Vertical Accuracy Standards for Geospatial Data

Some of the highlights of the new ASPRS Vertical Accuracy Standards for Geospatial Data are the following:

4. Unlimited vertical accuracy classes:

The new standard was designed to fit any vertical accuracy requirement, no matter what technology, current or future, is used. Table 5 represents the new ASPRS vertical accuracy classes.

Table 5: The new ASPRS vertical accuracy classes

Vertical Accuracy Class	Absolute Accuracy		Data Internal Precision (where applicable)
	NVA RMSEv (cm)	VVA RMSEv (cm)	Within-Swath Smooth Surface Precision Max Diff (cm)	Swath-to-Swath Non-Vegetated RMSDz (cm)	Swath-to-Swath Non-Vegetated Max Diff (cm)
			#-cm	≤ #	As found	≤ 0.60*#	≤ 0.80*#	≤ 1.60*#

1. Non-vegetated Vertical Accuracy (NVA) for any part of the project that is not covered by vegetation.
2. Vegetated Vertical Accuracy (VVA) for the part of the project that is partly or fully covered by vegetation.

6. The standards introduced relative accuracy for elevation data, besides the absolute accuracy.

Table 6 lists a new accuracy term, which is the relative accuracy. It mainly addresses the Lidar-derived elevation data. The table also provides vertical accuracy examples and other quality criteria for ten common vertical accuracy classes 

Table 6 Vertical Accuracy/Quality Examples for Digital Elevation Data

Vertical Accuracy Class	Absolute Accuracy		Data Internal Precision (where applicable)
	NVA RMSEv (cm)	VVA RMSEv (cm)	Within-Swath Smooth Surface Precision Max Diff (cm)	Swath-to-Swath Non-Vegetated RMSDz (cm)	Swath-to-Swath Non-Vegetated Max Diff (cm)
1-cm	≤ 1.0	As found	≤ 0.6	≤ 0.8	≤ 1.6
2.5-cm	≤ 2.5	As found	≤ 1.5	≤ 2.0	≤ 4.0
5-cm	≤ 5.0	As found	≤ 3.0	≤ 4.0	≤ 8.0
10-cm	≤ 10.0	As found	≤ 6.0	≤ 8.0	≤ 16.0
15-cm	≤ 15.0	As found	≤ 9.0	≤ 12.0	≤ 24.0
20-cm	≤ 20.0	As found	≤ 12.0	≤ 16.0	≤ 32.0
33.3-cm	≤ 33.3	As found	≤ 20.0	≤ 26.7	≤ 53.3
66.7-cm	≤ 66.7	As found	≤ 40.0	≤ 53.3	≤ 106.7
100-cm	≤ 100.0	As found	≤ 60.0	≤ 80.0	≤ 160.0
333.3-cm	≤ 333.3	As found	≤ 200.0	≤ 266.7	≤ 533.3

7. The standards introduced horizontal accuracy estimation for elevation data

1. For Photogrammetric elevation data, the horizontal accuracy equates to the horizontal accuracy class that would apply to planimetric data or digital orthoimagery produced from the same source imagery, using the same aerial triangulation/INS solution.
2. For Lidar elevation data: use the following formula:

$${\mathrm{RMSE}}_H=\sqrt{{\left(\mathrm{GNSS}\text{positional error}\right)}^2+{(\frac{\tan \left(\mathrm{IMU}\text{roll or pitch error}\right)+\tan \left(\mathrm{IMU}\text{heading error}\right)}{1.478}*\mathrm{flying}\mathrm{height})}^2}$$ Table 7 lists some horizontal accuracy values for lidar data based on the previous formula (the GNSS horizontal accuracy is assumed to be equal to 0.10 m, the IMU error is assumed to be 10.0 arc-seconds for the roll and pitch and 15.0 arc-seconds for the heading)

Table 7: Relationship between Flying Height, GNSS/IMU Errors, and Horizontal Root Mean Square Error

Flying Height (m)	GNSS Error (cm)	IMU Roll/Pitch Error (arc-sec)	IMU Heading Error (arc-sec)	RMSEH (cm)
500	10	10	15	10.7
1,000	10	10	15	12.9
1,500	10	10	15	15.8
2,000	10	10	15	19.2
2,500	10	10	15	22.8
3,000	10	10	15	26.5
3,500	10	10	15	30.4
4,000	10	10	15	34.3
4,500	10	10	15	38.2
5,000	10	10	15	42.0

8. The Standards Introduced a Formal Accuracy Testing Statement:

For the first time, the new standards provide users with formal data evaluation statements to be used by the data users and data producers. The following statements are examples of the accuracy statement of an elevation dataset:

8.1 Accuracy Reporting by Data User or Consultant

This type of reporting should only be based on a set of independent checkpoints. The positional accuracy of digital orthoimagery, planimetric data, and elevation data products shall be reported in the metadata in one of the manners listed below. For projects with NVA and VVA requirements, two three-dimensional positional accuracy values should be reported based on the use of NVA and VVA, respectively.

8.1.1 Accuracy Testing Meets ASPRS Standard Requirements

If testing is performed using a minimum of thirty (30) checkpoints, accuracy assessment results should be reported in the form of the following statements:

• Reporting Horizontal Positional Accuracy

“This data set was tested to meet ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023) for a __(cm) RMSE_H horizontal positional accuracy class. The tested horizontal positional accuracy was found to be RMSE_H = __(cm)”.

• Reporting Vertical Positional Accuracy

“This data set was tested to meet ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023) for a __(cm) RMSE_V Vertical Accuracy Class. NVA accuracy was found to be RMSE_V = __(cm).” VVA accuracy was found to be RMSE_V = __(cm).”

• Reporting Three-Dimensional Positional Accuracy

“This data set was tested to meet ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023) for a ___ (cm) RMSE_3D three-dimensional positional accuracy class. The tested three-dimensional accuracy was found to be RMSE_3D = ___(cm).”

8.1.2 Accuracy Testing Does Not Meet ASPRS Standard Requirements

If testing is performed using fewer than thirty (30) checkpoints, accuracy assessment results should be reported in the form of the following statements:

• Reporting Horizontal Positional Accuracy

“This data set was tested as required by ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023). Although the Standards call for a minimum of thirty (30) checkpoints, this test was performed using ONLY __ checkpoints. This data set was produced to meet a ___(cm) RMSE_H horizontal positional accuracy class. The tested horizontal positional accuracy was found to be RMSE_H = ___(cm) using the reduced number of checkpoints.”

• Reporting Vertical Positional Accuracy

“This data set was tested as required by ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023). Although the Standards call for a minimum of thirty (30) checkpoints, this test was performed using ONLY __ checkpoints. This data set was produced to meet a ___(cm) RMSE_V vertical positional accuracy class. The tested vertical positional accuracy was found to be RMSE_V = ___(cm) using the reduced number of checkpoints.”

• Reporting Three-Dimensional Positional Accuracy

“This data set was tested as required by ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023). Although the Standards call for a minimum of thirty (30) checkpoints, this test was performed using ONLY __ checkpoints. This data set was produced to meet a ___(cm) RMSE_3D three-dimensional positional accuracy class. The tested three-dimensional positional accuracy was found to be RMSE_3D = ___(cm) using the reduced number of checkpoints.”

8.2 Accuracy Reporting by Data Producer

In most cases, data producers do not have access to independent checkpoints to assess product accuracy. If rigorous testing is not performed by the data producer due to the absence of independent checkpoints, accuracy statements should specify that the data was “produced to meet” a stated accuracy. This “produced to meet’’ statement is equivalent to the “compiled to meet” statement used by prior Standards when referring to cartographic maps. The “produced to meet’’ statement is appropriate for data producers who employ mature technologies and who follow best practices and guidelines through established and documented procedures during project design, data processing, and quality control. However, if enough independent checkpoints are available to the data producer to assess product accuracy, it will do no harm to report the accuracy using the statement provided in section 4.1 above.

If not enough checkpoints are available, but the data producer has demonstrated that they are able to produce repeatable, reliable results and thus able to guarantee the produced-to-meet accuracy, they may report product accuracy in the form of the following statements:

• Reporting Horizontal Positional Accuracy

“This data set was produced to meet ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023) for a __(cm) RMSE_H horizontal positional accuracy class.

• Reporting Vertical Positional Accuracy

“This data set was produced to meet ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023) for a __(cm) RMSE_V vertical accuracy class.

• Reporting Three-Dimensional Positional Accuracy

“This data set was produced to meet ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2 (2023) for a ___ (cm) RMSE_3D three-dimensional positional accuracy class

9. The Standards introduced a new accuracy term, the Three-Dimensional Positional Accuracy:

The following formula defines the three-dimensional accuracy standard for any three-dimensional digital data as a combination of horizontal and vertical radial error. RMSE_3D is derived from the horizontal and vertical components of error according to the following formula:

$${\text{RMSE}}_{\text{3D}}=\sqrt{{{\text{RMSE}}_X}^2+{{\text{RMSE}}_Y}^2+{{\text{RMSE}}_Z}^2}\text{ or, }{\text{RMSE}}_{\text{3D}}=\sqrt{{{\text{RMSE}}_H}^2+{{\text{RMSE}}_V}^2}$$

10. The Standards introduced a new approach for assessing product accuracy by factoring in the accuracy of the surveyed checkpoints when computing product accuracy:

As we are producing more accurate products, errors in surveying techniques of the checkpoints used to assess product accuracy, although it is small, can no longer be neglected, and they should be represented in computing the product accuracy. Currently, we quantify products accuracy ignoring the errors in the surveyed checkpoints. In such practice, our surveying techniques approximate the datum, i.e., producing pseudo datum, and therefore, we are evaluating the closeness of data to the pseudo datum and not the true datum. The following figure illustrates the current practices and the new ones proposed in Edition 2 of the ASPRS standards.

Best Practices in Determining Product Accuracy*

1. Check data should not be used in calibrating the tested products:
   • Totally independent checkpoints
2. Check data must be more accurate than the tested data:
   • Two times more accurate
3. Check data must be well distributed around the project area:
4. Check data must be a valid statistical sample:
   • Minimum of 30 checkpoints for orthos
   • Minimum of 30 checkpoints for elevation data

* according to the ASPRS Positional Accuracy Standards for Digital Geospatial Data, Edition 2, v2 (2024)