Inertial position conversion

A first glance onto trial data

Receiver clock synchronization

While we have the luxury that position data are transmitted by ADS-B squitters, these positions are a bit different from what we need. As we will convert signal travel time to distance and v.v. this will assume that a position is described in space by latitude, longitude and altitude over the globe and distances are calculated as straight and slant.

Altitude is therefore very important. As an example, while a flight exactly overhead the SBS-1 would be described as 0 NM distance from it, the travel time of a transponder signal would be a product of the light of speed and the altitude over ground.

To calculate distances we will there for convert the position and altitude data we have to an inertial coordinate system. This cartesian system has the the center of the earth as a midpoint.

The conversion is

[Latitude, Longitude, Height (=Altitude (FL) + GNSS Altitude Difference + radius_Earth)]  >> [x, y, z]

The distance between two points x₁, y₁, z₁ and x₂, y₂, z₂ would then be

d₁₂ = sqrt [(x₂ - x₁)²  + (y₂ - y₁)² +(z₂ - z₁)²]

With a mean radius_Earth = 6371 km the conversion is

x = sin (Longitude) * cos (Latitude) * Height

y = sin (Latitude) * Height

z = cos (Longitude) * cos (Latitude) * Height

all in km.

[OPEN] The mean value of radius_Earth = 6371 km shall be subject to discussion later, because this may not be the appropriate value for the position of the flight target. .