Continuously monitoring patient vital signs in the neonatal intensive care unit (NICU) requires wired sensors that can irritate fragile skin, motivating the development of non-contact physiologic signal estimation approaches. Such estimators typically involve a pipeline of multiple data analysis stages, including pre-processing, region of interest detection and tracking, and physiologic parameter estimation. Uncertainty in the estimated physiologic signal is often quantified strictly from the signal quality indicator (SQI) generated by the final stage of the pipeline. This manuscript proposes a framework to account for SQIs generated by each stage in a physiologic signal estimation pipeline and using the fusion of all SQIs to arrive at a refined measure of uncertainty in the final estimated physiologic parameter. This framework is demonstrated for heart rate (HR) estimation of newborns admitted in the NICU, where the pipeline includes bed occupancy detection, face detection, face tracking, and physiologic signal estimation. Different SQIs are derived at each stage and a novel fusion of all SQI metrics is shown to produce a more effective estimate of uncertainty in the final estimated HR.