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We propose self-training with noisy student-teacher approach for streaming keyword spotting, that can utilize large-scale unlabeled data and aggressive data augmentation. The proposed method applies aggressive data augmentation (spectral augmentation) on the input of both student and teacher and utilize unlabeled data at scale, which significantly boosts the accuracy of student against challenging conditions. Such aggressive augmentation usually degrades model performance when used with supervised training with hard-labeled data. Experiments show that aggressive spec augmentation on baseline supervised training method degrades accuracy, while the proposed self-training with noisy student-teacher training improves accuracy of some difficult-conditioned test sets by as much as 60%.