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GAMF: Learned and Analytical Array Transfer Function Matching for Array-Generic Direction-of-Arrival Estimation
Zhiheng Jin, Shichao Hu, Chunyang Xu, Mengyao Zhu
TL;DR
Microphone coordinates alone do not fully describe array acoustics such as device shadowing and microphone directivity, limiting their description of new arrays. GAMF matches observations to directional ATFs through learned, analytical, and gated hybrid configurations. Both learned and hybrid variants beat the positional-encoding baseline across six synthetic conditions, and the hybrid reports low errors on eight-microphone LOCATA.
Problem
Microphone coordinates only partially describe array acoustics, while ATF-conditioned cross-attention had demonstrated generalization to unseen arrays with the same microphone count.
Source: §1 · p. 1Method
Results
Both GAMF variants beat the positional-encoding baseline in all six synthetic conditions; on eight-microphone LOCATA, GAMF-H leads with 3.76° spherical MAE and 2.87° azimuth MAE.
Source: §1 · p. 1, §3.4 · p. 4Takeaways & Limitations
Learned matching is effective under noise and reverberation, while analytical matching remains strong in favorable scenes, making their integration competitive across both regimes.
Source: §3.3 · p. 4, §4 · p. 4The formulation specifies complex STFT observations and ATFs using a shared Fourier convention.
Source: §2 · p. 2
Abstract
from arXiv · showhide
Microphone positional encoding supports cross-array direction-of-arrival (DOA) estimation, but coordinates alone cannot fully describe device shadowing or microphone directivity. We propose a Generalizable ATF Matching Framework (GAMF) for DOA estimation across array geometries and microphone counts, using array transfer functions (ATFs) as acoustic descriptors. The learned branch incorporates ATF embeddings into geometry-conditioned neural estimation to match acoustic observations with candidate directions. The analytical branch performs normalized ATF matching adapted from generalized steered response power. A hybrid configuration combines their scores through adaptive gating. Simulations across array configurations show that both learned and hybrid configurations outperform a representative positional-encoding-based neural baseline, remain competitive with analytical ATF matching in clean, low-reverberation scenes, and substantially improve upon it under stronger noise or reverberation. On eight-microphone LOCATA Task 1 recordings, the hybrid configuration outperforms the evaluated state-of-the-art baselines for three-dimensional DOA estimation, achieving mean errors of $3.76^\circ$ for three-dimensional DOA and $2.87^\circ$ for azimuth.
1. INTRODUCTION
Cross-array DOA estimation must handle changing microphone layouts and counts, but microphone coordinates only partially describe device-specific acoustics. GAMF adds directional ATFs to geometry-conditioned matching, and its learned and hybrid configurations outperform a positional-encoding baseline across six synthetic conditions.
1. INTRODUCTION
- Coordinates do not explicitly describe how device shadowing and microphone directivity alter interchannel amplitude and phase for a new array.Directional ATFs provide candidate-direction complex microphone responses as richer acoustic descriptors.Source: §1 · p. 1
- Earlier ATF-conditioned cross-attention generalized to unseen arrays with the same microphone count, leaving varying-count conditioning an open deployment need.GAMF targets DOA estimation across both array geometries and microphone counts.Source: §1 · p. 1
- GAMF matches contextual observation queries with candidate ATF-and-direction keys at corresponding microphones, then aggregates scores using shared encoders and masked aggregation.This design is intended to accommodate variable microphone counts.Source: §1 · p. 1
- Both GAMF configurations outperform the retrained positional-encoding baseline in all six synthetic conditions.GAMF-H combines gated learned scores with analytical scores adapted from GSRP-NMF-frob.Source: §1 · p. 1
2. METHOD
GAMF matches multichannel observations to candidate directional ATFs, using a learned path, an analytical path, or a hybrid that gates learned scores while retaining analytical scores. Its learned path builds microphone-frame queries and candidate keys, compares them at corresponding microphones, and aggregates the scores.
2. METHOD
- GAMF offers standalone learned matching (GAMF-L) and hybrid matching (GAMF-H), which integrates learned scores with an analytical branch adapted from GSRP-NMF-frob.The analytical branch is also evaluated separately as an ablation reference.Source: §2 · pp. 1–2
2.1.1. Observation queries
- Observation queries combine local spectral information with microphone-position, time, and sequence context, then form normalized multi-head features.The shared spectral encoder processes each microphone-frame spectrum; Transformer blocks model dependencies across microphones and time.Source: §2.1.1 · p. 2
2.1.2. Candidate ATF keys
- Candidate keys combine each microphone’s encoded ATF with an embedding of its candidate direction, and are reused across frames.Encoder weights are shared across microphones and candidates, with no candidate-specific output weights.Source: §2.1.2 · p. 2
2.1.3. Microphone-aligned direction scoring
- The learned path scores queries against keys at the same microphone, then uses masked microphone averaging and a learned merger to produce direction scores.Shared encoders and padded-token masking support variable microphone counts within the configured limit.Source: §2.1.3 · pp. 2–3
2.2. Analytical ATF matching
- The analytical branch adapts GSRP-NMF-frob with instantaneous covariance and valid-frequency averaging to measure spectral agreement between observations and candidate ATFs.It serves as both GAMF-H’s analytical component and an ablation reference.Source: §2.2 · p. 3
2.3. Integration and training
- GAMF-H uses a framewise gate to scale the learned contribution while retaining the analytical score, then averages fused scores over valid frames.The gate uses analytical-score concentration and stability, branch disagreement, signal energy, valid-frequency fraction, and active-microphone count; the combination is not a convex average.Source: §2.3 · p. 3
- Training supervises fused, physical, and learned scores with cross-entropy and adds an auxiliary speech-presence task; GAMF-L is trained independently.The fused, physical, and learned losses have weights 1, 0.2, and 0.1, respectively.Source: §2.3 · p. 3
3. EXPERIMENTS AND DISCUSSIONS
Experiments evaluate GAMF under varied simulated acoustic conditions and on LOCATA Task 1 recordings. The results show complementary strengths: learned matching handles noise and reverberation, while hybrid matching performs strongly on eight-microphone LOCATA.
3.1. Implementation and training
- Training uses 300,000 point-microphone and 300,000 rigid-sphere scenes with 3–8 microphones, while candidate ATFs use 384 directions.Training follows a three-stage clean-to-noisy curriculum; inputs are 250-ms, 16-kHz segments.Source: §3.1 · p. 3
3.2. Baselines and evaluation
- Evaluation combines simulations varying SNR, microphone count, source distance, and reverberation with LOCATA recordings; baselines include retrained PhaseCoder, MUSIC-ATF, SRP-PHAT, and GSRP-NMF-frob.LOCATA includes 16 Task 1 recordings; metrics include spherical MAE and Acc@10.Source: §3.2 · p. 3
3.3. Synthetic localization
- Across all six synthetic conditions, GAMF-L beats retrained PhaseCoder in MAE and has the lowest MAE in five; GAMF-L and GAMF-H rank top two on both metrics in all four noisy conditions.GAMF-L’s standalone results show learned ATF-conditioned matching performs effectively without analytical fusion.Source: §3.3 · pp. 3–4, Table 1 · p. 4
3.4. Real-recording localization
- 3.76° spherical MAE, 2.87° azimuth MAE, and 98.80% Acc@10: GAMF-H leads the eight-microphone LOCATA evaluation.With six microphones, the analytical branch slightly outperforms GAMF-H.Source: Table 2 · p. 4, §3.4 · p. 4
3.3. Synthetic localization
- 7.73° MAE: GSRP-NMF-frob leads in clean, low-reverberation scenes, versus 8.42° for GAMF-L and 8.68° for GAMF-H.Under medium reverberation, GAMF-L and GAMF-H achieve lower MAE than the analytical baselines, even without added interference.Source: §3.3 · p. 4
- 31.2%–49.5%: GAMF-H reduces analytical-branch MAE across noisy conditions; learned matching better accommodates interference and reverberation.The results indicate complementary strengths rather than one matching strategy that is uniformly superior.Source: §3.3 · p. 4
3.4. Real-recording localization
- On eight-microphone LOCATA, GAMF-H combines analytical accuracy on real recordings with learned robustness in noisy simulations, remaining competitive without always outperforming either branch.Reverberation and simulation mismatch also matter for real-recording performance.Source: §3.4 · p. 4
4. CONCLUSION
GAMF extends geometry-conditioned DOA estimation with directional ATFs, matching observations to candidate acoustic responses. Experiments show complementary strengths for learned and analytical matching, with their combination remaining competitive across tested conditions, including transfer to real LOCATA recordings.
4. CONCLUSION
- GAMF targets three-dimensional DOA estimation across array geometries and microphone counts by enriching geometry-conditioned neural estimation with directional ATFs.Microphone-aligned matching links contextual observation features to candidate acoustic responses; shared encoders and masked aggregation support variable microphone counts.Source: §4 · p. 4
- Learned matching is effective under noise and reverberation, while analytical matching remains strong when directional acoustic cues are reliable.The experiments support complementary strengths rather than a uniformly superior strategy.Source: §4 · p. 4
- Combining learned and analytical matching yields competitive performance across tested conditions, including transfer from simulated ATFs to real LOCATA recordings.Source: §4 · p. 4
- Future work will isolate ATF-conditioning benefits, test measured ATFs and new geometries, and improve mismatch robustness.Source: §4 · p. 4