Accuracy assessment — iPhone LiDAR vs. survey total station
The hook
Every measurement has error. The job isn't to eliminate it — it's to classify it (random / systematic / blunder), bound it (positional accuracy), and propagateit through computations. Surveyors who can't talk fluently about error get assigned the easy stuff.
Memorize these
Concepts that show up on the exam
Random error
Equally likely positive or negative; small errors more likely than large; cancels in the long run. Mean of many measurements approaches the true value.
Systematic error
Consistent bias — wrong tape length, uncalibrated EDM, refraction not corrected. Does NOT cancel by averaging. Found by calibration.
Blunder
Gross mistake: misread the rod, recorded the wrong station, used the wrong instrument constant. Detected by redundant measurements and outlier tests.
Accuracy
How close the measurement is to the TRUE value. Affected by all three error types but mostly systematic + blunders.
Precision
How tightly clustered repeated measurements are. Affected mostly by random error. A precise measurement can be inaccurate (tightly grouped on the wrong target).
Positional accuracy
2D / 3D bound on where a point really is. For (E, N): r = √(σ_E² + σ_N²). FGDC publishes circular bounds; ALTA/NSPS specifies 2 cm + 50 ppm relative.
Error propagation
When errors in inputs combine through a formula, propagate variances by σ_y² = Σ (∂y/∂xᵢ)² · σ_xᵢ². For a sum z = a + b, σ_z² = σ_a² + σ_b².
Keep these in muscle memory
Formulas to know cold
General error propagation
σ_y² = Σ (∂y/∂xᵢ)² · σ_xᵢ²Assumes inputs uncorrelated. For correlated inputs add cross-covariance terms.
Sum / difference
σ_(a±b)² = σ_a² + σ_b²Variances add even when subtracting (random errors don't know to cancel).
Product / quotient (relative form)
(σ_y / y)² = (σ_a / a)² + (σ_b / b)²For y = a·b or y = a/b. Relative errors add in quadrature.
Try it before you peek
Worked example
The problem
A traverse leg is the sum of three taped sections measured as 31.42, 28.07, and 41.50 ft, each with a standard error of 0.012 ft. What is the standard error of the total length?
Don't fall for these
What trips people up
Treating ppm as a fixed amount
"50 ppm" means 50 parts per million of the distance. On a 1,000 ft line, that's 0.05 ft. On a 10,000 ft line, 0.50 ft. ALTA/NSPS specifies 2 cm + 50 ppm — constant dominates short shots, ppm dominates long ones.
Adding standard deviations directly
σ_(a+b) ≠ σ_a + σ_b. Variances add (and σ is the square root), so combined σ = √(σ_a² + σ_b²). Adding directly is too pessimistic by ~30% for two equal terms.
Confusing accuracy with precision (again)
The dartboard analogy: tightly grouped darts in the wrong area = precise but inaccurate. Surveyors quote precision easily; accuracy needs an external check (independent control, GPS-OPUS, etc.).
Test yourself
How well did it stick?
A quick 5-question check on Measurement Science. See where you stand and what to review.