely correlated. By treating the model as random parameter matrices Kalman filtering with one-step correlated noises approximately, the new state estimators are presented. Numerical examples show that the new estimators work better than the existing algorithm in many cases.

The set-membership information fusion problem is investigated for general multisensor nonlinear dynamic systems. Compared with linear dynamic systems and point estimation fusion in mean squared error sense, it is a more challenging nonconvex optimization problem. Usually, to solve this problem, people try to find an efficient or heuristic fusion algorithm. It is no doubt that an analytical fusion formula should be much significant for raising accuracy and reducing computational burden. However, since it is a more complicated than the convex quadratic optimization problem for linear point estimation fusion, it is not easy to get the analytical fusion formula. In order to overcome the difficulty of this problem, two popular fusion architectures are considered: centralized and distributed set-membership information fusion. Firstly, both of them can be converted into a semidefinite programming problem which can be efficiently computed, respectively. Secondly, their analytical solutions can be derived surprisingly by using decoupling technique. It is very interesting that they are quite similar in form to the classic information filter. In the two analytical fusion formulae, the information of each sensor can be clearly characterized, and the knowledge of the correlation among measurement noises across sensors are not required. Finally, multi-algorithm fusion is used to minimize the size of the state bounding ellipsoid by complementary advantages of multiple parallel algorithms. A typical numerical example in target tracking demonstrates the effectiveness of the centralized, distributed, and multi-algorithm set-membership fusion algorithms. In particular, it shows that multi-algorithm fusion performs better than the centralized and distributed fusion.

The estimation fusion problem and posterior Cramer-Rao bound (PCRB) are presented for multi-sensor nonlinear systems with uncertain observations. In order to effectively deal with the difficulties caused by uncertainty, a novel method is proposed by introducing 0-1 latent variables. It has two nice properties. Firstly, the derived estimation fusion method can take full advantage of the character of the nonlinear function and uncertain observations. Secondly, the uncertain system with a discrete variable can be approximated by a continuous system, where the discrete distribution of the latent variable is approximated by a continuous one, then the PCRB can be achieved by a limiting process of PCRB for the continuous system. Since the derived PCRB has an analytical expression, it can reduce the computational burden much more. A typical numerical example in target tracking demonstrates the effectiveness of the estimation fusion method and the proposed PCRB for the uncertain observation systems.

A novel random data association algorithm is proposed in the framework of multiple hypothesis tracking which can be equivalent to an NP-hard multidimensional assignment problem. The key idea of this new algorithm is to relax the multidimensional assignment problem to a linear programming problem. The solution of the linear programming problem may be treated as the probability of potential tracks, which avoids the computation difficulties of rounding the probability solution to 0/1 satisfying the constraints. Then all tracks and measurements can be integrated to a new whole dynamic system with random coefficient matrices. Moreover, the random coefficient matrix Kalman filtering is applied to the integrated dynamic system to derive the state estimates of the tracks. The significant advantage of the random Kalman filter-based multiple hypothesis tracking data association is that the computation complexity is much less than that of Lagrangian relaxation of the multidimensional assignment problem. Simulation demonstrates the random data association algorithm works well and the running time can be shortened greatly compared with the Lagrangian relaxation algorithm of the multidimensional assignment problem.

In this paper, the problem of robust minimax testing of binary composite hypothesis is considered, while the actual probability densities are located in neighborhoods characterized by the Itakura-Saito divergence. And then the existence of a saddle value condition is proved under Sion's minimax theorem. Moreover, we derive the least favorable distributions and the robust decision rule involved four parameters, thus an infinite-dimensional optimization problem could be transformed into a nonlinear system of four equations with four unknown parameters, which can be solved numerically. Finally, experimental results evaluate and illustrate the theoretical derivations.

Although the globally optimal distributed Kalman filtering fusion has been proposed and studied for more than twenty years, the invertibility of estimation error and measurement noise covariances has been always a restrictive assumption to derive a globally optimal distributed Kalman filtering fusion equivalent to the centralized Kalman filtering fusion. This letter proposes an optimal distributed Kalman filtering fusion algorithm for general dynamic systems without invertibility of estimation error and measurement noise covariances. The new algorithm uses the convex combination fusion, whose fusion weights are recursively given. Computer experiments show that the performance of this fusion algorithm is very likely to be equivalent to that of the centralized Kalman filtering fusion. In practice, the new fusion algorithm can be applied to any distributed Kalman filtering fusion, such as the equality constrained distributed Kalman filtering fusion.

In this paper, a multisensor linear dynamic system with model uncertainty and bounded noises is considered. Based on previously developed set-valued estimation methods in terms of convex optimization, we propose several efficient algorithms of centralized sensor fusion, distributed sensor fusion, and multi-algorithm fusion to minimize the Euclidian estimation error of the state vector. Obviously, an ellipsoid/box with a larger “size” cannot be in general guaranteed to contain another ellipsoid/box with a smaller “size” since centers and shapes of the two ellipsoids/boxes may be different from each other. This fact and the complementary advantages of multiple sensors and multiple algorithms motivate us to construct multiple estimation ellipsoids/boxes squashed along each entry of the state vector as much as possible respectively by using the technique of multiple differently weighted objectives. Then intersection fusion of these estimation ellipsoids/boxes yields a final Euclidian-error-minimized state estimate. Numerical examples show that the new method with multi-algorithm at both the sensors and the fusion center can significantly reduce the Euclidian estimation error of the state.

In this paper, the robust estimation fusion problem in multisensor systems with norm-bounded uncertainties concerning the error covariance matrix between local estimates is addressed. A robust fusion method by minimizing the worst-case fused mean-squared error (MSE) for all feasible error covariance matrices of local estimates is proposed. The minimax robust fusion weighting matrices can be explicitly formulated as a function of solution of a semidefinite programming (SDP). Some numerical examples demonstrate that when the error covariance matrix suffers disturbance, the proposed fusion method is more robust than the nominal fusion method which ignores the uncertainties, and can improve the performance when the disturbance is considerably large.

In this paper, the communication direction problem of a two-sensor tandem binary decision system is considered. Rigorous analysis shows that the performance of communication from the sensor with higher noise power to the sensor with lower noise power is not always better than the performance of the reverse communication direction when the signal and sensor noises are both Gaussian. This result can be extended to a more general two-sensor tandem binary decision system without the assumption of a specific data distribution. This seems somewhat counterintuitive but has significance for optimization design of sensor communication direction. Computer experiments support our analytic results and illustrate interesting information which requires need further study.

Under the assumption of independent observation noises across sensors, Bar-Shalom and Campo proposed a distributed fusion formula for two-sensor systems, whose main calculation is the inverse of submatrices of the error covariance of two local estimates instead of the inverse of the error covariance itself. However, the corresponding simple estimation fusion formula is absent in a general distributed multisensor system. In this paper, an efficient iterative algorithm for distributed multisensor estimation fusion without any restrictive assumption on the noise covariance (i.e., the assumption of independent observation noises across sensors and the two-sensor system, and the direct computation of the Moore-Penrose generalized inverse of the joint error covariance of local estimates are not necessary) is presented. At each iteration, only the inverse or generalized inverse of a matrix having the same dimension as the error covariance of a single-sensor estimate is required. In fact, the proposed algorithm is a generalization of Bar-Shalom and Campo's fusion formula and reduces the computational complexity significantly since the number of iterative steps is less than the number of sensors. An example of a three-sensor system shows how to implement the specific iterative steps and reduce the computational complexities

This paper shows that a general multisensor unbiased linearly weighted estimation fusion essentially is the linear minimum variance (LMV) estimation with linear equality constraint, and the general estimation fusion formula is developed by extending the Gauss-Markov estimation to the random parameter under estimation. First, we formulate the problem of distributed estimation fusion in the LMV setting. In this setting, the fused estimator is a weighted sum of local estimates with a matrix weight. We show that the set of weights is optimal if and only if it is a solution of a matrix quadratic optimization problem subject to a convex linear equality constraint. Second, we present a unique solution to the above optimization problem, which depends only on the covariance matrix k . Third, if a priori information, the expectation and covariance, of the estimated quantity is unknown, a necessary and sufficient condition for the above LMV fusion becoming the best unbiased LMV estimation with known prior information as the above is presented. We also discuss the generality and usefulness of the LMV fusion formulas developed. Finally, we provide an off-line recursion of k for a class of multisensor linear systems with coupled measurement noises.

This paper deals with data (or information) fusion for the purpose of estimation. Three estimation fusion architectures are considered: centralized, distributed, and hybrid. A unified linear model and a general framework for these three architectures are established. Optimal fusion rules based on the best linear unbiased 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 more general and flexible, and have wider applicability than previous results. For example, they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time. They are also in explicit forms convenient for implementation. The optimal fusion rules presented are not limited to linear data models. Illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete, 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 observations 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 hence, 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.