Document MT0605P.E
© Xsens Technologies B.V.
MTi User Manual
29
This system is called the locally tangent plane (LTP) and is in fact a local linearization of the Ellipsoidal
Coordinates (Latitude, Longitude, Altitude) in the WGS-84 Ellipsoid.
When mapping the ellipsoidal coordinates defined by to latitude, longitude, and altitude to a local
tangent plane, a spatial distortion is introduced as shown in Figure 7.
Figure 7: Spatial Distortion as Result of Mapping Ellipsoidal Coordinates to Local Tangent Plane (LTP)
In order to minimize the linearization error, the reference coordinates should be chosen as close as
possible to the points that are being mapped. The MTi-G performs a local linearization for each valid
GPS update according to the following linearization scheme, given a reference coordinates defined by
a latitude-longitude pair (
ref
,
ref
). The height is the same for both coordinate systems.
{
𝐸 = 𝑅 . ∆𝜑. cos(𝜃)
𝑁 = 𝑅. ∆𝜃
Where R is the radius of Earth at a given latitude.
{
∆𝜃 = 𝜃 − 𝜃
𝑟𝑒𝑓
∆𝜑 = 𝜑 − 𝜑
𝑟𝑒𝑓
In this documentation we will refer to the WGS84 co-ordinates system as
G
. The output of position
data from the MTi-G is in Ellipsoidal Coordinates (Latitude, Longitude, Altitude) in the WGS84
Ellipsoid.
The MTi-G uses HE (Height over Ellipsoid)
– Altitude above
the ellipsoid (WGS84).
Furthermore, the local gravity vector may differ from the
vector perpendicular to the local tangent plane
(perpendicular to the plane tangent to the ellipsoid) as
shown in the figure below. The imaginary shape that is
perpendicular to the natural gravity vector is called
“geoid”. The value of vertical deviation (or also called
vertical deflection) can be a small fraction of a degree.
For the continental US, the maximum vertical deviation can be about +/- 0.01 degrees.
longitude
52
lat
itud
e
53
6
7
local meridian
linearized meridian
N
E
Figure 8: Difference between Geoid and
Ellipsoid
