1 Introduction

Using Global Navigation Satellite System, (GNSS) e.g. GPS systems, for surveying or machine control comes with the consideration of the accuracy and precision of the GNSS receiver’s position. The basic idea of GNSS systems is establishing a satellite network in which each satellite sends a signal at a defined time to receivers. The distance from the satellite to the receiver can be calculated, by measuring the time difference from the transmitter to receiver. Using at least 4 satellites simultaneous the 3D Position of the receiver (vertical and horizontal) can be calculated, if the position of each satellite is known. The accuracy of GNSS Systems is influenced by the realization of the needed infrastructure causing the influences on the transmitted signals that make the position calculation possible. Satellites used for GNSS Systems are moving at approx. 4 km per seconds (with respect to the earth) under varying conditions. Due to the movement of the receiver and the transmitter we need to take a look at the factors that determine the accuracy of GNSS Systems.

2 Atmospheric Influences

2.1 Ionosphere

The signal transmitted from the satellites travels through the different layers of the atmosphere. Some layers of the atmosphere have an impact on the speed of the signal. Normally, as any electronic signal, GNSS signals travel with the speed of light. Knowing that the speed of light is a physical constant it should never change, so why is the GNSS signal slowed down? The ionosphere is a layer of electrified particles at an altitude of 130 to 200km. The speed of light is constant, but only in a vacuum. Having to travel through several kilometers of a denser layer slows down the GNSS signal, which will result in an error in the calculation of the distance from the satellite to the receiver. A way to reduce the ionosphere error is to use two different frequencies of the GNSS Signal, and a receiver that is able to pick up both frequencies simultaneously. The fact is that signals traveling through the ionosphere are slowed down in relation to their frequencies. It is possible to eliminate most of the ionosphere error, using the deviation in the difference of speed in both signals. This method is implemented in most GNSS receivers used for surveying or machine control. Receivers with lower specifications, often use a standardized model given an average day under average conditions, for the ionospheres error.

2.2 Troposphere

Travelling closer to the earth the signal passes through the troposphere at an altitude of 10-12 km. The speed of the signal is slowed down in relation to temperature, pressure and humidity. It is possible to roughly estimate the influence of the troposphere on the speed of the signal by a model but not by measurements.

3. Geometry of the satellite constellation

Along with accuracy of the position, the precision is also important in understanding the limitations of GNSS Systems.

Fig. 1.1 Precision and accuracy

Simply speaking, if all available satellites are close together, the geometric constellation is bad. If the satellites are far apart from each other, the geometry is considered to be good. The following example gives an easy understanding as to the importance of the satellite geometry and how the error in the measured distance effects the calculated position in relation to the geometric constellation. The orange and green lines show the range of error in the distance measurement to the satellite (e.g. caused by atmospheric influences). Having a good satellite constellation in Figure 1.1 gives a high precision, symbolized by the intersection of the two circles.

Figure 1.2 shows an example of a bad satellite geometry having a much lower precision.

Fig. 1.2 Good satellite constellation Fig. 1.3 Bad satellite constellation

The following terms are used to describe the geometry: Geometric dilution of precision (GDOP) or Dilution of precision (DOP). Using receivers that calculate and select the satellites with the best GDOP value or even better, using receivers that uses the maximum number of visible satellites minimizes the GDOP value.

4. Orbital Error

To be able to calculate the position of the receiver the position of the satellites must be known.The satellites are positioned on precise orbits, however, due to gravitational forces, a deviation from these orbits can occur. The orbit of the satellites are constantly monitored and controlled by the ground segment of the satellite operator. The updated data is transmitted to the receiver in the ephemeris data broadcasted from the satellites within the navigation message. Still there are delays between the measurements of the real position and the transmitted position, which causes errors in the distance measurements.

5. Satellite Clock Error

Even though satellites use precise atomic clocks for the timing of the transmission, still the bias, drift and drift rate are changing and monitored by the ground segment. The parameters are broadcasted in the navigation message.

6. Phase Cycle Slips

The GNSS Signal is blocked for a short time, e.g. blocked by a tree. The receiver misses a part of the signal and calculates the distance to the satellite too short.

Fig. 1.4 Phase Cycle Slips

7. Multipath

This is the reflection of the signal on surfaces like buildings. When picking up the reflected signal the distance from the satellite to the receiver is calculated too long.

Fig. 1.5 Multipath

8. Receiver Noise

The receivers electronic components generates noise that affects the accuracy of the position by contaminates the observations.

9. Horizontal versus Vertical Accuracy

Using only satellites above the horizon (signals from satellites below the horizon are blocked by the earth), the geometric constellation to determine the horizontal position (Figure 1.3) is much better than for the vertical position (Figure 1.4). The vertical accuracy is about 1.5 times worse than the horizontal accuracy.

Fig 1.6 Horizontal Geometry, Plane View Fig.1.7 Vertical Geometry, Cross View

10. Total error

This is only an approximation and the numbers can differ significantly depending on the circumstances.

11. Conclusion

By having an approximately position accuracy about 10 meters horizontal and about 15 meters vertical it is necessary to establish further infrastructure, to eliminate errors. Some options for this infrastructure are: GNSS augmentation, Differential Global Positioning System, GNSS Basestation, NTRIP.

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The fluctuation of the receiver's position is caused by the moving satellites and the alternating impacts on the signal

Fig.1.8: Fluctuation GNSS Position