Other dilution of precision factors can be defined which are a subset of GDOP and

have a more specific physical meaning with respect to the x, y, and z axes in a local

coordinate system.  They include position dilution of precision (PDOP), horizontal

dilution of precision (HDOP), vertical dilution of precision (VDOP) and time dilution of

precision (TDOP).  Mathematically they are defined as follows:

PDOP =  (s

2

2

2

x

 + s

y

 + s

z

)

1/2

HDOP =  (s

2

2

x

 + s

y

)

1/2

VDOP =  (s

2

z

)

1/2

TDOP =  (s

2

t

)

1/2

HDOP can be further resolved into its X and Y components.  If the X axis is oriented in

an East West direction, an "East" DOP (EDOP) and "North" DOP (NDOP) can be

defined as follows:

EDOP =  (s

2

x

)

1/2

NDOP =  (s

2

y

)

1/2

Similarly, if the Y axis is oriented along the track of a moving vehicle, a "cross track"

DOP (XDOP) and an "along track" DOP (ADOP) can be defined:

XDOP =  (s

2

x

)

1/2

ADOP =  (s

2

y

)

1/2

The various elements of GDOP can also be calculated for an over determined position

solution, that is, where the available satellite or aiding measurements exceed the

required minimum of four, and an "all in view" solution is calculated.  The mathematical

formulations are similar, and generally result in a lower value of GDOP (hence better

solution accuracy) for each additional measurement that is added to the calculation.

GDOP can also be "weighted" with a vector of UERE values in the matrix

calculations for real time or short term error estimates where the satellite (or aiding)

UERE values are not equal.  As mentioned previously, this is generally the case for

instantaneous values of UERE,  and especially true for SPS where large differences

in instantaneous UERE can be caused by Selective Availability.  This is also true

for aiding situations where the equivalent "UERE" of the aid is usually different than

the typical satellite UERE.  This "weighted" variation of DOP is an estimate of User

Navigation Error (UNE) and is sometimes termed "KDOP".  KGDOP has the same

definition as GDOP except that the statistical satellite range  errors are not required

to be equal.  Similarly there are analogous subset definitions of  KPDOP, KHDOP,

etc.

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