This paper investigates and assesses neutron radiation effects on the attitude estimation (AE) processing, typically embedded in inertial navigation systems (INS) and upcoming autonomous things. Findings highlight the importance of radiation-induced critical failures that can upset the on-board AE processing, and consequently the inertial navigation. Radiation tests and analyses were conducted by considering as on-board AE processing the execution of classical AE algorithm on a multi-core computer hardware exposed to 14-MeV neutron and thermal neutron radiation. Three computing strategies and different case-study scenarios were tested and compared. Results suggest that the contribution of radiation-induced soft errors to be mitigated on the embedded AE processing is essentially related to single-event functional interrupts that can lead the inertial navigation to critical failures.