The exact inner workings of SpaceX's guidance computers are proprietary secrets, but we do know some facets based on information available in the public domain. The guidance system of the SpaceX Dragon vehicles, for example, use a Fault-Tolerant Inertial Navigation System (FTINS) primarily based on a triple set of accelerometers and gyroscopes and a GPS receiver for correction, with the readings from each sensor fused together using a Kalman filter algorithm for best accuracy and resilience against failures. This allows for determination of acceleration, orientation, and altitude information. For the communication with ground stations, SpaceX takes a software-defined radio approach, which allows for versatility in the types of signals it can send and receive, as well as resilience against potential issues. The onboard computer system uses a version of the Linux operating system with real-time extensions called "Real-Time Linux". It is mainly written in C++ and Python and operates in a redundant setup for fault tolerance - meaning, multiple computers that check each other's calculations to minimize the chance of failure. Lastly, the use of closed-loop guidance algorithms, which adapt to changing circumstances mid-flight, adjusts the path in realtime based on sensor data. This setup allows the rockets to automatically correct their trajectory if any deviations occur, such as a change in wind conditions or minor performance variations in the engines. Specific programming details are understandably not made public for both commercial and security reasons. However, the core concepts of SpaceX's guidance systems are rooted in industry-wide accepted best practices for real-time, safety-critical systems with a strong focus on fault tolerance and flexibility.