Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey

Principal component analysis (PCA) and subspace estimation (SE) are popular data analysis tools and used in a wide range of applications. The main interest in PCA/SE is for dimensionality reduction and low-rank approximation purposes. The emergence of big data streams have led to several essential issues for performing PCA/SE. Among them are (i) the size of such data streams increases over time, (ii) the underlying models may be time-dependent, and (iii) problem of dealing with the uncertainty and incompleteness in data. A robust variant of PCA/SE for such data streams, namely robust online PCA or robust subspace tracking (RST), has been introduced as a good alternative. The main goal of this paper is to provide a brief survey on recent RST algorithms in signal processing. Particularly, we begin this survey by introducing the basic ideas of the RST problem. Then, different aspects of RST are reviewed with respect to different kinds of non-Gaussian noises and sparse constraints. Our own contributions on this topic are also highlighted

A new adaptive Kalman filter-based subspace tracking algorithm and its application to DOA estimation

IEEE International Symposium on Circuits and Systems, Island of Kos, Greece, 21-24 May 2006This paper presents a new Kalman filter-based subspace tracking algorithm and its application to directions of arrival (DOA) estimation. An autoregressive (AR) process is used to describe the dynamics of the subspace and a new adaptive Kalman filter with variable measurements (KFYM) algorithm is developed to estimate the time-varying subspace recursively from the state-space model and the given observations. For stationary subspace, the proposed algorithm will switch to the conventional PAST to lower the computational complexity. Simulation results show that the adaptive subspace tracking method has a better performance than conventional algorithms in DOA estimation for a wide variety of experimental condition. © 2006 IEEE.published_or_final_versio

Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.Comment: Double-column 15 pages, 10 figures, submitted to IEEE Trans. Signal Processin

GUNSHOT DIRECTION OF ARRIVAL DETERMINATION USING BIO-INSPIRED MEMS SENSORS

A key component of battle space awareness is direction of arrival (DoA) determination of gunshots. In the initial stages of an engagement, quick and reliable DoA determination enhances a Marine’s ability to execute the observe-orient-decide-act (OODA) loop, increasing chances of survival and mission success. Naval Postgraduate School (NPS) has developed a novel, biomimetic acoustic sensor modeled after the auditory system of the Ormia Ochracea fly. This microelectromechanical system (MEMS)-based directional sound sensor, which consists of two wings connected to a substrate using two torsional legs in the middle, is well documented in previous NPS theses. Each sensor has a uniform dipole beam pattern. By combining two crossed MEMS sensors (crossed-dipoles) with an omni-directional microphone, 360° DoA determination can be fully resolved. The objective of this thesis is to evaluate, optimize, and develop DoA estimators for gunshots in the time- and frequency-domain, specifically for the crossed-dipoles sensors plus an omni-directional microphone configuration.ONR, Arlington, VA 22203Outstanding ThesisEnsign, United States NavyApproved for public release. Distribution is unlimited

Reports on industrial information technology. Vol. 12

The 12th volume of Reports on Industrial Information Technology presents some selected results of research achieved at the Institute of Industrial Information Technology during the last two years.These results have contributed to many cooperative projects with partners from academia and industry and cover current research interests including signal and image processing, pattern recognition, distributed systems, powerline communications, automotive applications, and robotics

Signal Subspace Processing in the Beam Space of a True Time Delay Beamformer Bank

A number of techniques for Radio Frequency (RF) source location for wide bandwidth signals have been described that utilize coherent signal subspace processing, but often suffer from limitations such as the requirement for preliminary source location estimation, the need to apply the technique iteratively, computational expense or others. This dissertation examines a method that performs subspace processing of the data from a bank of true time delay beamformers. The spatial diversity of the beamformer bank alleviates the need for a preliminary estimate while simultaneously reducing the dimensionality of subsequent signal subspace processing resulting in computational efficiency. The pointing direction of the true time delay beams is independent of frequency, which results in a mapping from element space to beam space that is wide bandwidth in nature. This dissertation reviews previous methods, introduces the present method, presents simulation results that demonstrate the assertions, discusses an analysis of performance in relation to the Cramer-Rao Lower Bound (CRLB) with various levels of noise in the system, and discusses computational efficiency. One limitation of the method is that in practice it may be appropriate for systems that can tolerate a limited field of view. The application of Electronic Intelligence is one such application. This application is discussed as one that is appropriate for a method exhibiting high resolution of very wide bandwidth closely spaced sources and often does not require a wide field of view. In relation to system applications, this dissertation also discusses practical employment of the novel method in terms of antenna elements, arrays, platforms, engagement geometries, and other parameters. The true time delay beam space method is shown through modeling and simulation to be capable of resolving closely spaced very wideband sources over a relevant field of view in a single algorithmic pass, requiring no course preliminary estimation, and exhibiting low computational expense superior to many previous wideband coherent integration techniques