In evaluating navigation estimators, which metric captures average error magnitude across many trials?

• A. Root-Mean-Square (RMS) error
• B. Absolute error
• C. Maximum error
• D. Standard deviation of measurement noise

Answer: (A)

When you want a single number that summarizes how far the estimator’s output is from the true state across many trials, you use the root-mean-square error. This metric takes each trial’s error, squares it, averages those squared errors, and then takes the square root. That gives a value in the same units as the quantity being estimated and reflects the typical deviation you’d expect, while still giving extra weight to larger errors so sporadic big mistakes stand out.

Other options don’t capture that average magnitude in the same way: a mean absolute error averages the absolute deviations but treats all errors equally without the extra emphasis on larger ones; a maximum error looks at the worst case only, not typical performance; the standard deviation of measurement noise describes how noisy the measurements are, not how far the estimator’s outputs stray from the true state across trials.