1

 

EVOLUTION OF GPS

INTRODUCTION

GPS has been born out of parallel evo­lution of surveying techniques and satellite communication systems. Also in association with this evolution is the principle of operation of long-range navigation systems like LORAN, DECCA and OMEGA. As the techniques to measure time and mark it at different places at the same instant developed, it was realized that the hyperbolic systems could be operated with two clocks running at different locations and in full synchronism with each other. Accuracy of time tagging confers accuracy of position determination. Then the advantage of global coverage from satellites removed the limitation of range. We shall consider in this chapter how different technologies have really joined together to emerge as Satellite Navigation.

FROM SURVEY TO NAVIGATION

            The subject of survey has undergone a continuous process of improvisations and technological improvements as far back as human memory can go. The techniques of survey included the ancient Egyptian method of marking control points to maintain property corners destroyed by the Nile. Another method was triangulation, in which a  series of triangles were fixed by astronomical points. These methods were restricted to small areas covered by line-of-sight and suffered from errors of hundreds of meters.

Surveying was further improved by using optical triangulation with the help of reflecting satellites and using observation sites on the earth as far apart as 4000 km. This, however, involved the use of heavy equipment and also suffered from the setback of visibility limitations that can further deteriorate in bad weather or by dust content of the atmosphere.

Disadvantages of optical triangulation were overcome by using electromagnetic global trilateration that came out of the use of HIRAN - a High Ranging System made during World War II - for position fixes of aircraft. It was perhaps at this point of time that relationship between the sciences of survey and navigation was established.  The reader can appreciate that a good survey depends on the degree of accuracy achieved in fixing the position of a point on earth. Hereafter, the technology of survey with the help of satellite ranging has simultaneously led to the development of navigation of high standards. The subject thus boils down to a basic requirement - that of measuring the distance between two points. Here, the two points are: (1) the satellite, and (2) the user on the earth (including aircraft).

            Some of the earlier positioning systems include Navy Navigation Satellite System developed by Applied Physics Laboratory of the USA. This system uses six satellites at an altitude of about 11000 km in near-circular polar orbits.  For position fixing on earth, accuracy of up 1 meter can be achieved through prolonged observations. The system is being used even today by a large number of aircraft and small vessels. It is also feasible to make prolonged observation for a single point on ships and vessels as well as on ground-based platforms where we can afford to wait for the position outputs to converge to a best value. We shall see in the coming chapters that positioning needs to be fast for high-dynamic vehicles like an aircraft or even a satellite itself.

            The TRANSIT system has a serious limitation of having long time gaps between sightings of satellites. The GPS/GLONASS system, as we shall see in later paragraphs, has been designed to overcome all earlier limitations of system availability, integrity and continuity of signals.

            After TRANSIT, another system, TIMATION, used atomic frequency standards and had three satellites. Two of them were at 500 nm, while the third one was at 7500 nm. The three satellites moved in inclined orbits. At this stage, the technique of PRN and CDMA was introduced. The scheme allowed even a signal power 1/100^th of ambient noise to be detected apart from using the same carrier frequency for a number of satellites.

            The present GPS was born with the formation of Joint Program Office (JPO) in 1973 under Dr. (Col.) Bradford W. Parkinson. Initially, only four satellites were approved, but soon need for more satellites was realized, as at least four satellites were required for a complete positioning solution. Another factor which has greatly contributed to the present state of navigation techniques is the development of software to process the signals and filtering the data, also by software, to free the signal from the effects of ionospheric and tropospheric propagation delays, clock biases, etc. As we shall see, data processing techniques help in building up confidence in position determination in the presence of random errors.

 

PRESENT NAVIGATION SYSTEMS

Long Range Navigation Systems

These systems like Decca, Loran C and Omega make use of ground wave propagation at low and very low radio frequencies. With sufficient radiated power, the ground waves travel thousands of miles. Position fixing in these navigation systems depends on:

2

TECHNICAL OVERVIEW OF SATELLITE NAVIGATION SYSTEM

INTRODUCTION

Satellite-based navigation (or survey) is based on a global system, which provides service to a user at any point on earth. That is why it is generally known as GPS (Global Positioning System). GPS signals are presently being provided by USA and Russian Federation from their satellite constellations named NAVSTAR (NAVigation by Satellite Tracking And Ranging) and GLONASS (Global Orbiting Navigation Satellite System) respectively. Other organizations like INMARSAT and Indian Space Research Organization are also developing the concept of putting navigational payloads on-board their satellites for augmentation of GPS performance at user level.  Although USA has given commitment through Presidential decision on 29 March 1996 to keep their GPS signals available for civil users for a period of ten years, the civil aviation community is well aware of the need to ensure that a constellation of navigation satellites is guaranteed for civil use. GPS technology is being continually improved by ground-based and satellite-based augmentation systems so as to enable real time navigation up to category III landings. Augmentation systems are discussed in detail in relevant chapters of this book.

SYSTEM CONFIGURATION

The whole GPS system is divided into three major segments: Space, Control & monitoring and User. The space segment and control & monitoring segment of the American system constitute NAVSTAR. Overview of NAVSTAR includes satellite dynamics, geometry of satellite, satellite position vector analysis, r.f. signal modulation and navigation data format.

NAVSTAR-GPS

Space segment of GPS (American) consists of a constellation of 24 satellites at 20200 km above the earth in six orbits inclined at 55 degrees to the Equator. 21 of these satellites are kept in active operation, while the others remain in standby mode. Each satellite completes one orbit of the earth in 11 hours and 58 minutes, i.e., two orbits in 23 hours and 56 minutes. Due to this difference between the period of the satellite and length of a day, each satellite leads its previous projection at a point on the surface of the earth by four minutes in a day. Table 1 shows allotment of orbit planes and slots of the satellites.

Note: Although GLONASS  is also a GPS, the latter term is normally used for the American system.

Table 1. GPS Satellite Planes/Slots

Notes:

1. Nomenclature used in this table: Block number (2, 2A or 2R), satellite within block. In parentheses, USAF space vehicle number of GPS satellite. Satellites GPS 2-1 (14), 2-3 (16), 2-6 (18), 2-7 (20) and 2A-13 (28) have been retired. GPS 2R-1 (42) was destroyed in a Delta launch failure in January 17, 1997.
2. In electronic form of this book, readers can click on individual cells for more on-line information on the satellites

 

NAVSTAR GPS Block I

GPS satellite vehicle numbers (SVN) 1 through 11 are designated as Block I. Block I satellites are/were positioned in the same orbital planes as Block II, but at an inclination angle of 63 degrees. Block I consisted of the original concept validation satellites and reflect various stages of system development. Lessons learned from the 11 satellites were incorporated into later blocks. In 1974, Rockwell International was awarded a contract to build 8 Block I satellites. In 1978, the contract was extended 

3

DYNAMICS OF SATELLITE

INTRODUCTION

            Satellites revolving around the earth are maintained in defined and closed paths under two major forces: earth's gravitation and centrifugal force. Trajectory of the satellites follows Kepler's law like planets revolving around the sun. Purely under this condition, a satellite could remain in its orbit for ever. However, the satellites are also subjected to a number of other forces, which tend to remove them from the original defined path. For communication satellites, it may be required only to bring the satellite back to its intended path by remote control. A deviation of a few meters from its known position may not matter seriously for communications. However, for navigation, it is necessary that all the orbit perturbations be taken into account. In this chapter, we shall analyze the geometry of satellite orbit and various perturbations caused on its position by external forces other than the main gravitation of the earth.

CONSTRUCTION OF ORBIT OF GPS SATELLITE (Fig. 1)

 

Fig.1. Construction of GPS satellite orbit

            We start with basic understanding of how orbits of GPS satellites are created. First consider axes x, y and z where equatorial plane of the earth is contained in the x-y plane and the center of the co-ordinates is the geo center of the earth. A rectangular plane LMNP makes part of the equatorial plane with LM and MN parallel to Y and X-axes, respectively. See Fig. 1(a).

We shall assign another set of axes to the plane LMNP as: e₁, e₂ and e₃. At this moment, e₁, e₂ and e₃ co-ordinates  coincide with X, Y and Z axes, respectively. The origin of 'e' co-ordinates is the same - the Geo center. Things are quite simple so far. We now begin with steps to form a satellite orbit. We look into the system along the y-axis towards the center. You will see the coordinates as in Fig. 1 (b)  Now, follow the steps given below.

Step 1 : Rotate plane LMNP about the Y -axis by an angle i. The plane is now inclined over the equator at this angle. The result of this step is:

 

4

TIME SYSTEMS

 

 

INTRODUCTION                                                               

The term TIME has been associated with our lives from day one of human history. This association has gone so deep into our thoughts that we, in fact, have accepted it as the master of all events. Time has even become a source of philosophical debates. I strongly believe that it is not fully understood yet. I consider that time is only a secondary offshoot of an even more basic power of nature: the rhythm. If some people have been successful in grasping the real form of time, Einstein must be one of them. According to Hindu philosophy also, time was first born from the enormity of Brahma, the creator. They say that one moment of Brahma is equal to a thousand years of our life. Do not be surprised. It may be true. For one thing, it has been proved through experiments that the velocity of light remains the same irrespective of movement of the point of observation. For another, nothing having a mass more (positive) than zero can be accelerated to the velocity of light. Mathematically, the mass of a particle increases to infinity at the velocity of light and then again starts decreasing beyond that velocity. Obviously, a mass cannot cross over. And if there are any particles already moving at a velocity above that of light, they would not be able to slow down. It seems that propagation of light as well as any electromagnetic wave has a lot to do with the RHYTHM of nature.

            In order to get close to the term time, we shall discuss beginning from present and move to the past. First consider how we measure it. In common parlance, time is measured by the number of clicks of a clock. The measurement becomes more and more reliable if a number of clocks are allowed to run together at one place of observation and their counts are equal. Resolution of the measurement is increased if the number of ticks is more between two given events. As such, today we have atomic clocks, which oscillate at the fastest known frequency. One second is defined as the time in which cesium atom oscillates 9,192,631,770 times. We admit this as the most accurate means to measure the time only because it is the best way available today.

            From what has been said above, it should be a better idea to begin with the rhythm rather than time. In my opinion, the former should be closer to the mother nature.

            We have said that one second is considered to have elapsed when a cesium atom has oscillated 9,192,631,770 times. We can surely count without mistake. But who knows whether the cesium atom was oscillating with truly the same period in all the cycles? Here again, we can say that a number of independent atomic clocks using cesium oscillations may display final counts with a good tolerance. This tolerance is not ideally zero. Therefore, we should go beyond cesium oscillations. We have defined above one second of time based on the oscillations of cesium atom. And what happens during one cycle of the oscillations? What clock does the atom follow? We need to take another source of oscillations whose frequency is higher than that of cesium atom. Then, the same logic can be extended further and further. There appears to be no end to this.

            Now we make a presumption that appearance of universe is jumping from one state to another at a frequency so high that, within any observable period, the number of ticks is nearly equal to, but not actually, infinity. The state of the universe in between two successive states can be assumed to be constant. At different points in the universe, there are various kinds of forces - mechanical, electrical, magnetic, gravitational and perhaps any other yet unknown to man. The magnitude of each force would decide how different the state of the point will be when the universe jumps to the next point. We should leave it to the mysteries of the nature as to what the frequency of the ticks is, and what clock the universe follows. But I would like to think that the secret lies there. Another argument in this direction is that the three-dimensional space can be filled by stacking cubes and not spheres. One jumps from a cube to another under the influence of a suitable force. Perhaps there is nothing like continuity of a function.

** observable oscillations should be bound to the basic rhythm.

One oscillation should take place when N ticks of the rhythm have occurred.

Fig. 1. Rhythm of nature

            Then, there can be natural oscillations taking place somewhere that we have not yet been able to notice. What we have noticed is the oscillations of atoms. In accordance with our scale of time, the oscillations are fast enough to build confidence of accuracy in our minds. However, when we think of changing the point of observation from our frame to a smaller frame, the oscillations would begin to appear slow. So, we can say that it is the point of observation in Fig.1 that determines the observed accuracy. When man is able to observe the basic oscillations, he may find out whether we are really seeing things happening as they actually are. 

5

WGS-84 COORDINATES SYSTEM

Bimal K. Srivastava

The position of any place, object or point can be represented by means of its geographical coordinates expressed in three-dimensional form of latitude, longitude and height. The latitude and longitude are measured from the intersection of lines of prime meridian (passing through Greenwich) and the Equator. Similarly, the height (or elevation) is normally measured from the mean sea level and is generally referred to as "Above Mean Sea Level" or AMSL. In other words, the origin of latitude, longitude and height is the intersection point of the Greenwich meridian, Equator and the mean sea level. Thus, it can be said that the geographical coordinates of Delhi are 28^o 34^' 07^'' North, 77^o 06^' 48^'' East, 227 meters amsl, and those of Lucknow are 26^o 45^' 42^'' North, 80^o 53^' 07^" East, 122 meters amsl; where all the measurements are related to the origin, as defined above, and all values are represented as arc-degrees, arc-minutes and arc-seconds (though not stated).

Geographical position of any place or object can also be expressed in terms of the relative distances and bearings from a given reference point.  For example, it can be said that Lucknow is located at a distance of 425 km (aerial distance) and on a bearing of 118 ^o from Delhi.  

Here, a particular point in Delhi has been assumed to be the reference point (or the origin) from which all measurements are taken. Another assumption that has been made here is that the surface of earth between Lucknow and Delhi is flat on which measurements have been taken by means of a tape or any other distance measuring equipment in straight line. However, it is a known fact that the surface of earth is not flat, but it is approximately of spheroid (or ellipsoid) shape having an assumed center of its own. Thus, with a view to get the accurate results of the distance between Delhi and Lucknow, a spheroid (or ellipsoid) which best fits the shape of earth between Delhi and Lucknow must also be assumed.

In a similar manner, it can be further extra-polated to represent all areas of our country into a common spheroid, which best fits the surface of earth existing in our country.  This spheroid can be defined in terms of its inherent characteristics, such as the semi-major axis, semi-minor axis, eccentricity, etc. on the basis of which it is possible to mathematically work out the distances and bearings of any two points by geometrically plotting these points on that spheroid. This spheroid provides the basis for mapping for that area.

Thus, it is evident that the geographical position of a place or object when expressed in terms of X, Y, Z coordinates (known as latitude, longitude and height of the place) are always based on a particular reference datum. These coordinates are called `ground derived coordinates' or `local coordinates' and the reference datum on which measurements are made is known as local datum. In other words, a geographical datum is a mathematical model representing the shape of the earth that is used as a reference or starting point for the determination or calculation of latitude, longitude and height.

Accordingly, a mathematical spheroid roughly representing the shape of Indian sub-continent has been assumed by the Survey of India and all measurements are related to this spheroid. The reference datum fixed by "Survey of India" is located near Kalyanpur in Madhya Pradesh. This is known as `Everest-1830' (Everest is the name of first Surveyor General of India, (Late) Mr. George Everest' and the term `1830' represents the year in which the spheroid was defined). This datum is also sometimes called `Indian datum'. The Indian spheroid has been marginally modified on a number of occasions so that the parameters assumed for the spheroid have been refined slightly from time to time. For example, such changes were made in the year 1930, 1956 and so on. Thus, sometimes the Everest spheroid (or Indian spheroid) is also referred to as Indian 1880, Everest 1930 or Indian 1956, etc. (Even now some changes in the original definition are under consideration by Survey of India).

Obviously, the Everest spheroid may not be having its center coinciding with the center of the earth.  However, this is the best fitting spheroid that works fairly well for our country. All the maps prepared by Survey of India and other agencies use `Everest-1830 datum' for expressing geographical coordinates of places in India. Based on this, a number of sub-datums** have also been established in our country (**although the grammatically correct word for the plural of `datum' is `data', for the sake of simplicity and for the purpose of distinguishing it from another frequently used word "data" or `a set of information' we would use the word `datums' throughout this chapter).  All measurements are taken from the main datum, sub-datums or tertiary datums. (Aerodrome Reference Points, which are established by Survey of India, are also one of the sub-datums).