Urban areas, occupying only 3% of the global land surface yet generating approximately 70% of anthropogenic carbon emissions, are critical targets for climate change mitigation. Accurate emission quantification remains challenging, as most atmospheric inversion studies neglect spatiotemporal correlations in prior fluxes and observation errors, inflating uncertainties in both the spatial distribution and magnitude of greenhouse gases. This study introduces an inversion framework integrating explicit correlation functions, hierarchical Bayesian modeling, and maximum-likelihood estimation, thereby removing reliance on empirical parameterization in error covariance matrices. Application to the urban core of Zhengzhou demonstrated superior performance over conventional approaches. In controlled experiments, the framework achieved superior precision in localizing high-emission sources, reducing root-mean-square error by 21.4% between posterior estimates and assumed true fluxes across multiple emission scenarios. Real-world validation at the two monitoring towers further confirmed the improvements under the EDGAR-based prior, with lower RMSE values (10.31 and 10.05 ppm) and higher correlation coefficients (0.91 and 0.81) than conventional benchmarks. Additionally, the relative uncertainty of posterior emissions declined by approximately 46.4% compared to the traditional method, reflecting the enhanced precision of the approach. Crucially, analysis indicated that the reduction in posterior uncertainty resulted from systematic examination of inter-grid correlations, demonstrating that spatial correlations are essential for rigorous uncertainty quantification.