Reliable human orientation estimation (HOE) is critical for autonomous agents to understand human intention and perform human-robot interaction (HRI) tasks. Great progress has been made in HOE under full observation. However, the existing methods easily make a wrong prediction under partial observation and give it an unexpectedly high probability. To solve the above problems, this study first develops a method that estimates orientation from the visible joints of a target person so that it is able to handle partial observation. Subsequently, we introduce a confidence-aware orientation estimation method, enabling more accurate orientation estimation and reasonable confidence estimation under partial observation. The effectiveness of our method is validated on both public and custom-built datasets, and it showed great accuracy and reliability improvement in partial observation scenarios. In particular, we show in real experiments that our method can benefit the robustness and consistency of the robot person following (RPF) task.