Chapter 23: Navigational Errors and Accuracy
Every position is an estimate with an uncertainty. Professional navigation means quantifying that uncertainty and planning margins around it.
Random and systematic error
Random errors scatter symmetrically about the truth and shrink with averaging; systematic errors (a wrong index correction, uncorrected deviation, a datum shift) bias every observation the same way and averaging does nothing. Blunders are neither — they are mistakes, detected by redundancy: a third LOP, a cross-check by a second means, or a sanity check against DR.
- Random — reduce by repetition
- Systematic — reduce by calibration and cross-checks
- Blunder — detect by redundancy
Error budgets and confidence
Position uncertainty is usually stated as a radius or ellipse at a stated confidence: 1σ is about 68%, 2σ about 95%. Standards such as the IMO accuracy requirement for harbour approaches are expressed at 95%. Combine independent error sources in quadrature: σ_total = √(σ₁² + σ₂² + …). The result defines the safety margin that must be added to charted dangers, along with allowances for chart accuracy (CATZOC) and survey age.
Formula cards
Combining independent errors
σ_total = √(σ₁² + σ₂² + … )
Only valid when the sources are independent.
Key takeaways
- • Averaging kills random error and does nothing to systematic error.
- • Combine independent errors in quadrature, never by simple addition.
- • 95% confidence ≈ 2σ — the standard for stated navigational accuracy.
Knowledge check
Immediate feedback with rationales. Answer each question to see the explanation.
Chapter 23 quiz
0 of 3 answered
1.Repeatedly averaging sights will reduce:
2.Two independent error sources of 3 m and 4 m combine to about:
3.A stated accuracy of '10 m at 95%' corresponds roughly to: