4. positioning systems for precision farming

Silsoe College Chapter 4

Mark Moore (1997) 55

4. Positioning systems for Precision Farming

4.1 Overview

To maximise the full potential of precision farming techniques, it is essential to be able to

determine as accurately as is possible the location of the farm vehicle carrying the system,

(tractor, combine, etc.) both on the farm and within the field. It is fundamental, therefore,

that any parameters to be measured can be “Geo-referenced” within the field to produce a

map. This is also essential if inputs (cultivation, seed, fertiliser, chemicals etc.) are to be

varied equally accurately within the field.

Mills (1986) first attempted to accurately monitor the location of a Massey Ferguson combine

harvester within four trial fields in 1985. A dead reckoning system was used to locate the

machine, and that year the four fields were yield mapped.

In 1986 the same four fields were yield mapped for a second time, but the location system on

the combine harvester was changed to a radio navigation system. This system was originally

developed for guiding tractors applying fertilisers in a field without tramlines. The location

system enabled the machine to be driven along straight parallel bouts. It comprised of three

elements; two stationary radio repeaters positioned at convenient points in the field and one

mobile transceiver and computer unit. During operation, the mobile unit was in constant

communication with the two stationary repeaters, thus enabling the position of the vehicle to

be calculated.

Mills found that first, the operation of the dead reckoning system proved very complex and

secondly, that the radio navigation system was technically unreliable. He concluded that a

more efficient method of locating the vehicle must be designed if precision farming was to be

adopted at a commercial level.



4.2 The Concept of Satellite Navigation

The development of the Global Position System (GPS) was established as result of funding

from the United States of America Department of Defence. It was recognised in the early

1950’s that a world-wide, 24 hour, positioning system would be an advantage to national

defence policy, Anon (1992). By 1964, the US Navy had introduced an operational satellite

navigational system called Transit, to be used for marine navigation. Using a combination of

dead reckoning and satellite fixes, it was possible to locate slow moving ships on the oceans.

Eleven years later, in 1973, the US government formed the Navigation Technology Program,

merging two experimental satellite navigation projects. Shortly after this, the GPS program

was officially launched, and controlled by the US Air Force.

Today, the main function of GPS is to provide the US Department of Defence with

continuous highly accurate world-wide three dimensional, (position, velocity and time)

information. The same service is available to civil users including those in the agricultural

industry. The accuracy of the system received by civil users is reduced by a system called

Selective Availability (S/A), but, nethertheless, it is available at no cost.

GPS is generally regarded to be divided into three parts:

• The space segment which includes 21 operational satellites and three active spares

orbiting the earth at approximately 20,000km, Anon (1989).

• The control segment which includes a master control station in Colorado, (North

America), and five linked monitoring stations.

• The user segment which consists of the receiver which provides accurate positioning,

velocity and time information to the user.

The constellation of 24 satellites became fully operational in 1993. Prior to that date, there

were instances when users experienced reduced accuracy simply because there where periods

during the 24 hour day when less than 4 satellites could be observed.

4.3 Datums



Any statement of geographical position must be referred to some co-ordinate system. On a

flat 2-dimensional surface, this is a relatively simple operation. The world, however, is not

flat, but an irregular shape that can be approximated to an ellipsoid which is approximately

0.3% or 31km larger in diameter at the equator that at its poles. A co-ordinate system that

“best fits” the shape of the world has been continually refined. The various Datums which are

adopted as reference co-ordinate systems are based on ellipsoids with slightly different

parameters. Prior to 1987. GPS operated on a datum called World Geodetic System 1972

(WGS-72). However, in early 1987, GPS changed from WGS-72 to a new system called

WGS-84. WGS-84 is the co-ordinate system which has been adopted as the datum for the

majority of GPS navigation systems today.

4.4 The Global Positioning System (GPS) - basic operating principles

GPS is based on satellite ranging. To locate an accurate position of an object using GPS, the

distance from a minimum of four satellites is measured to that object. The distance from the

orbiting satellites is calculated using the equation:

Velocity x Time = Distance

The GPS system works by recording the length of time taken for a radio signal to reach the

ground receiver from a satellite and by converting time into distance. All satellites continually

transmit radio signals that travel at the speed of light (299,300 km/second). Therefore, taking

the known time when the GPS satellite transmitted its radio signal and the actual time that

signal was picked-up by the ground receiver, it is possible to calculate the distance between

the two.

However, timing how long it takes a radio signal to reach the ground receiver is one of the

major errors in the GPS system. If the satellite and ground receiver were out of

synchronisation by a mere 1/100th of a second, the distance calculated could be off-set by

1,860 miles, Anon (1989).

By using a combination of trigonometry and an extra signal from a satellite it is possible to

over-come timing errors. Trigonometry proposes that if three perfect measurements locate a



point in three dimension space, then four imperfect measurements can eliminate any timing

error as the centre of a pyramid, formed by the four measurements, can be calculated using

trigonometry. For the most accurate GPS position to be fixed in three dimensional space

therefore, it would mean that a minimum of four satellites are required. To assist in the

purposes of explanation, the following description is given in two dimension, although the

principal for three dimension is exactly the same.

4 seconds6 seconds

x

A

B

Figure 4.1- Position “X” calculated from two perfect measurements (2 dimensional)

Figure 4.1 illustrates the calculation of point “X” using two perfect measurements converted

from the timing of two radio waves transmitted from two satellites. In this example, the

correct position represented by “X” is 4 seconds from satellite A, and 6 seconds from satellite

B. The intersection represents the true position “X”. Normally, the distances are

measurement in kilometres but for the purposes of explanation they are measured in seconds.

For a three dimension position an extra measurement from a third satellite would be required.

Figure 4.2 illustrates what happens in reality, as it is virtually impossible to obtain perfect time

measurements. In this example, there is a one second error in both measurements from

satellites A and B causing the circles to intersect at an incorrect point “XX”. By adding

another measurement from a third satellite, trigonometry can be used to correct the timing

error.



4 seconds 6 seconds

xx

A

B

5 seconds(wrong time)


Figure 4.2 - Incorrect position “XX” calculated from errors in time measurements

(2 dimension)

In Figure 4.3, the position of “X” has been recalculated using a third satellite C, from which

“X” is at 8 seconds distance. The position of “X” is the true position, as the point at which all

three circles intersect, each circle representing the true range from the three satellites.

4 seconds6 seconds

x

A

B

C

8 seconds

Figure 4.3. - Position “X” calculated from three perfect measurements (2 dimensional)

Figure 4.4 represents satellite C as having a timing error of an additional one second. There is

no direct intersection point of all three circles, hence there is no accurate positioning of “X” at



five seconds from satellite A, 6 seconds from satellite B and 9 seconds from satellite C. To

compensate for the lack of intersection point using these three measurements, the computer in

side the GPS receiver will acknowledge a mis-fit error and attempt to correct it. By applying

algebra to solve the problem, the computer will begin to subtract or add the same amount of

time to each measurement. It continues this process until it discovers the point at which all

measurements intersect, (four measurements in 3 dimensional situations). In the example

shown the computer discovers that by subtracting one second from each of the readings it can

make each of the circles intersect at one point.

5 seconds(wrong time) 7 seconds

(wrong time)

xx

A

B

C


Figure 4.4 - Inaccurate positioning due to timing errors (2 dimensional)

4.5 Knowing where satellites are

The basic principles of using GPS will only work if the position of the satellites are known.

Each satellite is launched into a very precise orbit of the earth at a height of 20,000km. The

orbit pattern and route is known in advance and some GPS receivers have an almanac

programmed into their computer memory, thus identifying the position of a satellite at any

given time.



The high altitude of 11,000 miles is necessary to maintain the satellite in a stable orbit. It also

means that the satellite is not influenced by other factors such as the earth’s gravitational pull.

Satellite orbits are therefore very precise and predictable.

All satellites are constantly monitored by the USA Department of Defence. Altitude, position

and speed are precisely measured and each satellite is updated if any slight change of orbit has

been detected. The satellites in turn relay the new information to ground GPS receivers as

navigational (NAV) messages.

Most GPS receivers utilise Kalman filters to process and compensate for the errors between

actual measured satellite data and the predicted measurement of the known location of the

satellites position and GPS receiver position.

4.6 GPS Accuracy and Error

The absolute accuracy of GPS is determined by the sum of several sources of error. The

contribution of each source may vary depending on atmospheric conditions and equipment

reliability.

4.6.1 Ionospheric propagation delays

The earth’s ionosphere - a blanket of electrically charged particles 130 to 200 km above the

earth’s surface - can have a considerable effect on the accuracy of GPS. The electrically

charged particles affect the speed of light (or radio signal) by slowing it down slightly. This

can introduce an error in the distance calculations, as it is generally assumed that the speed of

light is constant.

The error can be minimised by predicting the typical speed of light for an average day, under

average ionosphere conditions. The correction factor is applied to all measurements.

A more accurate but complex way of overcoming these errors is to use esoteric physics. The

principle behind this is that when light travels through the ionosphere it slows down at a rate

inversely proportional to its frequency squared. The lower the frequency of the signal, the



slower it becomes. Therefore, by comparing signal frequencies it is possible to determine the

effect of the ionosphere.

4.6.2 Atmospheric propagation delays

Water vapour in the earth’s atmosphere can also affect radio signals, resulting in errors similar

to that of the ionosphere, but impossible at present to correct.

4.6.3 Geometric Dilution of Precision

The geometric positions of the satellites used to fix a position on the earth’s surface can also

affect accuracy. This value can be quantified and is termed the Geometric Dilution of

Precision. The effect of Geometric Dilution of Precision is illustrated in Figure 4.5.

Good Geometry

Range Error

Bad Geometry

Figure 4.5. - Geometric Dilution of Precision

Every satellite range has a little uncertainty due to errors which cannot be foreseen. The

range error from a satellite is represented in Figure 4.5 by the thick grey line. The range

errors mean that the calculated position is not an exact single point. In reality, the position

lays somewhere in a box, represented in Figure 4.5 by the black area where the two circles

intersect. Depending upon the angle between the satellites, the box can be relatively small and

square, (good geometry) or large and elongated (poor geometry). Therefore, the wider the

angle between the satellites the more accurate are the measurements. The best DoP will occur



when 1 satellite is at zenith and 3 satellites are on the horizon 120 degrees in azimuth apart,

Rupert et al. (1994).

The GPS receiver will monitor the position of all the satellites that it can “see” at any one

moment, and automatically calculate from almanac data a reference to offer the best

geometry. Geometric Dilution of Precision can be recorded with position data, and is

represented by a value on a scale of 1 to 15, 1 being good geometry and 15 being poor

geometry, Anon (1989).

4.6.4 Selective Availability (S/A)

The accuracy of GPS is purposefully degraded by the USA Department of Defence using an

operational mode called “Selective Availability” (S/A). S/A denies “enemies” the ability to

acquire precise measurements from GPS.

GPS data can be acquired in either of two modes:

1. PPS (Precise Positioning Service) or P code.

2. SPS (Standard Positioning Service) or C/A code (Coarse Acquisition)

PPS or P code provides the USA Department of Defence and other authorised users with

very accurate and precise GPS position, velocity and time information. The Standard

Positioning Service or C/A code provides civil and other unauthorised users with limited GPS

accuracy. The scheme designed to limit GPS accuracy received by unauthorised users is

called Selective Availability (S/A). As stated above, S/A is imposed by the USA Department

of Defence by manipulating the navigational messages and introducing timing errors. The

result is to reduce resolution to approximately 100 metres. This resolution is inadequate for

the purposes of Precision Farming.

4.7 Differential Global Positioning System (DGPS)



To overcome the problem of a 100m resolution imposed by selective availability, a system

called Differential Global Positioning System (DGPS) can be employed.

MobileGPS reciever

StationaryGPS reciever

VHFTransmitter

Reference Station Farmer’s Field

CalculatedGPS Errors

VHFReciever

GPS Satellites

VHF Signal

11000miles

11000miles

Figure 4.6. - Differential Global Positioning System

With the Differential Global Positioning System, two GPS receivers are used, one stationary

and located at the reference point and the other mobile on the vehicle in the field. The

stationary receiver is placed in a known position. When the stationary GPS receiver

calculates a position fix from satellite data which has be down-graded by S/A, it compares the

GPS calculated position with the actual known position of the receiver contained in its

computer’s memory. By comparing the true position with the GPS calculated position, the

computer can work out a correction factor which will convert the GPS calculated position

into the true known position. The correction factor is transmitted to the mobile GPS receiver

in the field via a VHF radio link. The concept works, simply because the satellites are at such

an altitudes that any errors measured by the static GPS receiver will be almost exactly the

same as the mobile receiver. Both GPS receivers, which must be in the same area, are

therefore, receiving the same data and errors from the satellites. However, the mobile GPS



receiver has no reference point from which to calculate errors, by the very fact that it is

mobile, but does have the correction factor transmitted from the reference station. Therefore,

GPS resolution is reduced from 100m (Selective Availability) to a level which is acceptable

for Precision Farming.

It is known that the length of the distance that separates the base station and mobile unit has

an effect on the ability to differentially correct the mobile unit, resulting in reduced accuracy,

Rupert et al. (1994). The closer the mobile receiver to the base station, the more effective

differential corrections will be in removing the error in the mobile unit. On average, the error

increases about 0.6m for every 100 kilometres increase in distance between reference point

and mobile unit.

4.8 Positioning Resolution

Much research has been presented on the resolution that can be obtained from GPS. Murphy

et al. (1994) suggest that the accuracy obtained from GPS is price dependant - the more

expensive the GPS receiver, the more precise the position fixes. In a survey of GPS receivers

carried out in 1993, it was demonstrated that to obtain an accuracy of 10m with Differential

GPS would cost around $5,000. However, in this instance the purchase of the differential

signal was an additional cost. Cain et al. (1996) state that current positioning systems being

utilised for agricultural purposes offer a +/- 2 to 3m resolution.

Using a 6 channel GPS receiver for the mobile unit and an identical unit for the reference

station, Reitz et al. (1996) state that if the following demands are met, the deviation from the

true path of combine is less than 3m:

- At least four satellites are received

- Both mobile and stationary GPS receivers use the same satellites for at least 10 seconds

- The dilution of precision for the constellation of satellites must be below 2

- The data used to correct Selective Availability is not older than 2 seconds.

Rupert et al. (1994) provide a good summary of the typical error components and their

respective magnitudes. These error sources are illustrated in Table 4.1. All error sources are

squared, summed and square root of the sum taken. The resulting number is the User



Equivalent Range Error (UERE). Rupert et al. (1994) state that the DoP is of major concern,

as the UERE is multiplied by the DoP to give the positioning accuracy.

Table 4.1 - Typical Effect of major errors sources on GPS Horizontal Error

Segment Error Source Stand Alone Error (m) Error After Differential

Corrections (m)

Individual Segment Sources:

Space Satellite Clock 15 0

Control Ephemeris 25 0.4

Propagation Link:

(a) Ionosphere 5 1.2

(b) Troposphere 0.5 0.4

(c) Multipath 0.8 1

User Receiver Noise and Bias 1.3 1.6

Summary of Errors Sources:

User Range Error (UERE) 29.6 2.3

DoP 3 3

Processing 0 0.05

Total Error: 88.8 6.95

Note : Total Error = UERE x DoP + Processing

Source: Rupert et al. (1994)

4.8.1 The effect of satellite geometry on GPS accuracy



To quantify the effect random errors and Dilution of Precision (Satellite Geometry) have on

the nominal accuracy of the measured position of the combine whilst harvesting a field, a

number of tests were carried out.

In all radio navigation systems the measurement of position is influenced by various types of

error which have been discussed earlier. As a result, a series of measurements taken at one

stationary location will generally form a cluster of points around the position.

A six channel GPS receiver was removed from a yield mapping combine and placed in a

stationary position close to the differential reference station. Position data relating to WGS-

84 co-ordinates was recorded over a 24 hour period together with information on satellite

geometry.

The relative accuracy of the positions was calculated using the 2 drms method, Anon (1991).

The results of the data analyses are summarised in Table 4.2 and Figure 4.6 for a satellite

constellation consisting of 4 satellites which provides 3 dimensional location. The nominal

accuracy obtained from the Differential Global Positioning System with a Dilution of

Precision (DoP) of 1 to 1.99 was 6.0m for R67 of the position readings and 11.9m for R95 of

the position readings. The resolution obtained from a satellite constellation giving a Dilution

of Precision of 2 to 2.99 decreased by 28% to 7.7m and 15.4m, for R67 and R95 of position

readings, respectively. The nominal accuracy was further reduced with an increase in Dilution

of Precision. However, the value obtained for 2 drms stabilised at DoP 4 to 4.99. Up until

DoP 4 to 4.99, the movement of the mid value was stable even though the nominal accuracy

was decreasing. However, after DoP 4 to 4.99 the mid value becomes unstable as large

movements in horizontal distance were experienced.

Table 4.2 - The effect of satellite geometry on the accuracy of position information from

differential GPS - 3 dimensional

DGPS resolution for different values of Dilution of Precision



3 Dimensional (1992)DoP Number Min value Max value Movement from % of samples

of samples (m) (m) (m) (m) mid value (m)x y x y x y R67 R95

1-1.99 18867 22 85 61 141 0.0 0.0 6.0 11.92-2.99 3785 22 108 62 152 -1.1 0.4 7.7 15.43-3.99 798 24 100 63 163 -1.4 1.7 11.1 22.24-4.99 310 0 69 86 163 -2.5 0.7 18.0 36.05-5.99 57 25 98 65 167 -2.9 3.9 20.7 41.46-6.99 72 27 100 61 167 -4.5 4.4 18.7 37.47-7.99 72 12 95 81 150 0.5 -6.2 17.0 34.08-8.99 23 30 95 67 158 -4.0 9.3 17.6 35.29-9.99 11 13 134 39 182 -16.0 20.5 14.3 28.5

10-10.99 11 13 113 82 141 7.8 -3.1 24.3 48.6

0 10 20 30 40 50 60 70 80 90 10070

80

90

100

110

120

130

140

150

160

170

180

DGPS Accuracy for different values of Dilution of Precision3 Dimensional (1992)

12345678910

Value ofDilution ofPrecision

1

2

3

4

5

6

7

89

10

Figure 4.7 - The effect of satellite geometry on the accuracy of position information from

differential GPS

Therefore, position fixes with DoP of less than 4 show stable characteristics in terms of mid

point movement, with a slight decrease in nominal accuracy. Positions fixes with a DoP

greater than 4 show an increase in mid point movement, but the resolution is reasonably stable

although it has decreased by approximately 200% to 20.7m and 41.4m for R67 and R95 and

position readings.



In the above example, it would be recommended that position fixes with a DoP of greater

than 2 should be deleted in order to ensure a reasonably accurate position fix given the

technology being utilised within the GPS receivers.

Table 4.3 and Figure 4.8 illustrate the distribution of DoP values whilst harvesting a field. If

values for a DoP of 2 or less were acceptable, then for Oak Field (1993) 98% of the total

position fixes would be within acceptable limits. Similarly for Oak Field (1994) 94 % would

be within a pre-determined limit.

Table 4.3 - Satellite Geometry - Dilution of Precision - recorded for Oak Field (1993/1994)

whilst harvesting the field

Percentage of readingsDilution ofPrecision

Oak Field 1993 Oak Field 1994

1-1.99 90..54 84.192-2.99 7.15 10.183-3.99 0.31 2.464-4.99 1.20 1.565-5.99 0.29 0.646-6.99 0.13 0.517-7.99 0.16 0.288-8.99 0.05 0.009-9.99 0.13 0.13

10-10.99 0.00 0.0011-11.99 0.00 0.0012-12.99 0.00 0.0013-13.99 0.00 0.03

Table 4.4 shows the effect satellite geometry has on the accuracy of GPS fixes in a 2

dimensional situation. In these circumstances, the GPS receiver can only receive data from a

maximum of three satellites either due to some obstruction covering the GPS antenna, or lack

of satellites at that particular moment in time. The three satellites give a 2-dimensional fix as

opposed to four satellites giving a 3-dimensional fix.



0

2

4

6

8

10

12

14

Time

Dilu

tio

n o

f P

reci

sio

n

Oak Field 1993 Oak Field 1994

Note - Local reference station used to correct mobile GPS receiver

Figure 4.8 - Satellite Geometry - Dilution of Precision - recorded for Oak Field (1993/1994)

whilst harvesting the field

Table 4.4 - The effect of satellite geometry on the accuracy of position information from

differential GPS - 2-dimensional

DGPS resolution for different values of Dilution of Precision(2 dimensional)

DoP Number Min value Max value Movementfrom

% of sample

ofsamples

mid point

x y x y x y R67 R951-1.99 945 94 237 39 106 0.0 0.0 11.8 23.72-2.99 4994 119 337 43 109 6.5 -2.8 22.4 44.73-3.99 2522 71 235 48 106 -2.4 -0.2 16.8 33.54-4.99 1666 136 259 39 96 10.7 -0.8 21.0 41.95-5.99 2077 122 350 257 117 -15.0 1.5 20.6 41.26-6.99 527 137 246 43 102 10.8 1.2 24.9 49.77-7.99 459 104 283 48 126 -0.8 -0.2 23.6 47.38-8.99 178 130 262 46 108 5.1 0.7 28.6 57.29-9.99 209 93 273 48 117 -15.6 4.3 33.6 67.2

10-10.99 191 125 241 56 122 1.2 -2.2 29.1 58.111-11.99 152 68 220 54 128 -21.1 1.3 29.7 59.412-12.99 87 88 281 52 148 10.3 3.2 36.5 73.013-13.99 44 85 210 63 171 -3.2 7.7 37.6 75.314-14.99 44 141 281 56 135 29.9 -14.5 34.2 68.515-15.99 23 122 259 52 76 -1.5 -8.8 40.7 81.5



The resolution obtained from a 2-dimensional fix has reduced by some 96%. With an increase

in DoP there is also a reduction in accuracy obtained from the constellation of satellites.

Therefore, in harvesting situations where navigational messages can only be accessed from 3

satellites, position fixes are not reliable enough to reflect the actual position of the combine

within the field. The data should, therefore, be deleted.

4.9 Evaluation of DGPS systems

To evaluate the precision and accuracy obtained from a number of DGPS systems used in

commercial agriculture, a series of tests were established, Saunders et al. (1996).

The specification of the three commercial GPS systems under test was as follows:

System 1 - A 6 channel GPS receiver using differential corrections from a national radio

signal giving a claimed accuracy of 1 metre.

System 2 - A 6 channel GPS receiver also using differential corrections from a national radio

signal, but with a reduced claimed accuracy of 5 metres.

System 3 - A 6 channel GPS receiver, identical to system 1, using a differential correction

signal broadcast from a geo-stationary satellite.

4.9.1 Static Accuracy

This test was used to illustrate the overall accuracy of each system. The GPS receivers were

placed around a known base point which was surveyed from a known Ordnance Survey (OS)

benchmark. A two metre spacing was used between each DGPS system in order to avoid any

interference between antennae. All systems were switched on and 30 minutes was given for

the systems settle and to allow the almanacs to be updated, Rupert et al. (1994). Position

data relating to WGS-84 co-ordinates were recorded in a static situation for 15 minutes.

In the analyses of data, comparative accuracy and Euclidean distance were computed. The

former is the indicator of ninety fifth percentile horizontal error about the mean of all data



points. The latter is the distance between the established base point and the average of all

data points recorded.

The results of the analyses are shown in Table 4.5 and Figure 4.9. System 1 was the most

precise with a “R95” of 1.28m, whilst system 3 was the most precise with an Euclidean error

of 3.8m.

Table 4.5 - Static accuracy - R95 and Euclidean distances for DGPS

All distance (m) System 1 System 2 System 3

R95 1.28 4.45 2.54

Euclidean error 5.6 5.2 3.8

507977 507978 507979 507980 507981 507982 507983 507984

Eastings (m)

235319

235320

235321

235322

235323

235324

235325

235326

235327

Nor

thin

gs (

m)

System 1

All coordinates in OSGBReference Point

Mean value

Figure 4.9 - Static accuracy - R95 and Euclidean distances for DGPS



System 2

All coordinates in OSGBReference Point

Mean value

235310.00 235315.00 235320.00 235325.00 235330.00 235335.00 235340.00

Eastings (m)

507970.00

507975.00

507980.00

507985.00

Nor

thin

gs (

m)

507980 507981 507982 507983 507984 507985 507986 507987

Eastings (m)

235317

235318

235319

235320

235321

235322

235323

235324

235325

235326

235327

235328

Nor

thin

gs

(m)

All coordinates in OSGB

System 3

Reference Point

Mean value

Figure 4.9 cont. - Static accuracy - R95 and Euclidean distances for DGPS

4.9.2 Static Stability

The purpose of the test for cold settling time, was to determine the time required to receive a

full and stable DGPS signal for each system. Using the previously established base point, the

GPS receivers were positioned as in the static accuracy test. The systems were switched on



(cold) and the time required to get the full signal was recorded. The systems were then run

for a few minutes.

Table 4.6 displays the “cold settling” times, which is the time required to obtain a DGPS

signal and the time necessary for each system to achieve ten consecutive points within a ten

metre radius of the base point. This is a measure of how long the operator must wait from

switching on the GPS before field operations can be undertaken. System 2 showed the fastest

settling time, followed by system 3 and finally system 1. However, all systems fall within an

acceptable time for an operator to wait before commencing work.

Table 4.6 - Time required to reach various states for three different systems

Time to get fullDGPS signal (s)

Time to stabilise inten metre radius (s)

Total settling time (s)

System 1 37 43 80System 2 21 6 27System 3 28 38 64

Figure 4.10 illustrates how Euclidean distance and time relate for the three DGPS system.

Euclidean distance against time for 'cold settling'

0

5

10

15

20

25

30

35

40

0 25 50 75 100 125 150 175 200 225Time (s)

Eu

clid

ean

dis

tan

ce (

m)

System 1 System 2 System 3

Figure 4.10 - Euclidean distance against time for “cold settling”



4.9.3 Dynamic Repeatability

The dynamic repeatability of any DGPS system, used for yield mapping, is of great

importance to ensure that yield data is recorded in strips that do not cross over and thus

impair mapping effectiveness. Clark et al. (1994) examined the nature of error associated

with a C/A code GPS receiver with differential corrections from a moving vehicle. Using the

equipment specified, it was concluded that the maximum average error was less than 2m, with

a maximum point trajectory error of around 11m.

To test the dynamic repeatability of the three DGPS systems being evaluated, all three GPS

antennae were mounted on the roof of a vehicle and the systems were set to record

continuous data. The vehicle was driven at a constant speed around a pre-determined circuit.

This circuit was repeated three times for each test. The dynamic test was then repeated with

the differential corrections turned off to determine the dynamic repeatability of the systems in

stand-alone GPS mode.

Table 4.7 - Dynamic Repeatability - Euclidean distances for DGPS

All distance (m) System 1 System 2 System 3

Maximum Euclidean Error 10 18 5

System 1


507980.00 508030.00 508080.00 508130.00 508180.00

Easting (m)

235150.00

235200.00

235250.00

235300.00

235350.00

Nor

thin

g (m

)

- Loss of Differential signal on third circuit

507950.00 508000.00 508050.00 508100.00 508150.00

Eastings (m)

235150.00

235200.00

235250.00

235300.00

235350.00

235400.00

235450.00

No

rthi

ngs

(m)

System 1


System 1 - no differential correction System 1 - with differential correction

Figure 4.11 - Dynamic Repeatability



System 2


507950 508000 508050 508100 508150

Eastings (m)

235150.00

235200.00

235250.00

235300.00

235350.00

235400.00

235450.00

235500.00

Nor

thin

gs (

m)

System 2


508000.00 508050.00 508100.00 508150.00

Eastings (m)

235150.00

235200.00

235250.00

235300.00

235350.00

Nor

thin

gs (

m)


507950.00 508000.00 508050.00 508100.00 508150.00

Eastings (m)

235150.00

235200.00

235250.00

235300.00

235350.00

235400.00

235450.00

Nor

thin

gs (

m)


- Loss of Power on Logging Computer

507980.00 508030.00 508080.00 508130.00 508180.00

Easting (m)

235160.00

235210.00

235260.00

235310.00

235360.00

Nor

thin

g (m

)



Figure 4.11 cont. - Dynamic Repeatability

The results of the dynamic repeatability tests are illustrated in Table 4.7 and Figure 4.11.

From the plots obtained from the logged data it can be seen that system 1 and system 3

exhibited a stable repeatable signal which was slightly distorted by trees and buildings. This

was probably a result of a reduction in the number of “visible satellites” which in turn

influence satellite constellation. However, during the third circuit of system 1, the differential

signal was lost and not regained for the remainder of the test. It was concluded that system 2

was not very accurate, as large shifts in horizontal distance were experienced for all three

circuits. In all three systems, as expected, the lack of differential correction signal affected the



accuracy of the system enormously. The maximum Euclidean error was experienced by

system 2, followed by system 1 and 3 respectively.

4.10 Filters for removing position errors

The deletion of raw yield data containing position errors is well documented by Rands (1995).

The research formed a basis on which an expert filter for improving the quality of yield

mapping data was developed and tested in conjunction with Massey Ferguson.

The filter deals with two aspects of position errors: (i) points outside the field and (ii) points

too far apart; both of which are caused by errors in GPS and differential signals. With the

knowledge of the combine’s maximum speed, the time interval between points and the

expected resolution of the GPS signals, Rands modelled the greatest distance expected

between two points. Using this, any position that fell outside the model limits was marked

and deleted. Aspects relating to other forms of error are left for the user to specify the

maximum and minimum expected values. For each line and each variable, the value is

compared with these limits and anything outside is again marked and deleted. As a result of

his research, Rands concluded that it is possible to remove errors and improve the quality of

the raw data before interpolation into a yield map.

4.11 Yield Mapping Data

For the purposes of yield mapping, the combine harvester is fitted with a computer system

which records the necessary data on yield and position information to generate a yield map in

the farm office. The data from the combine is stored in a compressed format as limited

memory storage is available on the vehicle. Once the compressed file, denoted by extension

“.LSI”, has been entered onto the farm office computer, it is unpacked into a raw data file,

denoted by the extension “.RAA”. A sample is taken and stored at every 1.2 seconds in the

Datalog Module while the combine remains in the harvesting mode or condition. The criteria

for harvest condition is defined as:

• forward speed must be greater than 1km/hr

• the threshing mechanism must be engaged and running at full rpm.



• the header must be engaged

• the header must be below 50cm

4.11.1 .RAA Data Formats

An example of a .RAA raw data file is shown in Table 4.8. Each line of data represents one

sample which was recorded and stored after a time period of 1.2 seconds on board the

combine harvester.

Table 4.8 - Example of a raw data file (.RAA) -

recorded by a Massey Ferguson Combine Harvester

(Park Field - Shuttleworth Farms 1992)

1 2 3 4 5 6 7 8 9

N5205.170,W00021.731,06.0,SAT1203,000,000,02,4,3N5205.171,W00021.733,06.3,SAT1203,000,000,02,4,3N5205.166,W00021.734,06.5,SAT1203,000,000,02,4,3N5205.167,W00021.732,06.4,SAT1203,000,000,02,4,3N5205.171,W00021.734,06.2,SAT1203,000,000,02,4,3N5205.172,W00021.736,06.4,SAT1203,000,000,02,4,3N5205.173,W00021.738,06.3,SAT1203,000,000,02,4,3N5205.174,W00021.741,06.2,SAT1203,000,000,02,4,3N5205.172,W00021.749,06.3,SAT1203,000,000,02,4,3

The .RAA file format contains the following information:

1. Latitude in *DDmm.mmm where

* indicates the hemisphere (N = North, S= South)

DD = degrees

mm.mmm = decimal minutes

2. Longitude in *DDDmm.mmm where

* indicates either West (W) or East (E) of Greenwich

DDD = degrees

mm.mmm = decimal minutes

3. Yield in tonnes per hectare to 1 decimal place



4. Harvest time in DDDHHmm where

DDD = the day the sample was taken

HHmm = the time the sample was taken in hours and minutes

5. East/West ground speed in metres per second

6. North/South ground speed in metres per second

7. Geometric Dilution of Precision

8. Satellite mode or number of satellites used to calculate the position4 indicates 3 dimensional3 indicates 2 dimensional

9. Navigation mode2 indicates no differential GPS3 indicates differential corrections were being received

4. positioning systems for precision farming

Documents