Discussion
Consider the following statements about error growth:
1. A constant gyro bias gives attitude error growing linearly with time.
2. Angle random walk gives error growing with the square root of time.
3. Both mechanisms produce error growing at the same rate.
Which of the statements given above is or are correct?
Answer: D
Correct answer: 1 and 2 only
Statement 1 is correct: integrating a constant bias gives an attitude error \( bt \), linear in time. Statement 2 is correct: angle random walk comes from integrating white noise, whose independent increments accumulate as \( \sqrt{t} \).
Statement 3 is false and contradicts the first two, since linear and square-root growth are plainly different. The distinction is not academic: it is what allows a filter to estimate bias as a separate state, and it explains why bias dominates over long intervals while noise matters most over very short ones.
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