Clutter rejection for MTI radar using a single antenna and a long integration time

Moving Target Indicators (MTI) are airborne radar systems designed to detect and track moving vehicles or aircrafts. In this paper, we address the problem of detecting hazardous collision targets to avoid them. One of the best known solutions to solve this problem is given by the so-called Space-Time Adaptive Processing (STAP) algorithms which optimally filter the target signal from interference and noise exploiting the specific relationship between Direction Of Arrival (DOA) and Doppler for the ground clutter. However, these algorithms require an antenna array and multiple reception channels that increase cost and complexity. The authors propose an alternative solution using a single antenna only. In addition to the standard Doppler shift related to the radial speed, the orthoradial speed of any target can be estimated if using a long integration time. Dangerous targets and ground clutter have different signatures in the radial-orthoradial velocity plane. An optimal detector is then proposed based on the oblique projection onto the signal subspace orthogonal to the clutter subspace. The theoretical performances of this detector are derived and a realistic radar scene simulation shows the benefits of this new MTI detector

Sparse-Based Estimation Performance for Partially Known Overcomplete Large-Systems

We assume the direct sum o for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace and the goal is to estimate the LA am- plitudes corresponding to subspace . Taking into account the knowledge of the orthogonal "interfering" subspace \perp, the Bayesian estimation lower bound is de- rivedfortheLA-sparsevectorinthedoublyasymptoticscenario,i.e. N,LA,LB -> \infty with a finite asymptotic ratio. By jointly exploiting the Compressed Sensing (CS) and the Random Matrix Theory (RMT) frameworks, closed-form expressions for the lower bound on the estimation of the non-zero entries of a sparse vector of interest are derived and studied. The derived closed-form expressions enjoy several interesting features: (i) a simple interpretable expression, (ii) a very low computational cost especially in the doubly asymptotic scenario, (iii) an accurate prediction of the mean-square-error (MSE) of popular sparse-based estimators and (iv) the lower bound remains true for any amplitudes vector priors. Finally, several idealized scenarios are compared to the derived bound for a common output signal-to-noise-ratio (SNR) which shows the in- terest of the joint estimation/rejection methodology derived herein.Comment: 10 pages, 5 figures, Journal of Signal Processin

Joint ML calibration and DOA estimation with separated arrays

This paper investigates parametric direction-of-arrival (DOA) estimation in a particular context: i) each sensor is characterized by an unknown complex gain and ii) the array consists of a collection of subarrays which are substantially separated from each other leading to a structured noise covariance matrix. We propose two iterative algorithms based on the maximum likelihood (ML) estimation method adapted to the context of joint array calibration and DOA estimation. Numerical simulations reveal that the two proposed schemes, the iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint array calibration and DOA estimation, outperform the state of the art methods and the MIML algorithm reaches the Cram\'er-Rao bound for a low number of iterations

Prior Knowledge Optimum Understanding by Means of Oblique Projectors and Their First Order Derivatives

International audienceRecently, an optimal Prior-knowledge method for DOA estimation has been proposed. This method solely estimates a subset of DOA's accounting known ones. The global idea is to maximize the orthogonal-ity between an estimated signal subspace and noise subspace by constraining the orthogonal noise-made projector to only project onto the desired unknown signal subspace. As it could be surprising, no deflation process is used for. Understanding how it is made possible needs to derive the variance for the DOA estimates. During the derivation, oblique projection operators and their first order derivatives appear and are needed. Those operators show in consequence how the optimal Prior-knowledge criterion can focus only on DOA's of interest and how the optimality is reached

Matched direction detectors and estimators for array processing with subspace steering vector uncertainties

In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the steering vector but, on the other hand, some knowledge about the steering vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Cramer-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this problem is NP-hard to compute, relaxations of atomic $l_0$ norm, such as nuclear norm and reweighted atomic norm, have been employed for promoting sparsity. However, the relaxations give rise to a resolution limit, subsequently leading to biased model order and convergence error. To overcome the above shortcomings of relaxation, we propose a novel idea of simultaneously estimating the frequencies and model order by means of the atomic $l_0$ norm. To accomplish this idea, we build a multiobjective optimization model. The measurment error and the atomic $l_0$ norm are taken as the two optimization objectives. The proposed model directly exploits the model order via the atomic $l_0$ norm, thus breaking the resolution limit. We further design a variable-length evolutionary algorithm to solve the proposed model, which includes two innovations. One is a variable-length coding and search strategy. It flexibly codes and interactively searches diverse solutions with different model orders. These solutions act as steppingstones that help fully exploring the variable and open-ended frequency search space and provide extensive potentials towards the optima. Another innovation is a model order pruning mechanism, which heuristically prunes less contributive frequencies within the solutions, thus significantly enhancing convergence and diversity. Simulation results confirm the superiority of our approach in both frequency estimation and model order selection.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Parallel Factor-Based Model for Two-Dimensional Direction Estimation

Two-dimensional (2D) Direction-of-Arrivals (DOA) estimation for elevation and azimuth angles assuming noncoherent, mixture of coherent and noncoherent, and coherent sources using extended three parallel uniform linear arrays (ULAs) is proposed. Most of the existing schemes have drawbacks in estimating 2D DOA for multiple narrowband incident sources as follows: use of large number of snapshots, estimation failure problem for elevation and azimuth angles in the range of typical mobile communication, and estimation of coherent sources. Moreover, the DOA estimation for multiple sources requires complex pair-matching methods. The algorithm proposed in this paper is based on first-order data matrix to overcome these problems. The main contributions of the proposed method are as follows: (1) it avoids estimation failure problem using a new antenna configuration and estimates elevation and azimuth angles for coherent sources; (2) it reduces the estimation complexity by constructing Toeplitz data matrices, which are based on a single or few snapshots; (3) it derives parallel factor (PARAFAC) model to avoid pair-matching problems between multiple sources. Simulation results demonstrate the effectiveness of the proposed algorithm