Adversarial attacks pose a severe security threat to the state-of-the-art speaker identification systems, thereby making it vital to propose countermeasures against them. Building on our previous work that used representation learning to classify and detect adversarial attacks, we propose an improvement to it using AdvEst, a method to estimate adversarial perturbation. First, we empirically validate our claim that training representation learning network using adversarial perturbations as opposed to adversarial examples (consisting of a combination of clean signal and adversarial perturbation) is beneficial because it potentially eliminates nuisance information. At inference time, we use a time-domain denoiser to estimate the adversarial perturbations from adversarial examples. Using our improved representation learning approach to obtain attack embeddings (signatures), we evaluate their performance for three applications: known attack classification, attack verification, and unknown attack detection. We show that common attacks in the literature (Fast Gradient Sign Method (FGSM), Projected Gradient Descent (PGD), Carlini-Wagner (CW) with different Lp threat models) can be classified with an accuracy of ∼96%. We also detect unknown attacks with an equal error rate (EER) of ∼9%, an absolute improvement of ∼12% from our previous work.