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

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

Statistical Nested Sensor Array Signal Processing

Source number detection and direction-of-arrival (DOA) estimation are two major applications of sensor arrays. Both applications are often confined to the use of uniform linear arrays (ULAs), which is expensive and difficult to yield wide aperture. Besides, a ULA with N scalar sensors can resolve at most N − 1 sources. On the other hand, a systematic approach was recently proposed to achieve O(N 2 ) degrees of freedom (DOFs) using O(N) sensors based on a nested array, which is obtained by combining two or more ULAs with successively increased spacing. This dissertation will focus on a fundamental study of statistical signal processing of nested arrays. Five important topics are discussed, extending the existing nested-array strategies to more practical scenarios. Novel signal models and algorithms are proposed. First, based on the linear nested array, we consider the problem for wideband Gaussian sources. To employ the nested array to the wideband case, we propose effective strategies to apply nested-array processing to each frequency component, and combine all the spectral information of various frequencies to conduct the detection and estimation. We then consider the practical scenario with distributed sources, which considers the spreading phenomenon of sources. Next, we investigate the self-calibration problem for perturbed nested arrays, for which existing works require certain modeling assumptions, for example, an exactly known array geometry, including the sensor gain and phase. We propose corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares is used to deal with the phase error issue. We further propose a new class of nested vector-sensor arrays which is capable of significantly increasing the DOFs. This is not a simple extension of the nested scalar-sensor array. Both the signal model and the signal processing strategies are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. Last but not least, in order to make full use of the available limited valuable data, we propose a novel strategy, which is inspired by the jackknifing resampling method. Exploiting numerous iterations of subsets of the whole data set, this strategy greatly improves the results of the existing source number detection and DOA estimation methods

Detection of Wideband Signal Number Based on Bootstrap Resampling

Knowing source number correctly is the precondition for most spatial spectrum estimation methods; however, many snapshots are needed when we determine number of wideband signals. Therefore, a new method based on Bootstrap resampling is proposed in this paper. First, signals are divided into some nonoverlapping subbands; apply coherent signal methods (CSM) to focus them on the single frequency. Then, fuse the eigenvalues with the corresponding eigenvectors of the focused covariance matrix. Subsequently, use Bootstrap to construct the new resampling matrix. Finally, the number of wideband signals can be calculated with obtained vector sequences according to clustering technique. The method has a high probability of success under low signal to noise ratio (SNR) and small number of snapshots

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

Multiple source localization using spherical microphone arrays

Direction-of-Arrival (DOA) estimation is a fundamental task in acoustic signal processing and is used in source separation, localization, tracking, environment mapping, speech enhancement and dereverberation. In applications such as hearing aids, robot audition, teleconferencing and meeting diarization, the presence of multiple simultaneously active sources often occurs. Therefore DOA estimation which is robust to Multi-Source (MS) scenarios is of particular importance. In the past decade, interest in Spherical Microphone Arrays (SMAs) has been rapidly grown due to its ability to analyse the sound field with equal resolution in all directions. Such symmetry makes SMAs suitable for applications in robot audition where potential variety of heights and positions of the talkers are expected. Acoustic signal processing for SMAs is often formulated in the Spherical Harmonic Domain (SHD) which describes the sound field in a form that is independent of the geometry of the SMA. DOA estimation methods for the real-world scenarios address one or more performance degrading factors such as noise, reverberation, multi-source activity or tackled problems such as source counting or reducing computational complexity. This thesis addresses various problems in MS DOA estimation for speech sources each of which focuses on one or more performance degrading factor(s). Firstly a narrowband DOA estimator is proposed utilizing high order spatial information in two computationally efficient ways. Secondly, an autonomous source counting technique is proposed which uses density-based clustering in an evolutionary framework. Thirdly, a confidence metric for validity of Single Source (SS) assumption in a Time-Frequency (TF) bin is proposed. It is based on MS assumption in a short time interval where the number and the TF bin of active sources are adaptively estimated. Finally two analytical narrowband MS DOA estimators are proposed based on MS assumption in a TF bin. The proposed methods are evaluated using simulations and real recordings. Each proposed technique outperforms comparative baseline methods and performs at least as accurately as the state-of-the-art.Open Acces