Impact of derivative term noise on the uncertainty of metabolic rate estimates in whole-room indirect calorimetry

Whole-room indirect calorimeters (WRICs) estimate metabolic rate from time derivatives of gas concentrations, but derivative calculations are highly sensitive to measurement noise. We propose an analytical framework for the uncertainty of discrete derivatives under white and autocorrelated AR(1) noise and validate it through Monte Carlo simulations (1000 realizations across 64 combinations of window size, noise level, and autocorrelation) and experimental analysis. Simulation validation demonstrates theoretical predictions match the empirical results with relative errors . Experimental validation using propane combustion data shows excellent theory-empirical agreement across 3–15 min analysis windows, with relative errors below 11% when moderate autocorrelation (–0.8) is properly incorporated. Empirical derivative uncertainty scaled as , confirming the framework’s applicability to operational measurement systems. More generally, derivative uncertainty scales linearly with noise standard deviation and approximately as with window size (number of samples). The impact of autocorrelation is window-dependent: positive autocorrelation reduces uncertainty for short windows () via differencing-based cancellation, but increases uncertainty for longer windows (). Parameter effects combine multiplicatively, yielding uncertainty differences spanning over two orders of magnitude across realistic settings. The framework applies equally to dynamic transients and steady-state conditions. Furthermore, propagation of uncertainty through the measurement model based on the canonical WRIC gas-balance equations (including the dynamic Haldane correction) yields closed-form expressions for the derivative-term uncertainty in O, CO, metabolic rate, and respiratory exchange ratio (RER). At a representative propane-combustion operating point ( L, fraction), the derivative-term EE uncertainty ranges from 7.01 kcal/min (311% of metabolic rate) at min to 0.59 kcal/min (26% of metabolic rate) at min under white noise, confirming that window size is the dominant control parameter for metabolic-rate precision in large-volume chambers. These results provide quantitative guidance for WRIC design and analysis, enabling targeted derivative precision through informed trade-offs among window size, noise reduction, and autocorrelation management.