##### 05 Jun 2018 |

Research article |

Aerospace & Land Transportation

# Using GNSS in Space: Challenges

This follows the recent article entitled *Satellites also use GPS*. It explains the differences between spatial and terrestrial applications of GNSS signals in more detail, namely:

- Receiver position relative to the GNSS satellite antenna, which greatly affects the power received;
- The distances involved, which also affect the power received;
- Geometry, which affects the final accuracy;
- Dynamics, which require greater calculation and adaptation capacities of the receiver.

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## Antennas Calibrated for Earth

A GNSS satellite sends signals towards Earth, in other words, focusing transmission power in the shape of a cone of a certain angle, as shown in Figure 1. The angle varies depending on the constellation and satellite generation, but is about 32° for GPS. This emission is called the main lobe. Earth is covered with an angle of about 27°, so a portion of the main lobe is spread equally around Earth, covering the atmosphere for aeronautical applications and even beyond, reaching low altitudes known as LEO (Low Earth Orbit).

Outside this 32° zone, signals are still being emitted, but they are much weaker—these are called the side lobes—as can be seen on the diagram on satellite antenna emission in Figure 2. The diagram shows more or less regular side lobes, varying depending on the signals and the satellites. However, all emission diagrams will show a significant gain at angles smaller than ± 16°, which decreases rapidly beyond this radiation aperture [3].

Therefore, one consequence for a GNSS receiver in space is that if it is not located in the main transmission cone of a GNSS satellite, the power of the received signal will be much lower, from 15 dB to 40 dB below normal levels. This will require many more calculations to detect and process the signals. And this is even more problematic knowing that GPS signals, projected by satellites at about 480 W, are received on Earth at a power of −160 dBW (−130 dBm) in optimal conditions. The power received on Earth corresponds to about 10^{–16} W, making it difficult to compare to the power of a signal received by a mobile phone, which is in the range of nanowatts (10^{−9} W) or picowatts (10^{–12} W), for example.

**Much Greater Distances to Cover**

A second important difference in space is the distance travelled by the GNSS signal. For example, a GNSS signal travels distances from 19^{ }000 km to 28^{ }000 km, varying according to the constellation and satellite elevation as seen from Earth. Such distances cause power losses of about 180 dB, that is, the power of the received signal is 10^{18} times lower than when emitted by the satellite. The loss L caused by distance is proportional to the square of the carrier frequency f used and the square of the travelled distance d :

*c* being the propagation speed. Therefore, for spacecraft in High Earth Orbit, the distance can be multiplied by a factor of 2, 3, … up to 16 for missions around the Moon (located at about 400^{ }000 km from Earth), which means a signal that is 4, 9, …, 256 times weaker than normal or, in dB: 6, 9, … 24 dB.

However, this problem does not generally occur for low-orbit satellites, where a sufficient number of signals is almost always received with adequate power.

**Highly Unfavourable Geometry**

To determine its position, a receiver calculates its distance from each satellite by measuring the signal propagation delay and then solves a system of equations. Take a simple two-dimensional example (Figure 3): if we know the distance (*d*_{1}) separating us from a given source (S1), then we know that we are located on a circle centred on this source. With a second source (S2), we obtain a second circle, which intersects the first one in two points (A and B), thus reducing the number of possible positions to two. A third measurement (*d*_{3}) will remove any ambiguity. This is the basic principle of trilateration.

In satellite navigation, distances are calculated by measuring signal travel time. This measurement is not perfect and always contains errors due to the environment or the technology used (ionosphere, troposphere, noise, receiver errors, etc.). Let’s compare two cases, the first where the sources (satellites) are placed in different areas (Figure 4 a). Each measurement involving two satellites shows some uncertainty, as seen in Figure 4 b), which implies a certain level of uncertainty regarding the mobile’s position. Now, let’s take a second case where the source signals come from almost the same direction (Figure 4c), which happens when a spacecraft is located at a very high orbit. Figure 4 d) shows that when distances present the same uncertainty, the positional uncertainty will be much greater, especially on the plane parallel to the satellite orientation. That is why even if four satellites are enough to calculate a position in principle, a GNSS receiver uses more to obtain more measurements and improve its accuracy.

Mathematically, positional precision is the precision of distance measurements multiplied by a geometric factor, called dilution of precision (DOP). On Earth, a good DOP is less than 3 (with a full view of the sky), while a DOP above 10 results in poor accuracy—this is particularly the case in city centres where large areas of the sky are blocked by buildings, for example. In space, it has been shown that for high Earth orbit missions, the DOP can reach the 100s or even exceed 1000 [4]. In other words, even with a distance measurement accuracy of 1 m, the positional accuracy could be anywhere from about one hundred metres to kilometres. This explains the need to reduce distance measurement errors as much as possible (which will be possible with the new GNSS signals) and to maximize the number of usable satellites (which will also be possible by using all available constellations). Of course, it will be impossible to obtain the same precision in space as on Earth with a GNSS receiver.

**Much Larger Dynamics**

The last important difference is mobile dynamics, or signal dynamics. A GPS satellite rotates around the Earth at a speed of about 4 km/s, but for a static user on Earth, the relative speed will be at most 900 m/s. This relative speed causes an offset in emission frequency due to the Doppler effect, a maximum of 5 kHz in the case of terrestrial applications using a static receiver. This offset must be estimated by the receiver, and the larger it is, the longer it takes for the receiver to detect the signals. Another important parameter is the change rate of the Doppler shift, which remains within 1 Hz/s for a static user, and 10 Hz/s for a car, for example. The stronger the dynamics, the more difficult it will be to detect weak signals, and the design of the receivers will be strongly influenced by these parameters.

On the other hand, for satellite applications, it is quite a different matter and depends on the orbit. In low orbit, satellite velocities are very high, up to 10 km/s, resulting in Doppler shifts of up to 60 kHz, and very rapid changes that can increase Doppler shifts to up to 70 Hz/s. In high orbit, speeds are more limited (e.g.: 3 km/s in geostationary orbit), resulting in higher Doppler shift values than on Earth, but less than in low orbit [4].

Designers of receivers are in luck because, in low orbit, where dynamics are greater, the signal strength is generally adequate; in high orbit, where the signals received are very weak, the relative dynamics are weak. As a result, there are virtually no cases where power is very low and dynamics very strong, since in such cases the signals would be even more difficult to detect and use.

**Research at ÉTS**

It is within this context that LASSENA is working on GNSS signal detection and processing in space. There are many challenges, because as we have seen, in the future, the goal will be to use a maximum of signals from different constellations, each signal having its own specificities, and these signals could be very weak or have very strong dynamics. These new space GNSS receivers will require very powerful flexible architectures and highly efficient algorithms.

## Additional InformationMore information on GNSS uses in space

- NASA MMS Mission: https://www.nasa.gov/feature/goddard/2016/nasa-s-mms-breaks-guinness-world-record
- Real radiation pattern of GPS antennas: https://www.lockheedmartin.com/us/products/gps/gps-publications.html
- More on GNSS applications in space: http://itsnt.recherche.enac.fr/index.php/download_file/view/196/174
- ÉTS GFS Project (GNSS For Space):https://lassena.etsmtl.ca/spip.php?rubrique233

#### Jérôme Leclère

Jérôme Leclère is a postdoctoral researcher at the LASSENA laboratory. Previously, he obtained his Ph.D. at EPFL (Switzerland) on the acquisition of GNSS signals. He was also involved in the development of GPS and GNSS receivers on FPGAs.

Program : Aerospace Engineering

Research laboratories : LASSENA – Laboratory of Space Technologies, Embedded Systems, Navigation and Avionic

#### René Jr Landry

René Jr Landry is a professor in the Electrical Engineering Department at ÉTS and the Director of LASSENA . His expertise includes embedded systems, navigation, and avionics.

Program : Electrical Engineering

Research laboratories : LACIME – Communications and Microelectronic Integration Laboratory LASSENA – Laboratory of Space Technologies, Embedded Systems, Navigation and Avionic

Research laboratories :