This work deals with the estimation fusion for distributed multisensor systems under the framework of local estimates being taken as probability density functions. The estimation fusion is formulated to an optimization problem that minimizes the sum of squared distances between the fused probability density and each local probability density. The maximum mean discrepancy, which is a distance between two probability density functions, is considered. It is defined by the kernel mean embeddings from the probability density function space to a reproducing kernel Hilbert space. For the quadratic, cubic and Gaussian kernels, either the analytical solutions are derived or the numerical methods are developed for solving the aforementioned optimization problem. Numerical experiments are provided to illustrate the performance of the proposed estimation fusion methods.

Fusing a hyperspectral image (HSI) and a multispectral image (MSI) to generate a super-resolution image (SRI) with refined spatial and spectral resolution is a popular technique in hyperspectral super-resolution (HSR). Most HSR methods accomplish this task by matrix or tensor decomposition in the framework of linear unmixing. Although these methods are effective to some extent, serious challenges remain. In this work, the linear unmixing is extended to nonlinear unmixing framework and a novel HSR method based on a generalized bilinear unmixing model in tensor format is proposed. Apart from the linear part, it additionally considers bilinear interactions between endmembers. A low-rank prior is incorporated into the abundance maps and nonlinear interaction abundance maps, which can adequately model non-local similarities in images. In addition, the total variance is used to explore the local spatial relationships of the image. The optimization is implemented using the alternating direction method of multipliers (ADMM) algorithm with analytical expressions for each iterative update step, which is difficult to implement even for algorithms that focus on nonlinear unmixing. The proposed method overcomes the inherent linear limitations of the linear unmixing framework and avoids the information loss caused by matrixing the HSI and MSI with 3D-structure. The experimental results of simulations on real hyperspectral datasets demonstrate the superiority of the proposed approach over the compared HSR methods.

The problem of detecting unknown signals using the observations received from an array system with or without perfectly calibrated sensors is addressed. It is formulated as a statistical hypothesis testing on the covariance structure of the received signal. For the received signals following the elliptically symmetric distributions, the generalized likelihood ratio test (GLRT) statistics are derived. Specially, the GLRT detectors for uniform linear arrays are provided. Numerical experiments show the effectiveness of the proposed detectors.

In this paper, an improved shrinkage-to-tapering oracle approximating approach for estimating high-dimensional covariance matrices is proposed. Since the oracle shrinkage coefficient of shrinkage-to-tapering oracle (STO) estimator is greater than one for some tapering parameter, the optimal shrinkage coefficient is obtained by thresholding the oracle coefficients. The corresponding normalized mean-squared error (MSE) is also obtained. Moreover, an improved shrinkage-to-tapering estimator is proposed by plugging the unbiased and consistent estimators of some functions of unknown covariance matrix into the optimal coefficient and corresponding normalized MSE. Compared with the STO approximating approach using iteration to approximate the oracle coefficient, a closed-form formula of the estimated coefficient and the normalized MSE are derived for given tapering parameter. Numerical simulations and an application to adaptive beamforming show the comparable performance of the proposed estimator.

In the multiple target tracking scenarios, the correct matching between targets and measurements is critical. There have been many approaches to resolve this problem called data association. In this paper, a regression method is proposed to resolve the data association problem. In the logistic regression model, nine potential predictor variables are designed which are related to the geometric information of measurements and estimated states of multiple targets, including the distance, intersection angle of position vectors and smoothness of tracks at current time instant and several previous time steps, and the dependent variable is the association probability of matching the measurement with all targets. The regression coefficients are trained through a designed multiple target tracking system. For the new unknown tracking systems with the given number of tracked targets, the measurement having the highest association probability with a target is considered as the true measurement about such target using the trained empirical regression model. Moreover, various filtering algorithms can be invoked to tracking targets. Simulation studies show the proposed novel mechanism for tackling with data association problem in multiple target tracking is effective.

This paper addresses the shrinkage estimation problem of high-dimensional covariance matrices with low sample size data. A class of structured target matrices that include banding, thresholding, diagonal and block diagonal matrices is proposed, and an optimal oracle shrinkage coefficient is derived. To approximate the oracle estimator, an iterative method is presented and proved to be convergent. Moreover, a closed-form solution of its limit, which is guaranteed to be in the unit interval, is obtained. For the banding and thresholding target matrices with unknown bandwidth and threshold respectively, two adaptive algorithms are presented to estimate the covariance matrix, and some properties on the estimation error are discussed theoretically. Some simulations are given to illustrate the competitive performances of proposed covariance matrix estimators.