A Steered-Response Power Algorithm Employing Hierarchical Search for Acoustic Source Localization Using Microphone Arrays

Abstract

The localization of a speaker inside a closed environment is often approached by real-time processing of multiple audio signals captured by a set of microphones. One of the leading related methods for sound source localization, the steered-response power (SRP), searches for the point of maximum power over a spatial grid. High-accuracy localization calls for a dense grid and/or many microphones, which tends to impractically increase computational requirements. This paper proposes a new method for sound source localization (called H-SRP), which applies the SRP approach to space regions instead of grid points. This arrangement makes room for the use of a hierarchical search inspired by the branch-and-bound paradigm, which is guaranteed to find the global maximum in anechoic environments and shown experimentally to also work under reverberant conditions. Besides benefiting from the improved robustness of volume-wise search over point-wise search as to reverberation effects, the H-SRP attains high performance with manageable complexity. In particular, an experiment using a 16-microphone array in a typical presentation room yielded localization errors of the order of 7 cm, and for a given fixed complexity, competing methods' errors are two to three times larger.Index Terms-Sound source localization, steered-response power, microphone array, computational complexity, hierarchical search, branch-and-bound.

Acoustic Sensor Self-Localization: Models and Recent Results

“…The concise approach adopted here provides beginners with a glimpse of the main problems and solutions in the ASL field. Experienced researchers can also benefit from the unified approach covering recent ideas that are not standard in the area, as the ones described in [22][23][24]. In fact, many research opportunities may open up thanks to the unified way ASL problems and related solutions are described here.…”

“…For example, the impact of the affine model in (9) on the performance of SRP-inspired solutions should be studied, especially with regard to the bias (this problem does not appear in SSL techniques, for they use TDOFs). This seems to be a reasonable research direction, which could also benefit from modifications on the SRP proposed to circumvent the high computational burden when solving SSL problems [24,[30][31][32][33]. Some of these strategies avoid the exhaustive search throughout the entire grid, like in [30], and therefore cannot guarantee accurate position estimates, as parts of the search space are not explored.…”

“…Some of these strategies avoid the exhaustive search throughout the entire grid, like in [30], and therefore cannot guarantee accurate position estimates, as parts of the search space are not explored. More interesting results were obtained by the strategies that perform the exhaustive search throughout a grid of regions covering the entire search space, such as in [24,32,33]. The advantage over the standard SRP comes from the fact that the grid of regions can be made much coarser than the grid of points and still reach accurate estimates.…”

“…Each TDOF gives rise to a hyperboloid that is the locus of all candidate spatial points that are consistent with that TDOF. If the hyperboloid related to TDOF 1 2 intersects cuboid V , then TDOF 1 2 is coherent with that cuboid [24]. It can be proven using the Karush-Kuhn-Tucker (KKT) conditions [34] that the coherence test can be implemented in a very efficient way-see Theorem 3 and Corollary 1 of [24].…”

“…If the hyperboloid related to TDOF 1 2 intersects cuboid V , then TDOF 1 2 is coherent with that cuboid [24]. It can be proven using the Karush-Kuhn-Tucker (KKT) conditions [34] that the coherence test can be implemented in a very efficient way-see Theorem 3 and Corollary 1 of [24]. This result shows that the TDOF (x) of any point x inside V is within the interval (observe that the TDOF notation was replaced by , with , ∈ S, to emphasize that the second loudspeaker acts as a reference speaker):…”