Subject: [IGSMAIL-353] Satellite Accuracy Exponents
From: J. Feltens
Date: 22 OCT 1993 16:30:38

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IGS Electronic Mail       22-OCT-1993 16:30:38       Message Number 353
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From: J. Feltens 
Subject: Satellite Accuracy Exponents
-------------------------------------

 -------------------------
 ANALYSIS CENTRE: ESA/ESOC
 -------------------------

 INCLUSION OF "SATELLITE ACCURACY EXPONENTS" INTO THE HEADER OF OUR
                         DAILY ORBIT FILES

 J.M.Dow, J.Feltens, T.J.Martin-Mur, C.Garcia-Martinez

 Starting with  the week 0718 we  are including orbit sigma estimates  in
 the SP3 header format  (lines 8-12)  of our daily orbit files. The orbit
 sigma estimates are represented by  "satellite accuracy exponents"  (see
 NOAA Technical Report NOS 133 NGS 46).  The  orbit  sigma estimates  are
 computed at ESOC as can be seen from the figure:

             day|(i-1)               day|(i)
   12h          0h         12h   18h    0h    6h   12h
 a) +-----------|-----------+-----:-----|-----:-----+
                                  :<=========>:
                                  :<=========>:
 b)                         +-----:-----|-----:-----+-----------|-----------+
                           12h   18h    0h    6h   12h          0h         12h
                                     day|(i)                 day|(i+1)

 As already pointed out in earlier IGS-reports (e.g. report no. 224),  we
 are processing  the GPS-data in 48-hour-fits,  i.e. the orbit determina-
 tion of a day (i)  starts  on  day (i-1) at 12 hours noon  and  ends  on
 day (i+1) at 12 hours noon,  resulting in 24-hour overlaps for sucessive
 days. The figure shows  the situation for the two successive  days (i-1)
 and (i).
      For the computation of day (i)'s orbit sigma estimates, the overlap
 extending from 18 hours on day (i-1) to 6 hours on day (i)  will be con-
 sidered. This time interval covers 12 hours  and is marked by :<======>:
 in the figure. Starting at 18 hours on day (i-1),  every 15 minutes  the
 differences  deltaX, deltaY and deltaZ  between the earth fixed position
 vector components from the orbital fits of day (i) and of day (i-1)  are
 computed and summed up into squared sums:

            SX = sum(deltaX**2) every 15 minutes,
            SY = sum(deltaY**2) every 15 minutes,
            SZ = sum(deltaZ**2) every 15 minutes.

 This is  performed  individually  for every satellite  until 6 hours  on
 day (i) are reached. The number N of epochs are counted.  Then the orbit
 sigma estimates  OSIG  are  computed  as follows  (also individually for
 every satellite):

            sx = SX/(N-1)
            sy = SY/(N-1)
            sz = SZ/(N-1)

            OSIG = sqrt((sx + sy + sz)/3)

 And since the  satellite accuracy exponents  are defined as  2**OSIG  in
 the SP3 convention:

            SAE = nearest integer(ln(OSIG)/ln(2))

 These SAE (Satellite Accuracy Exponents) are the values that will appear
 appear from now on in the headers of our daily orbit files.

                                           The GPS group at ESOC