PS Exam Preparation

Comprehensive preparation for the NCEES Principles and Practice of Surveying (PS) exam. 5 modules covering all 5 exam domains with 50 in-depth topics.

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Lesson 14

Geospatial Positioning Accuracy Standards

Learning Objectives

After completing this topic, you should be able to:

Explain the purpose and structure of the FGDC Geospatial Positioning Accuracy Standards
Describe the National Standard for Spatial Data Accuracy (NSSDA) methodology
Calculate horizontal and vertical accuracy from RMSE values
Explain accuracy classification systems for geodetic control
Understand accuracy reporting conventions at the 95% confidence level
Compare NSSDA to NMAS and explain why NSSDA was developed
Apply accuracy standards to surveying projects and deliverables

Overview

The Federal Geographic Data Committee (FGDC) Geospatial Positioning Accuracy Standards provide a modern, statistically rigorous framework for evaluating and reporting the positional accuracy of geospatial data. The most widely applied component is the National Standard for Spatial Data Accuracy (NSSDA), which replaced NMAS for federal geospatial data production. Unlike the binary pass/fail approach of NMAS, NSSDA requires reporting the actual accuracy achieved, expressed in ground units at the 95% confidence level.

The PS exam tests your understanding of FGDC standards because they represent the current standard of practice for accuracy assessment in surveying and mapping.

Key Concepts

Figure PS.5.14 — NSSDA Accuracy Testing Methodology

FGDC Framework

The Federal Geographic Data Committee (FGDC) publishes a family of accuracy standards organized into three parts:

Part 1: Reporting Methodology

Establishes the general framework for accuracy reporting
Defines the 95% confidence level as the reporting standard
Provides the statistical methodology for computing accuracy from test data

Part 2: Standards for Geodetic Networks (FGCS Standards)

Accuracy standards for horizontal and vertical geodetic control
Classification by accuracy level
Network adjustment and testing requirements

Part 3: National Standard for Spatial Data Accuracy (NSSDA)

Accuracy standard for maps, digital geospatial data, and survey products
Testing methodology using independent check points
Reporting format for accuracy values

National Standard for Spatial Data Accuracy (NSSDA)

NSSDA is the primary accuracy standard for geospatial data in the United States.

Key principles:

Accuracy is reported in ground units (feet or meters), not map units
All accuracy values are reported at the 95% confidence level
Accuracy is computed from Root Mean Square Error (RMSE) of test points
Independent check points are used for testing (not the same points used to create the data)
Both horizontal and vertical accuracy are addressed separately

RMSE Calculations

Root Mean Square Error (RMSE) is the fundamental statistic used in NSSDA:

RMSE in one dimension (e.g., vertical):

RMSE_z = sqrt[ sum(z_data - z_check)^2 / n ]

Where:

z_data = elevation from the dataset being tested
z_check = elevation from the independent check source
n = number of check points

RMSE in two dimensions (horizontal):

RMSE_x = sqrt[ sum(x_data - x_check)^2 / n ] RMSE_y = sqrt[ sum(y_data - y_check)^2 / n ] RMSE_r = sqrt[ RMSE_x^2 + RMSE_y^2 ]

Where RMSE_r is the horizontal RMSE (radial).

Converting RMSE to 95% Confidence

Horizontal accuracy at 95% confidence:

Accuracy_horizontal = 1.7308 x RMSE_r

This assumes errors are normally distributed and equal in both x and y directions (circular error). The factor 1.7308 converts from RMSE_r to the 95% confidence level.

If RMSE_x and RMSE_y are significantly different, the circular normal assumption is less valid, but NSSDA still uses this formula for simplicity.

Vertical accuracy at 95% confidence:

Accuracy_vertical = 1.9600 x RMSE_z

The factor 1.9600 is the z-value for 95% confidence in a normal distribution (one-dimensional).

NSSDA Testing Methodology

Step 1: Collect independent check points

Minimum of 20 check points (NSSDA requirement)
Check points must be well-defined, clearly identifiable features
Check points must be surveyed using methods at least 3 times more accurate than the data being tested
Check points should be distributed across the project area

Step 2: Compare data positions to check point positions

For each check point, compute the difference between the data position and the check position
Record x, y, and z differences separately

Step 3: Compute RMSE values

RMSE_x, RMSE_y, and RMSE_z from the differences
RMSE_r for horizontal accuracy

Step 4: Convert to 95% confidence

Horizontal: Accuracy = 1.7308 x RMSE_r
Vertical: Accuracy = 1.9600 x RMSE_z

Step 5: Report accuracy

State the accuracy values in ground units with the confidence level
Example: "Tested 3.5 feet horizontal accuracy at 95% confidence level"
Example: "Tested 1.2 feet vertical accuracy at 95% confidence level"

Common wrong path — applying the horizontal factor to vertical data (or vice versa). The two conversion factors in NSSDA are different because they apply to different statistical distributions. Horizontal accuracy uses 1.7308 (derived from a 2D circular normal distribution at 95%). Vertical accuracy uses 1.9600 (the 1D normal z-value at 95%). Students frequently mix them up — multiplying horizontal RMSE by 1.96 to get horizontal 95% accuracy, or multiplying vertical RMSE by 1.7308. The first produces a slightly too-high horizontal accuracy (≈ +13%), the second produces a slightly too-low vertical accuracy (≈ −12%). Both are wrong answers on the exam. Memorize the pairing: 1.7308 for horizontal (2D, circular), 1.9600 for vertical (1D, linear). And never apply either factor to an already-at-95% accuracy value — the factors convert RMSE to 95%, not 95% to something else.

Quick retrieval check — try before reading on.

▶An airborne LiDAR dataset has RMSE_x = 0.35 ft, RMSE_y = 0.40 ft, RMSE_z = 0.55 ft, based on 25 check points. What are the horizontal and vertical accuracies at 95% confidence?

Horizontal: RMSE_r = √(0.35² + 0.40²) = √(0.1225 + 0.1600) = √0.2825 = 0.5315 ft. Multiply by 1.7308: horizontal accuracy at 95% = 0.5315 × 1.7308 = 0.92 ft.

Vertical: Multiply RMSE_z by 1.9600: vertical accuracy at 95% = 0.55 × 1.9600 = 1.08 ft.

Report as: "Tested 0.92 ft horizontal accuracy at the 95% confidence level; tested 1.08 ft vertical accuracy at the 95% confidence level." If you had applied 1.96 to horizontal instead, you'd report 1.04 ft (about 13% too high) — a wrong answer on the exam. Also note: the minimum 20 check points was exceeded (25) and the check points must have been independently surveyed at 3× the accuracy of the LiDAR for the test to be valid.

Example Calculation

Given 25 check points with the following computed statistics:

RMSE_x = 0.45 feet
RMSE_y = 0.52 feet
RMSE_z = 0.38 feet

Horizontal RMSE: RMSE_r = sqrt(0.45^2 + 0.52^2) = sqrt(0.2025 + 0.2704) = sqrt(0.4729) = 0.687 feet

Horizontal accuracy at 95% confidence: Accuracy_horizontal = 1.7308 x 0.687 = 1.19 feet

Vertical accuracy at 95% confidence: Accuracy_vertical = 1.9600 x 0.38 = 0.74 feet

Reported as: "Tested 1.19 feet horizontal accuracy at the 95% confidence level, compiled to meet 2-foot horizontal accuracy at the 95% confidence level." "Tested 0.74 feet vertical accuracy at the 95% confidence level, compiled to meet 1-foot vertical accuracy at the 95% confidence level."

FGDC Accuracy Standards for Geodetic Control

For geodetic control networks, FGDC Part 2 defines accuracy in terms of the 95% confidence region:

Horizontal accuracy classifications:

Accuracy Class	95% Confidence (local)	Typical Application
1-mm	1 mm	Deformation monitoring, high-precision scientific
2-mm	2 mm	High-order geodetic control
5-mm	5 mm	Primary geodetic control
1-cm	1 cm	Geodetic densification
2-cm	2 cm	Survey-grade GNSS, ALTA surveys
5-cm	5 cm	Mapping-grade GNSS
1-dm	10 cm	GIS feature collection
2-dm	20 cm	Resource-grade GNSS
5-dm	50 cm	Recreation-grade GPS
1-m	1 m	Navigation

Network accuracy vs. local accuracy:

Network accuracy -- The accuracy of a point position relative to the NSRS datum (geodetic accuracy)
Local accuracy -- The accuracy of a point position relative to other directly connected points (relative accuracy)
Both are expressed at the 95% confidence level
For most surveying applications, local accuracy is the more relevant measure

Vertical Accuracy Classification

Classification	Typical RMSE_z	95% Accuracy	Application
1-cm vertical	0.5 cm	1 cm	Precise leveling
2-cm vertical	1 cm	2 cm	First-order leveling
5-cm vertical	2.5 cm	5 cm	Second-order leveling
10-cm vertical	5 cm	10 cm	Third-order leveling, GNSS
25-cm vertical	12.7 cm	25 cm	Topographic mapping
50-cm vertical	25.5 cm	50 cm	Regional mapping

NGS Accuracy Reporting

The National Geodetic Survey reports accuracy on published datasheets using the FGDC framework:

Horizontal accuracy in meters at 95% confidence (network and local)
Vertical accuracy in meters at 95% confidence
These values reflect the accuracy of the published coordinates relative to the NSRS

Accuracy vs. Precision

These terms are frequently confused but have distinct meanings:

Term	Definition
Accuracy	Closeness of a measured value to the true value
Precision	Closeness of repeated measurements to each other
Bias	Systematic offset between measured and true values

A survey can be precise but not accurate (consistently wrong by the same amount). NSSDA measures accuracy, not just precision, because it compares to independently determined "true" positions.

Relationship to Project Specifications

When specifying accuracy requirements for a survey or mapping project:

Using NSSDA:

Specify the required horizontal and vertical accuracy at 95% confidence
Example: "Horizontal accuracy shall be 0.50 feet at the 95% confidence level"
The surveyor must then achieve RMSE_r less than or equal to 0.50/1.7308 = 0.289 feet

Using NMAS (for comparison):

Specify the map scale and contour interval
Accuracy is implied by the standard (1/30 inch horizontal, 1/2 contour interval vertical)
Pass/fail determination

Best practice:

Specify accuracy in ground units at 95% confidence (NSSDA approach)
This is independent of map scale and directly meaningful for field work
Allows the data to be used at any display scale without ambiguity

ASPRS Positional Accuracy Standards

The American Society for Photogrammetry and Remote Sensing (ASPRS) publishes its own accuracy standards for digital geospatial data (updated in 2014):

Uses RMSE-based methodology consistent with NSSDA
Defines accuracy classes based on RMSE thresholds
Applicable to orthoimagery, digital planimetric data, digital elevation data, and LiDAR
Horizontal accuracy classes are defined by RMSE_x and RMSE_y values
Vertical accuracy addresses both vegetated and non-vegetated terrain

Exam Tips

Memorize the conversion factors: Horizontal accuracy at 95% = 1.7308 x RMSE_r; Vertical accuracy at 95% = 1.9600 x RMSE_z
NSSDA requires a minimum of 20 check points, independently surveyed at 3 times the accuracy of the data being tested
RMSE_r = sqrt(RMSE_x^2 + RMSE_y^2) -- be ready to compute this from given data
NSSDA reports accuracy in ground units at 95% confidence; NMAS reports accuracy as a function of map scale at an implied 90% threshold
"Network accuracy" is relative to the NSRS datum; "local accuracy" is relative to nearby points -- know the difference
Accuracy measures closeness to truth; precision measures consistency of repeated measurements -- they are not the same thing
The FGDC 2-cm accuracy class corresponds to the ALTA/NSPS RPP standard of 2 cm (at close range)
Always check whether an exam question asks for RMSE or 95% accuracy -- they are different values
If given RMSE values, multiply by the appropriate factor to get 95% accuracy; if given 95% values, divide to get RMSE