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.




Velocity errors:


Pitch and roll errors:


Notice how the Yaw error converges to zero when the aircraft executes the serpentine manuever:


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:




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