Present Surveying Instrumentation

Different realization of the combination use of angles and distance (Staiger, 2009)

Total Station

1. Cooperative: Yes/No
   
2. Range: 2-5000m
   
3. Accuracy: >0.5mm
   
4. Frequency: 0.2 – 10Hz
   
5. Distance method: Phase/Pulse
   
6. Application: Known; manifold
   

 

Binocular (With integrated compass and reflectorless distance-measurement)

1. Cooperative target: No
   
2. Range: 2-300m
   
3. Accuracy: >1m
   
4. Frequency: 0.3Hz
   
5. Distance method: Pulse
   
6. Applications: GIS
   

 

Laser Tracker

1. Cooperative target: Yes
   
2. Range: 0.4 – 80m
   
3. Accuracy: >0.05mm
   
4. Frequency: 0.5 – 2kHz
   
5. Distance method: Interferometer/Absolute distance measurement (probably: phase-technique)
   
6. Applications: Industrial Measurement
   

 

Laser Radar

1. Cooperative target: No
   
2. Range: 1 – 50m
   
3. Accuracy: >0.05mm
   
4. Frequency: 1 – 0.05Hz (Depending on accuracy)
   
5. Distance method: Chirp
   
6. Applications: Industrial Measurement
   

 

Laser Scanner

1. Cooperative target: No
   
2. Range: 1 – 500m
   
3. Accuracy: >1 – 20mm
   
4. Frequency: >1 – 500kHz
   
5. Distance method: Phase/Pulse
   
6. Applications: Manifold
   

 

Source: Staiger, R. (2009). Push the Button – or Does the "Art of Measurement" Still Exist. International Federation of Surveyor, Article of the Month – June 2009.

Electronic Distance Measurement - EDM

The velocity of light – History Review

• The accuracy of EDM instrument depends ultimately on the accuracy of the estimated velocity of light (velocity of the electromagnetic wave) through atmosphere.
  
• The first estimates of the velocity of electromagnetic wave were derived from astronomical observation – very large distances were necessary to produce effects measurable.
  
• In 1676 - By studying the time of the eclipses of the satellites of Jupiter, Romer first calculated the value to be about 187 000 miles per second.
  
• In 1727 – Bradley improved – by using observations made on the aberration of the light received from star – he obtained of 308 000km/s.    
  
  • Bradley method : because the motion of the earth round the sun, star in a direction at right angles to the motion will appear to have a small circular orbit and by measuring the diameter of     this circle, Bradley was able to calculate a value for the velocity light.    
    
• In more recent time – this Bradley method has been used to obtain a value of 299 714 – close agreement with values derived from other method.
  
• In 1849 – Fizeau making first direct terrestrial measurement. Fizeau method is in essence the one still employed in the modern EDM instrument – WHELL MODULATION.
  
• Fizeau estimated the velocity to be 313 000km/s
  
• Fizeau answer on WHEEL MODULATION was of no great accuracy – in experiment the timing of the eclipses was estimated by eye and any error in the light path length would contribute     directly to the error.
  
• With modern terminology – using visible light as a carrier wave, modulated to give a approximately square wave by a mechanical method – the phase of returning signal was estimated by     eye using a null-point method and a variable modulation frequency.
  
• In 1906 – Rusa and Dorsey – using ration of electromagnetic to electrostatic units – 299 784km/s ±10.
  
• In 1929 – Michelson, Pearson and Pease – using rotation mirror device– obtained 299 796km/s ±15
  
• In 1933 - Michelson, Pearson and Pease – mile long tube reduced to . of low vacuum in order to minimise errors due to atmospheric effect – 299 774km/s ±4
  
• During the 1939 – 1945 war, radar devices using microwaves were introduced into rangefinding techniques.
  
• In 1940 - Anderson – using Kerr Cells device – 299 776km/s ±6.
  
• In 1941 – Birge – using weighted mean from past result and obtained 299 776km/s ±4.
  
• In 1947 – Essen and Gordon-Smith – using cavity resonator – 299 792km/s ±4.
  
• In 1949 – 1951     i) Aslakson – radar measurement – 299 792km/ ±1.4 (1949) and 299 794.2km/s ±1.9 (1951).
  

          ii) Bergstand – Kerr Cell – Geodimeter device – 299 793km/s ±2 (1949) and 299 793.1km/s ±0.2 (1951).
  

• In 1950 – Essen – Cavity resonator – 299 792.5km/s ±1.
  
• In 1954 – Froome – microwave interferences – 299 792.7km/s ±0.3.
  
• In 1955 – Scholdstrom – Kerr Cell device - 299 792.4km/s ± 0.4.
  
• In 1956 – Ordnance Survey – Geodimeter 4 - 299 792.4km/s ±0.5.
  
• In 1957 – Froome – Microwave interferometer – 299 792.5km/s ±0.10.
  
• In 1957, the XIIth General Assembly of the International Scientific Radio Union recommended that the best available value for the velocity of electromagnetic waves in vacuum was : 299 792.5km/s ±0.4km/s.
  
• This value (299 792.5±0.4km/s) was also accepted by the International Union for Geodesy and Geophysics.
  
• Standard of velocity is itself dependent on two others
  

1. Standard of length and that of time – is based upon an atomic standard – the wavelength of the orange line of the krypton atom, known to accuracy of about on part in one hundred million (1 x 10^-8).
   
2. Atomic clock provide a standard of time accurate to about one part in a hundred thousand million (1 x 10^-11).

Understanding the Residual Errors - v

Simple Task

Given L=(l1,l2,l3,.....,ln). Assumption all measurements are free of gross errors and corrected for all systematic errors.

Processing using Microsoft Excel and Matlab

Observations of angles (sec)

L=[22.7 22.3 25.5 23.8 22.9 22.2 21.9 26.1 22.6 21.7 25.4 24.2 24.7 24.4 23.4 23.3 24.3 21.2 25.3 23.9 24.0 24.8 23.2 23.7 25.9 24.6 23.8 23.0 25.0 22.3 20.5 23.5 22.0 24.1 23.1 24.1 23.1 25.9 22.8 25.3 22.5 22.9 23.8 22.6 21.8 23.2 25.2 22.8 23.6 20.1]

After sorting – Matlab: sort=sort(L)then

Observation	u
1	20.1
2	20.5
3	21.2
4	21.7
5	21.8
6	21.9
7	22
8	22.2
9	22.3
10	22.3
11	22.5
12	22.6
13	22.6
14	22.7
15	22.8
16	22.8
17	22.9
18	22.9
19	23
20	23.1
21	23.1
22	23.2
23	23.2
24	23.3
25	23.4
26	23.5
27	23.6
28	23.7
29	23.8
30	23.8
31	23.8
32	23.9
33	24
34	24.1
35	24.1
36	24.2
37	24.3
38	24.4
39	24.6
40	24.7
41	24.8
42	25
43	25.2
44	25.3
45	25.3
46	25.4
47	25.5
48	25.9
49	25.9
50	26.1

Numerical Analysis

	min, ū=	∑u / n
	=	1175/50
	=	23.5
	Standard deviaton,σ=	√∑v² / ∑(n-1)
	=	√[ (92.36 / (50-1) ]
	=	± 1.373
	PROBABLE ERROR AT 68.3%
	t=	1.0009
	E68.3=	t ( σ )
	=	1.0009 ( ± 1.373 )
	=	± 1.37
	min range =	ū-E68.3
	=	23.5-1.37
	=	22.13
	max range =	ū+E68.3
	=	23.5+1.37
	=	24.87
=	between 22.13 ‒– 24.87 , 34 observations ( 68 % )
	PROBABLE ERROR AT 95%
	t=	1.96
	E95=	t ( σ )
	=	1.96 ( ± 1.373 )
	=	± 2.69
	min range =	ū-E95
	=	23.5-2.69
	=	20.81
	max range =	ū+E95
	=	23.5+2.69
	=	26.19
=	between 20.81 –‒ 26.19 , 47 observation ( 94 % )
	PROBABLE ERROR AT 99%
	t=	2.576
	E99=	t ( σ )
	=	2.576 ( ± 1.373 )
	=	± 3.53
	min range =	ū-E99
	=	23.5-3.53
	=	19.97
	max range =	ū+E99
	=	23.5+3.53
	=	27.03
=	between 19.97 –‒ 27.03 , 50 observations ( 100 % )
	PROBABLE ERROR AT 99.7%
	t=	2.965
	E99.7=	t ( σ )
	=	2.965 ( ± 1.373 )
	=	± 4.06
	min range =	ū-E99.7
	=	23.5-4.06
	=	19.44
	max range =	ū+E99.7
	=	23.5+4.06
	=	27.56
=	between 19.44 –‒ 27.56 , 50 observations ( 100 % )
	PROBABLE ERROR AT 99.9%
	t=	3.29
	E99.7=	t ( σ )
	=	3.29 ( ± 1.373 )
	=	± 4.51
	min range =	ū-E99.9
	=	23.5-4.51
	=	18.99
	max range =	ū+E99.9
	=	23.5+4.51
	=	28.01
=	between 18.99 –‒ 28.01 , 50 observations ( 100 % )

Histogram