Features were developed which accounted for the changing orientation of the inertial measurement unit (IMU) relative to the body, and demonstrably improved the performance of models for human activity recognition (HAR). The method is proficient at separating periods of standing and sedentary activity (i.e., sitting and/or lying) using only one IMU, even if it is arbitrarily oriented or subsequently re-oriented relative to the body; since the body is upright during walking, learning the IMU orientation during walking provides a reference orientation against which sitting and/or lying can be inferred. Thus, the two activities can be identified (irrespective of the cohort) by analyzing the magnitude of the angle of shortest rotation which would be required to bring the upright direction into coincidence with the average orientation from the most recent 2.5 s of IMU data. Models for HAR were trained using data obtained from a cohort of 37 older adults (83.9 ± 3.4 years) or 20 younger adults (21.9 ± 1.7 years). Test data were generated from the training data by virtually re-orienting the IMU so that it is representative of carrying the phone in five different orientations (relative to the thigh). The overall performance of the model for HAR was consistent whether the model was trained with the data from the younger cohort, and tested with the data from the older cohort after it had been virtually re-oriented (Cohen's Kappa 95% confidence interval [0.782, 0.793]; total class sensitivity 95% confidence interval [84.9%, 85.6%]), or the reciprocal scenario in which the model was trained with the data from the older cohort, and tested with the data from the younger cohort after it had been virtually re-oriented (Cohen's Kappa 95% confidence interval [0.765, 0.784]; total class sensitivity 95% confidence interval [82.3%, 83.7%]).