Embedded devices are frequently used to deploy adaptive learning systems for several applications, such as anomaly detection models in automotive or aerospace domains. These models can detect anomalous data from the sensors to predict hazardous situations ahead of time. However, training on-the-edge requires the use of efficient learning algorithms, able to run on low-powered devices while keeping a high accuracy. In this paper, we propose the use of Echo State Networks (ESN), a randomized family of efficiently trainable recurrent networks, for anomaly detection on-the-edge in aerospace applications. The anomaly detection method uses a nonparametric dynamic threshold to detect anomalous behaviours from the observed data by comparing it to the model's predictions. The proposed model is empirically assessed on aerospace data against state-of-the-art LSTM networks. The results show that the proposed method grants a 6x speedup in training time, while also improving the outlier detection performance.