Bionic limb control through myoelectric pattern recognition, offering intuitive decoding of motor intent, can improve the quality of life for individuals with amputations. However, most work on pattern recognition only uses a small subset of the myoelectric data generated during daily life, to train an Artificial Neural Network (ANN) via Supervised Learning (SL). Scenarios substantially different from the recording session e.g. different limb positions, can lead to misclassifications by the ANN during everyday usage of the bionic limb. Recording labeled data from all scenarios encountered in daily life could alleviate the problem, but would be prohibitively time consuming. Unsupervised Domain Adaptation (UDA) offers a solution by leveraging unlabeled data from a target domain, not represented in the labeled dataset i.e. the source domain, to calibrate ANNs for improved performance. In this study we explore the potential of two UDA algorithms for domain shifts in myoelectric pattern recognition: Domain Adversarial Neural Networks (DANN) and Sliced Wasserstein Discrepancy (SWD). Offline evaluation identified SWD as the best-performing algorithm, which was subsequently validated in online experiments with 11 participants. Using UDA substantially improved the performance, not only on the target domain, but also on the source domain. Indeed, it nearly matched the performance of an ANN trained through SL on labeled data from both the source and target domain. This is the first time UDA was validated in online experiments as a viable approach to overcome domain shift problems caused by changes in limb position.