In a real-world environment, Dialogue State Tracking (DST) should use speech recognition results to perform tasks. However, most existing DST research has been conducted in text-based environments. This study aims to build a model that efficiently performs Automatic Speech Recognition-based DST. To operate robustly against speech noise, we used CopyT5, which adopted a copy mechanism, and trained the model using augmented data including speech noise. Furthermore, CopyT5 performed post-training using the masked language modeling method with the MultiWOZ dataset in T5 in order to learn the dialogue context better. The copy mechanism also mitigated name entity errors that may occur during DST generation. Experiments confirmed that data augmentation, post-training, and the copy mechanism effectively improve DST performance.