Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 476

The measurement noise is received with the pseudorange and pseudorange rate
measurement. When we process the measurement and form the observation, we will
set the R ( t 1 ) matrix, where

σ

2

0

()

R t 1 =

ρ

0 σ

2

&

9.2.4.5 Data Synchronization
One issue that we must deal with is that of data synchronization. The Kalman filter,
being a sampled state system, assumes the time of the GPS measurement and that of
the inertial measurement are identical. Failure to synchronize the measurement data
results in unmodeled errors and requires the user to increase the process noise vari-
ances to compensate for this error. To accomplish this, two issues must be
addressed. The first is the timing of inertial data with the GPS receiver time. The sec-
ond is the buffering of inertial data to allow synchronization of the inertial data with
the GPS data.
Timing of the inertial data is accomplished by having the GPS receiver transmit
a 1-second timing pulse to the navigation processor. This signal, tied to a high-level
interrupt, forces the inertial clock to the next second. The inertial clock is a software
clock that is incremented by each inertial measurement received by the navigation
processor (typically at a rate of 100 Hz to 800 Hz). The inertial clock is thus
resynchronized to GPS receiver clock time once per second. To initialize the inertial
clock, the GPS receiver must implement a specific message that will inform the navi-
gation processor of the GPS receiver time at the next interrupt. This must be accom-
plished well before the receipt of the interrupt to give the navigation processor time
to respond to the interrupt and the message, and prepare to set the inertial clock
before the next interrupt is received.
Since the GPS receiver and the inertial are asynchronous, a circular
queue—called a history queue—contains 1 or 2 seconds of inertial position data. By
examining the time of the GPS measurement, the latest inertial position whose time
tag is less than that of the GPS measurement can be extracted from the queue. Using
the next queue entry, the data is then interpolated to the time of the GPS measure-
ment. Using raw data taken from the GPS satellite measurements given in Table 9.2,
we can start to see how our system will respond. In our system, the user inputs the
estimated initial position as 42.1º latitude, 71.2º longitude and zero altitude. This,

in ECEF coordinates, is: (1,527,397; -4,486,699; 4,253,850). When the GPS mea-
surement data is received by the navigation processor, the measurement matrix (9.5)
is formulated.
To do this, we utilize the position of the satellite x sv , y sv , z sv and subtract the user's
inertial-based position at the time of the GPS measurement x ui , y ui , z ui . To obtain the
user's inertial-derived position at the time of the GPS measurement, we utilize the
previously mentioned history buffer. By obtaining this inertial position in ECEF
coordinates just before the time of the GPS measurement and using the next history
buffer entry, the data is interpolated to give an accurate inertial user position at the

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