  We consider a model of optimal investment and consumption with both habit
formation and partial observations in incomplete It\^{o} processes market. The
investor chooses his consumption under the addictive habits constraint while
only observing the market stock prices but not the instantaneous rate of
return. Applying the Kalman-Bucy filtering theorem and the Dynamic Programming
arguments, we solve the associated Hamilton-Jacobi-Bellman (HJB) equation
explicitly for the path dependent stochastic control problem in the case of
power utilities. We provide the optimal investment and consumption policies in
explicit feedback forms using rigorous verification arguments.
