Online DOA estimation using real eigenbeam ESPRIT with propagation vector matching

International audienceThe Eigenbeam estimation of signal parameters via rotational invariance technique (EB-ESPRIT) [1] is a method to estimate multiple directions-of-arrival (DOAs) of sound sources from a spherical microphone array recording in the spherical harmonics domain (SHD). The method, first, constructs a signal subspace from the SHD signal and then makes use of the fact that, for plane-wave sources, the signal subspace is spanned by the (complex conjugate) spherical harmonic vectors at the source directions. The DOAs are then estimated from the signal subspace using recurrence relations of spherical harmonics.In recent publications, the singularity and ambiguity problems of the original EB-ESPRIT have been solved by jointly combining several types of recurrence relations. The state-of-the-art EB-ESPRIT, denoted as DOA-vector EB-ESPRIT, is based on three recurrence relations [2,3]. This EB-ESPRIT variant can estimate the source DOAs with significantly higher accuracy compared to the other EB-ESPRIT variants [3]. However, a permutation problem arises, which can be solved by using, for example, a joint diagonalization method [3].For parametric spatial audio signal processing purposes in the short-time Fourier transform (STFT) domain, DOA estimates are usually needed per time-frame and frequency bin. In principle, one can use the DOA-vector EB-ESPRIT method to estimate the source DOAs per time-frequency bin in an online manner. However, due to the eigendecompostion of the PSD matrix and the joint diagonalization procedure, the computational cost might be too large for many real-time applications.In this work, we propose a computationally more efficient version of the DOA-vector EB-ESPRIT based on real spherical harmonics recurrence relations. First, we separate the real and imaginary parts of the real SHD signal in the STFT domain and then construct a real signal subspace thereof, which can be recursively estimated using the deflated projection approximation subspace tracking (PASTd) [4] method. For the case of one source per time-frequency bin, the joint diagonalization is not necessary and we can simplify the EB-ESPRIT equations. For the case of two sources, the plane-wave propagation vectors can directly be estimated from the signal subspace eigenvectors by employing properties of the propagation vectors. This method can be seen as a higher order ambisonics extension of the robust B-format DOA estimation in [5]. The proposed method for estimating two DOAs can be summarized as follows:1. Separate real and imaginary parts of the real SHD signal in the STFT domain.2. Recursively estimate the signal subspace eigenvectors using PASTd.3. Estimate the two plane-wave propagation vectors from the signal subspace eigenvectors by using that they span the same subspace and by using properties of the propagation vectors (subspace-propagation vector matching).4. Estimate the DOAs by using three types of real spherical harmonics recurrence relations.Alternatively, one can estimate the DOAs analogously to the complex DOA-vector EB-ESPRIT using the joint diagonalization method proposed in [3].For the evaluation, we simulate SHD signals up to third order with one and two speech sources in reverberant and noisy environments. For the one-source scenarios, we compare the real DOA-vector EB-ESPRIT with subspace estimation based on singular value decomposition (SVD) against PASTd. For the two-source scenarios, we compare the real DOA-vector EB-ESPRIT with joint diagonalization against subspace-propagation vector matching and the robust B-format DOA estimation method.We analyze the angular distributions of the DOA estimates and find, that the DOA estimation using PASTd for the signal subspace estimation is slightly less accurate than the SVD based method but computationally much more efficient. For the estimation of two DOAs, the EB-ESPRIT based methods outperform the robust B-format estimation method when higher SHD orders are considered. The joint diagonalization method is more accurate than the subspace-propagation vector matching method. However, the latter is computationally more efficient.References:[1] H. Teutsch and W. Kellermann, “Detection and localization of multiple wideband acoustic sources based on wavefield decomposition using spherical apertures,” in Proc. IEEE Intl. Conf. Acoust., Speech Signal Proc. (ICASSP), Mar. 2008, pp. 5276–5279.[2] B. Jo and J. W. Choi, “Nonsingular EB-ESPRIT for the localization of early reflections in a room,” J. Acoust. Soc. Am., vol. 144, no. 3, p. 1882, Sep. 2018.[3] A. Herzog and E. A. P. Habets, “Eigenbeam-ESPRIT for DOA-vector estimation,” IEEE Signal Process. Lett., vol. 26, no. 4, pp. 572-576, April 2019.[4] B. Yang – “Projection Approximation Subspace Tracking, IEEE Trans. Sig. Proc.,” vol. 43, no. 1, Jan. 1995.[5] O. Thiergart and E.A.P. Habets, “Robust direction-of-arrival estimation of two simultaneous plane waves from a B-format signal,” IEEE 27th Conv. of Electrical and Electronics Engineers in Israel, Nov. 2012

Blind identification of Ambisonic reduced room impulse response

Recently proposed Generalized Time-domain Velocity Vector (GTVV) is a generalization of relative room impulse response in spherical harmonic (aka Ambisonic) domain that allows for blind estimation of early-echo parameters: the directions and relative delays of individual reflections. However, the derived closed-form expression of GTVV mandates few assumptions to hold, most important being that the impulse response of the reference signal needs to be a minimum-phase filter. In practice, the reference is obtained by spatial filtering towards the Direction-of-Arrival of the source, and the aforementioned condition is bounded by the performance of the applied beamformer (and thus, by the Ambisonic array order). In the present work, we suggest to circumvent this problem by properly modelling the GTVV time series, which permits not only to relax the initial assumptions, but also to extract the information therein is a more consistent and efficient manner, entering the realm of blind system identification. Experiments using measured room impulse responses confirm the effectiveness of the proposed approach.Comment: Submitte

時間と周波数領域情報に基づいたシステムモデリングとその応用

System modeling is required to deal with the time-varying system dynamics or the experimental data with insufficient information. However, the existing methods cannot construct satisfactory models for rapidly varying systems or severely band-limited signals. This thesis focuses on the new approaches to solve such system modeling problems based on time and frequency-domain information and illustrates their applications in time-varying channel identification and localization system. For the rapid time-varying systems, parameters can be approximated by the cosine series using virtual even periodic functions. Following the orthogonality of the trigonometric functions, the parameter estimation is recursively implemented by estimating the coefficients of each degree of the cosine harmonic term. For the localization system with insufficient frequency components, the spectral characteristics including phase information in frequency domain and the information evaluation in time domain are applied to improve the convergence performance. Numerical simulations demonstrate the effectiveness of the new approaches.北九州市立大

Proceedings of the EAA Spatial Audio Signal Processing symposium: SASP 2019

International audienc