Wideband Source Localization Research Articles

Sparse reconstruction methods for wideband source localization in spherical harmonics domain

Wideband acoustic source localization is a challenging task especially in the presence of noise. Generally wideband source localization is done by averaging the Direction of Arrival (DOA) estimates obtained over multiple frequencies or narrow subbands by the method of frequency smoothing. Localization of multiple wideband sources which are correlated is even more challenging. In this work acoustic source localization under these challenging conditions is addressed. A sparse reconstruction framework is developed for wideband source localization in the Spherical Harmonics (SH) domain. The proposed framework jointly computes both the azimuth and elevation. In contrast to earlier methods of source localization in the SH domain, this work utilizes the expression for the SH coefficients of the amplitude density of the plane wave, to develop the sparse reconstruction framework. An expression for Cramér Rao Lower Bound (CRLB) on the DOA using this framework is also derived for the wideband sources. This CRLB is shown to easily generalize for narrowband sources as well. The performance of the proposed method is compared with MUltiple Signal Classification in SH domain (MUSIC-SH), Steered Response Power in SH domain (SRP-SH), MUSIC with Direct Path Dominance test in SH domain (MUSIC-DPD-SH) and Pressure based Compressive Sensing in SH domain (PCS-SH). The performance is evaluated for correlated narrowband and wideband sources through simulations, conducting experiments in an anechoic chamber and under reverberant conditions. Using the proposed framework, it is shown that correlated narrowband and wideband sources can be resolved reasonably well when compared to conventional methods of acoustic source localization in SH domain.

Advancements in wideband source localization with an acoustic vector sensor line array

A method is presented for localizing wideband acoustic sources using an array of acoustic vector sensors (AVS). The method focuses on leveraging the lack of correlation between acoustic pressure and particle velocity in the underwater environmental noise field. Coherent processing is introduced in the signal processing stage to suppress noise components in the observed data. By employing a focused transform that maps various frequency components of the wideband signal into the same signal subspace, an asymptotically unbiased Direction of Arrival (DOA) estimation is achieved using a multidimensional subspace method. A concise expression for the Cramér-Rao Bound (CRB) on the estimation errors is provided within the framework of the wideband multi-vector-sensor model. The performance of the proposed method for localizing sources is assessed through simulation and experimental data analysis. The research indicates that coherent processing effectively suppresses isotropic components in background noise, the proposed method achieves a lower estimation error, closer to the CRB, compared to the scalar array counterpart under identical signal-to-noise ratio (SNR) conditions.

Performance Comparison of Several Algorithms for Localization of Wideband Sources

In recent years, researchers have tried to estimate the direction-of-arrival (DOA) of wideband sources and several novel techniques have been proposed. In this paper, we compare six algorithms for calculating the DOA of broadband signals, namely coherent subspace signal method (CSSM), two-sided correlation transformation (TCT), incoherent multiple signal classification (IMUSIC), test of orthogonality of frequency subspaces (TOFS), test of orthogonality of projected subspaces (TOPS), and squared TOPS (S-TOPS). The comparison is made through computer simulations for different parameters, such as signal-to-noise ratio (SNR), in order to establish the efficiency and performance of the discussed methods in noisy environments. CSSM and TCT require initial values, but the remaining approaches do not need any preprocessing.

S$^2$H Domain Processing for Acoustic Source Localization and Beamforming Using Microphone Array on Spherical Sector

Spherical microphone arrays (SMAs) are widely used for the localization of acoustic sources and beamforming. However, building an SMA over a rigid sphere is a challenging task, and it is uneconomic to build full SMAs when the sources are in some restricted regions of the environment. This paper addresses the issue of multiple source localization and beamforming using a microphone array on a spherical sector. The discontinuity over the boundary is handled by solving the Helmholtz equation over the sector. As the sound pressure is present only on the microphones over that sector, novel orthonormal spherical sector harmonics (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> H) basis functions are developed. The basis functions defined over the sector are in generalized form, for which the usual spherical harmonics are a special case. To ensure orthonormality of S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> H basis functions, the orthogonality of the shifted associated Legendre polynomials and scaled exponential functions are established for the same sector. The new S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> H basis functions are utilized for far-field data model development. Subsequently, multiple signal classification and minimum variance distortionless response spectra are formulated in the S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> H domain for wideband and narrowband source localization. An ideal direction-invariant beampattern using S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> H basis functions is also derived. The performance of the proposed methods is analyzed using various source localization experiments. The acoustic image principle for beamforming is extended herein for source localization. Additionally, the proposed methods are compared with acoustic image principle-based source localization using spherical harmonics.

A source range and depth estimation method based on modal dedispersion transform

The wideband source localization is analysed widely in shallow water. It is pointed out that its performance is poor when the number of array elements is few or the ocean environment is uncertain. A method of estimating the range and depth is studied by using a single hydrophone based on the relationship of the horizontal wavenumber difference between two modes with the waveguide invariant for low frequency underwater acoustic pulse signals in a range-independent shallow water waveguide. This localization method estimates the source range by using the rangedispersion two-dimensional（2D) plane focus phenomenon and also the source depth by matching the modal energy. So it can separately estimate the source range and source depth by single hydrophone. First, the signal received on a single hydrophone can be decomposed into a series of modes within the framework of normal mode theory. In order to obtain a better localization performance, the first few order modal dispersion parameters and waveguide invariant are regarded as the unknown parameters. And then the first few order modal dispersion parameters and waveguide invariant can be estimated by comparing the differences between the modal phase velocity calculated by Eq.(8) and that calculated by the Kraken model. Second, using the estimated dispersion parameters and waveguide invariant for dedispersion transform, the amplitudes of each normal mode can achieve maximum values but only when the range of the received signal after dedispersion transform is equal to the range of source. On range-dispersion 2D plane, there appears the sound pressure focus phenomenon, and this phenomenon can be used to estimate the source range. Simulation results from a shallow water Pekeris waveguide show that the time-frequency distribution represents well the dispersion characteristics of the underwater acoustic pulse signal and the dedisperision transform can eliminate this dispersion at the range of source, so that the source range can be estimated. Besides, the first few order modal signals received are clearly separated in time domain after dedispersion transform, and the first few order modal energy can be calculated accurately. So the source depth can be estimated by matching the modal energy. The errors in range estimation and depth estimation are little in simulation. Finally, the data collected from airgun sources during an experiment in the shallow water are used to verify the presented method, and the experimental results obtained using airgun sources on a straight line are shown. The presented method is very significant for estimating the range and depth in shallow water.

Wideband source localization using sparse learning via iterative minimization

In this paper, two extensions of the Sparse Learning via Iterative Minimization (SLIM) algorithm are presented for wideband source localization using a sensor array. The proposed methods exploit the joint sparse structure across all frequency bins, and estimate the spatial pseudo-spectra at various frequency bins jointly and iteratively. Via several numerical examples, we show that the proposed methods can provide high-resolution angle estimates and excellent source localization performance, and are able to resolve the left–right ambiguity problem, when used together with the vector sensor array technology.

A Subspace Algorithm for WideBand Source Localization Without NarrowBand Filtering

The popular algorithms for wideband source localization pass the data through a bank of narrowband filters, and use the narrowband signal model for subsequent processing of the filter-bank output. This requires a large time window over which the data must be collected. We propose a new low-rank signal model, which does not rely on the narrowband signal model. In this way we can avoid narrowband filtering. The model is applicable to arbitrary array geometries, and is useful in both far-field and near-field problems. A subspace algorithm for source localization using the new model is proposed, which requires significantly smaller time window to yield reliable results.

Robust Expectation-Maximization Algorithm for Multiple Wideband Acoustic Source Localization in the Presence of Nonuniform Noise Variances

Wideband source localization using acoustic sensor networks has been drawing a lot of research interest recently. The maximum-likelihood is the predominant objective which leads to a variety of source localization approaches. However, the robust and efficient optimization algorithms are still being pursuit by researchers since different aspects about the effectiveness of such algorithms have to be addressed on different circumstances. In this paper, we would like to combat the source localization based on the realistic assumption where the sources are corrupted by the noises with nonuniform variances. We focus on the two popular source localization methods for solving this problem, namely the SC-ML (stepwise-concentrated maximum-likelihood) and AC-ML (approximately-concentrated maximum likelihood) algorithms. We explore the respective limitations of these two methods and design a new expectation maximization (EM) algorithm. Furthermore, we provide the Cramer-Rao lower bound (CRLB) for all these three methods. Through Monte Carlo simulations, we demonstrate that our proposed EM algorithm outperforms the SC-ML and AC-ML methods in terms of the localization accuracy, and the root-mean-square (RMS) error of our EM algorithm is closer to the derived CRLB than both SC-ML and AC-ML methods.

High-Resolution Multiple Wideband and Nonstationary Source Localization With Unknown Number of Sources

In this paper, a new algorithm for high-resolution multiple wideband and nonstationary source localization using a sensor array is proposed. The received signals of the sensor array are first converted into the time-frequency domain via short-time Fourier transform (STFT) and we find that a set of short-time power spectrum matrices at different time instants have the joint diagonalization structure in each frequency bin. Based on such joint diagonalization structure, a novel cost function is designed and a new spatial spectrum for direction-of-arrival (DOA) estimation at hand is derived. Compared to the maximum-likelihood (ML) method with high computational complexity, the proposed algorithm obtains the DOA estimates via one-dimensional (1-D) search instead of multidimensional search. Therefore its computational complexity is much lower than the ML method. Unlike the subspace-based high-resolution DOA estimation techniques, it is not necessary to determine the number of sources in advance for the proposed algorithm. Moreover, the proposed method is robust to the effects of reverberation caused by multipath reflections. Hence it is suitable for multiple acoustic source localization in a reverberant room. The results of numerical simulations and experiments in a real room with a moderate reverberation are provided to demonstrate the good performance of the proposed approach.

Robustness analysis and new hybrid algorithm of wideband source localization for acoustic sensor networks

Wideband source localization using acoustic sensor networks has been drawing a lot of research interest recently in wireless communication applications, such as cellular handset localization, global positioning systems (GPS), and land navigation technologies, etc. The maximum-likelihood is the predominant objective which leads to a variety of source localization approaches. However, the appropriate optimization (search) algorithms are still being pursuit by researchers since different aspects about the effectiveness of such algorithms have to be addressed on different circumstances. In this paper, we focus on the two popular source localization methods for wideband acoustic signals, namely the alternating projection (AP) algorithm and the expectation maximization (EM) algorithm. We explore the respective limitations of these two methods and design a new hybrid approach thereupon. Through Monte Carlo simulations, we demonstrate that the trade-off can be achieved between the computational complexity and the localization accuracy using our newly proposed scheme. Moreover, we present the new robustness analysis for the source localization algorithms. We derive the Cramer-Rao lower bound (CRLB) involving the source spectral estimation error and thus prove that the new hybrid algorithm is more efficient than the EM algorithm. By employing the Gaussianity test, we also quantify the statistical mismatch between the actual statistics of the sensor signals and the underlying Gaussian model. We show that the Gaussianity measure can be a reliable robustness figure for source localization.

Efficient and Robust EM Algorithm for Multiple Wideband Source Localization

Source-localization techniques are crucial in transportation applications such as navigation or Global Positioning Systems (GPS). A computationally efficient technique for multiple wideband source localization is presented in this paper using the expectation-maximization (EM) algorithm in the near field of a sensor array/area. Our basic idea is to decompose the recorded sensor data, which is a superimposition of multiple sources, into individual components in the frequency domain and then separately estimate the corresponding location parameters associated with each source. Instead of the conventional alternating projection (AP) method, we propose to adopt the EM algorithm in this paper; our 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 (ML) estimates of the source-location parameters are obtained. These two steps are iteratively and alternatively executed until the user's predefined convergence is reached. The computational complexity comparison between our proposed EM algorithm and the existing AP scheme is also investigated. Provably, it is shown through Monte Carlo simulations that the computational complexity of the proposed EM algorithm is significantly lower than that of the conventional AP scheme. We also derive the Cramer-Rao lower bound (CRLB) for the source-location estimates.

Localization of short-range acoustic and seismic wideband sources: Algorithms and experiments

We consider the determination of the location (source localization) of a disturbance source which emits acoustic and/or seismic signals. We devise an enhanced approximate maximum-likelihood (AML) algorithm to process data collected at acoustic sensors (microphones) belonging to an array of, non-collocated but otherwise identical, sensors. The approximate maximum-likelihood algorithm exploits the time-delay-of-arrival of acoustic signals at different sensors, and yields the source location. For processing the seismic signals, we investigate two distinct algorithms, both of which process data collected at a single measurement station comprising a triaxial accelerometer, to determine direction-of-arrival. The direction-of-arrivals determined at each sensor station are then combined using a weighted least-squares approach for source localization. The first of the direction-of-arrival estimation algorithms is based on the spectral decomposition of the covariance matrix, while the second is based on surface wave analysis. Both of the seismic source localization algorithms have their roots in seismology; and covariance matrix analysis had been successfully employed in applications where the source and the sensors (array) are typically separated by planetary distances (i.e., hundreds to thousands of kilometers). Here, we focus on very-short distances (e.g., less than one hundred meters) instead, with an outlook to applications in multi-modal surveillance, including target detection, tracking, and zone intrusion. We demonstrate the utility of the aforementioned algorithms through a series of open-field tests wherein we successfully localize wideband acoustic and/or seismic sources. We also investigate a basic strategy for fusion of results yielded by acoustic and seismic arrays.

Wide-band source localization in the presence of internal waves

The effects of internal waves on low-frequency (25-Hz) wide-band source localization performance are investigated at a very long range (1000 km). Sound-speed perturbations induced by internal waves obeying the Garrett–Munk spectral model are incorporated into the normal mode solution to the wave equation using the adiabatic approximation. Source range estimates are limited by very random internal waves and do not improve with increasing SNR. In an attempt to combat this limitation due to environmental uncertainty, processors can benefit from the spectrum of the acoustic source. According to the hybrid Cramer–Rao lower bound (CRLB), significant improvements on range estimates are possible when using a coherent wide-band acoustic source with bandwidth of 10 Hz on the 25-Hz source. The CRLB provides valuable analytical insight into the limits on source range estimates, but the optimal signal processing algorithm is necessary to compute the actual limits on source localization. Using a coherent wide-band source with many discrete frequencies spanning the bandwidth, significant gains in range estimates are achieved by optimally incorporating this signal spectrum into the localization algorithm a priori.

Wavefield modeling and array processing .II. Algorithms

For pt.I see ibid. vol.42, no.10, p.2549, 1994. We present several novel algorithms for array processing, as well as extensions of existing methods based on this approach. We first consider the problem of localization of wideband sources via coherent processing, and show how wavefield modeling enables us to derive expressions for the frequency transformation (focusing) matrices. This method is extended to three dimensions and to sector processing. We then develop computationally efficient implementations of MUSIC and Root-MUSIC for the narrowband and the coherent and incoherent wideband cases, as well as a natural extension of Root-MUSIC to any 2-D array. In addition, wavefield modeling allows us for the first time to extend Root-MUSIC to 3-D arrays and wavefields. We also present a low complexity variant of Root-MUSIC for direction finding within a limited angular sector. Finally, we derive a low-dimensional sufficient statistic and reduced rank processing schemes for the case of oversampled arrays and/or limited angular sector scenarios.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>