With the ubiquity of smartphones, the interest in indoor localization as a research area grew. Methods based on radio data are predominant, but due to the susceptibility of these radio signals to a number of dynamic influences, good localization solutions usually rely on additional sources of information, which provide relative information about the current location. Part of this role is often taken by the field of activity recognition, e.g., by estimating whether a pedestrian is currently taking the stairs. This work presents different approaches for activity recognition, considering the four most basic locomotion activities used when moving around inside buildings: standing, walking, ascending stairs, and descending stairs, as well as an additional messing around class for rejections. As main contribution, we introduce a novel approach based on analytical transformations combined with artificially constructed sensor channels, and compare that to two approaches adapted from existing literature, one based on codebooks, the other using statistical features. Data is acquired using accelerometer and gyroscope only. In addition to the most widely adopted use-case of carrying the smartphone in the trouser pockets, we will equally consider the novel use-case of hand-carried smartphones. This is required as in an indoor localization scenario, the smartphone is often used to display a user interface of some navigation application and thus needs to be carried in hand. For evaluation the well known MobiAct dataset for the pocket-case as well as a novel dataset for the hand-case were used. The approach based on analytical transformations surpassed the other approaches resulting in accuracies of 98.0% for pocket-case and 81.8% for the hand-case trained on the combination of both datasets. With activity recognition in the supporting role of indoor localization, this accuracy is acceptable, but has room for further improvement.