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GPSoft Closed-Loop Filtering

The inertial error model utilized by the integration filter has a linearity assumption built into it. So long as the inertial errors are sufficiently small, the assumption holds. As a result in actual practice, the Kalman filter corrections must be fed back periodically to keep the errors small.

To illustrate this, a loosely-coupled integration was performed utilizing a long (i.e., 45 minute) trajectory. With no feedback, the vertical solution eventually diverges:

GPSoft No Feedback Positioning Error
GPSoft No Feedback Velocity Error
GPSoft No Feedback Attitude Error

The divergence problem can be solved by feeding back the error estimates once the filter has converged:

GPSoft LC Feedback Position Error
GPSoft LC Feedback Velocity Error
GPSoft LC Feedback Attitude Error
GPSoft LC Feedback Acceleration Estimate
GPSoft LC Feedback Gyro Estimate
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