Least Squares Network Adjustment Simplified Solver

Restricted weighted least-squares common3Dtranslation adjustment only, actual independently matched control-minus-survey residuals, positive total inversevariance. Not arbitrary network/rotation/scale adjustment, datum establishment or uncertainty estimation.

Description

A common translation fits one offset shared by several three-dimensional residual observations.

A common translation fits one offset shared by several three-dimensional residual observations.^[1]

It differs from adjusting an entire cave network with station, angle and distance constraints.

When to use Least Squares Network Adjustment Simplified Solver

Use this tool to obtain fittedTranslation, postAdjustmentResiduals from the supplied records using the stated calculation. Establish the survey or observation scope, reference frame, units and independently applicable calibration or qualified plan.

How to use Least Squares Network Adjustment Simplified Solver and understand its results

Establish the survey or observation scope, reference frame, units and independently applicable calibration or qualified plan.
Enter actualCommonTranslationResidualsXyzMeters, callerIndependentInverseVarianceWeights, using the field meanings and rules below, then run the tool.
Read result.fittedTranslation, result.postAdjustmentResiduals. Use the units and sign conventions below, and review any unknown records separately.
Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.

Input field	Meaning	Value type	Requirement
actualCommonTranslationResidualsXyzMeters	Actual common translation residuals xyz meters	numeric matrix	Required
callerIndependentInverseVarianceWeights	Caller independent inverse variance weights	list of number	Required

Supply nonempty aligned three-component residual rows and nonnegative inverse-variance weights with positive total weight. Fit the weighted mean of each coordinate as one common translation, then subtract it from every residual row, including zero-weight rows. No station-network or angle adjustment is solved.

translation_j=Σ(weight_i×residual_ij)/Σweights; postResidual_ij=residual_ij−translation_j

Use the matching field units and the exact boundary, ordering and reference rules above.

Output field	Meaning	Value type
result	Qualified observed calculation or explicit reference	object
result.fittedTranslation	Weighted common offset for each of the three residual coordinates.	list
result.postAdjustmentResiduals	Each supplied residual row minus fittedTranslation, retaining input order.	list

json

{
  "input": {
    "actualCommonTranslationResidualsXyzMeters": [
      [
        1,
        2,
        3
      ],
      [
        3,
        4,
        5
      ]
    ],
    "callerIndependentInverseVarianceWeights": [
      1,
      1
    ]
  },
  "output": {
    "result": {
      "fittedTranslation": [
        2,
        3,
        4
      ],
      "postAdjustmentResiduals": [
        [
          -1,
          -1,
          -1
        ],
        [
          1,
          1,
          1
        ]
      ]
    }
  }
}

Limitations and assumptions

The actual observation coverage, calibration and qualified plan determine applicability. A numerical result does not establish survey accuracy, route suitability, atmosphere conditions or equipment adequacy beyond the declared comparison.

Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries, subject to the narrower lengths and code rules above. Numeric matrices allow at most 128 rows and 128 columns, subject to the narrower shape requirements above. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use Blunder Detection Residual Outlier Flag Calculator: Adjustment residuals can be screened against an independently justified absolute review threshold. For a complementary comparison, use Survey Loop Misclosure Error Calculator: A closed-loop survey ideally returns to its start in the adopted coordinate frame.

References

Least Squares Network Adjustment Simplified Solver — tool.io

Similar or alternative tools

Blunder Detection Residual Outlier Flag Calculator
Adjustment residuals can be screened against an independently justified absolute review threshold.
Survey Loop Misclosure Error Calculator
A closed-loop survey ideally returns to its start in the adopted coordinate frame.