Heart rhythm and respiration rate are two vital signs that are of interest for ambulatory monitoring. However, noise due to activity in ambulatory monitoring complicates the ECG interpretation. This paper describes a set of algorithms to robustly monitor a subject's heart rhythm and respiration rate in an ambulatory environment. To ensure robustness against motion artifacts, we have developed an algorithm for motion artifact reduction based on independent component analysis with a multi-lead ECG system. From the robust heart-rate calculations, we use an ECG derived respiration (EDR) algorithm based on heart-rate variability (HRV) to estimate the respiration rate.