ALTAIR is a European Commission Horizon 2020 project that proposes a space launch system composed of an autonomous aircraft-rocket assembly, dedicated to the market share of small satellites (50-150 kg) in Low Earth Orbit. The rocket, or Space Launch Vehicle (SLV), comprises a cost-effective lightweight navigation system that fuses Global Navigation Satellite System (GNSS) data and readings from an Inertial Measurement Unit (IMU). The combination of these two technologies allows for a significant cut of the system mass budget with respect to traditional inertial-only navigation systems, without consequential accuracy loss. Additionally, ALTAIR embeds the alignment process on-board the SLV, which is performed during captive flight. Transferring this task to after take-off significantly simplifies ground operations in terms of both time and safety, hence further decreasing the cost of each launch campaign. This paper is divided into two parts: navigation performance assessment and its application for autonomous on-board safety algorithms. First, it presents the sensor fusion algorithm used to hybridize GNSS and IMU during the SLV free flight, including the captive alignment process. It describes a loosely coupled architecture of the hybrid navigation system, which combines a profile-free alignment with a profile-based GNSS/IMU data fusion. It then analyses the performance of this implementation that uses the Indirect (error-based) and Extended Kalman filters. Second, it evaluates the impact of sensor fusion on the safety algorithms that assess the nominal launcher state and engine failure free-fall scenario. Results show that hybrid navigation can be used to maintain a bounded error navigation solution throughout the in-flight initialization, the alignment manoeuvre and the free fall before ignition. Furthermore, transfer-alignment previous to SLV release prevents transient errors during the most critical initial seconds of free flight.