Inertial measurement units (IMUs) together with advanced machine learning algorithms have enabled pervasive gait analysis. However, the worn positions of IMUs can be varied due to movements, and they are difficult to standardize across different trials, causing signal variations. Such variation contributes to a bias in the underlying distribution of training and testing data, and hinder the generalization ability of a computational gait analysis model. In this paper, we propose a position-independent IMU based gait analysis framework based on unsupervised domain adaptation. It is based on transferring knowledge from the trained data positions to a novel position without labels. Our framework was validated on gait event detection and pathological gait pattern recognition tasks based on different computational models and achieved consistently high performance on both tasks.