In this paper, we propose an estimation method that allows for unrestricted interactions between worker and firm unobserved characteristics in both wages and the mobility patterns. Related to Bonhomme, Lamadon and Manresa (2014) (BLM), our method identifies double sided unobserved heterogeneity through an application of the EM-algorithm where the firm classification is repeatedly updated so as to improve on the likelihood function. In Monte Carlo simulations we demonstrate that the cyclic updating of the firm classification provides a significant performance improvement. Firm classification is a result of both wage and mobility patterns in the data. We estimate the model on Danish matched employer-employee data for the period 1985-2013. The estimation includes gender, education, age and time controls. We find an increased sorting pattern over time, although overall sorting is modest. Joint with Suphanit Piyapromdeey and Jean-Marc Robinz.