# INS take Gravity, Earth Rotation and Coriolis into account

Inertial Navigation Systems (INS) have to take the Gravity Vector g, Earth Rotation Rate ω and the Coriolis Effect $-2\mathbf{\omega}\times\mathbf{v}$ into account to be able to correctly calculate the movement and orientation of the aircraft over the globe without any reference to the outside.

The accelerometers are affected by the Coriolis force which depends on the velocity $\dot{\mathbf{r}}$ and earth's rotation ω. The accelerometers also measure the gravity vector, which is calculated from the known position of the aircraft $\mathbf{r}$ and has to be canceled to get the pure aircraft accelerations.

The gyroscopes 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.

There are explicit control loops in the electronics and navigation equations in the software to account for Gravity, Earth's rotation and Coriolis.

"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"

"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

## Introductions to INS

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