Search

In this letter we address the problem of multistatic target localization using time-delay measurements corrupted by noise with unknown non-uniform variances. More concretely, we consider the problem of joint maximum likelihood (ML) estimation of the target position and the noise variances, for which we propose a majorization-minimization based algorithm. The proposed approach is compared with state-of-the-art algorithms, and the simulation results show the excellent accuracy of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose an iterative algorithm named PGPAL for the phase-retrieval problem under the scenario when the measurements follow Poisson plus Gaussian (PG) distribution, which is a more realistic model in applications like astronomy, microscopy, medical imaging, and remote sensing. The proposed algorithm is based on majorization-minimization (MM) framework, in which a simple surrogate function that tightly upperbounds the challenging underlying maximum-likelihood (ML) objective is constructed and minimized iteratively. The proposed algorithm monotonically decreases the ML objective and the algorithm is guaranteed to converge to a stationary point of the ML objective. Numerical simulations are performed for the one-dimensional phase-retrieval case, and the performance of the proposed method is compared with the recently proposed Poisson phase-retrieval algorithm, which assumes the measurement model to be only Poisson distributed. The performance of the proposed MM-based algorithm in terms of the normalized root mean square error (NRMSE) is found to be much better in comparison to the method for Poisson phase-retrieval. [ABSTRACT FROM AUTHOR]

In this letter, we develop a low-complexity algorithm named maximum-likelihood estimation of low-rank Toeplitz covariance matrix (MELT) to solve the maximum-likelihood estimation of a low-rank Toeplitz covariance matrix. Our derivation of MELT is based on the technique of majorization–minimization (MM), in which we design and optimize a novel tight upper-bound function. MELT is an iterative algorithm, and its each iterative step is a closed-form update, which can be implemented efficiently by fast Fourier transforms. As MELT is based on MM, it enjoys nice properties such as monotonicity and guaranteed convergence to a stationary point. Finally, we numerically show that the performance of MELT is much better than some of the algorithms currently available in the literature. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of the clutter subspace projector estimation in the context of a disturbance composed of a low rank heterogeneous (Compound Gaussian) clutter and white Gaussian noise. In such a context, adaptive processing based on an estimated orthogonal projector onto the clutter subspace (instead of an estimated covariance matrix) requires less samples than classical methods. The clutter subspace estimate is usually derived from the eigenvalue decomposition of a covariance matrix estimate. However, it has been previously shown that a direct maximum likelihood estimator of the clutter subspace projector can be obtained for the considered context. In this paper, we derive two algorithms based on the block majorization-minimization framework to reach this estimator. These algorithms are shown to be computationally faster than the state of the art, with guaranteed convergence. Finally, the performance of the related estimators is illustrated on realistic Space Time Adaptive Processing for airborne radar simulations. [ABSTRACT FROM PUBLISHER]

In this paper, the joint mean-covariance estimation problem is considered under the scenario that the number of samples is small relative to the problem dimension. The samples are assumed drawn independently from a heavy-tailed distribution of the elliptical family, which can model scenarios where the commonly adopted Gaussian assumption is violated either because of the data generating process or the contamination of outliers. Under the assumption that prior knowledge of the mean and covariance matrix is available, we propose a regularized estimator defined as the minimizer of a penalized loss function, which combines the prior information and the information provided by the samples. The loss function is chosen to be the negative log-likelihood function of the Cauchy distribution as a conservative representative of heavy-tailed distributions, and the penalty term is constructed with the prior being its global minimizer. The resulting regularized estimator shrinks the mean and the covariance matrix to the prior target. The existence and uniqueness of the estimator for finite samples are established under certain regularity conditions. Numerical algorithms are derived for the estimator based on the majorization-minimization framework with guaranteed convergence and simulation results demonstrate that the proposed estimator achieves better estimation accuracy compared to the benchmark estimators. [ABSTRACT FROM PUBLISHER]

The Bayesian Information Criterion (BIC) is often presented in a form that is only valid in large samples and under a certain condition on the rate at which the Fisher Information Matrix (FIM) increases with the sample length. This form has been improperly used previously in situations in which the conditions mentioned above do not hold. In this correspondence, we describe the proper forms of BIC in several practically relevant cases that do not satisfy the above assumptions. In particular, we present a new form of BIC for high signal-to-noise ratio (SNR) cases. The conclusion of this study is that BIC remains one of the most successful existing rules for model order selection, if properly used. [ABSTRACT FROM PUBLISHER]

This paper introduces a maximum-likelihood method for the nonparametric estimation of smooth spectra from irregularly sampled observations, which is abbreviated as LIMES (LIkelihood-based Method for Estimation of Spectra). As a byproduct, LIMES also provides an estimate of the data covariance matrix that may be of interest in its own right. Spectral estimation from irregularly sampled data is a rather difficult problem and there are only a handful of methods in the literature that can be used for such a task. Of these already existing methods we consider the Daniell method (DAM) for comparison with LIMES. Computationally, LIMES is more complex than DAM. On the other hand, DAM is much less accurate than LIMES in the irregularly sampled data case and for spectra with a relatively large bandwidth. In a nutshell, LIMES should be the method of choice in the unevenly sampled data applications that require high statistical performance and can tolerate an increased computational burden. [ABSTRACT FROM AUTHOR]