In the neonatal intensive care unit (NICU), preterm infants are usually unable to fulfil their sleep demands due to frequent disruptions. Real-time sleep monitoring could be an essential tool not only to shift elective care to their wake periods but also to track their developmental sleep profile as an indicator of healthy brain maturation. The current gold standard for sleep measurement, polysomnography, is invasive and labour-intensive, limiting its applicability for continuous monitoring. We propose an automatic sleep stage classification method using only the routinely available electrocardiogram (ECG) and patient movement data recorded with a piezo mat. For this study we recorded data from 28 preterm infants (13 females and 15 males) at 35.7 \pm 0.5 weeks postmentrual age. We employed a support vector machine (SVM) to classify sleep stages into wakefulness (W), active sleep (AS), and quiet sleep (QS). The combined piezo + ECG model demonstrated superior accuracy (92 \%) and strong agreement with expert annotations (Cohen's kappa = 0.83) compared to ECG-only or piezo-only models. This approach offers a reliable, unobtrusive solution for continuous sleep monitoring in NICUs, facilitating individualised, sleep-based medical care for preterm infants.