Module 2 : Global Positioning System
  Lecture 12 : GPS Measurements Techniques
Code based measurements
  • Code measurements (also referred to as pseudorange measurements) enable instantaneous position determinations using GPS satellites.
  • Pseudoranges to four satellites are used to determine position by removing uncertainties in (a) X, Y, Z and (b) receiver clocks and then corrected to produce the range. Positioning accuracy is a function of intersection geometry and range measurement accuracy.
  • Code measurements are the difference in time between when the code is transmitted from a satellite and received at a GPS receiver, multiplied by the speed of light.
                                                     measured code pseudorange (P) = c (t i - tj )

P     measured code
c      speed of light
t i     signal reception time
t j     signal transmission time

  • It represents a direct measurement of satellite to receiver range and can be expressed as
                           measured code pseudorange = range + errors
                                                                               P = ρ + errors
As shown earlier in Lecture 11, a simplified code pseudorange at an epoch t between receiver i and satellite j can be given by the following equations
   Measured code pseudorange between the receiver i and the satellite j
   Geometric distance between the satellite j and the receiver i
  Combined clock offset of the satellite and the receiver clock, with respect to GPS time.
C   Speed of light
(X j (t), Y j (t), Z j(t))              satellite coordinates at epoch/time t
(X i , Y i , Z i )                        receiver coordinates
A general pseudorange equation with different errors can be written as (Leick, 2004)

 
 
  • Pseudorange between receiver i and satellite p at time t for L1 frequency
  • Geometric vacuum range
  • Ionospheric delay at L1, depends on ionospheric conditions along the path and on frequency, always positive since code is slowed down by the ionosphere
  • Tropospheric delay, depends on tropospheric conditions along path but independent of carrier frequency. Hence, no subscript to identify it, always positive
  • Receiver hardware delay, independent of satellite observed
  • Multipath delay, depends on direction of satellite observed
  • Satellite hardware delay
  • Pseudorange measurement noise (approx 30 cm for P(Y) code more for C/A code depending on technique used)
 
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