Abstract

State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to construct a Gaussian approximation to the posterior. In this paper, we propose to use invertible particle flow methods, derived under the Gaussian boundary conditions for a flow equation, to generate a proposal distribution close to the posterior. The resultant particle flow Gaussian particle filter (PFGPF) algorithm retains the asymptotic properties of Gaussian particle filters, with the potential for improved state estimation performance in highdimensional spaces. We compare the performance of PFGPF with the particle flow filters and particle flow particle filters in two challenging numerical simulation examples. Index Terms—Particle filters, particle flow filters, Gaussian particle filters, particle flow particle filters.

Abstract

Sparse Bayesian learning (SBL) has been successful in direction of arrival (DOA) estimation due to its robustness and high resolution using a few snapshots. Most wideband SBL algorithms make the simplifying assumption that distinct sources have the same power spectrum across frequency bands. However, this assumption may not be true in practice (for example speech signals). We analyze three wideband signal models and compare variants of wideband SBL (called SBL1, SBL2, and SBL3) with different assumptions on source signal power spectrum. The localization performance of SBL algorithms is compared with wideband processing of conventional beamforming (CBF) and multiple signal classification (MUSIC). The experimental validation is presented using simulated data and experimental LOCATA data. This comparative study shows that SBL3 which simultaneously enforces sparsity and models frequency-dependent signal spectrum shows superior performance in most scenarios. Index Terms—Compressive sensing, Sparse Bayesian learning, DOA estimation, MUSIC, CBF.

Abstract

Sound source localization is crucial in acoustic sensing and monitoring-related applications. In this paper, we do a comprehensive analysis of improvement in sound source localization by combining the direction of arrivals (DOAs) with their derivatives which quantify the changes in the positions of sources over time. This study uses the SALSA-Lite feature with a convolutional recurrent neural network (CRNN) model for predicting DOAs and their first-order derivatives. An update rule is introduced to combine the predicted DOAs with the estimated derivatives to obtain the final DOAs. The experimental validation is done using TAU-NIGENS Spatial Sound Events (TNSSE) 2021 dataset. We compare the performance of the networks predicting DOAs with derivative vs. the one predicting only the DOAs at low SNR levels. The results show that combining the derivatives with the DOAs improves the localization accuracy of moving sources. Index Terms— Deep learning, Microphone array, SALSALite, Sound event localization and detection (SELD).

Abstract

Directions of arrival (DOA) estimation or localization of sources is an important problem in many applications for which numerous algorithms have been proposed. Most lo- calization methods use block-level processing that combines multiple data snapshots to estimate DOA within a block. The DOAs are assumed to be constant within the block duration. However, these assumptions are often violated due to source motion. In this paper, we propose a signal model that cap- tures the linear variations in DOA within a block. We applied conventional beamforming (CBF) algorithm to this model to estimate linear DOA trajectories. Further, we formulate the proposed signal model as a block sparse model and sub- sequently derive sparse Bayesian learning (SBL) algorithm. Our simulation results show that this linear parametric DOA model and corresponding algorithms capture the DOA tra- jectories for moving sources more accurately than traditional signal models and methods.

Abstract

Sparse arrays are special geometrical arrangements of sensors which overcome some of the drawbacks associated with dense uniform arrays and require fewer sensors. For direction finding applications, sparse arrays with the same number of sensors can resolve more sources while providing higher resolution than a dense uniform array. This has been verified numerically and with real data for one-dimensional microphone arrays. In this study the use of nested and co-prime arrays is examined with sparse Bayesian learning (SBL), which is a compressive sensing algorithm, for estimating sparse vectors and support. SBL is an iterative parameter estimation method and can process multiple snapshots as well as multiple frequency data within its Bayesian framework. A multi-frequency variant of SBL is proposed, which accounts for non-flat frequency spectra of the sources. Experimental validation of azimuth and elevation [two-dimensional (2D)] direction-of-arrival (DOA)estimation are provided using sparse arrays and real data acquired in an anechoic chamber with a rectangular array. Both co-prime and nested arrays are obtained by sampling this rectangular array. The SBL method is compared with conventional beamforming and multiple signal classification for 2D DOA estimation of experimental data.

Abstract

The localization of acoustic sources is a parameter estimation problem where the parameters of interest are the direction of arrivals (DOAs). The DOA estimation problem can be formulated as a sparse parameter estimation problem and solved using compressive sensing (CS) methods. In this paper, the CS method of sparse Bayesian learning (SBL) is used to find the DOAs. We specifically use multi-frequency SBL leading to a non-convex optimization problem, which is solved using fixed-point iterations. We evaluate SBL along with traditional DOA estimation methods of conventional beamforming (CBF) and multiple signal classification (MUSIC) on various source localization tasks from the open access LOCATA dataset. The comparative study shows that SBL significantly outperforms CBF and MUSIC on all the considered tasks.

Abstract

The localization of acoustic sources is a parameter estimation problem where the parameters of interest are the direction of arrivals (DOAs). The DOA estimation problem can be formulated as a sparse parameter estimation problem and solved using compressive sensing (CS) methods. In this paper, the CS method of sparse Bayesian learning (SBL) is used to find the DOAs. We specifically use multi-frequency SBL leading to a non-convex optimization problem, which is solved using fixed-point iterations. We evaluate SBL along with traditional DOA estimation methods of conventional beamforming (CBF) and multiple signal classification (MUSIC) on various source localization tasks from the open access LOCATA dataset. The comparative study shows that SBL significantly outperforms CBF and MUSIC on all the considered tasks.

Abstract

This paper develops efficient channel estimation techniques for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems under practical hardware limitations, including an arbitrary array geometry and a hybrid hardware structure. Taking on an angle-based approach, this work adopts a generalized array manifold separation approach via Jacobi-Anger approximation, which transforms a non-ideal, non-uniform array manifold into a virtual array domain with a desired uniform geometric structure to facilitate super-resolution angle estimation and channel acquisition. Accordingly, structure-based optimization techniques are developed to effectively estimate both the channel covariance and the instantaneous channel state information (CSI) within a short sensing time. The different time-varying scales of channel path angles versus path gains are capitalized to design a two-step CSI estimation scheme that can quickly sense fading channels. Theoretical results are provided on the fundamental limits of the proposed technique in terms of sample efficiency. For computational efficiency, a fast iterative algorithm is developed via the alternating direction method of multipliers. Other related issues such as spurious-peak cancellation in non-uniform linear arrays and extensions to higher-dimensional cases are also discussed. Simulations testify the effectiveness of the proposed approaches in hybrid mmWave massive MIMO systems with arbitrary arrays.

Abstract

Sparse arrays such as co-prime and nested arrays can identify more sources than the number of sensors. This is because their difference co-arrays contain a uniformly spaced virtual array with more elements than the number of sensors in the array. In this paper we demonstrate this using two dimensional co-prime and nested sparse arrays combined with sparse Bayesian learning (SBL) for 2D beamforming in azimuth and elevation. SBL can directly process the sparse array data and significantly outperform conventional beam-forming and MUSIC as seen from simulations.

Abstract

Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, iteratively solves a non-convex optimization problem using fixed point updates. It provides comparable performance and is significantly faster than convex optimization techniques used in sparse processing. We propose a multi-dictionary SBL algorithm that simultaneously can process observations generated by different underlying dictionaries sharing the same sparsity profile. Two algorithms are proposed and corresponding fixed point update equations are derived. Noise variances are estimated using stochastic maximum likelihood. The multi-dictionary SBL has many practical applications. We demonstrate this using direction-of-arrival (DOA) estimation. The first example uses the proposed multi-dictionary SBL to process multi …