Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 483

phase error is the LOS INS velocity error times the time constant of this simple loop
model (the time constant is just the inverse of the gain K θ in this first order loop
model). Thus, limiting carrier phase error to 90º (assuming a time constant of 10
seconds is used) requires a LOS velocity error in steady state of no greater than 5.0
mm/sec, a very tight requirement indeed. As the aided loop time constant is
increased (and the corresponding loop bandwidth is reduced to further attenuate
the effects of jamming), the INS velocity requirement becomes more difficult to
meet. Of course, corresponding requirements for peak transient velocity errors are
less stringent (e.g., a velocity error component as large as 5 cm/s, if it persists for less
than 1 second, may not induce loss of track, depending on the tracking state when
the velocity transient occurred).
This very tight requirement for INS velocity error implies that certain error
sources are carefully controlled, including the nonstatic component of accelerome-
ter bias (the static component is generally cancelled by the platform misalignments
generated during initial alignment), accelerometer scale factor and misalignments,
and even the quantization level associated with the delta velocity derived from each
accelerometer. For example, consider a residual accelerometer scale factor of 100
parts per million (ppm). Assume the host vehicle is a high-performance fighter air-
craft doing a highly dynamic maneuver, producing a 5g acceleration along its lateral
axis for 5 seconds. This single error source integrates to a velocity error of 2.5 cm/s,
which could jeopardize carrier phase aiding with a bandwidth as narrow as that
considered in our simplified analysis. Recall in the introduction that it was men-
tioned that oscillator instability also limited the potential bandwidth reduction that
can be generally be achieved when receiver aiding. For the dynamic example here, it
is possible that the g sensitivity of the local oscillator (see Section 5.6.1.5) will limit
the utility of carrier phase aiding to as great an extent as the identified INS error
sources. This point will be addressed in more detail in Section 9.2.4.8.
Common output rates of delta angle and delta velocity information from an
IMU range from 10 to 100 Hz. These output rates may be unacceptable for carrier
phase aiding and can lead to large transient errors in the aiding source under
worst-case dynamics. This transient error can be reduced using an extrapolation
algorithm. For example, a constant jerk model could be hypothesized for the delta
velocity history, and the coefficient of the jerk term can be periodically determined
from sets of delta-velocities output from the IMU; the model would then be used to
generate modeled delta velocities to supply to the carrier loop at a higher rate. Not-
withstanding these technical challenges, carrier phase aiding is possible and can
extend track by as much as 9 dB [10].
Given the difficulties associated with aiding the phase lock loop, it is attractive
to consider aid of the frequency tracking loop as a “fall back” position. Frequency
track, as discussed in Section 5.3.3 , is more tolerant of dynamic and interference
induced errors than is phase track. A typical error detector (see Table 5.4) used for
frequency track can tolerate up to 50 Hz of frequency error. It is in fact the use of
frequency track that enables many commercial GPS receivers to maintain track
under foliage. Obviously, maintaining an INS velocity aiding error less than 10 m/s
(corresponding to the 50-Hz limit at L1) is relatively easy to do and will guarantee
frequency lock as long as excessive frequency error is not induced by the receiver's
oscillator. Enhancements of at least 10 dB in antijam performance are expected.