Description
Return eastSigma² cos²(angle) plus northSigma² sin²(angle) plus twice correlation times both sigmas times cosine and sine.
Coordinate uncertainty can be expressed as angular halfwidths, linear components, or variances. A local spherical conversion and a covariance projection use different conventions; neither alone defines a complete confidence region.
Return eastSigma² cos²(angle) plus northSigma² sin²(angle) plus twice correlation times both sigmas times cosine and sine.
When to use this tool
Use Geographic Axis Uncertainty Projection when you need a local uncertainty or rounding term with supplied geometry and statistics.
How to use the tool and how it works
- Enter eastSigma, northSigma, correlation, angleRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read projectedVariance. Use the output convention below.
Require nonnegative eastSigma and northSigma and correlation within [-1, 1]. Return eastSigma² cos²(angle) plus northSigma² sin²(angle) plus twice correlation times both sigmas times cosine and sine.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| eastSigma | East Sigma | Required. Finite number; minimum 0. |
| northSigma | North Sigma | Required. Finite number; minimum 0. |
| correlation | Dimensionless supplied correlation, not estimated from raw observations. | Required. Finite number; minimum -1; maximum 1. |
| angleRadians | Projection direction from east toward north, in radians. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| projectedVariance | Variance in squared component units; not standard deviation. | Required. Finite number. |
{
"input": {
"eastSigma": 2,
"northSigma": 3,
"correlation": 0,
"angleRadians": 0
},
"output": {
"projectedVariance": 4
}
}Limitations and assumptions
- Angle is in radians from the east axis toward north, unlike a clockwise-from-north bearing. Output is projected variance in squared coordinate units, not standard deviation or a confidence interval; floating-point cancellation can affect nearly zero results.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete error-propagation model with known coordinate reference and covariance. Distinguish resolution from measurement uncertainty and variance from standard deviation or confidence limits.
References
Similar or alternative tools
- Coordinate Uncertainty Angular Halfwidth
Divide halfwidth by radius for radians and multiply by 180/π for degrees.
- Coordinate Rounding Ground Error Bound
Return radius times angular step divided by two as latitudeHalfwidth and multiply it by cosine latitude for longitudeHalfwidth.