What are the fundamental navigation equations in the navigation frame for INS?

• A. The rate of change of attitude is given by a function of body angular rates; velocity update uses specific force transformed to navigation frame minus gravity; position update integrates velocity in navigation frame.
• B. Attitude remains constant.
• C. The velocity update depends on inertial forces.
• D. Motion described by a simple linear model with no gravity.

Answer: (A)

In the navigation-frame formulation, the fundamental INS equations describe how orientation, velocity, and position evolve using gyros and accelerometers. The rate of change of attitude comes from the angular rates measured by the gyros, expressed in the body frame and mapped into the navigation frame by the current orientation. Once the attitude is known, the accelerometer output (specific force) is rotated into the navigation frame and, after subtracting gravity, gives the acceleration of the platform in the navigation frame. Integrating that acceleration updates velocity, and integrating velocity updates position in the navigation frame. This sequence—attitude change driven by body angular rates, velocity update from transformed specific force minus gravity, and position update by integrating velocity—is the standard set of INS navigation equations in the navigation frame. Other statements omit essential pieces (attitude can change with motion; velocity depends on gravity-corrected specific force, not inertial forces alone; and gravity-free models don’t describe real motion).