The invention provides a neck-worn sensor (referred to herein as the ‘necklace’) that is a single, body-worn system that measures the following parameters from an ambulatory patient: heart rate, pulse rate, pulse oximetry, respiratory rate, temperature, thoracic fluid levels, stroke volume, cardiac output, and a parameter sensitive to blood pressure called pulse transit time. From stroke volume, a first algorithm employing a linear model can estimate the patient's pulse pressure. And from pulse pressure and pulse transit time, a second algorithm, also employing a linear algorithm, can estimate systolic blood pressure and diastolic blood pressure. Thus, the necklace can measure all five vital signs along with hemodynamic parameters. It also includes a motion-detecting accelerometer, from which it can determine motion-related parameters such as posture, degree of motion, activity level, respiratory-induced heaving of the chest, and falls.