Discussion
A gyro has a constant bias of 0.01 degrees per second. After 5 minutes of unaided integration the attitude error is
Answer: A
Correct answer: 3 degrees
A constant bias integrates linearly with time. Five minutes is \( 300 \) seconds, so
\[ \Delta\theta = 0.01\ \mathrm{deg/s} \times 300\ \mathrm{s} = 3\ \mathrm{degrees} \]
The result shows why unaided integration is untenable: a bias small enough to be hard to measure produces an unacceptable attitude error within minutes. This is exactly the growth the accelerometer-derived vertical reference is there to bound, and why a Kalman filter estimates the bias as a state rather than trusting a factory calibration to hold.
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