TR-ENF: A Trust-Region Optimization Framework for Peak-Agnostic Electric Network Frequency Detection in Audio

Electric Network Frequency (ENF) acts as a fingerprint in multimedia forensics. ENF detection remains challenging in short audio segments at low signal-to-noise ratios (SNR) because frequency and amplitude estimation are non-convexly coupled. Existing detectors commonly separate spectral frequency estimation from amplitude fitting, introducing discretization and initialization effects that are most pronounced on short windows. The proposed TR-ENF framework jointly estimates ENF frequency and amplitude in a continuous three-parameter space using exact gradients and Hessians, positive-definite Hessian shifting, and frequency box constraints. Experiments on the ENF-WHU benchmark show a TR-ENF accuracy of 87.0% on 5 s segments and accuracies above 90% for 8–10 s segments, with the 9 s condition providing the most concentrated bootstrap distribution. Under the common empirical median operating rule, the point estimates are competitive with the evaluated likelihood-ratio baselines. A matched 5 s paired bootstrap shows that TR-ENF retains the highest point accuracy, with differences of $+1$ to $+4$ percentage points. Threshold-free ROC/DET analyses provide complementary evidence, with the strongest 5 s AUC and EER obtained by TR-ENF. Robustness is further characterized through SNR sensitivity, frequency-box and hyperparameter ablations, convergence trajectories, and bootstrap analysis.