  In this paper we mainly propose efficient and reliable numerical algorithms
for solving stochastic continuous-time algebraic Riccati equations (SCARE)
typically arising from the differential statedependent Riccati equation
technique from the 3D missile/target engagement, the F16 aircraft flight
control and the quadrotor optimal control etc. To this end, we develop a fixed
point (FP)-type iteration with solving a CARE by the structure-preserving
doubling algorithm (SDA) at each iterative step, called FP-CARE SDA. We prove
that either the FP-CARE SDA is monotonically nondecreasing or nonincreasing,
and is R-linearly convergent, with the zero initial matrix or a special initial
matrix satisfying some assumptions. The FP-CARE SDA (FPC) algorithm can be
regarded as a robust initial step to produce a good initial matrix, and then
the modified Newton (mNT) method can be used by solving the corresponding
Lyapunov equation with SDA (FPC-mNT-Lyap SDA). Numerical experiments show that
the FPC-mNT-Lyap SDA algorithm outperforms the other existing algorithms.
