Data fusion is the joint analysis of multiple inter-related datasets that provide complementary views of the same phenomenon. The process of correlating and fusing information from multiple sources generally allows more accurate inferences than those that the analysis of a single dataset can yield. Data fusion is a multifaceted concept with clear advantages but at the same time with numerous challenges that need to be carefully addressed. Coupled tensor decompositions have been proved successful in a plethora of data fusion applications, in view of their uniqueness properties and their unique ability to discover and fuse latent multidimensional information from inter-linked datasets. The aim of this chapter is to provide a brief overview of the data fusion concept and its advantages and challenges, with a discussion of coupled tensor decomposition models and methods, showing their power in solving data fusion tasks, as compared to matrix decomposition-based approaches. A few relevant applications are overviewed, particularly the fusion of electroencephalography and functional magnetic resonance imaging data. 

Coupled tensor decompositions for data fusion

The existing multi-sensor control algorithms for multi-target tracking (MTT) within the random finite set (RFS) framework are all based on the distributed processing architecture, so the rule of generalized covariance intersection (GCI) has to be used to obtain the multi-sensor posterior density However, there has still been no reliable basis for setting the normalized fusion weight of each sensor in GCI until now Therefore, to avoid the GCI rule, the paper proposes a new constrained multi-sensor control algorithm based on the centralized processing architecture A multi-target mean-square error (MSE) bound defined in our paper is served as cost function and the multi-sensor control commands are just the solutions that minimize the bound In order to derive the bound by using the generalized information inequality to RFS observation, the error between state set and its estimation is measured by the second-order optimal sub-pattern assignment metric while the multi-target Bayes recursion is performed by using a δ-generalized labeled multi-Bernoulli filter An additional benefit of our method is that the proposed bound can provide an online indication of the achievable limit for MTT precision after the sensor control Two suboptimal algorithms, which are mixed penalty function (MPF) method and complex method, are used to reduce the computation cost of solving the constrained optimization problem Simulation results show that for the constrained multi-sensor control system with different observation performance, our method significantly outperforms the GCI-based Cauchy-Schwarz divergence method in MTT precision Besides, when the number of sensors is relatively large, the computation time of the MPF and complex methods is much shorter than that of the exhaustive search method at the expense of completely acceptable loss of tracking accuracy

https://www.mdpi.com/1424-8220/18/7/2308/pdf

Constrained Multi-Sensor Control Using a Multi-Target MSE Bound and a δ-GLMB Filter

A new optimization algorithm of sensor selection is proposed in this paper for decentralized large-scale multi-target tracking (MTT) network within a labeled random finite set (RFS) framework. The method is performed based on a marginalized δ-generalized labeled multi-Bernoulli RFS. The rule of weighted Kullback-Leibler average (KLA) is used to fuse local multi-target densities. A new metric, named as the label assignment (LA) metric, is proposed to measure the distance for two labeled sets. The lower bound of LA metric based mean square error between the labeled multi-target state set and its estimate is taken as the optimized objective function of sensor selection. The proposed bound is obtained by the information inequality to RFS measurement. Then, we present the sequential Monte Carlo and Gaussian mixture implementations for the bound. Another advantage of the bound is that it provides a basis for setting the weights of KLA. The coordinate descent method is proposed to compromise the computational cost of sensor selection and the accuracy of MTT. Simulations verify the effectiveness of our method under different signal-to- noise ratio scenarios.

Sensor Selection for Decentralized Large-Scale Multi-Target Tracking Network.

The posterior Cramer–Rao bound (PCRB) is a fundamental tool to assess the accuracy limit of the Bayesian estimation problem. In this article, we propose a novel framework to compute the PCRB for the general nonlinear filtering problem with additive white Gaussian noise. It uses the Gaussian mixture model to represent and propagate the uncertainty contained in the state vector and uses the Gauss–Hermite quadrature rule to compute mathematical expectations of vector-valued nonlinear functions of the state variable. The detailed pseudocodes for both the small and large component covariance cases are also presented. Three numerical experiments are conducted. All of the results show that the proposed method has high accuracy and it is more efficient than the plain Monte Carlo integration approach in the small component covariance case.

/pdf/approximating-posterior-cramer-rao-bounds-for-nonlinear-2eq332g76g.pdf

Approximating Posterior Cramér–Rao Bounds for Nonlinear Filtering Problems Using Gaussian Mixture Models

This paper considers the problems of the posterior Cramer–Rao bound and sensor selection for multi-sensor nonlinear systems with uncertain observations. In order to effectively overcome the difficulties caused by uncertainty, we investigate two methods to derive the posterior Cramer–Rao bound. The first method is based on the recursive formula of the Cramer–Rao bound and the Gaussian mixture model. Nevertheless, it needs to compute a complex integral based on the joint probability density function of the sensor measurements and the target state. The computation burden of this method is relatively high, especially in large sensor networks. Inspired by the idea of the expectation maximization algorithm, the second method is to introduce some 0–1 latent variables to deal with the Gaussian mixture model. Since the regular condition of the posterior Cramer–Rao bound is unsatisfied for the discrete uncertain system, we use some continuous variables to approximate the discrete latent variables. Then, a new Cramer–Rao bound can be achieved by a limiting process of the Cramer–Rao bound of the continuous system. It avoids the complex integral, which can reduce the computation burden. Based on the new posterior Cramer–Rao bound, the optimal solution of the sensor selection problem can be derived analytically. Thus, it can be used to deal with the sensor selection of a large-scale sensor networks. Two typical numerical examples verify the effectiveness of the proposed methods.

The Cramér-Rao Bounds and Sensor Selection for Nonlinear Systems with Uncertain Observations.

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.

The estimation fusion and Cramer-Rao bounds for nonlinear systems with uncertain observations

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The Cramér-Rao Bounds and Sensor Selection for Nonlinear Systems with Uncertain Observations.

The estimation fusion and Cramer-Rao bounds for nonlinear systems with uncertain observations