Can Expectation Maximization estimate truth and confusion matrix from multiple noisy sources?
I don't have a full answer to your question, but I wanted to help (and would love to know a complete answer). In a simpler case when you have one source $m=i=1$, it seems to me you are describing a scenario that resembles a hidden Markov model which uses a EM algorithm-based solution (Baum–Welch algorithm) – that is if you make the further hypothesis that a Markov property is satisfied. Because convergence properties of the stationary distribution of Markov chains are exponentially fast the algorithm convergence may be limited to the implemented algorithm. I hope that info helps point you in the right direction.