Satellite retrievals of carbon monoxide (CO) are routinely assimilated in atmospheric chemistry models to improve air quality forecasts, produce reanalyzes and to estimate emissions. This study applies the quantile‐conserving ensemble filter framework, a novel assimilation algorithm that can deal with non‐Gaussian and modestly nonlinear distributions. Instead of assuming normal distributions like the Ensemble Adjustments Kalman Filter (EAKF), we now apply a bounded normal rank histogram (BNRH) distribution for the prior. The goal is to efficiently estimate bounded quantities such as CO atmospheric mixing ratios and emission fluxes while maintaining the good performance achieved by the EAKF. We contrast assimilating meteorological and MOPITT (Measurement of Pollution in the Troposphere) observations for May 2018. We evaluate the results with the fourth deployment of the NASA Atmospheric Tomography Mission (ATom‐4) airborne field campaign. We also compare simulations with CO tropospheric columns from the network for the detection of atmospheric composition change and surface in‐situ observations from NOAA carbon cycle greenhouse gases. While the differences remain small, the BNRH approach clearly works better than the EAKF in comparison to all observation data sets.