Geoida Help

Least Squares Adjustment - Tips and Suggestions

Question: Please provide some tips and suggestions for locating and eliminating problems and refining a Least Squares Network Adjustment

Answer:

• Errors, blunders, incorrect point numbers, entry errors
  1. If an adjustment will not converge within a few iterations but rather increasingly diverges with unacceptable values for variance factor etc, then probably there is at least one erroneous measurement or blunder, or an observation with incorrectly-numbered points. Examine the adjustment summary and scrutinise observations close to where outlier tests have failed or where observations have excessive residuals or corrections. To test their influence on the network, suspect observations may be disabled or have their a-priori standard deviations relaxed.
  2. Provided that provisional coordinates are reasonable, the Relax Std Dev for tolerance errors (LS Options button) option can be very helpful in locating outliers due to these errors by concentrating most of the necessary adjustment into affected observations for easier detection. Observations whose standard deviations have been relaxed by this option may be located by examining the summary for evidence of observations with large residuals/corrections, large computed standard deviations or standardised residuals, test failures, etc.
  
  
• Outliers and failed residual tests - Observations marked as having failed the outlier test may not be in error themselves but may have been influenced adversely by one or more adjacent observations that are in error. Examine other surrounding observations while applying the principles appropriate to the type of test applied; for example where residuals are of excessive size, the Baarda W-test and Pope's Tau-test assume that only one observation contains a gross error so the observation with the largest error or correction should be eliminated first. For an excessive number of failed outlier tests it may be appropriate to relax the confidence level for outlier detection to a more reasonable value
  
  
• Poor quality observations - Combining observations of poor or questionable quality with other observations of normal precision may degrade the overall quality of the adjustment
  
  
• Minimally-constrained adjustment - It is good practice to first check a network for internal consistency with a minimally-constrained adjustment. Do this by limiting the number of points or observations held fixed. For example, in a 2D network hold only one point fixed and set one fixed azimuth for orientation; in a 3D network with GNSS observations unfix all points. By this means any undue strain in the network due to low quality control points will be eliminated. Note that if the network consists of more than one area with no connecting observations then each area must have at least one constrained (fixed) point
  
  
• GNSS vector loop checks - Where GNSS vector observations are included, turn on Check Loops and supply a suitable Loop-check Tolerance PPM value prior to Compute. This will check many of the vector loops and will list the details of any loops that exceed the PPM tolerance and may help locate observational or point numbering errors or entry blunders. Suspect observations may be disabled to test their influence on the network
  
  
• Consistently-signed DX, DY and DZ - Duplicated or repeated GNSS vector observations between the same points must have consistently-signed DX, DY and DZ values - different signs between the observations will cause conflict
  
  
• Re-scale vector observations - GNSS vector observations may require their variance-covariances to be rescaled if the values appear too tight. Rescaling them all by the same amount may not make any difference but by selectively rescaling according to their reliability the adjustment may be improved
  
  
• Convergence Criteria - If the observations are of poor quality in general, then relaxing the Convergence Criteria in LS Options might help to get a workable convergence
  
  
• Disproportionate error ellipses - Disproportionate error ellipses on certain points compared to most other adjusted points suggests that there may be poor observations nearby; temporarily holding different points 'Fixed' may help to isolate the problem area
  
  
• Including/excluding observations - If the network contains a range of observation types, including or excluding one type at a time ( Observations Active checkbox) may help to isolate where anomolous observations may be located. If both terrestrial and GNSS observations are used together, changing the dimension of the adjustment from 3D to 2D may be helpful
  
  
• Changing dimension - Where GNSS observations are used, changing the dimension of the adjustment from 3D Terrestrial + GPS to 3D Spatial may produce a better convergence
  
  

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