Which of the following is not a radio-based navigation system?

The inertial navigation system (INS) is indeed not a radio-based navigation system, which makes it the correct choice in this context. INS operates based on data generated from onboard sensors that track the vehicle's position, speed, and orientation using accelerometers and gyroscopes. This system calculates the aircraft's position over time through inertial measurement without relying on external radio signals.

In contrast, VOR (VHF Omnidirectional Range), NDB (Non-Directional Beacon), and TACAN (Tactical Air Navigation) are all radio-based navigation systems. VOR provides directional information based on radio frequency signals, enabling pilots to determine their position relative to various VOR stations. Similarly, NDB uses radio signals for navigation but is more simplistic, allowing aircraft equipped with a radio receiver to hone in on the beacon's location. TACAN is more advanced, combining distance measuring (DME) capabilities with VOR, specifically for military aircraft, hence offering both range and bearing information.

Understanding the differences between these systems clarifies why INS is the outlier in this question, relying entirely on internal mechanics rather than external radio frequencies for navigation.