This paper addresses the nonlinear attitude-tracking control problem of a rigid spacecraft with large-angle manoeuvres under actuator saturation and partial state measurement. A combined control and state-estimation framework is developed by combining feedback linearisation, Linear Quadratic Regulation (LQR), and a reduced-order Luenberger observer. First, the feedback linearisation is used to transform the nonlinear attitude dynamics into a linear equivalent form, which allows the LQR controller to be designed systematically to balance the attitude-tracking performance and control effort. The developed control architecture is implemented subject to actuator torque constraints to reflect the practical limitations encountered during large-angle manoeuvres. A reduced-order observer is added to the system to estimate the required unmeasured states from the available measurements and the system dynamics, reducing dependence on direct attitude measurements. The proposed framework is validated with numerical simulations using the TURKSAT-1B spacecraft parameters. The simulation results are used to evaluate the attitude-tracking accuracy, transient response, control effort, actuator saturation, and observer convergence. The results demonstrate the potential of combining nonlinear feedback linearisation and optimal linear control with reduced-order state estimation to achieve satisfactory attitude tracking under the given operating conditions. The paper proposes a computationally structured approach to spacecraft attitude control when not all required states can be measured directly.