3.1.3  Geometric Dilution of Precision

As described in paragraph 3.1.1, GDOP is a dimensionless multiplicative factor that

is an instantaneous measure of the error in the positioning solution, contributed by

the geometric relationships of the GPS satellites, as seen by the receiver.  As an

example, if two lines of position are necessary to establish a user position, the least

amount of error is present when the lines cross at right angles.  The greatest error

is present as the lines approach parallel.  (See Figure 3 1.)  Similarly, for GPS, the

greatest amount of error is present when the lines of sight between the user and 2

or more satellites approach parallel, or when all four satellites approach the same

plane.

Figure 3 1.  Dilution of Precision

"Technical Characteristics of the Navstar GPS" contains the mathematical definition

and derivation of GDOP.  In short, if the one sigma pseudorange measurement errors

for all satellites are assumed to be unity, GDOP is defined to be the square root of the

sum of the variances of the position and time error estimates.

GDOP =  (s

2

2

2

2

x

 + s

y

 + s

z

 + c

2

s

t 

)

1/2

(Where "c" is the speed of light and "t" is the user clock bias.)

GDOP is therefore considered to relate the standard deviation of the satellite range

errors (UERE) to the standard deviation of the position solution errors.  GDOP is

normally considered to be unitless; the units (metres) being carried by the range error

and position solution errors.  Expressed as a mathematical formula:

s

UERE

 x GDOP = s

POSITION SOLUTION ERROR

3 4