Discussion
A gyro has an angle random walk of \( 0.1 \) degrees per root hour. After 4 hours the attitude error from this source is about
Answer: B
Correct answer: 0.2 degrees
Angle random walk accumulates as the square root of elapsed time, and the coefficient is quoted in degrees per root hour:
\[ \sigma = 0.1 \times \sqrt{4} = 0.1 \times 2 = 0.2\ \mathrm{degrees} \]
The value \( 0.4 \) would follow from growth linear in time, which is the bias law, not the random walk law. The contrast is instructive: over four hours, random walk contributes only a fifth of a degree, whereas a bias of \( 0.5 \) degrees per hour would contribute two degrees. Bias, not noise, dominates the long-term error.
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