Launch vehicles and aerospace structures trend towards slender and more lightweight designs to reduce mass and aerodynamic drag. Slender structures are more affected by structural vibrations that interfere with both inertial sensing and navigation performance. Slender aerospace structures (launch vehicles, aircraft, and others) would greatly benefit from means for real-time monitoring of the flexible dynamics: real time modal sensing, as well as estimation of acceleration and rate of rotation at any point in the structure. This paper proposes the use of fiber-Bragg (FBG) sensor arrays for real-time monitoring and control of a flexible subscale test article representative of a launch vehicle. A virtual sensor for estimating acceleration and rate of rotation at any point in the structure is presented: the FBG Inertial Measurement Unit. The FBG-IMU is a real-time estimator based on a finite element model of the structure, the state-space equations of the flexible dynamics, and a finite number of strain measurements provided by the FBG array. The FBG-IMU allows accurate estimation of the states of the flexible structure with no need of estimation of load forces or damping matrix, as current structural models of flexible structures are forced to assume. The FBG-IMU is a contribution to the real-time estimation of the flexible dynamics in structures without the need of estimating loads or damping.