Deltarange measurements can be computed by summing up the carrier voltage 

controlled oscillator (VCO) commands in the carrier tracking loop which tracks the

phase of the received signal.  The changes in measured phases are fed back to the

VCO to zero out these changes.

As with the pseudorange measurements, four deltarange measurements to four

different satellites allow velocity and user clock drift to be computed analytically,

although an iterative procedure is typically employed.

9.3.2  The GPS Navigation Equation

Figure 9 2 shows the basic relation between the line  of sight pseudorange

measurement PR

i

 (i=1,..,4 satellites), the satellites positions (S

xi

, S

yi

, S

zi

), and the

(antenna) user position coordinates (U

x

, U

y

, U

z

).  The equation for the pseudorange

is as follows:

1/2

2

2

2

i

PR    =    [(S

xi

     U

x

)   +  (S

yi

     U

y

)   +   (S

zi

     U

z

) ]   +  

u

b

where

PR

i 

= pseudorange to the i

th

 satellite, measured in the code

correlation process

S

xi

, S

yi

, S

zi

=

position coordinates of the i

th

  satellite, known from the

decoded navigation message

U

x

, U

y

, U

z  

=

three coordinates of the user position, to be found

b

u 

=

contribution to pseudorange caused by the user clock offset

error, to be found

The equations for deltarange are similar:

1/2

2

2

2

i

dPR    =    [(V

xi

      V

x

)   +  (V

yi

      V

y

)   +  (V

zi

      V

z

) ]   +  f

u

where

dPR

i 

=

deltarange to the i

th

 satellite, measured in the phase lock

loop

V

xi

, V

yi

, V

zi

=

velocity coordinates of the i

th

  satellite, derived from the

decoded navigation message

V

x

, V

y

, V

z  

=

three coordinates of the user velocity, to be found

9 7