Robustness of subspace-based algorithms with respect to the distribution of the noise: application to DOA estimation

International audienceThis paper addresses the theoretical analysis of the robustness of subspace-based algorithms with respect to non-Gaussian noise distributions using perturbation expansions. Its purpose is twofold. It aims, first, to derive the asymptotic distribution of the estimated projector matrix obtained from the sample covariance matrix (SCM) for arbitrary distributions of the useful signal and the noise. It proves that this distribution depends only of the second-order statistics of the useful signal, but also on the second and fourth-order statistics of the noise. Second, it derives the asymptotic distribution of the estimated projector matrix obtained from any M-estimate of the covariance matrix for both real (RES) and complex elliptical symmetric (CES) distributed observations. Applied to the MUSIC algorithm for direction-of-arrival (DOA) estimation, these theoretical results allow us to theoretically evaluate the performance loss of this algorithm for heavy-tailed noise distributions when it is based on the SCM, which is significant for weak signal-to-noise ratio (SNR) or closely spaced sources. These results also make it possible to prove that this performance loss can be alleviated by replacing the SCM by an M-estimate of the covariance for CES distributed observations, which has been observed until now only by numerical experiments

Robust Multiple Signal Classification via Probability Measure Transformation

In this paper, we introduce a new framework for robust multiple signal classification (MUSIC). The proposed framework, called robust measure-transformed (MT) MUSIC, is based on applying a transform to the probability distribution of the received signals, i.e., transformation of the probability measure defined on the observation space. In robust MT-MUSIC, the sample covariance is replaced by the empirical MT-covariance. By judicious choice of the transform we show that: 1) the resulting empirical MT-covariance is B-robust, with bounded influence function that takes negligible values for large norm outliers, and 2) under the assumption of spherically contoured noise distribution, the noise subspace can be determined from the eigendecomposition of the MT-covariance. Furthermore, we derive a new robust measure-transformed minimum description length (MDL) criterion for estimating the number of signals, and extend the MT-MUSIC framework to the case of coherent signals. The proposed approach is illustrated in simulation examples that show its advantages as compared to other robust MUSIC and MDL generalizations

Analysis of Geolocation Approaches Using Satellites

A space based system capable of geolocating radio frequency signals of interest has wide reaching application to the Air Force. This system would provide increased situational awareness to the warfighter on the battlefield. The Air Force Institute of technology is developing a satellite to conduct research on geolocation using CubeSats. A methodology to evaluate space based geolocation systems by varying orbital altitude and transmitter position for a given geolocation algorithm and satellite configuration was developed. This method allows multiple satellite configurations and geolocation algorithms to be compared during the design process of a space based geolocation system. The method provides a tool to facilitate decision making on the configuration design and geolocation methods chosen for a given system design. This research explains the geolocation methods and provides comparisons for one through four satellite configurations for time difference of arrival and angle of arrival geolocation algorithms

Array and multichannel signal processing using nonparametric statistics

In array signal processing a group of sensors located at distinct spatial locations is deployed to measure a propagating wavefield. The multichannel output is then processed to provide information about parameters of interest. Application areas include smart antennas in communications, radar, sonar and biomedicine. When deriving array signal processing algorithms the noise is typically modeled as a white Gaussian random process. A shortcoming of the estimation procedures derived under Gaussian assumption is that they are extremely sensitive to deviations from the assumed model, i.e. they are not robust. In real-world applications the assumption of white Gaussian noise is not always valid. Consequently, there has been a growing interest in estimation methods which work reliably in both Gaussian and non-Gaussian noise. In this thesis, new statistical procedures for array and multichannel signal processing are developed. In the area of array signal processing, the work concentrates on high-resolution subspace-based Direction Of Arrival (DOA) estimation and estimation of the number of source signals. Robust methods for DOA estimation and estimation of the number of source signals are derived. Spatial-smoothing based extensions of the techniques to deal with coherent signals are also derived. The methods developed are based on multivariate nonparametric statistics, in particular sign and rank covariance matrices. It is shown that these statistics may be used to obtain convergent estimates of the signal and noise subspaces for a large family of symmetric noise distributions. Simulations reveal that the techniques developed exhibit near-optimal performance when the noise distribution is Gaussian and are highly reliable if the noise is non-Gaussian. Multivariate nonparametric statistics are also applied to frequency estimation and estimation of the eigenvectors of the covariance matrix. Theoretical justification for the techniques is shown and their robust performance is illustrated in simulations.reviewe