Description
Calculate 2DRMS from horizontal standard deviations and report Gaussian coverage only for the stated isotropic case.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Calculate 2DRMS from horizontal standard deviations and report Gaussian coverage only for the stated isotropic case.
When to use this tool
Use this tool when you need to calculate 2DRMS from horizontal standard deviations and report Gaussian coverage only for the stated isotropic case.
How to use the tool and how it works
- Enter eastSigmaMeters, northSigmaMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.twoDrmsMeters, result.isotropicGaussianCoverage, using the stated boundary, ordering, sign and absence conventions.
Calculate 2×hypot(eastSigmaMeters,northSigmaMeters). Return isotropicGaussianCoverage=1−exp(−4) only when both supplied positive sigmas are exactly equal; otherwise return null coverage.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| eastSigmaMeters | Nonnegative one-axis east standard deviation in meters, at most 10⁷. | Finite numeric value satisfying the stated comparisons. |
| northSigmaMeters | Nonnegative one-axis north standard deviation in meters, at most 10⁷. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.twoDrmsMeters | Two times the root sum of squared east/north sigmas, in meters. |
| result.isotropicGaussianCoverage | 1−exp(−4) when positive sigmas are exactly equal, otherwise null. |
{
"input": {
"eastSigmaMeters": 3,
"northSigmaMeters": 4
},
"output": {
"result": {
"twoDrmsMeters": 10,
"isotropicGaussianCoverage": null
}
}
}Limitations and assumptions
- Sigmas lie from zero through 10⁷ m. The isotropic Gaussian coverage is approximately 98.17%, not a general 95% claim. Anisotropy, bias, correlation and the empirical distribution are not estimated.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
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