We consider the optimal investment and consumption problem for the pooled annuity funds, in which both the financial market and the mortality hazard rate of participants in the pool are partially observable. We manage to achieve the explicit expressions for optimal consumption and investment strategies employing filtering techniques and Hamilton-Jacobi-Bellman (HJB) equation. What is more, we also discuss the models where both the instantaneous rate of return of financial market and mortality of plan members are observable and obtain the optimal investment strategies accordingly. In addition, we look into this optimization problem under different exit mechanism including infinite exit time for the plan members. Last, but not the least, we carry out numerical analysis demonstrating the impact of observability of information.