Continuous monitoring of respiratory rate in ambulatory conditions has widespread applications for screening of respiratory diseases and remote patient monitoring. Unfortunately, minimally obtrusive techniques often suffer from low accuracy. In this paper, we describe an algorithm with low computational complexity for combining multiple respiratory measurements to estimate breathing rate from an unobtrusive chest patch sensor. Respiratory rates derived from the respiratory sinus arrhythmia (RSA) and modulation of the QRS amplitude of electrocardiography (ECG) are combined with a respiratory rate derived from tri-axial accelerometer data. The three respiration rates are combined by a weighted average using weights based on quality metrics for each signal. The algorithm was evaluated on 15 elderly subjects who performed spontaneous and metronome breathing as well as a variety of activities of daily living (ADLs). When compared to a reference device, the mean absolute error was 1.02 breaths per minute (BrPM) during metronome breathing, 1.67 BrPM during spontaneous breathing, and 2.03 BrPM during ADLs.