Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 334

estimation may be used and the same DOPs apply. The only difference is that in the
linearization process, satellite velocities and initial estimates of user velocity and
clock drift are employed. Also, for precise velocity estimation it is important to
account for the fact that satellite geometry is slowly changing with time (e.g., see
[34]).
Additional state variables may also be included for vertical tropospheric delays
[35] or system time offsets when using measurements from both GPS and a separate
satellite navigation system [36].

7.3.5 Kalman Filtering
The least-squares and WLS solutions that were described in Chapter 2 and previ-
ously in this chapter have utilized a set of pseudorange measurements at one snap-
shot in time, along with initial estimates of the user position and clock, to derive an
improved estimate of the user's position and clock error at that instant. In practice,
the user frequently has access to an entire sequence of measurements over time. Past
measurements may often be useful for obtaining a more accurate PVT estimation.
For instance, a stationary user can average least-square position estimates over an
hour, a day, or longer to obtain a more accurate estimate of his or her position than
would be possible using just the latest set of measurements. In principle, even the
most agile user can obtain some benefit from incorporating past measurements into
his or her position estimator, provided that it is possible to accurately model the
motion of the platform over time and to model the progression of user clock errors
with time. The most common algorithm used to incorporate past measurements in
GPS PVT applications is referred to as a Kalman filter . Kalman filters also facilitate
the blending of GPS measurements with measurements from other sensors and are
discussed in detail in Chapter 9.

7.4 GPS Availability

Availability of a navigation system is the percentage of time that the services of the
system are usable. Availability is an indication of the ability of the system to provide
a usable navigation service within a specified coverage area. Availability is a func-
tion of both the physical characteristics of the environment and the technical capa-
bilities of the transmitter facilities [37]. In this section, GPS availability is discussed
under the assumption that usable navigation service can be equated to GPS accuracy
meeting a threshold requirement. It should be noted that some applications include
additional criteria (e.g., the provision of integrity—see Section 7.5) that must be met
for the system to be considered available).
As discussed in Section 7.3.1, GPS accuracy is generally expressed by

σ = DOP ⋅ σ

p UERE

where σ UERE is the stan-

dard deviation of the satellite pseudorange measurement error. Representative

σ p is the standard deviation of the positioning accuracy, and

σ UERE
values are provided in Tables 7.3 and 7.4 for PPS and SPS, respectively. The DOP
factor could be HDOP, VDOP, PDOP, and so forth, depending on the dimension for