In this paper, we establish a Nash equilibrium in a market with N agents, all with CARA utility with relative performance criteria, when only partial information is available. Each investor has identical Gaussian prior belief on the return rate of the risky asset. The investor updates her belief modelled according to a Kalman filter and dynamically adjusts the amount she invests in the risky asset. A multidimensional coupled FBSDE is used to characterize the optimal investment strategy for stochastic and possibly unbounded return rate. We find that while investors trade more aggressively under relative performance, the effect is mitigated by partial information. Numerical solution is provided for multidimensional FBSDEs using a deep learning method. We demonstrate the efficiency and accuracy by comparing with the numerical solution from PDE. Moreover, our FBSDE framework can be used to solve for equilibriums in multi-asset cases.