Each - Draper Laboratory

where
dt = 20 ms
S = signal power
R = pseudorandom code correlation function
e = LOS delay error in chips
D = correlator spacing = 0.5 chip
b = bias
n = noise
The bias and noise both derive from squaring the raw I
and Q noise and equations for their distributions may
be derived. The ideal correlation function is:
Finally, the LOS error is modeled as:
38 A Deep Integration Estimator for Urban Ground Navigation
(8)
(9)
(10)
where u is a unit vector from the IMU to the satellite,
dba is the residual atmospheric delay error, and dtR is
user clock residual error.
The DI filter first uses the dz measurements to estimate
the signal-to-noise ratio (SNR), allowing for smooth
adaptation to jamming or low signal strength. Then, the
DI filter performs an update of the filter error state. The
details of this update algorithm are omitted here. Since
the measurement model is highly nonlinear due to the
form of R and its square, common Kalman methods
must be replaced by algorithms from nonlinear estimation
theory. Further discussion is in Ref. [4].
The remaining arrow in Figure 2 shows the low to
medium rate transfer of corrections. After all estimates
are processed for one 10-Hz filter pass (all satellites,
plus radar and altimeter measurements), the error state
is used to calculate these corrections. At the end of the
next 10-Hz interval, the navigation system incorporates
these corrections in a reset. The following items
are reset based on filter error states: position, velocity,
quaternion, gyroscope, and accelerometer compensators,
user clock error estimates, and LOS delay errors
for satellites being tracked.
The two-rate scheme of Figure 2 is critical to the operation
of DI GPS. The data from the filter are not sent
directly to the receiver. Rather, the corrections go to
medium rate, and then indirectly affect NCO commands
via the 10-Hz resets. The 50-Hz receiver control allows
for tracking high-frequency dynamics in the correlators,
while the lower rate filter execution allows for a
more advanced estimation algorithm with more accurate
estimates.
Clock errors: Initialization and reacquisition
Timing and clock errors are critical to deep
integration.
The previous section indicated how the navigation filter
kept up accurate clock error estimates while tracking
satellites in deep integration. Two closely related problems
are clock initialization and clock recapture after
satellite signal loss.
Time is determined in navigation on the basis of highspeed
interrupts from the Rockwell Collins receiver,
referred to as t10 (10 ms apart) and t1000 (1 second
apart). These are driven directly by the receiver
oscillator.
Navigation time, or user time, is based directly on
a count of t10 interrupts. The user clock bias and
frequency errors are defined in speed-of-light units as:
dtR = user time – GPS time
= user time frequency – true frequency
For practical purposes, GPS time is considered perfect.
True frequency is, in speed-of-light units, 1 + Doppler.
As seen above, estimates of these enter into navigationissued
NCO commands. From this follows the deep
integration requirement: clock estimates must always
be within about a chip (approximately 100 ft) of accuracy
to retain code lock in deep integration.
Initialization: At initial operation, the receiver is
in control of its NCOs, and the navigation software
receives t1000 interrupts and messages with the matching
GPS times. The navigation wrapper software does
careful bookkeeping of these data over at least three
low-rate passes (t1000 interrupts). From this, a linear
relationship between user and GPS time can be determined
algebraically. The data are then passed to the
navigation algorithm, which in turn (after navigation
initialization), issues a command to the receiver to
accept host control.
Reacquisition: After a long period of time without visible
GPS satellites, it was found that the receiver clock can
drift nonlinearly to a point well outside the 100-ft accuracy
requirement. An immediate return to DI updates
would result in the loss of lock and poor performance
of the PNS navigator.