**Inertial Navigation Systems** (INS) have to take the **Gravity Vector** **g**, **Earth Rotation Rate** **ω** and the **Coriolis Effect**

The accelerometers **Acc** are affected by the **Coriolis force** which depends on the velocity **ω**. The accelerometers also measure the **Gravity** vector, which is calculated from the known position of the aircraft

The gyroscopes **Gyros** not only measure the rotation of the aircraft but also the rotation of the earth. To get the pure aircraft rotation, earth's rotation has to be subtracted from the rotation rate measured by the gyros.

Source: Integration of a GPS aided Strapdown Inertial Navi

You find some more INS block diagrams below.

"Inertial Navigation (IN) is the type of navigation that uses accelerometers and a computer to calculate via dead reckoning one’s position. IN is fundamentally achieved by the double integration of acceleration and correcting for gravitational fields in the computations along with other considerations such as **coriolis acceleration**. Currently IN is used for navigation in astronautics, aeronautics, marine and land, but the technology goes beyond navigation"

- Optimization of a Strapdown Inertial Navigation System; Mario Ruiz; University of Texas at El Paso, mariobikes@hotmail.com

See page 23, **Navigation Equations**

"The navigation computer uses these equations to compute the vehicle’s position taking measurements form the sensors, correcting them to account gravity, coriolis, and the earth’s rotation, and then computing the vehicles movements."

"A moving vehicle experiences forces like Coriolis and centripetal which related to the vehicle’s craft rate. These forces need to be accounted for to accurately navigate." page 65

Search for *Coriolis*:

- INERTIAL NAVIGATION SYSTEMS; IVAO INTERNATIONAL VIRTUAL AVIATION ORGANISATION
- Inertial Navigation System (INS); SKYbrary

Inertial navigation system algorithm block diagram. Taken from Titterton & Weston (2004) The navigation equations presented in the image above is collectively known as the INS (Inertial Navigation System). The output of INS consists of the complete system position, velocity, acceleration, orientation and angular rates of rotation. These parameters are used by the control system as the measurements of the system motion on which the control action will be performed.

Source: Design Considerations for Long Endurance Unmanned Aerial Vehicles

The IMU is an underlying element of each INS. Sensors whose output is influenced only by the motion of the object, on which the IMU is placed, are regarded as primary sensors of the IMU. Sensors of angular velocity whose output signals after integrating are used for determining the orientation in space, and accelerometers whose output signals after precise compensating the **gravitational acceleration** and **Coriolis force** can be integrated for speed and position are the primary sensors in the inertial navigation. 4 Such an IMU has six degrees of freedom, which means that it enables measuring the translational and rotary motion in three orthogonal axes.

Source: Enhancing the reliability of mobile robots control

When the accelerometer and gyroscope in the motion sensor measure specific forces and angular rates, respectively, the navigation solutions including position, velocity, and attitude are computed using the inertial navigation system (INS) mechanization.