Calibration of measurement delay in global positioning system/strapdown inertial navigation system

The effect of a constant transmission delay that occurs in delivering measurements from a global positioning system receiver to a Kalman filter for an aided strapdown inertial navigation is analyzed. Steady-state conditions under the measurement delay are derived based on measurement residual observation. A new error model for circular trajectories is derived to show that the currently, computed navigation variables converge not to the current true variables but to the neighborhood of the past true variables at the instant the delayed measurements were actually sampled. Based on the stead-state conditions and the new error model, causes and effects of an erroneously large estimation error of forward accelerometer bias are presented. To eliminate the undesirable delay effects given any combination of a global positioning system receiver and a strapdown inertial measurement unit, a simple delay calibration algorithm is proposed. The proposed algorithm is based on the characteristics that the heading error is biased by a controlled vehicle maneuver and advantageously requires no modification in onboard hardware.