Tightly-Coupled INS/GPS Kalman Filter Simulation:
Here we are simulating a 29-state tightly-coupled GPS/INS Kalman Filter.
There are 9 inertial error states (3-D position, velocity and attitude),
3 gyro bias states, 3 accelerometer bias states, 2 GPS clock error states
and 12 GPS range bias states.
In this simulation, an aircraft is traveling east and a serpentine
maneuver is executed before the aircraft continues to the east. This
maneuver is executed exactly 10 minutes into the flight and this time
correlates to some interesting Kalman Filter performance seen in later plots.
This simulation differs from the loosely-coupled simulation, however, in
that the number of satellites tracked is reduced significantly at the
end of the run (see later plots):
The tightly-coupled integration processes the GPS data in the range domain.
As a result, the input to the filter are the differences between the
GPS pseudorange measurements and the computed range from the GPS satellites
to the INS estimated position. Thus one of the significant
advantages of the tightly-coupled approach is the fact that the integration
still works even when the GPS receiver is tracking less than four satellites.
In this simulation, a high-grade (a.k.a., nav-grade) inertial navigation system
is being simulated and thus the integration is calibrating out the effects of
the small but non-trivial gyro and accelerometer errors. The following plots
compare the Kalman Filter performance to the unaided INS performance.
Pitch and roll errors:
Notice how the Yaw error converges to zero when the aircraft executes the
Horizontal position error:
The Kalman Filter position error covariance shows the effect of the
reduced number of satellites tracked at the end of the run (also see last
plot on this page):
Kalman Filter Velocity errors:
As indicated earlier, the tightly-coupled approach allows the filter
to continue to operate even when there are less than four satellites
being tracked. As this plot indicates, the performance does not
degrade appreciably when the number of satellites reduces to 3 but
finally does start to deteriorate when all satellites are lost and
the filter is purely coasting:
Back to the NSI&KF Page
Back to the Main Page