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Objective: The objective of this paper is to obtain accurate estimation of breathing rate (BR), using only the electrocardiogram (ECG) or the photoplethysmogram (PPG) signals, to avoid wearing cumbersome and uncomfortable sensors for direct measurements. Methods: Several respiration waveforms are derived from ECG or PPG signals based on amplitude, frequency, and baseline wander modulations. It is, however, difficult to determine their optimal combination for BR estimation due to the noise and patient specificity. We first propose to quantify the quality of modulation waveforms using respiratory quality indices (RQIs). We then present two methods: the first automatically selects the modulation signal with highest RQI for BR estimation, and the second tracks the respiration signal using the Kalman smoother to fuse modulation signals with highest RQI. Results: These two methods are evaluated on two independent datasets, one benchmark database (DB) with immobilized patients recordings and the second with those performing daily activities. Our results outperform existing methods in the literature in both the cases. Conclusion: Experimental results show that the RQIs coupled with a fusion algorithm increases the accuracy for BR estimations in dealing with derived modulation signals. Significance: This work describes a robust Kalman Smoother method applicable in multiple clinical contexts to improve breathing rate estimation from data fusion. [ABSTRACT FROM AUTHOR]