Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 303

δ t noise&int = errors due to receiver noise and interference

δ t mp = multipath offset

δ t hw = receiver hardware offsets

A delay expression with the same form as (7.2) but with generally different
numerical values is incurred on the RF carrier component of each signal.
Before May 2000, (7.2) included the effects of SA, an error intentionally
induced by the DOD to degrade the user's navigation solution. The degradation was
accomplished primarily through dithering of the satellite clock (clock error compo-
nent), although the manipulation of the broadcast ephemeris data (orbital error
component) was also possible but not observed [2]. On May 1, 2000 SA was
officially removed [3].
The pseudorange time equivalent is the difference between the receiver clock
reading when the signal (i.e., a particular code phase) was received and the satellite
clock reading when the signal was sent. These timing relationships are shown in Fig-
ure 7.1, where:

∆ t = geometric range time equivalent

T S = system time at which the signal left the satellite

T u = system time at which the signal would have reached the user receiver in

the absence of errors (i.e., with δ t D equal to zero)

′ = system time at which the signal reached the user receiver with δ t D

T u

offset of the satellite clock from system time—advance is positive;
retardation (delay) is negative
t u =

δ t =

offset of the receiver clock from system time
T S + δ t = satellite clock reading at time which the signal left the satellite

Tt
u

′ + = user receiver clock reading at time when the signal reached the user

u

receiver
c = speed of light

(Geometric range time equivalent)

∆ t

t u

δ t

δ t D

Time

T s

Tt

s + δ

T u T u T u + t

u

(Pseudorange time equivalent)

Figure 7.1 Range measurement timing relationships.