Applanix POS MV V5 Installation And Operation Manual page 213

has an angular rate with respect to the inertial frame of reference frame because the Earth rotates about
is north-south axis at 15°/hour.
An INS that is designed to operate on the surface of the Earth must first subtract the gravitational force
and Coriolis acceleration from the sensed specific forces, to obtain the acceleration of the INS with
respect to the Earth.
• Gravitational acceleration - Essentially a constant over the surface of the Earth (although small
variations exist from one place to another). The standard acceleration of gravity
. 9 80665
g
. 9 81
g
• Coriolis acceleration - The apparent tendency of a freely moving body to swing to one side when
its motion is referred to a set of axis that is itself rotating in space. The magnitude of Coriolis
acceleration measured by an INS moving horizontally on the surface of the Earth is:
Where:
The acceleration is perpendicular to the direction of
Hemisphere.
The INS must also subtract the 15°/hour Earth rotation rate from the sensed angular rates to obtain the
angular rate of the INS relative to the Earth.
After it has performed these functions, the INS integrates the corrected accelerations and angular rates to
compute changes in velocity, position, attitude and heading relative to the Earth.
Figure 81 on page B-5 is a simplified view of inertial navigation on a spherical non-rotating Earth. The
vessel is moving north at an initial velocity
The INS housing and its internal accelerometers are fixed to the vessel, forming a 'strap-down'
arrangement. One accelerometer aligns with the fore-aft line of the vessel, another aligns with the vertical
and a third accelerometer aligns with the port-starboard axis of the vessel. For convenience, this
explanation considers only the fore-aft and the vertical accelerometers (although the INS uses all three to
compute the solution).
With the vessel on a northerly course as shown, the fore-aft accelerometer also aligns with true north and
therefore senses any change in the northerly velocity.
Copyright © Applanix Corporation, 2017
POS MV V5 Installation and Operation Guide
2 . The convention used throughout this manual defines gravitational acceleration
ms
.
= is the angular magnitude of the angular
velocity of rotation of the Earth
= is the speed of the INS
= is the latitude
2 sin
c
and is towards the right in the Northern
.
n
Theory
of Operation
B-3