Sleep posture is linked to several health conditions such as nocturnal cramps and more serious musculoskeletal issues. However, in-clinic sleep assessments are often limited to vital signs (e.g. brain waves). Wearable sensors with embedded inertial measurement units have been used for sleep posture classification; nonetheless, previous works consider only few (commonly four) postures, which are inadequate for advanced clinical assessments. Moreover, posture learning algorithms typically require longitudinal data collection to function reliably, and often operate on raw inertial sensor readings unfamiliar to clinicians. This paper proposes a new framework for sleep posture classification based on a minimal set of joint angle measurements. The proposed framework is validated on a rich set of twelve postures in two experimental pipelines: computer animation to obtain synthetic postural data, and human participant pilot study using custom-made miniature wearable sensors. Through fusing raw geo-inertial sensor measurements to compute a filtered estimate of relative segment orientations across the wrist and ankle joints, the body posture can be characterised in a way comprehensible to medical experts. The proposed sleep posture learning framework offers plug-and-play posture classification by capitalising on a novel kinematic data augmentation method that requires only one training example per posture. Additionally, a new metric together with data visualisations are employed to extract meaningful insights from the postures dataset, demonstrate the added value of the data augmentation method, and explain the classification performance. The proposed framework attained promising overall accuracy as high as 100% on synthetic data and 92.7% on real data, on par with state of the art data-hungry algorithms available in the literature.