Breathing frequency (f) is an important vital sign that-if appropriately monitored-may help to predict clinical adverse events. Inertial sensors open the door to the development of low-cost, wearable, and easy-to-use breathing-monitoring systems. The present paper proposes a new posture-independent processing algorithm for breath-by-breath extraction of breathing temporal parameters from chest-wall inclination change signals measured using inertial measurement units. An important step of the processing algorithm is dimension reduction (DR) that allows the extraction of a single respiratory signal starting from 4-component quaternion data. Three different DR methods are proposed and compared in terms of accuracy of breathing temporal parameter estimation, in a group of healthy subjects, considering different breathing patterns and different postures; optoelectronic plethysmography was used as reference system. In this study, we found that the method based on PCA-fusion of the four quaternion components provided the best f estimation performance in terms of mean absolute errors (<2 breaths/min), correlation (r > 0.963) and Bland⁻Altman Analysis, outperforming the other two methods, based on the selection of a single quaternion component, identified on the basis of spectral analysis; particularly, in supine position, results provided by PCA-based method were even better than those obtained with the ideal quaternion component, determined a posteriori as the one providing the minimum estimation error. The proposed algorithm and system were able to successfully reconstruct the respiration-induced movement, and to accurately determine the respiratory rate in an automatic, position-independent manner.