The Universal Transverse Mercator (UTM) coordinate system has at its core, equations that enable ... more The Universal Transverse Mercator (UTM) coordinate system has at its core, equations that enable the transformations from geographic to grid coordinates and vice versa. These equations have a long history stretching back to Gauss and his survey of Hannover in the early 1800's but their modern formulation is due to L. Krueger (1912) who synthesised Gauss' and other work on the transverse Mercator (TM) projection of the ellipsoid. Krueger developed two methods of transformation and the equations of his second method have become the de facto standard for the UTM and other TM projection systems. Unfortunately these are complicated and have limited accuracy. But the equations for Krueger's first method which do not suffer from these accuracy limitations are undergoing a renaissance and a recent study by Charles Karney (2011) has given these equations a 'make over'. This paper gives some insight into the development and use of the Karney-Krueger equations.
Transformations of coordinates are common geodetic operations. For example, networks of GPS measu... more Transformations of coordinates are common geodetic operations. For example, networks of GPS measurements are processed in X,Y,Z Cartesian coordinates but locations of network stations are usually transformed to geodetic coordinates , , h φ λ (latitude, longitude and height) related to the reference ellipsoid. And , φ λ may be transformed to E,N grid coordinates on a map projection. Such transformations are shown symbolically as ( ) ( ) , , , , X Y Z h φ λ ⇔ and ( ) ( ) , , E N φ λ ⇔ where ⇔ represents sets of equations linking coordinates. If the precisions of coordinates are known in one system, then precisions in the transformed system can be evaluated by propagation of variances expressed mathematically as a sequence of matrix operations. One of the matrices involved is the Jacobian matrix of first-order partial derivatives, and this paper gives the derivation of various partial derivatives as well as examples of their application. Introduction Something to be added here
The Kalman filter is a set of equations, applied recursively, that can be used in surveying appli... more The Kalman filter is a set of equations, applied recursively, that can be used in surveying applications to obtain position, velocity and acceleration of a moving object from traditional surveying measurements. The aim of this paper is to introduce the surveyor to the Kalman filter by examination of two simple applications, (i) Electromagnetic Distance Measurement (EDM) and (ii) the position and velocity of a ship in a navigation channel.
Cartography and Geographic Information Science, 1990
The point pole of a pseudocylindrical map projection may be expanded to a line to alleviate disto... more The point pole of a pseudocylindrical map projection may be expanded to a line to alleviate distortions in the map at high latitudes. The ratio between the length of the pole line and the length of the equator may be determined so as to give a minimum-error pseudocylindrical map projection. A variation of the minimum-error technique, as proposed by Sir George Airy, is applied to the sinusoidal projection to demonstrate the method.
A three-dimensional (3D) conformal coordinate transformation, combining axes rotations, scale cha... more A three-dimensional (3D) conformal coordinate transformation, combining axes rotations, scale change and origin shifts is a practical mathematical model of the relationships between different 3D coordinate systems. Applications in geodesy and photogrammetry often use simplified transformation models under the assumption of small or negligible rotations, but in other areas of interest rotations may be large. In such other cases, approximate values of rotations are required to perform initial transformations before the simplified models are employed. This paper uses an example applicable to the construction industry to demonstrate methods of calculating approximate rotations and performing initial transformations prior to computing transformation parameters. A rigorous development and proof of the 3D conformal transformation is given as well as the necessary assumptions for the simplified model. In addition, this paper also explains how least squares may be used in determining transfo...
FROM DIRECTIONAL ANTENNA R.E. Deakin Geospatial Science, RMIT University email: rod.deakin@rmit.e... more FROM DIRECTIONAL ANTENNA R.E. Deakin Geospatial Science, RMIT University email: rod.deakin@rmit.edu.au [Proceedings of Victorian Survey Conference: Industry and Environment, Traralgon, Victoria, 23-25 May, 2003 Institution of Surveyors Victoria & the Institution of Engineering and Mining Surveyors, Victoria Division.] ABSTRACT To monitor the position of athletes during sporting contests it is proposed to equip the athletes with small radio transmitters whose signal is received by several directional radio antennae located at known locations. This paper provides a method of determining the athletes horizontal position as well as the precision of position given the precision of the directional measurements. In addition an analysis of precision of position fixing for different antennae locations is provided
The highest recorded speed reached by any craft under sail is 46.52 knots (86 km/h). This record ... more The highest recorded speed reached by any craft under sail is 46.52 knots (86 km/h). This record was set at Shallow Inlet Victoria in 1993 by Simon McKeon and Tim Daddo sailing the yacht Yellow Pages Endeavour; a triplanar wing sail yacht, designed and constructed in Australia. In 2002, they will attempt to raise the record above 50 knots with a new yacht, Macquarie Innovation, an improved version of Yellow Pages Endeavour. To determine the speed the Macquarie team has developed their own low-tech approach using a digital video recorder aboard the yacht and sighting posts at fixed distances on shore. With the latest development of GPS technology, speed and distance travelled can be measured in an efficient and precise manner and this paper compares both techniques on simulated runs of the yacht before a recent record attempt. INTRODUCTION World Sailing Speed Records are awarded by the World Sailing Speed Record Council (WSSRC 2002), an affiliated body of the International Sailing Fe...
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tab... more The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table...
The concept of a centroid is useful for many spatial applications, and the determination of the c... more The concept of a centroid is useful for many spatial applications, and the determination of the centroid of a plane polygon is standard functionality in most Geographic Information System (GIS) software. A common reason for determining a centroid is to create a convenient point of reference for a polygon, often for positioning a textual label. For such applications, the rigour
The Universal Transverse Mercator (UTM) coordinate system has at its core, equations that enable ... more The Universal Transverse Mercator (UTM) coordinate system has at its core, equations that enable the transformations from geographic to grid coordinates and vice versa. These equations have a long history stretching back to Gauss and his survey of Hannover in the early 1800's but their modern formulation is due to L. Krueger (1912) who synthesised Gauss' and other work on the transverse Mercator (TM) projection of the ellipsoid. Krueger developed two methods of transformation and the equations of his second method have become the de facto standard for the UTM and other TM projection systems. Unfortunately these are complicated and have limited accuracy. But the equations for Krueger's first method which do not suffer from these accuracy limitations are undergoing a renaissance and a recent study by Charles Karney (2011) has given these equations a 'make over'. This paper gives some insight into the development and use of the Karney-Krueger equations.
Transformations of coordinates are common geodetic operations. For example, networks of GPS measu... more Transformations of coordinates are common geodetic operations. For example, networks of GPS measurements are processed in X,Y,Z Cartesian coordinates but locations of network stations are usually transformed to geodetic coordinates , , h φ λ (latitude, longitude and height) related to the reference ellipsoid. And , φ λ may be transformed to E,N grid coordinates on a map projection. Such transformations are shown symbolically as ( ) ( ) , , , , X Y Z h φ λ ⇔ and ( ) ( ) , , E N φ λ ⇔ where ⇔ represents sets of equations linking coordinates. If the precisions of coordinates are known in one system, then precisions in the transformed system can be evaluated by propagation of variances expressed mathematically as a sequence of matrix operations. One of the matrices involved is the Jacobian matrix of first-order partial derivatives, and this paper gives the derivation of various partial derivatives as well as examples of their application. Introduction Something to be added here
The Kalman filter is a set of equations, applied recursively, that can be used in surveying appli... more The Kalman filter is a set of equations, applied recursively, that can be used in surveying applications to obtain position, velocity and acceleration of a moving object from traditional surveying measurements. The aim of this paper is to introduce the surveyor to the Kalman filter by examination of two simple applications, (i) Electromagnetic Distance Measurement (EDM) and (ii) the position and velocity of a ship in a navigation channel.
Cartography and Geographic Information Science, 1990
The point pole of a pseudocylindrical map projection may be expanded to a line to alleviate disto... more The point pole of a pseudocylindrical map projection may be expanded to a line to alleviate distortions in the map at high latitudes. The ratio between the length of the pole line and the length of the equator may be determined so as to give a minimum-error pseudocylindrical map projection. A variation of the minimum-error technique, as proposed by Sir George Airy, is applied to the sinusoidal projection to demonstrate the method.
A three-dimensional (3D) conformal coordinate transformation, combining axes rotations, scale cha... more A three-dimensional (3D) conformal coordinate transformation, combining axes rotations, scale change and origin shifts is a practical mathematical model of the relationships between different 3D coordinate systems. Applications in geodesy and photogrammetry often use simplified transformation models under the assumption of small or negligible rotations, but in other areas of interest rotations may be large. In such other cases, approximate values of rotations are required to perform initial transformations before the simplified models are employed. This paper uses an example applicable to the construction industry to demonstrate methods of calculating approximate rotations and performing initial transformations prior to computing transformation parameters. A rigorous development and proof of the 3D conformal transformation is given as well as the necessary assumptions for the simplified model. In addition, this paper also explains how least squares may be used in determining transfo...
FROM DIRECTIONAL ANTENNA R.E. Deakin Geospatial Science, RMIT University email: rod.deakin@rmit.e... more FROM DIRECTIONAL ANTENNA R.E. Deakin Geospatial Science, RMIT University email: rod.deakin@rmit.edu.au [Proceedings of Victorian Survey Conference: Industry and Environment, Traralgon, Victoria, 23-25 May, 2003 Institution of Surveyors Victoria & the Institution of Engineering and Mining Surveyors, Victoria Division.] ABSTRACT To monitor the position of athletes during sporting contests it is proposed to equip the athletes with small radio transmitters whose signal is received by several directional radio antennae located at known locations. This paper provides a method of determining the athletes horizontal position as well as the precision of position given the precision of the directional measurements. In addition an analysis of precision of position fixing for different antennae locations is provided
The highest recorded speed reached by any craft under sail is 46.52 knots (86 km/h). This record ... more The highest recorded speed reached by any craft under sail is 46.52 knots (86 km/h). This record was set at Shallow Inlet Victoria in 1993 by Simon McKeon and Tim Daddo sailing the yacht Yellow Pages Endeavour; a triplanar wing sail yacht, designed and constructed in Australia. In 2002, they will attempt to raise the record above 50 knots with a new yacht, Macquarie Innovation, an improved version of Yellow Pages Endeavour. To determine the speed the Macquarie team has developed their own low-tech approach using a digital video recorder aboard the yacht and sighting posts at fixed distances on shore. With the latest development of GPS technology, speed and distance travelled can be measured in an efficient and precise manner and this paper compares both techniques on simulated runs of the yacht before a recent record attempt. INTRODUCTION World Sailing Speed Records are awarded by the World Sailing Speed Record Council (WSSRC 2002), an affiliated body of the International Sailing Fe...
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tab... more The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table...
The concept of a centroid is useful for many spatial applications, and the determination of the c... more The concept of a centroid is useful for many spatial applications, and the determination of the centroid of a plane polygon is standard functionality in most Geographic Information System (GIS) software. A common reason for determining a centroid is to create a convenient point of reference for a polygon, often for positioning a textual label. For such applications, the rigour
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Papers by Rod Deakin