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Ambient assisted living (AAL) technology is often proposed as a way to tackle the increasing cost of healthcare caused by population aging. However, the sensing technology for continuous respiratory monitoring at home is lacking. Known approaches of respiratory monitoring are based on measuring either respiratory effect, e.g. tracheal sound recording by a bio-acoustic sensor, or respiratory effort, e.g. abdomen movement measurement by a tri-axial accelerometer. This paper proposes a home respiration monitoring system using a tri-axial accelerometer. Three different methods to extract a single respiratory signal from the tri-axial data are proposed and analyzed. The performance of the methods is evaluated for various possible respiration conditions, defined by the sensor orientation and respiration-induced abdomen movement. The method based on principal component analysis (PCA) performs better than selecting the best axis. The analytical approach called full angle shows worse results than the best axis when the gravity vector is close to one of the sensor's axes (<15 degrees). Hybrid-PCA, which is a combination of both methods, performs comparable to PCA. The system is evaluated using simulated data from the most common postures, such as lying and sitting, as well as real data collected from five subjects. The results show that the system can successfully reconstruct the respiration-induced movement, which is necessary to determine the respiratory rate accurately.