Joint DOA and multi-pitch estimation using block sparsity

Abstract

In this paper, we propose a novel method to estimate the fundamental frequencies and directions-of-arrival (DOA) of multi-pitch signals impinging on a sensor array. Formulating the estimation as a group sparse convex optimization problem, we use the alternating direction of multipliers method (ADMM) to estimate both temporal and spatial correlation of the array signal. By first jointly estimating both fundamental frequencies and time-of-arrivals (TOAs) for each sensor and sound source, we then form a non-linear least squares estimate to obtain the DOAs. Numerical simulations indicate the preferable performance of the proposed estimator as compared to current state-of-the-art methods.

Multi-pitch estimation exploiting block sparsity

“…However, in this case, the analysis holds for any kind of non-overlapping sub-division of the sub-vectors, not only into the two variables corresponding to the same complex variables. This insight was used in [59] to generalize the above results to the case of multiple measurements vectors (array) case.…”

An adaptive penalty approach to multi-pitch estimation

“…The simulation and estimation procedure is performed for two cases; one where the number of harmonics L k are set to [5,6] and one where L k are set to [10,11]. In the former case, we set L max = 10 and in the latter we set L max = 20, i.e.…”

“…(`), ±2 Hz from the true values for the six compared methods, for the case of [5,6] and [10,11] harmonics, respectively. As is clear from the figures, the proposed method performs as well, or better, than the PEBS-TV algorithm, although requiring fewer tuning parameters.…”

“…We are only interested in such approximations where few, ideally K, of the fundamentals will have non-zero power, and so steps must be taken to ensure this sparse behavior of the to be estimated amplitudes a p,l . This approach may be seen as a sparse linear regression problem reminiscent of [4] and has been thoroughly examined in the context of pitch estimation in, e.g., [5,10,11]. For notational convenience, we define the set of all amplitude parameters to be estimated as…”