Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 548

θ

a

b

1 1

22
ne

2222
ne

a = (+)+ (+)+ σσ σσ σ

e

4

2

1 1

22
ne

2

) 22

b = (+) (+ + σσ − σσ σ

ne e

2 4

2 σ ne

1

tan − 1 = θ −

2

22
e

σ−σ

n

Figure 9.44 Error ellipse relationship to covariance matrix.

ranging off the cellular signals). In the figure, σ ne denote the elements of

the covariance matrix corresponding to east and north position error. In the case of
an error ellipse, the east and north position error components will generally be cor-
related (i.e., a nondiagonal measurement error variance will be needed if the con-
straints are expressed directly in terms of east and north position error components).
Preferably, the measurement error variance matrix can remain diagonal if the mea-
surements are expressed in the principal axes. Adding the approximate location
information as measurements cannot be expected to improve the accuracy of the
resultant fix, but it can assist in the identification of failed pseudorange measure-
ments corresponding to false signal detections.
In a manner completely analogous to the addition of position constraints as
additional measurements in the WLS solution for location, a timing constraint can
be added to the clock offset solution, if fine timing information is available and suffi-
ciently accurate (i.e., submillisecond).
Finally, the mobile's navigation solution can be aided by the transmission of sat-
ellite clock correction and ephemeris data, which may already be part of the acquisi-
tion assistance. However, for a handset-based solution in response to an emergency
call, both are generally required for an accurate solution, since time does not permit
decoding of the equivalent information from the navigation data bits.

σ 2 , σ 2 , and

9.4.5.1 Over-the-Air Location Protocol Standards
It is important to develop common over-the-air messaging standards to support
assisted GPS technology in a handset in order to guarantee interoperability among
various handset and location technology developers. As such, telecommunication