Spatial Sound Localization via Multipath Euclidean Distance Matrix Recovery

Abstract

Abstract-A novel localization approach is proposed in order to find the position of an individual source using recordings of a single microphone in a reverberant enclosure. The multipath propagation is modeled by multiple virtual microphones as images of the actual single microphone and a multipath distance matrix is constructed whose components consist of the squared distances between the pairs of microphones (real or virtual) or the squared distances between the microphones and the source. The distances between the actual and virtual microphones are computed from the geometry of the enclosure. The microphonesource distances correspond to the support of the early reflections in the room impulse response associated with the source signal acquisition. The low-rank property of the Euclidean distance matrix is exploited to identify this correspondence. Source localization is achieved through optimizing the location of the source matching those measurements. The recording time of the microphone and generation of the source signal is asynchronous and estimated via the proposed procedure. Furthermore, a theoretically optimal joint localization and synchronization algorithm is derived by formulating the source localization as minimization of a quartic cost function. It is shown that the global minimum of the proposed cost function can be efficiently computed by converting it to a generalized trust region sub-problem. Numerical simulations on synthetic data and real data recordings obtained by practical tests show the effectiveness of the proposed approach.

Structured total least squares based internal delay estimation for distributed microphone auto-localization

“…Most literatures, like [9,25], use signal-to-noise ratio (SNR) to represent the measurement noise level. With measurement noise present, the TOAs can be expressend aŝ…”

“…Recently, many methods have been derived for microphone auto-localization, which can be generally categorised into methods based on received signal strength (RSS) [5], time-of-arrival (TOA) [6], angle-of-arrival (AOA) [7], time difference of arrival (TDOA) [8] and Euclidean distance matrices (EDM) [9,10]. TOA and TDOA based techniques are popular in many applications because they are less vulnerable to multipath reflections, and they only require one receiver per sensor.…”

“…However, MDS is based on an implicit assumption that the sensors and sources are co-located, thus limiting its use in practical applications. Alternatively, auto-localization can also be solved by using non-linear least-squares (LS), e.g., [9,[12][13][14].…”