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We study the detection and estimation of the parameters related to the deterministic model of the reflections of room impulse responses measured with a spherical microphone array. More specifically, we investigate the problem of detecting and estimating several reflections of a single snapshot of data in the spherical harmonic (SH) domain with four detection and four estimation methods, presented previously in the array processing research. Three of the estimation methods are based on Bayesian Maximum a Posteriori (MAP) estimation, and they employ a prior normal distribution on the signals. The estimation methods are compared with the deterministic maximum likelihood (DML) method [Tervo & Politis 2015]. In the detection task, two information criteria-based methods, minimum description length (MDL) and Akaike information criteria (AIC), a normalized likelihood (NL) based method, and a Bayesian detection scheme (BDS) are explored. The experiments study the performance of the methods with simulated and real data experiments. The simulation results show that the MAP estimation methods have a lower root mean squared error (RMSE) than DML in the reflection signal amplitude estimation, but all three have similar performance in the direction of arrival (DOA) and noise variance estimation, although in general RMSE of DOA estimation of MAP methods is slightly lower that that of DML. In addition, in the detection task, the BDS and AIC are the most robust against additive noise, and NL and AIC have the best detection rate when more than two reflections are simulated. The results of the real data experiments show that all the estimation methods have similar performance for DOA and noise variance estimation, while the Bayesian MAP methods have a clearly lower RMSE for reflection signal amplitude estimation than DML. In total, NL has the highest detection rate in the real data experiments.

Single Snapshot Detection and Estimation of Reflections From Room Impulse Responses in the Spherical Harmonic Domain