The invention provides a multi-sensor system that uses an algorithm based on adaptive filtering to monitor a patient's respiratory rate. The system features a first sensor which is selected from the group consisting of an impedance pneumography sensor, an ECG sensor, and a PPG sensor; and a motion sensor (e.g., an accelerometer) configured to attach to the patient's torso and measure therefrom a motion signal. The system further comprises (iii) a processing system, configured to operably connect to the first and motion sensors, and to determine a respiration rate value by applying filter parameters obtained from the first sensor signals to the motion sensor signals.