Abstract: An improved method and apparatus for the photoplethysmographic monitoring of blood analyte parameters, specifically oxyhemoglobin, deoxyhemoglobin (reduced hemoglobin), carboxyhemoglobin and methemoglobin, uses a plurality of beams of light having different spectral contents to trans-illuminate the tissue of a patient. Received light is measured and the normalized differential absorption is used in a forward calibration equation to generate estimated relative blood analyte concentration values. Error in the blood analyte concentration values is minimized by applying constraints to the estimated analytes. Specifically, the constraints require that all relative analyte concentration values are greater than or equal to zero and sum to one hundred percent.