<p>Anomaly detection in multivariate time series (MTS) data is pivotal for ensuring the integrity and reliability of real-time systems across diverse domains. Existing approaches for anomaly detection often rely on clean normal data to learn temporal and intervariable relationships. However, such datasets is nearly unavailable in real scenarios. Moreover, the presence of temporal distortions like warp variations and their impact on anomaly detection accuracy remains unexplored, potentially leading to more erroneous detections. In this work, we propose a Warping resilient Robust Anomaly Detection (WRADMts) method with two major modules: 1) Warp Aligning Temporal Transformation to eliminate warp distortions and efficiently capture the normal pattern in the data, and 2) Graph Structure and Node Embedding Learning to capture temporal and intervariable dependencies with unique sparse adjacency matrix learning mechanism. Our model is resilient to warp distortions and also robust to noise contamination in the data. We compare our model with eight baselines on five real-world datasets, demonstrating significant improvements, with up to 7% F1 score enhancement over the best baseline.</p>