Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

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

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

FRIDA: FRI-Based DOA Estimation for Arbitrary Array Layouts

In this paper we present FRIDA---an algorithm for estimating directions of arrival of multiple wideband sound sources. FRIDA combines multi-band information coherently and achieves state-of-the-art resolution at extremely low signal-to-noise ratios. It works for arbitrary array layouts, but unlike the various steered response power and subspace methods, it does not require a grid search. FRIDA leverages recent advances in sampling signals with a finite rate of innovation. It is based on the insight that for any array layout, the entries of the spatial covariance matrix can be linearly transformed into a uniformly sampled sum of sinusoids.Comment: Submitted to ICASSP201

EM Algorithm for Multiple Wideband Source Localization

A computationally efficient algorithm using the expectation-maximization (EM) algorithm for multiple wideband source localization in the near field of a sensor array/area is addressed in this thesis. Our idea is to decompose the observed sensor data, which is a superimposition of multiple sources, into the individual components in the frequency domain and then estimate the corresponding location parameters associated with each component separately. Instead of the conventional alternating projection (AP) method, we propose to adopt the EM algorithm in this work; our new method involves two steps, namely Expectation (E-step) and Maximization (M-step). In the E-step, the individual incident source waveforms are estimated. Then, in the M-step, the maximum likelihood estimates of the source location parameters are obtained. These two steps are executed iteratively and alternatively until the pre-defined convergence is reached. The computational complexity comparison between our proposed EM algorithm and the existing AP scheme is investigated. It is shown through Monte Carlo simulations that the computational complexity of the proposed EM algorithm is significantly lower than that of the existing AP algorithm

Direct and Residual Subspace Decomposition of Spatial Room Impulse Responses

Psychoacoustic experiments have shown that directional properties of the direct sound, salient reflections, and the late reverberation of an acoustic room response can have a distinct influence on the auditory perception of a given room. Spatial room impulse responses (SRIRs) capture those properties and thus are used for direction-dependent room acoustic analysis and virtual acoustic rendering. This work proposes a subspace method that decomposes SRIRs into a direct part, which comprises the direct sound and the salient reflections, and a residual, to facilitate enhanced analysis and rendering methods by providing individual access to these components. The proposed method is based on the generalized singular value decomposition and interprets the residual as noise that is to be separated from the other components of the reverberation. Large generalized singular values are attributed to the direct part, which is then obtained as a low-rank approximation of the SRIR. By advancing from the end of the SRIR toward the beginning while iteratively updating the residual estimate, the method adapts to spatio-temporal variations of the residual. The method is evaluated using a spatio-spectral error measure and simulated SRIRs of different rooms, microphone arrays, and ratios of direct sound to residual energy. The proposed method creates lower errors than existing approaches in all tested scenarios, including a scenario with two simultaneous reflections. A case study with measured SRIRs shows the applicability of the method under real-world acoustic conditions. A reference implementation is provided