Building on previous works, this paper introduces a novel continuous-time stochastic optimal linear quaternion estimator under the assumptions of rate gyro measurements and of vector observations of the attitude. A quaternion observation model, which observation matrix is rank degenerate, is reduced to a two-dimensional model via a maximum information rate approach. The resulted filter combines the exact treatment of the quaternion process state-dependent noise and the quaternion measurement state-dependent noise under the framework of continuous-time optimal linear filtering. This yields statistically consistent covariance computations within the proposed filter without requiring tuning. The case of white noises in the gyro and vector measurements are considered in this work. This paper also presents the development of a Sun vector determination subsystem for the nanosatelite Delfi-N3xt. Simulations and preliminary experimental validation show that this subsystem, which consists of six four-quadrant Sun sensors, can deliver a Sun-spacecraft line of sight with an averaged equivalent angular error of approximately 0.2 deg without the Earth albedo. The performances of the novel filter are illustrated via extensive Monte-Carlo simulations in the case of Delfi-N3xt, where Sun vector measurements, Earth magnetic measurements and gyro measurements are acquired along a 600 km height Sun synchronous orbit. The proposed filter appears to be insensitive to poor initial conditions and low sampling rates. It converges where a standard extended Kaiman filter fails to do so under the same conditions.