Discussion
Assertion (A): Gyro bias and angle random walk produce errors that grow identically.
Reason (R): Bias is a constant offset while random walk comes from integrated white noise.
Select the correct answer from the options below.
Answer: D
Correct answer: A is false but R is true
The assertion is false. Gyro bias produces attitude error growing linearly with time, whereas angle random walk produces error growing as the square root of time - quite different laws.
The reason is true and is exactly why they differ: a bias is a constant offset, which integrates to \( bt \), while random walk comes from integrating white noise, whose independent increments accumulate as \( \sqrt{t} \). Over four hours a gyro with \( 0.1 \) degrees per root hour contributes \( 0.2 \) degrees of random walk, while a bias of \( 0.5 \) degrees per hour contributes \( 2 \) degrees - which is why bias dominates the long-term error.
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