Loosely-Coupled INS/GPS Kalman Filter Simulation:
Here we are simulating an 18-state loosely-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, and 3 GPS position 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:





The loosely-coupled integration processes the GPS data in the position domain. As a result, the input to the filter is the x, y and z differences between the GPS position solution and INS position solution. Thus one of the significant limitations in the loosely-coupled approach is the fact that one must compute a GPS-only position solution and thus must be making measurements from at least 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:


Kalman Filter position error covariance:


Kalman Filter Velocity errors:




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