Sleep apnea is a breathing disorder that affects many individuals and has been associated with serious health conditions such as cardiovascular disease. Clinical diagnosis of sleep apnea requires that a patient spend the night in a sleep clinic while being wired up to numerous obtrusive sensors. We are developing a system that utilizes respiration rate and breathing amplitude inferred from non-contact bed sensors (i.e. load cells placed under bed supports) to detect sleep apnea. Multi-harmonic artifacts generated either biologically or as a result of the impulse response of the bed have made it challenging to track respiration rate and amplitude with high resolution in time. In this paper, we present an algorithm that can accurately track respiration on a second-by-second basis while removing noise harmonics. The algorithm is tested using data collected from 5 patients during overnight sleep studies. Respiration rate is compared with polysomnography estimations of respiration rate estimated by a technician following clinical standards. Results indicate that certain subjects exhibit a large harmonic component of their breathing signal that can be removed by our algorithm. When compared with technician transcribed respiration rates using polysomnography signals, we demonstrate improved accuracy of respiration rate tracking using harmonic artifact rejection (mean error: 0.18 breaths/minute) over tracking not using harmonic artifact rejection (mean error: -2.74 breaths/minute).