Least Squares Adjustment Method
Input Observation File
The adjustment relies on station, observation and options data given in the observations file (<object>.lsa_dat). This file has a fixed format so far as column positions are concerned, but is free in the ordering of its data blocks, that is, blocks can be arranged in any order in the file. It is a text file and is thus easily edited with any text editor.
There are eleven different types of data blocks; two for administrative purposes, one for defining the grid on which the adjustment is to be calculated, one for defining the options chosen, two for declaring the stations being used, and five for the observations.
Blocks are initiated and terminated with an asterisk in column one. The block heading of five significant letters follows the asterisk on the first line that is, in columns 2-6.
All information of any one type must be in its specific data block. Only the first data block of a specific type is read; all others are ignored.
Following is a description of each data block, giving the columnar format of the data expected. An example of the
.lsa_dat
file is included in
Appendix A
.
| Data Block | Description |
| Survey Name |
This is an administrative block consisting of the survey name or number to be used in the adjustment report. It is mandatory for all adjustments. The format of this block is: 1-10 Survey name |
| Date |
This is the second administrative block consisting of the date to be used in the adjustment report. It is mandatory for all adjustments. The format of this block is: 1-9 Date of survey |
| Grid |
This block supplies the grid on which the horizontal adjustment is to be calculated. It is mandatory for all horizontal adjustments. It can have the following values:
'AMG'
If the field is left blank, then all distances and angles are assumed to be planar. If 'AMG' or 'ISG' are chosen then line scale factors and arc-chord corrections are applied to distances and angles. The distances are thus assumed to be spheroidal and all angles are assumed on the grid, with bearings being grid bearings, etc. The format of this block is: 1-3 Survey grid |
| Options |
This data block contains the options associated with the horizontal adjustment, and is thus mandatory for a horizontal adjustment.
Columns 1-2
In general, this field will be left blank, as an erroneous result may occur if the adjustment is terminated prematurely, especially in the case where the approximate coordinates are highly inaccurate. Historically, restricting the number of iterations has been necessary due to the lack of computing power in processing large networks; on the Silicon Graphics computers it may be deemed obsolete.
Column 3
The graphical display is colour and line style coded for the three cases of observed lines with distance observations only, angular observations only, and with both distance and angle observations. Fixed stations are also highlighted.
Column 4
Column 5
Columns 6-7
Columns 8-9
Columns 10-11
Columns 12-16
See Warnings during the adjustment in the description of the least squares adjustment (Appendix B - second part) for an explanation. |
| Fixed stations |
All stations that are to be held fixed in the adjustment are listed here, along with their eastings and northings. If an elevation adjustment is being performed, then the reduced levels of the fixed stations will also be required. [Note that for a horizontal adjustment, no reduced levels are necessary as the distances given are assumed spheroidal]. If no reduced level is given, a value of zero will be assumed. Up to 50 fixed stations is allowed in one adjustment. The format of the fixed station data is:
1-10 station name (L)
L = Left justified, R = Right justified |
| Free stations |
All stations that are not to be held fixed should be listed here, along with their approximate eastings and northings. These coordinates can be obtained in a variety of ways, For example, scaled off a map, calculated from a radiation, etc. No reduced level for the free stations is required. Up to 250 free stations are allowed in one adjustment. The format of the free station data is equivalent to that for fixed stations, except for the need for a reduced level, that is,
1-10 station name (L)
L = Left justified, R = Right justified |
| Distance observations |
Distance observations are given in metres and are assumed spheroidal if UTM corrections are to be applied, or else planar. That is, they are assumed fully corrected and reduced to sea-level. Each distance observation requires the a priori standard deviation of the measurement, taking into account errors, such as centring and those inherent in the equipment. A blank or zero value for the standard deviation implies a fixed distance. The format of the data is as follows:
1-10 AT station (L)
L = Left justified, R = Right justified |
| Angle Observations |
Angle observations are given in degrees, minutes, seconds and tenths of seconds. Each measurement must also have an a priori standard deviation associated with it. A blank or zero value for the standard deviation implies a fixed angle. The format of the angle observation data block is as follows:
1-10 AT station (L)
L = Left justified, R = Right justified |
| Bearing Observations |
Bearing observations are given in degrees, minutes, seconds and tenths of seconds. Each measurement must also have an a priori standard deviation associated with it. A blank or zero value for the standard deviation implies a fixed bearing. The format of the bearing observation data block is as follows:
1-10 AT station (L)
L = Left justified, R = Right justified |
| Direction Observations |
Direction observations are given in degrees, minutes, seconds and tenths of seconds. Each measurement must also have an a priori standard deviation associated with it. Fixed directions are obviously meaningless, and will terminate the program. Different sets of directions can be entered by utilising the set number field. The use of directions causes implied angles to be formed by the program. These angles are the result of subtracting one direction from another. The program always takes as its RO the direction with the smallest angular value, which is consistent with the practice of reducing one's directions to the RO. The format of the direction observation data block is as follows:
1-10 AT station (L)
L = Left justified, R = Right justified |
| Height difference Observations |
Height difference observations are given in metres, and define the observed height difference between two stations. A negative height difference implies a 'drop' in elevation from the AT station to the TO station. As with the horizontal adjustment, an a priori standard deviation is required with each observation, and no value or a value of zero implies a fixed height difference. The format of the height difference observation data block is as follows:
1-10 AT station (L)
L = Left justified, R = Right justified |
