  Financial markets are often driven by latent factors which traders cannot
observe. Here, we address an algorithmic trading problem with collections of
heterogeneous agents who aim to perform optimal execution or statistical
arbitrage, where all agents filter the latent states of the world, and their
trading actions have permanent and temporary price impact. This leads to a
large stochastic game with heterogeneous agents. We solve the stochastic game
by investigating its mean-field game (MFG) limit, with sub-populations of
heterogeneous agents, and, using a convex analysis approach, we show that the
solution is characterized by a vector-valued forward-backward stochastic
differential equation (FBSDE). We demonstrate that the FBSDE admits a unique
solution, obtain it in closed-form, and characterize the optimal behaviour of
the agents in the MFG equilibrium. Moreover, we prove the MFG equilibrium
provides an $\epsilon$-Nash equilibrium for the finite player game. We conclude
by illustrating the behaviour of agents using the optimal MFG strategy through
simulated examples.
