When discussing coordinates and refence frames Sonardyne always applies the ‘right-hand rule’, which can be seen below.

The ‘right-hand rule’ can be explained by holding one’s right-hand hand outward, palm up, with the fingers curled, and the thumb outstretched. If the curl of the fingers represents a movement from the first or x-axis to the second or y-axis, then the third or z-axis can point along either thumb

Applying this to a common Forward, Starboard, Down reference frame can be seen below:

Several reference frames are used within inertial navigation.

Vehicle Frame
Axes are along the vehicle axis, typically Forward, Starboard and Down. The vehicle frame is typically used for navigation outputs, e.g. roll, pitch, and heading, and for defining various sensor lever arms and mounting angles.

Navigation Frame
Frame used for the inertial navigation computation of position and velocity, most often local level, e.g. North, East and Down.

IMU Frame
Axes are along the inertial sensor axes as typically marked on the IMU/INS housing. IMU frame is primarily used for internal INS computations.