  In this paper, we study an optimal control problem of linear backward
stochastic differential equation (BSDE) with quadratic cost functional under
partial information. This problem is solved completely and explicitly by using
a stochastic maximum principle and a decoupling technique. By using the maximum
principle, a stochastic Hamiltonian system, which is a forward-backward
stochastic differential equation (FBSDE) with filtering, is obtained. By
decoupling the stochastic Hamiltonian system, three Riccati equations, a BSDE
with filtering, and a stochastic differential equation (SDE) with filtering are
derived. We then get an optimal control with a feedback representation. An
explicit formula for the corresponding optimal cost is also established. As
illustrative examples, we consider two special scalar-valued control problems
and give some numerical simulations.
