with dx, dy and dz the errors in the BOFrequently asked questions about our orbit accuracies
What do the tables show?
The tables give the minimal and maximal errors in the X, Y and Z directions and also for the 3D-vector. Further it shows the root mean square (RMS) errors in those directions over the whole day.
Why are some numbers red?
The numbers become red when they are equal or higher than 6 meters.
How are these statistics computed?
The IGS orbit is available at an interval of 15 minutes. The Broadcast Orbits are therefore also calculated in Cartesian coordinates every 15 minutes. The errors are computed by subtracting the X,Y,Z coordinates of the IGS orbit from the X,Y,Z coordinates determined from the broadcast orbit. No transformations are carried out. The difference between the WGS 84 system used for the BO and ITRF used for the IGS orbits is well below 10 cm.
The 3D error is then computed as follows:
with dx, dy and dz the errors in the BO
This gives a set of 4 x 96 differences for every satellite during a day.
Then the root mean square (RMS) is calculated and the minimum and maximum values can be computed. The RMS in the X direction is defined as:
|
where |
k = the satellite number |
|
|
n = the number of valid values for satellite k |
|
|
dxi = the error in the orbit in the X-direction |
A similar formula is used for the Y and Z directions. The RMS for the 3D direction is defined as follows:
The overall RMS for the whole day for all the satellites can then be computed in the following way.
where s = the number of satellites with a valid RMS
The statistics between the WAAS-corrected orbit and the IGS orbit are computed in a similar way.
When does the data become available?
Because the IGS final orbit only becomes available after 20 days (worse case), the most recent statistics table has a day-of-year of 20 days previous to the present day. To fill this gap, there is also a comparison made with the IGS rapid orbit. This file comes available after 2 days. So the delay in the statistics table for the rapid orbit comparison is 2 days. The rapid orbit statistics are overwritten by the final orbit statistics when they become available.
The statistics are calculated every day at 8:00 (final orbit comparison) and 8:05 (rapid orbit comparison) Atlantic Time.
How are the WAAS-corrections applied?
Long Term WAAS-corrections are made available in WAAS Message Type 24 and Message Type 25. A Long Term WAAS-correction can be applied to the appropriate satellite when the PRN of the corrections is established using Message Type 1. The corrections are only valid when the Issue of Data (IOD) of the broadcast ephemeris matches with the IOD in the correction message, and only when the time interval of applicability is not larger than 360 seconds.
The position error correction vector is computed as follows:
with tk = the current time
This correction vector is added to the satellite coordinate vector [xk yk zk]T. If the velocity code is set to 0, the rate-of-change vector is set to 0.