<p>The concentrations and sources of particulate matter in the atmosphere are temporally auto-correlated. Here, we present a Bayesian matrix factorization model (BAMF) that considers the temporal auto-correlation of the components (sources) and provides a direct error estimation. The performance of BAMF is compared to positive matrix factorization (PMF) using synthetic Time-of-Flight Aerosol Chemical Speciation Monitor data, representing different urban environments from typical European towns to megacities. We find that BAMF resolves sources better than PMF on all datasets with auto-correlated components, but highly cross-correlated components continue to be challenging. However, we demonstrate that adding even partial prior information about the chemical composition of the components to BAMF improves the factorization. Overall, BAMF-type models are promising tools for source apportionment and merit further research.</p>