DETERMINATION OF PSEUDORANGE- AND CARRIER PHASE NOISE

Introduction.

With the current quality of GPS receivers, multipath on the pseudorange may very well be the determining factor for (sub) meter level code differential GPS, and multipath and receiver noise on both pseudorange and carrier phase may determine the ability of the receiver for cm level carrier phase differential  GPS. It is therefore required: A. to gain knowledge about these quantities and B. to control multipath by a careful antenna selection and antenna location. This page gives guidelines on how to determine pseudorange- and carrier phase noise. For guidelines on the determination of multipath, go to the multipath page.
Experience shows, that the noise level of both pseudorange and carrier phase often depends on the satellite elevation: low elevation satellites have a longer path through the atmosphere, and are thus more damped, and can be more noisy because of ionospheric scintillation, and thus deliver more noisy observations than high elevation satellites.

Forming double differences (DD's) removes common errors such as satellite clock error, satellite position error, ionospheric error, tropospheric error, receiver multipath error and receiver clock error. Remaining errors are the DD receiver noise, and, in case of the carrier phase, the DD cycle ambiguity. However, the noise level on a DD is higher than the noise level on an undifferenced observation.
Usually, the noise of observations of satellites with a high elevation (say more than 60 deg) is constant, say S.
If one assumes that the noise between satellites and between receivers is uncorrelated and gaussian (a reasonable assumption), the noise of a Double Differenced (DD) observation of two high satellites can be determined with the propagation law: SDD = sqrt(S2 + S2 + S2 + S2) = 2 * S, or : S = SDD / 2.
This property is used to determine the noise of high satellites first.
Next, the noise of lower satellites is determined using the high sat noise and again the propagation law. 

Recipe:

  1. Find a friend with an identical receiver.
  2. Buy (WR Inc), or build an antenna splitter.
  3. Connect the receivers to the splitter outputs, connect an (active) antenna to the splitter input, and connect PC's with download s/w to the receiver outputs.
  4. Power up the receivers, start the downloading s/w on both PC's (download should include pseudoranges and carrier phases).
  5. Record data at a rate of 1/sec for several time slices of about 5 minutes, until a full range of satellite elevations has been covered (this may take several hours).
  6. Select for each time slice the satellite with the highest elevation - this is the reference satellite for that time slice.
  7. Form DD's of the pseudorange- and carrier phase observations.
  8. Determine for each DD in the time slice the average and the standard deviation. (note : the average of the pseudo range should be close to zero, the average of the carrier phase (expressed in cycles) should be close to an integer value). Note: in the case of DD carrier phase: check that the time slices are free from sudden jumps, caused by cycle slips.
  9. Start with a high (> 60 deg) satellite, determine the noise level of the reference satellite as described above (Sref).
  10. For all other satellites and time slices the noise is calculated using Ssat = sqrt (SDD2 / 2 - Sref2). This calculation can be carried out for both pseudorange and carrier phase.
  11. Finally plot the satellite noise as a function of the elevation.


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