Surveying

Present Surveying Instrumentation

2010-12-14T10:14:00.001+08:00

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

Total Station

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

Binocular (With integrated compass and reflectorless distance-measurement)

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

Laser Tracker

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

Laser Radar

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

Laser Scanner

Cooperative target: No
Range: 1 – 500m
Accuracy: >1 – 20mm
Frequency: >1 – 500kHz
Distance method: Phase/Pulse
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

2010-11-10T11:13:00.001+08:00

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

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).
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

2010-08-06T16:43:00.002+08:00

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

Behaviour of Random Error

2010-08-02T16:12:00.005+08:00

Assume that all measurements are free of gross error and corrected for all systematic error.

	Practical Case	Theoretical Case
No. Of Observation	n->finite number	n→∞
Variable	Random Sample	Random Variable
Estimate	Mean	True value
Errors	Residuals	True Errors
Spread of Errors	Relative Frequency	Relative Frequency
	Probability Distribution Histogram	Probability Distribution Function

where,

Graphical example of

i. Probability distribution histogram

ii. Probability distribution function

Zenith and Vertical Angles

2010-07-19T16:37:00.001+08:00

Zenith angle is measure down from the zenith point directly above the instruments – Positive and negative are not needed

Vertical angle is measure off the horizon with up being positive and down from the horizon being negative.

Properties of a Random Variable - Definition

2010-04-30T10:48:00.002+08:00

A random variable is one whose value depends upon chance and in statistic, such a variable is often called stochastic (equal to guess). Situation where, a set of measured values,

obtained "under the same condition" constitutes a sample of the random variable, x, which is being measured. If the measurement were to be repeated an infinite number of times, the resulting infinite number of values,

would constitutes the population of the random variable x. In surveying, from repeated measurement, this sample we have to deduce characteristic of the population. From the population characteristics (or parameter) we can make deductions about the relative reliability of different measurement and about the most likely value of the random variable x.

Reference: Cooper, M. A. R. (1974). Fundamental of Survey Measurement and Analysis. Great Britain.: Granada Publishing Ltd

Notation used in Least Square Estimation

2010-03-17T16:31:00.001+08:00

Parameter – The unknown quantities, will be donated by

X = [x₁, x₂, x₃, x₄, ....., x_u]^T

Observation

l = [l₁, l₂, l₃, l₄, ....., l_n]^T

Part 4 - Types of Error - Random Errors

2010-02-22T16:49:00.003+08:00

Characteristic

- the remaining error after gross and systematic errors have been eliminated.

- No functional relationship based upon a deterministic system - modelled by stochastic model.

Source

- Personal (observer), natural and instrumentation

Fact

- Cannot be generally removed, however it can be minimised by

i) taking redundant observation

ii) applying least square estimation (LSE)

Part 4 : Types of Error – Systematic Errors

2010-01-14T13:29:00.001+08:00

Systematic errors exist from instrument calibration, observational procedures and the data pre-processing for atmospheric and other effects.
Physical sources of systematic errors are
1. Temperature,
2. Humidity,
3. Pressure changes.
All physical sources will affect :-
1. angle measurement, distance measurement either by tapes or EDM
2. will cause the bending of photogrammetry light rays due to atmospheric refraction,
3. lack of adequate adjustment of equipment
Can be eliminated by :-
1. Adjusting the instruments
2. Using certain procedure during measurement, example: levelling survey collimation errors can be minimized by taking measurement at equal distance from the level.

Mikhail, (1974) said " systematic effect take on different forms depending on the value and sign of each of the effects. If the value and sign remain the same all through the measuring process, we would have the so-called constant error. An example of this is making distance measurement with a tape that is either too short (or too long) by a constant value. All length measured by that tape will undergo the same systematic effect due to the tape alone. If the sign of the systematic effect changes, perhaps due to personal bias of an observer, the resulting systematic errors are often called counteracting. For example, on a aerial photograph earth curvature and atmospheric refraction cause opposite displacement of image points. Thus the systematic effect due to the first counteracts that due to the second."

Mikhail, E. M. (1974). Observation and Least Square, A Dun-Donnelley Publisher, New York

Abstract : Least Squares Formula for Zero Error of Electromagnetic Distance Measuring Instruments

2010-01-11T14:40:00.002+08:00

AliReze Amiri-Simkooei (2003). Least Squares Formula for Zero Error (Z₀) of Electromagnetic Distance Measuring Instruments. Journal of Surveying Engineering. Vol. 129, No 4, November 1, 2003

Abstract: The zero error of electromagnetic distance measuring instruments is a near-constant systematic error, which has the same effect on the measured distances. This paper presents a least-squares formula for this correction based on the division of a baseline into m subbaselines, and measuring all possible distances between the marked points. The validity of the formulation is verified by two examples.

Email me if interested.

Part 3 : Types of Errors – Gross Errors

2010-01-05T16:06:00.001+08:00

Gross errors – blunders – mistakes

Examples (Cooper, 1974):

A tape reading of 38.23m may be recorded as 38.32m in the field book,
The thermometer may be misread
Measurement may be made between the wrong pegs

Characteristics - its magnitude is significantly very large or different in comparison to the measured values

Sources – Personal errors (careless of the observer)

Effect – Inhomogeneous observables

In practice there are variety of ways that can be employed to reduced gross errors (Mikhail, 1974)

Taking multiple reading and checking for reasonable consistency
Careful checking of both pointing and recording
Using simple and quick technique for verification
Applying logic and common sense
Checking and verifying the performance of equipment, particularly those with automatic readout
Repeating the experiment with perhaps slightly different technique
Increasing redundancy of the observation used in a model

References

Cooper, M.A.R. (1974). Fundamental of Survey Measurement and Analysis. Crosby Lockwood Staples, Great Britain
Mikhail, E.M. (1974). Observations and Least Squares. A Dun-Donnelley Publisher, New York

Part 2 – Sources of Errors

2010-01-04T13:27:00.001+08:00

In observations, errors sources can be from:-

Personal – limitation of the observer, where the ability to repeat the same measurement

Careless of the observer

Instrumental - Due to imperfect construction of incomplete adjustment of the instrument (eg, incorrect graduation)
Natural - Due to changing environmental condition (eg, temperature)

Part I - About Observations

2010-01-01T12:58:00.002+08:00

Geodesy, Geodetic or Geospatial data are composed of points, lines and area relations which rich attributes.

In other word, surveyor are usually faced with the problem of estimating unknown quantities (paramaters). This is done through collecting several measurement known as observations.

Then adopting the appropriate mathematical model relating both observation and unknowns.

Observation generally requires some form instrumentations that is used by an observer in certain environment.

All observations contain errors. An error is different between an observation of a quantity and the true value. True value can never be known.

True error (e) = l – t, where l is observed value and t is true value

Both quantities, e and t can be estimated ..

Geodetic Models

2009-05-28T10:29:00.000+08:00

Geodetic Data

Geodetic or geospatial data are composed of point, lines and area relations. These data are rich with attributes. As in many other sciences, geodetic problems are located in a real world.

The concept – the problem need to be modeled.

The Solution – have to be put in a geometrical and physical formulation by mathematical means

The purpose is either description or explanation and allow to

i) estimate non-observable state and

ii) predict future state

Typical types of models in geodesy are:-

i) Measurement model (observation model)

ii) Geodetic model (theoretical model)

Both models are connected via the geodetic observable.

The task of measurement – to correct and evaluate the raw observation (true observation) to adapt them to the geodetic model

Introduction to Least Squares

2009-05-27T10:29:00.000+08:00

Least Squares – Original and Advancement

In history....original method

1795 : Karl Friederich Gauss & Adrien Marie Legendre (refer : Gauss, K.F. (1963). Theory of Motion of the Heavenly Bodies. Dover, New York

Advancements made to the original method
1905 : Kruger (refer : Kruger, L. (1905). Uber die Ausgleichung von bedingten Beobachtungen in zwei Gruppen, Postdam.

1930 : Tobey (refer : Tobey, W.M. (1930). The Differential Adjustment of Normally Distributed Observations. Geodetic Survey of Canada Pub. 27. Ottawa

1950 : Tienstra (refer : Tienstra, J.M. (1956). Theory of the Adjustment of Normally Distributed Observations. Argus, Amsterdam

- Tienstra explains that a least squares problem can be rigorously solved in “phases” – by treating the already estimated parameter and corrected observations of a previous phase as quasi-observation in the subsequent phase.

Advancement – Kalman Filtering
1960 : Kalman (refer : Kalman, R.E. (1960). A New Approach to Linear Filtering and Prediction. Journal of Basic Engineering, ASME, 82D

- extended to i) adding a second model – vector parameters to vary with time, ii) inserting covariance matrix in second model and iii) solving the problem in part

Advancement – Bayesian Procedure

1972 : Morrison ( refer : Morrison, N. (1972). Introduction to Sequential Smoothing and Prediction. McGraw-Hill Book Company, New York

Advancement – Sequential Procedure

1965 : Schmid & Schmid (refer : Schmid, H.H. & Schmid, E. (1965). A Generalized Least Squares Solution for a Hybrid Measuring System. The Canadian Surveyor, XIX, No. 1, Ottawas

- formulated with weight ranging from zero to infinity and rigorously solved “sequentially”. Sequential procedure achieved by updating the original estimate by a corrective term.

Advancement – Collocation Procedure

1969 & 1970 : Krarup ( refer : Krarup, L. (1969). A Contribution to the Mathematical Foundation of Physical Geodesy. Publication No. 44 of the Danish Geodetic Institute, Copenhagen & Krarup, L. (1970). The Method of Least Square Collocation. Studi Geophysica, No. 2, Roc. 14.

1972 : Moritz (refer : Moritz, H. (1972). Advanced Least Squares Method. Report of the Department id Geodetic Science, No. 75, The Ohio State University, Columbus.

Advancement – Stepwise & Sequential Procedure

1973 : Moritz (refer : Moritz, H. (1973). Stepwise and Sequential Collocation. Report of the Department of Geodetic Science. No. 203, The Ohio State University, Columbus

History....Documentation

2009-05-11T14:56:00.001+08:00

1. The best-known writting on surveying was by Frontinus.

The engineering ability of the Romans was demonstrated by their construction work throughout the empire.

The famous instruments is groma. This instrument used for sighting (Wolf & Ghilani, 2002).

note: others information about groma.

a) . http://www.legiiavg.org.uk/military/groma.html

b) . Source from Wikipedia - The Groma or gruma (altered from Greek gnmon γνόμων "indicator", possibly through Etruscan) was the principal Roman surveying instrument. It was composed of a vertical staff with horizontal cross pieces mounted on a bracket. Each cross piece had a plumb line and plumb bob hanging vertically. Its main use was to survey straight lines, squares, and rectangles.

c) . Britannica - use in ancient Egypt
There is some evidence that, in addition to a marked cord, wooden rods were used by the Egyptians for distance measurement.

2. Oldest Latin manuscript - Codex Acerianus, contaion an account of surveying as practised by the Romans and includes several pages from Frontinus work.

This manuscript found in the tenth century by Gerbert.

3. Middles Ages - Arabs in Islam world was making more progress in art of surveying - "practical geometry".

4. In 13th Century - Von Piso wrote Practica Geometria which contained instruction of surveying.

He also authored Liber Quadratorum - dealing with the quadran, a square brass frame having 90degree angle and other graduated scales

5. Instruments - Astrolabe.- a metal circle with apointer hinged at its center and held by a ring at the top, and the cross staff, a wooden rod about 4-ft long with an adjustable cross-arm ar right angles to it (Wolf & Ghilani, 2002). This instruments widely used in Islamic empire.

source of image: http://www.agmgifts.co.uk/resources/astrolabe_5.jpg

References

1. Wolf, P.R. & Ghilani, C.D. (2002) Elementary Surveying An Introduction to Geomatic. Prentice Hall, Upper Saddle River, New Jersey

2. Wikipedia : An astrolabe is a historical astronomical instruments used by classical astronomer, navigator and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets and stars determining local time given local latitude and vice-versa; surveying; and triangulation.
In the medieval Islamic world, they were used primarily for astronomical studies, as well as in other areas as diverse as astrology, navigationm, surveying, timekeeping, Salah prayer and Qibla. Astrologers of the European nations used astrolabes to construct horoscopes.
There is often confusion between the astrolabe and the mariner's astrolabe. While the astrolabe could be useful for determining latitude on land, it was an awkward instrument for use on the heaving deck of a ship or in wind. The mariner's astrolabe was developed to address these issues.

History...The Dioptra

2009-05-11T12:46:00.000+08:00

The oldest historical record - begin in Egypt, Hetorodotus recorded

i. Sesostris (about 1400 B.C) - Devided the land of Egypt into plots for the purpose of taxation

ii. Early surveyor were called ropestretcher - measurement were made with ropes

iii. Greek thinker - Heron, the author The Dioptra, which related to method of surveying a field, drawing a plan and making related calculations.

(note : wikipedia source - A dioptre, or diopter, is a unit of measurement of the optical power of a lens or curved mirror, which is equal to the reciprocal of the focal length measured in metres (that is, 1/metres). For example, a 3 dioptre lens brings parallel rays of light to focus at 1/3 metre. )

Taken from T. P. Tassios , Ancient Greek Technology - Measuring Instruments, FIG Working Week in Athens, May 22-27, 2004 (http://www.fig.net/news/news_2004/athens/ancient_exhibit.htm)

The "dioptra" devised by Heron is a portable surveying instrument for making accurate geodetic measurements. It measures azimuths, heights, lengths and angular distances.
The apparatus, which was mounted on a tripod about 50 cm tall, pivoted on a circular plate and was moved around horizontally by a worm screw , driven by a small handle. The top plate was mounted on a toothed semicircular plate and was adjusted in the vertical plane by another worm drive. Angles could be read off the top disc, which was scored with two lines crossing at right angles. The sighting and reading elements were made of bronze.

Definition...

2009-05-11T11:32:00.000+08:00

Just for introduction...

Surveying has been important since the begining of civilization. In early applications were in measuring and marking boundaries of property ownerships.

Surveying, recently also been interchangeably called geomatics, has traditionally been defined as the science, art and technology of determining the relative positions of point above, on, or beneath the earth's surface or of establishing such points (Wolf & Ghilani, 2002).

Surveyor traditionally and historically made their measurement using gorund-based method such as transit and tape. This is a surveyor primary instruments. The product such as computation sheet, analyses, and the report and maps they delivered to their client were prepared through manual process.

Todays, modern surveyors start to measuring and collecting using electronic instrumenatation, satellite surveying system and modern aerial imaging. The data process with high speed computer system.