Estimation of respiratory rate (RR) from photoplethysmography (PPG) signals has important applications in the healthcare sector, from assisting doctors onwards to monitoring patients in their own homes. The problem is still very challenging, particularly during the motion for large segments of data, where results from different methods often do not agree. The authors aim to propose a new technique which performs motion reduction from PPG signals with the help of simultaneous acceleration signals where the PPG and accelerometer sensors need to be embedded in the same sensor unit. This method also reconstructs motion corrupted PPG signals in the Hilbert domain. An auto-regressive (AR) based technique has been used to estimate the RR from reconstructed PPGs. The proposed method has provided promising results for the estimation of RRs and their variations from PPG signals corrupted with motion artefact. The proposed platform is able to contribute to continuous in-hospital and home-based monitoring of patients using PPG signals under various conditions such as rest and motion states.