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  • INTRODUCTION OF SURVEYING
    • INTRODUCTION
    • REFERENCE ELLIPSOID
    • BASIC MEASUREMENTS
    • The geoid
    • PROTECTION AND REFERENCING
    • CONTROL NETWORKS
    • The ellipsoid
    • BASIC SETTING-OUT PROCEDURES USING COORDINATES
    • LOCATING POSITION
    • COORDINATE SYSTEMS
    • USE OF GRIDS
    • PLOTTING DETAIL
    • Geodetic coordinates
    • SETTING OUT BUILDINGS
    • Computer-aided design (CAD)
    • Cartesian coordinates
    • Error and uncertainty
    • Plane rectangular coordinates
    • SIGNIFICANT FIGURES
    • Height
    • ERRORS IN MEASUREMENT
    • WEIGHT MATRIX
    • LOCAL SYSTEMS
    • Probability
    • ERROR ANALYSIS
    • Deviation of the vertical
    • INDICES OF PRECISION
    • VARIANCE-COVARIANCE MATRIX OF THE PARAMETERS
    • COMPUTATION ON THE ELLIPSOID
    • COMBINATION OF ERRORS
    • Uncertainty of addition or subtraction
    • Eigenvalues, eigenvectors and error ellipses
    • BLUNDER DETECTION
    • RELIABILITY OF THE OBSERVATIONS
    • PRACTICAL CONSIDERATIONS
    • ESTIMATION IN THREE DIMENSIONS

  • LEVELLING
    • LEVELLING
    • OPTICAL METHODS
    • CURVATURE AND REFRACTION
    • MECHANICAL METHODS
    • EQUIPMENT
    • Weiss quadrilateral
    • INSTRUMENT ADJUSTMENT
    • PARAMETER VECTOR
    • Single wires in two shafts
    • Automatic level
    • DESIGN MATRIX AND OBSERVATIONS VECTOR
    • GYRO-THEODOLITE
    • PRINCIPLE OF LEVELLING
    • Plan network
    • SOURCES OF ERROR
    • Distance equation
    • LEVELLING APPLICATIONS
    • Direction & Angle equation
    • Direct and Indirect contouring
    • Controlling earthworks
    • RECIPROCAL LEVELLING
    • PRECISE LEVELLING
    • Parallel plate micrometer
    • ERROR ELLIPSES
    • Field procedure
    • Booking and computing
    • DIGITAL LEVELLING
    • Factors affecting the measuring procedure
    • TRIGONOMETRICAL LEVELLING

  • CONTOURING
    • TAPES
    • Introduction of Satellite positioning
    • FIELD WORK
    • GPS SEGMENTS
    • Measuring in catenary
    • GPS
    • DISTANCE ADJUSTMENT
    • SATELLITE ORBITS
    • Sag
    • BASIC PRINCIPLE OF POSITION FIXING
    • ERRORS IN TAPING
    • DIFFERENCING DATA
    • Tension,Sag and Slope
    • GPS OBSERVING METHODS
    • ELECTROMAGNETIC DISTANCE MEASUREMENT (EDM)
    • Kinematic positioning
    • ERROR SOURCES
    • Global datums
    • GPS SYSTEM FUTURE
    • DATUM TRANSFORMATIONS
    • GALILEO
    • ORTHOMORPHIC PROJECTION
    • APPLICATIONS
    • ORDNANCE SURVEY NATIONAL GRID
    • (t – T) correction
    • PRACTICAL APPLICATIONS
    • Contouring
    • HEIGHTING WITH GPS

  • Theodolite Surveying
    • PLANE RECTANGULAR COORDINATES
    • PRINCIPLE OF LEAST SQUARES
    • PRINCIPLE OF LEAST SQUARES
    • TRAVERSING
    • LINEARIZATION
    • LEAST SQUARES APPLIED TO SURVEYING
    • Reconnaissance
    • NETWORKS
    • LINEARIZATION
    • Sources of error
    • Traverse computation
    • TRIANGULATION
    • Resection and intersection
    • Resection
    • NETWORKS
    • INSTRUMENT ADJUSTMENT
    • FIELD PROCEDURE
    • Setting up using the optical plumb-bob
    • MEASURING ANGLES
    • Measurement by directions
    • SOURCES OF ERROR

  • Simple Curves
    • CIRCULAR CURVES
    • Plotted areas
    • RESPONSIBILITY ON SITE
    • PHOTOGRAMMETRY
    • SETTING OUT CURVES
    • PARTITION OF LAND
    • COMPOUND AND REVERSE CURVES
    • CROSS-SECTIONS
    • SHORT AND/OR SMALL-RADIUS CURVES
    • VOLUMES
    • TRANSITION CURVES
    • Effect of curvature on volumes
    • Centrifugal ratio
    • MASS-HAUL DIAGRAMS
    • CONTROLLING VERTICALITY
    • The equation of motion
    • Coefficient of friction
    • CONTROLLING GRADING EXCAVATION
    • Sources of error
    • SETTING-OUT DATA
    • ROUTE LOCATION
    • LINE AND LEVEL
    • Highway transition curve tables (metric)
    • THE OSCULATING CIRCLE
    • Transitions joining arcs of different radii (compound curves)
    • Coordinates on the transition spiral
    • VERTICAL CURVES
    • Vertical curve design
    • Sight distances
    • Permissible approximations in vertical curve computation

Branch : Civil Engineering
Subject : Surveying-I
Unit : CONTOURING

DIFFERENCING DATA


Description:

Whilst the system was essentially designed to use pseudo-range for navigation purposes, it is the carrier phase observable which is used in engineering surveying to produce high accuracy relative positioning. Carrier phase measurement is similar to the measuring process used in EDM. However, it is not a twoway process, as with EDM. The observations are ambiguous because of the unknown integer number of cycles between the satellite and receiver at lock-on. Once the receiver has acquired the satellite signals, the number of cycles can be tracked and counted (carrier phase) with the initial integer number of cycles, known as the integer ambiguity, still unknown (Figure ).

 

By a process of differencing between the phase received at one station from two satellites, from one satellite at two stations, and between each of these over a period of time it is possible to solve for the relative position of one station with respect to the other. There are two major problems here. One is that, although the position on a single radio sine wave from the satellite may be determined to about 1% of the wavelength, it is not possible to differentiate one sine wave from another.

 

Therefore, although the distance from a satellite may be computed to a few millimetres (the wavelength on the L2 frequency is approximately 19 cm) there is an ‘ambiguity’ in that distance of a whole number (an integer) of 19 cm wavelengths. A major part of the solution is to solve for this integer ambiguity. This is done by a series of ‘difference’ solutions that are described below. The other major problem is that of ‘cycle slips’. In the ‘triple difference solution’, which is differencing  time, the cycles are counted from the start to the end of the observing period. If one or more of the cycles are missed then the measure will be in error by the number of cycle slips multiplied by the wavelength of the signal. Cycle slips may be ‘repaired’ if more than the minimum number of observations.

 

Integer ambiguity

is taken and observations are recorded on a continuous basis. More flexible methods of using the carrier phase observable have been developed. Kinematic surveying involves taking observations at two stations for a period of time, say 10 minutes. One instrument is then moved from station to station remaining for
only a short period at each station. The post-processing again is all on a differencing basis. Semi-kinematic surveying uses the whole number nature of the integer ambiguity and even allows for switching off the instrument between repeated visits to the stations. What follows is a demonstration of the concepts involved in the differencing processes and shows how a solution may be achieved. It does not represent how the software of any specific instrument works. In Figure and in the text that follows, elements associated with satellites have superscripts and elements associated with ground stations have subscripts.

 

Rj = position vector of ground station j
ra = position vector of satellite a
paj = actual range from satellite a to ground station j

Paj = pseudo-range
c = speed of radio waves in vacuo
Tj = receiver clock time of receipt of signal at station j from satellite a
ta = satellite clock time of transmission of signal at satellite a
gj = GPS time of receipt of signal at station j

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