This paper presents an experimental and comparative study of several spherical microphone array eigenbeam (EB) processing techniques for localization of early reflections in room acoustic environments, which is a relevant research topic in both audio signal processing and room acoustics. This paper focuses on steered beamformer-based and subspace-based localization techniques implemented in the spherical EB domain, including the plane-wave decomposition, eigenbeam delay and sum, eigenbeam minimum variance distortionless response, eigenbeam multiple signal classification (EB-MUSIC), and eigenbeam estimation of signal parameters via rotational invariance techniques (EB-ESPRIT) methods. The directions of arrival of the original sound source and the associated reflection signals in acoustic environments are estimated from acoustic maps of the rooms, which are obtained using a spherical microphone array. The EB-domain-based frequency smoothing and white noise gain control techniques are derived and employed to improve the performance and robustness of reflection localization. The applicability of the presented methods in practice is confirmed by experiments carried out in real rooms.

Spherical microphone array eigenbeam (EB)-ESPRIT gives an elegant closed-form solution for 3D broadband source localization based on the spherical harmonics (eigenbeam) framework. However, in practical implementations, there are still several issues not being rigorously studied, e.g. how to avoid the ill-conditioning of an EB-ESPRIT matrix, solve the ambiguity problem, handle a large number of sources, and localize coherent broadband sources, etc. In this work, we propose to use the condition number of the EB-ESPRIT matrix as a robustness measure, and to use Wigner-D weighting to avoid the ill-conditioning issue and improve the robustness. In addition, power spectrum testing, frequency smoothing, and manifold vector extension techniques are employed to address the ambiguity, coherent source localization, and large source number problems, respectively. Experimental results based on measurements taken with a real spherical microphone array in a room environment show the effectiveness of the proposed methods.Index Terms-Spherical microphone array, eigenbeam, EB-ESPRIT, spherical harmonics. INTRODUCTIONEB-ESPRIT algorithms have recently been proposed for spherical and cylindrical microphone arrays [1, 2], and spherical antenna arrays [3]. The spherical array EB-ESPRIT can provide elegant closed-form solutions for three-dimensional (3D) source localization. The highly efficient closed-form solution is the major advantage of the spherical array EB-ESPRIT over other existing spherical array source localization methods, e.g. EB-MUSIC [4, 5] and EB-Beamformers [6-10], where the full 3D power spectrum computation and 3D peak searching are needed, which usually lead to a high computational complexity.In this paper, we address hitherto unsolved problems and performance limitations of the spherical array EB-ESPRIT, which are very critical in practical implementations, and experimental results for a real spherical array in a real room are presented. We first review briefly the implementation procedure of the spherical array EB-ESPRIT, and address several practical issues of this algorithm. Moreover, for the first time, the experimental results obtained using a real array (Eigenmike [6]) in a real room are presented to validate both the original EB-ESPRIT and the proposed methods. EB-ESPRIT WITH SPHERICAL MICROPHONE ARRAYSThe background and the implementation procedure of the spherical array EB-ESPRIT is introduced in this section. The reader is referred to [1][2][3][4] for more details of the spherical array EB-ESPRIT algorithm and spherical harmonics processing techniques.The spherical array EB-ESPRIT algorithm is basically performed in the spherical harmonics (eigenbeam) domain. Based on a well-known recurrence relation for associated Legendre polynomials [1], an EB-ESPRIT equation can be formulated, which can be easily solved. Then, by computing the eigenvalues of the solution from the EB-ESPRIT equation, the direction of arrival (DOA) information can be obtained from the phases and amplitudes of the eigenvalues.The convent...

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Temporal knowledge graph (TKG) reasoning is a crucial task that has gained increasing research interest in recent years. Most existing methods focus on reasoning at past timestamps to complete the missing facts, and there are only a few works of reasoning on known TKGs to forecast future facts. Compared with the completion task, the forecasting task is more difficult and faces two main challenges:(1) how to effectively model the time information to handle future timestamps? (2) how to make inductive inference to handle previously unseen entities that emerge over time? To address these challenges, we propose the first reinforcement learning method for forecasting. Specifically, the agent travels on historical knowledge graph snapshots to search for the answer. Our method defines a relative time encoding function to capture the timespan information, and we design a novel time-shaped reward based on Dirichlet distribution to guide the model learning. Furthermore, we propose a novel representation method for unseen entities to improve the inductive inference ability of the model. We evaluate our method for this link prediction task at future timestamps. Extensive experiments on four benchmark datasets demonstrate substantial performance improvement meanwhile with higher explainability, less calculation, and fewer parameters when compared with existing stateof-the-art methods.

The knowledge of parameters characterizing an acoustic environment, such as the geometric information about a room, can be used to enhance the performance of several audio applications. In this paper, a novel method for three-dimensional room geometry inference based on robust and high-resolution beamforming techniques for spherical microphone arrays is presented. Unlike other approaches that are based on the measurement and processing of multiple room impulse responses, here, microphone array signal processing techniques for uncontrolled broadband acoustic signals are applied. First, the directions of arrival (DOAs) and time differences of arrival (TDOAs) of the direct signal and room reflections are estimated using high-resolution robust broadband beamforming techniques and cross-correlation analysis. In this context, the main challenges include the low reflected-signal to background-noise power ratio, the low energy of reflected signals relative to the direct signal, and their strong correlation with the direct signal and among each other. Second, the DOA and TDOA information is combined to infer the room geometry using geometric relations. The high accuracy of the proposed room geometry inference technique is confirmed by experimental evaluations based on both simulated and measured data for moderately reverberant rooms.

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