When TPC computes any Least Squares solution it doesn’t actually change any of the current survey points. Instead, you have to explicitly update the survey with the adjusted coordinates. This extra step of updating the survey allows you to review the solution. Once you have reviewed and accepted the solution you can apply it to the survey.
To aid in this review, TPC provides a Least Squares report that can include any of the following information.
Each report begins with the survey and file information for the analysis. The example shown here is a Network adjustment for the WILLOW DUNES EAST FIRST ADDITION survey.
[[ Least Squares Network Analysis ]]
WILLOW DUNES EAST FIRST ADDITION
C:\DOCUMENTS AND SETTINGS\SURVEYS\03-90\CONTROL.TRVDepending on the type of analysis, the settings sections lists basic information you can use to evaluate the data in the report.
[ Settings ]
Distance Units: Feet
Angle Data Station Order: At-From-To
Adjustment Type: 2D
[ Standard Error Settings ]
Horizontal Distance (const) 0.030000 Feet
Horizontal Distance (ppm) 0.000000
Horizontal Angle 4.000000 Seconds
Vertical Angle 4.000000 Seconds
Azimuth/Bearing 4.000000 Seconds
Vertical Distance (const) 0.030000 Feet
Vertical Distance (ppm) 0.000000
Reference Variance 1.000000The unadjusted data section lists the initial coordinates and raw observations used in the analysis. If you were to write a Starnet file from a Least Squares analysis, this is the data it would contain.
[[ Unadjusted Data ]]
[ Number of Entered Stations = 8 ]
Fixed Stations Y X Desc
CP107 5113.4130 6148.2190 = CP5
CP108 5042.4490 5894.6770 =CP8
Free Stations Y X Desc
CP211 4960.7420 6344.1310 Found 1" I.P. with Brass Cap
CP212 5367.5530 7098.5300
CP213 4935.3250 7187.1150
CP214 5194.2230 7255.7280
CP215 5850.3820 6729.2750
CP216 6579.1840 6527.5430
[ Number of Horiz Angle Observations = 8 ]
At From To Horiz Angle Precision
CP107 CP108 CP211 233°30'48.00" 5.000000
CP211 CP107 CP212 113°45'48.00" 5.000000
CP212 CP211 CP213 286°45'12.00" 5.000000
CP213 CP212 CP214 26°25'32.00" 5.000000
CP214 CP213 CP215 126°24'56.00" 5.000000
CP215 CP214 CP107 76°59'00.00" 5.000000
CP215 CP214 CP216 203°16'08.00" 5.000000
CP216 CP215 CP107 29°59'00.00" 5.000000
[ Number of Horiz Dist Observations = 8 ]
From To Horiz Dist Precision
CP107 CP211 248.3270 0.051242
CP211 CP212 857.0960 0.054285
CP212 CP213 441.2120 0.052206
CP213 CP214 267.8350 0.051339
CP214 CP215 841.2480 0.054206
CP215 CP107 938.1910 0.054691
CP215 CP216 756.2070 0.053781
CP216 CP107 Redundant 1513.6580 0.057568Redundant observations are indicated by the word ‘Redundant’ following the foresight label.
If you select any of the solution reports, TPC displays the basic information about the solution as follows
[[ Least Squares Solution ]]
Solve for 6 of 8 points 16 Observations with 4 Deg Of Freedom
Solution converged in 2 iterations
This section lists the residuals of each observation used in the solution along with the corrected observation.
[ Number of Horiz Angle Corrected Observations = 8 ]
At From To Residual Correct
CP107 CP108 CP211 -0°00'00.00" 233°30'48.00"
CP211 CP107 CP212 -0°00'01.44" 113°45'46.56"
CP212 CP211 CP213 -0°00'01.03" 286°45'10.97"
CP213 CP212 CP214 -0°00'03.85" 26°25'28.15"
CP214 CP213 CP215 -0°00'02.49" 126°24'53.51"
CP215 CP214 CP107 0°00'12.23" 76°59'12.23"
CP215 CP214 CP216 -0°00'09.38" 203°15'58.62"
CP216 CP215 CP107 -0°00'13.62" 29°58'46.38"
[ Number of Horiz Dist Corrected Observations = 8 ]
From To Residual Correct
CP107 CP211 -0.0666 248.2604
CP211 CP212 -0.1590 856.9370
CP212 CP213 0.0321 441.2441
CP213 CP214 -0.0897 267.7453
CP214 CP215 0.0400 841.2880
CP215 CP107 0.1340 938.3250
CP215 CP216 -0.1978 756.0092
CP216 CP107 0.1197 1513.7777
The adjusted coordinates section lists the values that will be used to update the survey if you choose to do so.
[ Adjusted Coordinates ]
Station Y X
CP211 4960.9893 6344.1789
CP212 5368.0454 7098.2653
CP213 4935.8247 7187.0436
CP214 5194.6663 7255.5164
CP215 5850.6103 6728.7308
CP216 6579.1184 6526.6770The standard deviations are listed for each coordinate that was computed in the solution.
[ Standard Deviation of Coordinates ]
Station Y X
CP211 0.098623 0.125480
CP212 0.179752 0.144195
CP213 0.232175 0.141986
CP214 0.244924 0.133491
CP215 0.152554 0.175014
CP216 0.169762 0.318569If you choose to include statistics, TPC reports the Standard Deviation of Unit Weight for all observations.
[ Standard Deviation of Unit Weight ]
Observation Count Std Dev
Total 16 3.741536You must include statistics in the report to get the Chi squared test. TPC uses the estimated reference variance value of 1.0 for the Chi Squared test.
[ Chi Squared ]
Failed Chi Squared test at 99% significance level !
Chi Squared = 22.28
Chi Squared Lower value = 0.21
Chi Squared Upper value = 14.86[ Station Coordinate Error Ellipse ]
95% Error Ellipse Dimensions
Ellipse Scale = 3.7267
Station Semi-Major Semi-Minor Theta
CP211 0.943059 0.203791 42°45'28.23"
CP212 0.477439 0.230202 37°56'47.86"
CP213 0.704900 0.239512 -15°19'37.82"
CP214 0.918831 0.223432 -5°19'14.64"
CP215 0.482880 0.213381 64°33'18.36"
CP216 0.238705 0.096205 33°50'28.86"The blunder factor can be changed in the Miscellaneous page dialog.
[ Horiz Angle Blunders ]
At From To Residual Correct
CP215 CP214 CP107 0°00'24.89" 76°58'54.89"
CP216 CP215 CP107 -0°00'21.70" 29°58'38.30"
2 Horiz Angle Blunders Detected (blunder > 5 X StdError
[ Horiz Dist Blunders ]
From To Residual Correct
CP211 CP212 -0.1811 856.9149
CP215 CP216 -0.1885 756.0185
2 Horiz Dist Blunders Detected (blunder > 5 X StdError
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