Background: Satellite imagery will offer unparalleled global spatial coverage at high-resolution for long term cost-effective monitoring of CO2 concentration plumes generated by emission hotspots. CO2 emissions can then be estimated from the magnitude of these plumes. In this paper, we assimilate pseudo-observations in a global atmospheric inversion system to assess the performance of a constellation of one to four sun-synchronous low-Earth orbit (LEO) imagers to monitor anthropogenic CO2 emissions. The constellation of imagers follows the specifications from the European Spatial Agency (ESA) for the Copernicus Anthropogenic Carbon Dioxide Monitoring (CO2M) concept for a future operational mission dedicated to the monitoring of anthropogenic CO2 emissions. This study assesses the uncertainties in the inversion estimates of emissions ("posterior uncertainties"). Results: The posterior uncertainties of emissions for individual cities and power plants are estimated for the 3 h before satellite overpasses, and extrapolated at annual scale assuming temporal auto-correlations in the uncertainties in the emission products that are used as a prior knowledge on the emissions by the Bayesian framework of the inversion. The results indicate that (i) the number of satellites has a proportional impact on the number of 3 h time windows for which emissions are constrained to better than 20%, but it has a small impact on the posterior uncertainties in annual emissions; (ii) having one satellite with wide swath would provide full images of the XCO2 plumes, and is more beneficial than having two satellites with half the width of reference swath; and (iii) an increase in the precision of XCO2 retrievals from 0.7 ppm to 0.35 ppm has a marginal impact on the emission monitoring performance. Conclusions: For all constellation configurations, only the cities and power plants with an annual emission higher than 0.5 MtC per year can have at least one 8:30-11:30 time window during one year when the emissions can be constrained to better than 20%. The potential of satellite imagers to constrain annual emissions not only depend on the design of the imagers, but also strongly depend on the temporal error structure in the prior uncertainties, which is needed to be objectively assessed in the bottom-up emission maps.