High accuracy GNSS based navigation in GEO

Acta Astronautica 136 (2017) 332–341

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High accuracy GNSS based navigation in GEO

MARK

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Vincenzo Capuano , Endrit Shehaj, Paul Blunt, Cyril Botteron, Pierre-André Farine École Polytechnique Fédérale de Lausanne (ESPLAB), Switzerland

A R T I C L E I N F O

A BS T RAC T

Keywords: GNSS GPS Galileo GEO Navigation Orbit Determination

Although significant improvements in efficiency and performance of communication satellites have been achieved in the past decades, it is expected that the demand for new platforms in Geostationary Orbit (GEO) and for the On-Orbit Servicing (OOS) on the existing ones will continue to rise. Indeed, the GEO orbit is used for many applications including direct broadcast as well as communications. At the same time, Global Navigation Satellites System (GNSS), originally designed for land, maritime and air applications, has been successfully used as navigation system in Low Earth Orbit (LEO) and its further utilization for navigation of geosynchronous satellites becomes a viable alternative offering many advantages over present ground based methods. Following our previous studies of GNSS signal characteristics in Medium Earth Orbit (MEO), GEO and beyond, in this research we specifically investigate the processing of different GNSS signals, with the goal to determine the best navigation performance they can provide in a GEO mission. Firstly, a detailed selection among different GNSS signals and different combinations of them is discussed, taking into consideration the L1 and L5 frequency bands, and the GPS and Galileo constellations. Then, the implementation of an Orbital Filter is summarized, which adaptively fuses the GN1SS observations with an accurate orbital forces model. Finally, simulation tests of the navigation performance achievable by processing the selected combination of GNSS signals are carried out. The results obtained show an achievable positioning accuracy of less than one meter. In addition, hardware-in-the-loop tests are presented using a COTS receiver connected to our GNSS Spirent simulator, in order to collect real-time hardware-in-the-loop observations and process them by the proposed navigation module.

1. Introduction Although in the last decades, significant improvements in efficiency and performance of communication satellites have been achieved, it is expected that the demand for new platforms in Geostationary Orbit (GEO) will continue to rise [1]. At the same time, with the larger request of GEO satellites, the number of available orbital slots in such orbit is significantly decreasing. On-Orbit Servicing (OOS) may offer the possibility of re-fueling and/or even repairing some existing expensive GEO satellites otherwise nonoperational, and de-orbiting the ones that cannot be reused. In this context, both for new GEO platforms and for the ones to be used for OOS in GEO, GNSS-based navigation is no doubt becoming a viable and attractive alternative, offering many advantages over present ground based methods. Indeed, GNSS, originally designed for land, maritime and air –applications, has been already successfully used as navigation system in Low Earth Orbit (LEO) minimizing ground operations and reducing the associated costs. However, its further utilization for navigation of geosynchronous satellites and in general

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Corresponding author. E-mail address: vincenzo.capuano@epfl.ch (V. Capuano).

http://dx.doi.org/10.1016/j.actaastro.2017.03.014 Received 27 October 2016; Accepted 12 March 2017 Available online 18 March 2017 0094-5765/ © 2017 IAA. Published by Elsevier Ltd. All rights reserved.

above the GNSS constellations is still at the research stage and has not yet been fully accepted by the GNSS community as well as by the spacecraft designers, manufacturers and operators. Several research papers have already presented a feasibility study of GNSS for positioning and timing determination in GEO, highlighting different aspects. The concept was already introduced in [2,3] and later further investigated in other studies. For instance, in [4], the effect of the GPS constellation availability, antenna gain patterns and GPS receiver clock stability on position and timing accuracies in GEO are investigated. While more recently in [5], a feasibility of GNSS receiver and orbital filter for autonomous orbit determination is presented, reporting the main expected performances under different missions, environment and receiver architectures. Results of tests performed with the TOPSTAR 3000 receiver in a GEO configuration are presented in [6], while the Navigator space-qualified GPS receiver, developed at the at the NASA Goddard Space Flight Center (GSFC) is described in [7]. However, so far, maybe the only source that presents experimental results obtained collecting real GNSS signals in GEO is [8], where the experimental results from the SGR-GEO GPS receiver carried on board

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the GIOVE-A Galileo pathfinder satellite are described. Following our previous studies of GNSS signal characteristics in Medium Earth Orbit (MEO), GEO and beyond [9,10], in this research we specifically investigate the processing of different GNSS signals in a GEO mission, through an orbital filter, in order to achieve the best possible performance with an autonomous GNSS-based navigation system. Note that while in this paper we focus on the GNSS use for orbit determination only (position and velocity of the spacecraft), GNSS can also be used for attitude determination of the spacecraft [11]. We refer the interested reader to [11] or to our previous study [12]. The rest of the paper is organized as follows. Section 2 describes the assumed orbit of the GNSS receiver and all the assumptions about the GNSS constellations and signals models. A detailed selection among different GNSS signals and different combinations of them is discussed, taking into consideration the L1 and L5 frequency bands, and the GPS and Galileo constellations. Section 3 presents the simulated GNSS signal characteristics in GEO, in terms of signal power at the receiver position, Doppler shift and Doppler rate affecting the signals, availability and relative geometric dilution of precision (GDOP). Section 4 summarizes the implementation of an Orbital Filter, which adaptively fuses the GNSS observations with an accurate orbital forces model. Finally, in Section 5 the navigation performances achievable by processing the selected combinations of GNSS signals are described. In order to better validate the performance, we carried out simulation tests using modelled GNSS observations and also experimental tests using a real hardware COTS receiver, connected to our GNSS Spirent simulator in order to collect real-time hardware-in-the-loop observations, then processed by the navigation module.

Fig. 2:1. Assumed trajectory (GEO) for the receiver (in green) above the GPS constellation.

simulate and generate realistic RF GNSS signals, used in our simulation tests and hardware-in-the-loop experiments. Fig. 2:1 illustrates the assumed GEO orbit of the receiver, above the GPS constellation.

2.2. GNSS constellations According to [15], we assumed a GPS constellation consisting of 31 operational GPS satellites, allocated in six orbital planes, and as defined in [16], a Galileo constellation including 27 satellites, allocated in 3 orbital planes.

2.3. GNSS signals 2.3.1. Signal preselection In this study, we took into consideration the two frequency bands E5/L5 and E1/L1, since they are or will be transmitted by all the GNSS constellations (i.e. GPS, GLONASS (CDMA), Galileo, BeiDou and QZSS), not considering the L2 and E6 bands, which only contain a few civil signals. The L5-band civilian signals are particularly interesting. Indeed, their power is slightly higher than the L1/E1 signals and they have a higher chipping rate, yielding a lower tracking noise jitter for weak signal conditions in the ranging measurements. In addition, as well as the Galileo E1 signal, the L5-band civilian signals have a pilot (data-free) channel that allows for longer integration time, enabling higher sensitivity of the receiver. However, we also wanted to consider the E1/L1-band, in order to exploit dual frequency signals for ionospheric error mitigation and for aiding the acquisition of the E5/L5 frequency band signals. Then, we considered the tracking of the wideband GPS L5Q and Galileo E5aQ +E5bQ, as well as the Galileo E1c and the GPS L1 C/A signals and in particular we carried out our simulations for the following signals combinations:

2. Simulation models and assumptions 2.1. Receiver kinematics and dynamics The orbit assumed for the receiver was the one of the Intelsat 904 (IS-904) communication satellite owned by the International Telecommunications Satellite Organization, launched on February 23rd, 2002 and still active [13]. The initial kinematic state of the receiver at time 00:00 of May 26th, 2016, is identified by the Keplerian orbital parameters reported in Table 2:1, downloaded from the Standard Object Data Service of AGI's (Analytical Graphics INC) library. Then, the motion of the receiver was propagated for three days, by the very precise STK HPOP propagator [14] from the initial condition as function of perturbing accelerations (such as the full Earth gravitational field, third-body gravity, atmospheric drag and solar radiation pressure). The attitude of the spacecraft hosting the receiver and then of the receiver itself were assumed to be Earth pointing, as typical condition for the communication satellites in GEO, in such a way to always steer the antenna boresight towards the Earth center. The complete kinematic state of the receiver for the full three days GEO trajectory was converted to a Spirent-compatible format (user vehicle motion file) and used as reference for the Spirent simulator to

○ GPS L1 C/A ○ GPS L5Q-Galileo E5aQ +E5bQ ○ GPS L1 C/A- L5Q - Galileo E1c-E5aQ +E5bQ According to [17,18], the modern GPS L5 and Galileo E1 and E5 signals should be transmitted by at least 24 satellites in 2018. Also note that, for the purpose of decoding ephemeris and other navigation data necessary to compute the navigation solution, it is possible to easily demodulate the L5 data channel by using the assistance of the pilot channel, since the pilot channels and data channels in the L5 band are well synchronized. In the same way it is possible to demodulate the data in Galileo E5aI by using the assistance of the E5aQ pilot channels. Furthermore, once a given satellite signal frequency is tracked, it is much easier to acquire another signal frequency from the same satellite, as the code phase search can be significantly reduced.

Table 2:1 Initial Keplerian orbital parameters of the considered orbit. Initial orbital parameters Semi major axis: Eccentricity: Inclination: Argument of perigee: Right ascension of the ascending node (RAAN): Mean anomaly:

42167.043348 km 0.000289 0.081° 354.152° 68.784° 240.837°

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Table 2:2 Assumed power reference levels of the four considered GNSS signals. Signal

Minimum received signal power PICD (dBm)

Global signal strength offset OG (dB)

GPS L1 C/A GPS L5Q Galileo E1c Galileo E5aQ +E5bQ

–128.5 –127 –130 –125

+3 +3 +3 +3 Fig. 2:3. Assumed GNSS receiver antenna pattern as function of the elevation, according to [26].

2.3.2. Signals power models For our simulations, we made use of the Spirent GSS8000 GNSS simulator, able to model and generate realistic GNSS signals that would be present at the receiver antenna position, over time, for different kinds of scenarios, including in the space, above the GNSS constellations. The signal power received at the receiver position is modelled as described in equation (1) of our previous work [10], taking into account the gain patterns of both transmitter and receiver antennas and the free space signal propagation losses. For the considered signals, Table 2:2 indicates the guaranteed minimum received signal power on the Earth PICD , according to [19,20], and [16]. As shown in Table 2:2, a global signal strength offset OG was used in the Spirent simulator, in our simulations, to take into account for the difference between the guaranteed minimum signal level and the expected real one (typically, according to [21], the transmitted signal powers are from 1 to 5 dB higher than the minimum received signal power level, therefore we used a middle value of 3 dB). In order to take into account the signals transmitted by the side lobes of the transmitters, we modelled 3D receiver and transmitters antenna patterns. Fig. 2:2 shows the assumed GNSS transmitter antenna patterns as function of the elevation, for GPS L1, GPS L5, Galileo E1, and Galileo E5, respectively according to [22–25]. Fig. 2:3 displays the antenna pattern assumed for the receiver, designed specifically for the reception of GNSS signals at GEO in [26], in order to increase the power of only the signals coming from the transmitter's side lobes with higher gain. This strategy is useful to level the power levels at the receiver and avoid near-far effects. It is important to mention that the available RF signal power level range that the Spirent simulator can generate is [PICD + OG −49.9, PICD + OG +20] dBm. This means that, for instance, for GPS L1 C/A, the minimum power in output, will be −128.5 + 3−49.9 = − 175.4 dBm.

measured by the receiver) [11]. Such integer ambiguity can be calculated with two primary approaches as explained in [27]: – Using differential measurements through a reference station (technique known as real time kinematic (RTK)) – Using precise information about the orbit and clock of the GNSS satellites (known as precise point-positioning (PPP)). RTK can provide instantaneous high accuracy positioning, but only near to a reference station. PPP also can yield near real time highly accurate positioning, and does not require a reference station, but it relies on the streaming of ultra-precise ephemeris and clock corrections, for which an additional communication channel would be required. In both cases the GNSS receiver would not be autonomous, since it would rely on information which are not integral part of the data messages of the GNSS signals. In our simulations, pseudoranges and pseudorange rates observations were implemented according to [21] as follows. For the ith satellites, the pseudorange measured at the receiver position is modelled as:

ρi =

⎞2 ⎛ (xsat i − xu )2 + ⎜ysat − yu ⎟ + (zsat i − zu )2 + b + errorsρ i ⎠ ⎝ i

(2:1)

While the pseudorange rate is modelled as:

ρi̇ = (vsat i − vu)⋅ai + b ̇ + errorsρ ̇

i

(2:2)

T where in Eq. (2:1), [ xsat i ysat i zsat i ] is the position vector of the ith T x y z GNSS satellite, [ u u u ] is the user's position vector, and b is the receiver's clock offset (in m). While in Eq. (2:2), vsat i and vu are, respectively, the velocity vector of the ith transmitting GNSS satellite and of the spacecraft, b ̇ is the clock's drift (in m/s), and ai is the line-ofsight (LOS) unit vector from the receiver to the ith GNSS satellite. Systematic and non-systematic errors denoted as errorsρ in Eq. (2:1), affect pseudorange observations. They can be classified into:

2.4. GNSS observations In order to provide a flexible, autonomous, real time on board GNSS-based navigation, we did not consider carrier-phase observations, which would prevent a complete autonomy of the GNSS-based navigation system. Indeed, although GNSS carrier phase observations are more accurate than GNSS code observations, they are affected by unknown integer ambiguities (since only their fractional part is

○ Signal-in-Space Ranging Error (SISRE), which includes satellite clock error and broadcast satellite ephemeris error ○ Atmospheric delay ○ Multipath effect ○ Receiver error

Fig. 2:2. Assumed GNSS transmitter antenna patterns as function of the elevation, for GPS L1 [22], GPS L5 [23], Galileo E1 [24], and Galileo E5 [25]. The gain is normalized to 0 dB at boresight (located at 0°elevation).

According to [21], these error contributions can be modelled as white Gaussian noise with a certain standard deviation (although this is not strictly true, it is sufficient for this analysis). The overall pseudorange error can be expressed with the user equivalent range error (σUERE ), defined as the root sum square of the different range error contributions. For the GPS constellation, according to [28], we have considered a standard deviation value of 0.5 m for the transmitter's clock and broadcast ephemeris errors, often described as Signal-in-Space Ranging Error (SISRE) [29], assuming instead 0.65 m for Galileo according to [29]. We assumed a standard deviation of 0.2 m for possible multipath, 334

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according to [21]. Concerning the atmospheric delay, it is important to note that when the receiver is located above the ionosphere upper bound (at approximately 1000 km [21]), the GNSS signals at the receiver position, may have crossed the ionosphere (and other lower layers of the atmosphere) only when transmitted by satellites located on the other side of the Earth. This means that the ionosphere or the troposphere layers if crossed, they may have been crossed twice with larger delay of the crossing signal. However, when the receiver is in GEO, it is far enough from the Earth so that it only rarely receives signals that, transmitted from GNSS satellites at MEO altitudes of approximately 19000 – 23000 km altitude, cross the ~19–23 times smaller ionosphere layer. Even less probability exist to cross the troposphere. This is confirmed in Section 3.3, in Fig. 3:13, where the number of available satellites is plotted when considering all satellites available and also when discarding the ones that cross the ionosphere. For this reason, since the receiver in GEO is always above the ionosphere, in this analysis when processing only one frequency from the same GNSS satellite, all the signals that cross the ionosphere (and the troposphere as well below) are simply discarded. Instead, when two frequencies fm1 and fm2 from the same GNSS satellite are processed at the receiver position providing two measurements m1 and m2 , we also process the signals crossing the ionosphere, assuming a ionosphere-free combination of the two measurements, since it is possible to eliminate the first order ionosphere effects (99.9%) on code and carrier-phase measurements [30]. In this latter case, according to [31], the variance of the ionosphere-free pseudoranges error is:

σif2 =

1 (ωm1, m2 −1)2

σtDLL =

σtDLL =

σtDLL =

(2:4)

⎛ BnD 1 ⎞ × ⎜1+ ⎟ 13. 45 C / N0 ⎝ TC / N0 ⎠

(2:5)

∼ Bn(1 − RQ(D )) 2 × α 2C / N0

⎛ 1 ⎞ × ⎜1 + ⎟ TC / N0 ⎠ ⎝

(2:6)

∼ ∼ RQ(D ) = R (D )×cos (2πfsc D )

⎛ D⎞ ∼ R (D ) = A2 × ⎜1 − ⎟ ⎝ T ⎠ For all the signals we assumed integration time T =20 ms. Modern GNSS receivers obtain pseudorange rate observations from the Doppler shift measurements of the received carrier frequency, by simply multiplying the Doppler shift measure with the wavelength of the carrier [21]. We assumed the same approach in this study; therefore, the pseudorange rate error errorsρ̇ in Eq. (2:2) is function of the frequency estimation error. We assumed the Doppler tracking jitter as the main source of error in Doppler frequency estimation and we modelled its standard deviation as function of the C /N0 according to [35], for instance, assuming a standard PLL, as follows:

σf =

[ωm21, m2σm21 + σm2 2]

⎛ ⎞ Bn ⎜ πRc 2 ⎟ D 1 + valid for D ≥ C 2C ⎜ ⎟ Bfe T N (2 − D) ⎠ N0 ⎝ 0

(2:3)

1 T

Bn ⎛ 1 ⎞ ⎡ rad ⎤ ⎟⎢ ⎜1+ ⎥ C / N0 ⎝ 2TC / N0 ⎠ ⎣ s ⎦

(2:7)

An equivalent formula when using a FLL can be found in [35]. Note that the velocity can also be computed taking successive phase measurements when they are available and differentiating with time, obtaining a more accurate measure, less sensitive to the tracking loop jitter.

where ωm1, m2 = fm12 / fm2 2 , for fm1 > fm2 and σm2 is the variance at frequency fm . In nominal signal conditions, for typical modern GNSS receivers on Earth, a pseudorange observation is affected by a receiver noise and resolution error of approximately 0.1 m or less (1σ ) [21]. However, for very weak signals, as the ones above the GNSS constellations, the receiver noise can be much higher. In order to account for higher receiver noise when processing weaker signals, we modelled the standard deviation of the DLL code thermal noise jitter σtDLL as a function of the C /N0 , adding it to the 0.1 m assumed conservatively for any other noise source in the receiver. Assuming a code-tracking loop bandwidth of Bn =0.1 Hz, a correlation spacing of D =0.25 chips, and a double-sided front-end bandwidth Bfe =13 MHz, for GPS L1 C/A, characterized by BPSK(1) modulation, we used Eq. (2:4) from [32], valid for BPSK(n) modulations, and for πR D≥ B c , where Rc is the chipping rate.

2.5. Receiver characteristics We assumed for each signal, a receiver able to process signals down to 20 dB-Hz. Note that this is not a strong assumption. E.g., in [36], a sensitivity of 15 dB-Hz with the legacy GPS L1 C/A has been demonstrated, and such sensitivity level is even easier to achieve with the modernized signals (as they use longer PRN codes and provide a pilot channel). We also assumed that the receiver has enough tracking channels, to be capable of computing simultaneous observations from all the available signals, from both GPS and Galileo satellites. In addition, we assumed that the observations collected from GPS are synchronized with the ones collected from Galileo. Other assumptions required in this study about the tracking loops have already been specified in Section 2.4.

fe

Same code-tracking loop bandwidth but a correlation spacing of D =0.8 chips and a double-sided front-end bandwidth of Bfe =40 MHz were assumed for GPS L5, characterized by BPSK(10) modulation. πR Thus, we used again Eq. (2:4) from [32] (since again D≥ B c ); but fe

according to [21], in the same equation we considered the bracketed term on the right equal to unity, since when using a coherent DLL discriminator there are no squaring loss. For E1c instead, which has a CBOC(6,1,1/11) modulation, we used equation Eq. (2:5) from [33], assuming Bn =0.1 Hz, D =0.25 and Bfe =13 MHz. Finally for E5a +E5b, characterized by AltBOC(15,10) modulation, Eq. (2:6) from [34] was used, assuming code loop bandwidth Bn ∼ =0.1 Hz and D =0.2 and Bfe =80 MHz. Where R (D ) is the autocorrelation function, A=1 is the amplitude, fsc is the subcarrier frequency, α is the autocorrelation slope (in our case α =6.7785 as we can see in [34], because D =0.2 and Bfe =80 MHz).

3. GNSS signal characteristics in GEO 3.1. Received signals power levels In this section we show the received signals power levels at the receiver position, accounting for the gain/attenuation of the transmitters and receivers assumed antenna and for the free space propagation losses. Figs. 3:1–3:4 respectively display the strongest, the second strongest, the third strongest and the fourth strongest signal power level at the receiver position, for each of the considered signal, for one day of the defined GEO. Depending on which signal the receiver can process, from these figures it is possible to know what is the different acquisition and 335

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Fig. 3:1. Strongest received power level (Pr) at the receiver position in dBm, for each considered signal, during one day of the defined GEO.

defined GEO.

Fig. 3:2. Second strongest received power level (Pr) at the receiver position in dBm, for each considered signal, during one day of the defined GEO.

defined GEO.

Fig. 3:5. Carrier-to-noise ratio C /N0 for all the GPS L1 signals during one day of the

Fig. 3:6. Carrier-to-noise ratio C /N0 for all the Galileo E1 signals during one day of the

According to [37], assuming the effective temperature of the antenna TA=130K (typical for GNSS satellites) and the ambient temperature T0 = 290K , for a front-end noise figure of 2 dB, the power values in terms signal strength in dBm, can also be expressed in terms of the carrier-to-noise ratio C /N0 in dB-Hz as follows:

C / N0 = Pr +174

(3:1)

The full range of power levels for each considered signal from each GNSS satellite is also reported. Figs. 3:5–3:8 display the carrier-tonoise ratio C /N0 for all the considered signals from each GNSS satellite, during one day of the defined GEO.

Fig. 3:3. Third strongest received power level (Pr) at the receiver position in dBm, for each considered signal, during one day of the defined GEO.

3.2. Doppler shifts and Doppler rates Doppler shifts and Doppler rates were computed for each of the considered signals, for one day of defined GEO. Fig. 3:9 and Fig. 3:10 illustrate respectively the Doppler shifts and the Doppler rates affecting the carrier of the GPS L1 C/A signals during one day of the defined GEO. The ranges of possible Doppler shift and Doppler rate values for all the considered signals are reported Table 3:1. Unlike in LEO, the possible Doppler shift and Doppler rate ranges are not larger than respectively ± 15 kHz and ± 5.4 Hz/s. Such values are not that far from the ones experienced by a receiver on the Earth, as the receiver in GEO is fixed in the Earth-centered Earth-fixed (ECEF) frame. We can also see that, as expected, the Doppler effect affects slightly more the higher frequency bands L1/E1 and slightly less the Galileo signals, since they are transmitted from slightly higher altitude at lower velocity. Note that much larger Doppler shifts and Doppler rates of

Fig. 3:4. Fourth strongest received power level (Pr) at the receiver position in dBm, for each considered signal, during one day of the defined GEO.

tracking sensitivity required to acquire and track the signals from at least a total number of four different GNSS satellites. For instance, we can see that a receiver able to acquire and track GPS L1 C/A signals down to −137 dBm, would provide one pseudorange and one pseudorange rate from at least four GPS satellites. It is remarkable also to observe how the GNSS transmitters’ antenna patterns defined in Fig. 2:2 affect the range of signal power levels at the receiver position. For instance, we can see that for most of the orbit, the strongest Galileo E5 signals reach maximum power levels (about −122 dBm) higher than the one reached by the strongest GPS L1 C/A signals; but at the same time, the fourth strongest Galileo E5 signals also reach often power levels ( < −143 dBm) significantly lower than the minimum ones reached by the fourth strongest GPS L1 signals (~ −137 dBm). This is due to the significant gain difference between the transmitter's main lobe and the side lobes in E5, but also to the fact that the assumed receiver antenna pattern has higher gain at the elevations where it receives the GPS L1 C/A side lobes signals rather than ones where it receives the Galileo side lobes signals.

Fig. 3:7. Carrier-to-noise ratio C /N0 for all the GPS L5 signals during one day of the defined GEO.

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Fig. 3:8. Carrier-to-noise ratio C /N0 for all the Galileo E5 signals during one day of the

Fig. 3:11. Number of available satellites (or PRNs), when using only GPS L1 C/A, GPS L5-Galileo E5 combined and GPS L1 C/A- L5- Galileo E1- E5 combined signals for one day of the defined GEO.

defined GEO.

Fig. 3:12. GDOP when using only GPS L1 C/A, GPS L5-Galileo E5 combined and GPS L1 C/A- L5- Galileo E1- E5 combined signals for one day of the defined GEO.

Fig. 3:9. GPS L1 Doppler shifts, during one day of the defined GEO.

L5-Galileo E5 combined and GPS L1 C/A- L5- Galileo E1- E5 combined signals for one day of the defined GEO. For the same signals combinations, Fig. 3:12 shows the corresponding GDOP. As expected, using signals from more than one constellation increases the availability significantly and accordingly reduces the GDOP. An improvement also is achieved when considering more than one signal from the same constellation. This is partially due to the different transmitter's antenna patterns, which for a certain relative attitude between transmitter and receiver may allow or not the signal at the receiver position to be strong enough to be available. Another reason is that in our simulations, when two frequencies from the same GNSS satellite are used, we also consider the signals crossing the ionosphere. However, these signals are only a few. Indeed, for instance, for the GPS L1 C/A signal, Fig. 3:13 displays the number of available signals crossing the ionosphere, of available signals not crossing the ionosphere and of total available signals crossing and not crossing the ionosphere. As expected maximum three signals cross the ionosphere simultaneously, and very often none of them.

Fig. 3:10. GPS L1 Doppler rates, during one day of the defined GEO. Table 3:1 Doppler shifts and Doppler rates ranges for all the considered signals during one day of the defined GEO.

L1 E1 L5 E5

Doppler shift [kHz]

Doppler rate [Hz/s]

[−15.15] [−14.14] [−11.4, 11.4] [−10.8, 10.8]

[−5.4,1.2] [−5.4,1.2] [−4.0, 1] [−4.0, 1]

4. GNSS-based orbital filter In our previous research works [39,40], we implemented an adaptive orbital filter for lunar missions, based on a dynamic approach. The filter has been tuned and adapted to be used in GEO. A model of the orbital forces acting on the spacecraft is used to predict the GNSS observations. An Extended Kalman Filter (EKF) is used to fuse the GNSS observations and their prediction. Being the GNSS observations and their dynamics–based prediction characterized by dissimilar error

respectively ±40 kHz and ±15 Hz/s must be considered for a Geostationary Transfer Orbit (GTO) as also reported in [38]. 3.3. Availability and GDOP The ith GNSS signal si for a defined power level threshold, is available at time t for the receiver, only if both following two conditions are verified: 1. at t, the ith GNSS satellite from which the ith signal is transmitted, is in the line of sight of the receiver; 2. at t, the received power of the ith signal is higher than the defined power level threshold. Assuming a receiver able to process signals down to 20 dB-Hz, Fig. 3:11 shows the number of available satellites (each identified by one PRN (Pseudo Random Code)), when using only GPS L1 C/A, GPS

Fig. 3:13. Number of available signals (in blue), of available signals not crossing the ionosphere (in brown) and of available signals crossing the ionosphere.

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constellation for ionospheric delay mitigation. Indeed, the improvement in positioning that the processing of the additional few signals crossing the ionosphere can bring, is small compared to the worsening in positioning due to the additional ranging noise introduced when combining the L5/E5 range observations with the L1/E1 ones. In fact, as shown in Eq. (2:3), the ranging noise will be larger than the one obtained when processing only the L5/E5 observations and it will be particularly amplified by the code tracking noise of the L1/E1 observations. Indeed, as highlighted in Section 2.3, signals in the frequency band L1/E1 are characterized by a ten times lower chipping rate, which can result up to ten times larger ranging error (see Eqs. (2:4) to (2:6). However, as we can see in Table 5:1 for the single-epoch leastsquare solution, processing GPS L5-Galileo E5 does not bring to the best velocity estimation. Processing Doppler measurements from the L1/E1 frequency band for estimating the velocity appears to be more efficient; in fact the same frequency estimation error results in larger range rate error for smaller carrier frequencies (indeed here the pseudorange rate is estimated by multiplying the Doppler shift estimation to the wavelength of the carrier, or by dividing it with the carrier frequency). This effect is not completely visible when the Doppler measurements are processed in the orbital filter, where the predictions of the observations based on the spacecraft dynamics model can have a stronger impact on the velocity estimation.

characteristics, their fusion can provide a position and velocity estimation more accurate than the one achievable individually. The implemented orbital filter provides a real time complete autonomous on board GNSS-based orbit determination unit as described in [36,41]. Two input-configurations of the filter were developed, one that processes GNSS-based single-epoch least-squares position and velocity estimates and one that processes directly GNSS pseudoranges and pseudorange rates. For this study we adopted the developed orbital filter using the second input-configuration, which, although, more complex, generally results to be more efficient. A complete description of the orbital filter implementation is provided in [41], as well as in [40]. However, it is important to mention here that the implemented orbital filter makes use of an adaptive tuning of the covariance matrix of the measurements, as function of the pseudorange and pseudorange rate predicted errors, as well as of the predicted GDOP. A more advanced implementation, which augments the state vector with empirical accelerations, in order to compensate for the errors of the model of the spacecraft dynamics, has been designed and implemented and it is currently under validation. Such approach is commonly known as reduced-dynamic approach.

5. Navigation performance 5.1. Simulation results for 20 dB-Hz receiver sensitivity

5.2. Hardware-in-the-loop tests results using a COTS receiver

Fig. 5:1 shows the Radial, In-track, Cross-track estimation error components for three days of the defined GEO, when using a GPS L1 C/ A – based single-epoch least squares estimator (LS) or a GPS L1 C/A – based orbital filter (OF). The position error is illustrated on the left and the velocity on the right. While the norm of the 3D error for the same estimators is shown in Fig. 5:2. More precise quantitative information in terms of statistics of the error are reported in Table 5:1 for the single-epoch least square solution and in Table 5:2 for the filtered solution, for the three different signals combinations considered. From such results it is firstly possible to see how the implemented orbital filter improves the achievable accuracy, both in position and velocity estimation. The sub-meter level is achieved in positioning, while the order of mm/s is reached in velocity estimation, for all of the considered signals combinations. The best positioning accuracy is achieved when processing GPS L5Galileo E5, without using any signal that cross the atmosphere and then without the need of processing a second frequency for each

The implemented orbital filter was tested also by processing real observations provided by a COTS receiver, characterized by a sensitivity close to the 20 dB-Hz assumed to carry out the simulation results in the Sections 3.3 and 5.1. More specifically, the COTS receiver was connected to our Spirent simulator to process the RF GPS L1 C/A signals generated by the simulator according to the defined receiver trajectory in GEO, and the raw data (pseudoranges and pseudorange rates) obtained from the receiver were post-processed on a computer. Fig. 5:3 and Fig. 5:4 illustrate respectively the GDOP and the number of satellites available for the COTS receiver during the three days of the defined GEO. Note that our Spirent simulator, can generate a maximum number of 12 RF signals per constellation simultaneously. In this test, it was set to generate the 12 strongest signals at the receiver position. For this reason, here, as we can see from Fig. 5:4, the number of available satellites (or PRNs) is smaller than the one of Fig. 3:11 for GPS L1 C/A, obtained using all the available signals (that don’t cross the ionosphere) and not only the 12 strongest ones. Of course, the

Fig. 5:1. Radial, In-track, Cross-track estimation error components for three days of the defined GEO, when using a GPS L1 C/A – based single-epoch least squares estimator (LS) or a GPS L1 C/A – based orbital filter (OF). The position error is illustrated on the left while the velocity on the right.

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Fig. 5:2. Norm of the estimation error, for three days of the defined GEO, when using a GPS L1 C/A – based single-epoch least squares estimator (LS) or a GPS L1 C/A – based orbital filter (OF). The position error is illustrated at the top while the velocity at the bottom. Table 5:1 Statistics of the single-epoch least-squares solution error for three days of the defined GEO. Signals

State component

Radial

In-track

Norm

std

Crosstrack std

std

std

mean

Table 5:3 Statistics of the single-epoch least-squares solution error for three days of the defined GEO. Signals

L1

Position (m) Velocity (m/s)

5.234 0.039

0.963 0.013

1.038 0.014

2.984 0.039

4.527 0.059

L5 - E5

Position (m) Velocity (m/s)

1.563 0.044

0.298 0.017

0.308 0.017

0.887 0.044

1.356 0.068

L1-L5E1-E5

Position (m) Velocity (m/s)

4.327 0.013

1.149 0.006

1.169 0.007

2.421 0.013

3.944 0.022

L1

State component

Radial

In-track

Signals

std

L1

Norm

std

Crosstrack std

std

mean

L1

Position (m) Velocity (m/s)

0.507 0.004

0.178 0.001

0.190 0.001

0.322 0.004

0.470 0.001

L5 - E5

Position (m) Velocity (m/s)

0.183 0.002

0.069 0.001

0.070 0.001

0.114 0.002

0.175 0.002

L1-L5E1-E5

Position (m) Velocity (m/s)

0.418 0.001

0.228 0.0004

0.226 0.0004

0.229 0.001

0.475 0.001

Position (m) Velocity (m/s)

Radial

In-track

Norm

std

Crosstrack std

std

std

mean

24.08 1.150

3.31 0.206

2.89 0.193

16.64 1.143

18.09 1.001

Table 5:4 Statistics of the filtered solution error for three days of the defined GEO.

Table 5:2 Statistics of the filtered solution error for three days of the defined GEO. Signals

State component

State component

Position (m) Velocity (m/s)

Radial

In-track

Norm

std

Crosstrack std

std

std

mean

2.52 0.001

0.72 0.0003

0.67 0.0003

2.52 0.001

4.05 0.002

components and of the filtered solution error components are illustrated in Fig. 5:6. Also in this case, the filtered solution is more accurate than the single-epoch least-squared one, reaching a few meters in positioning and a few mm/s in velocity estimation, as shown in Table 5:3 and Table 5:4. In a comparison between the performance obtained for the modelled GPS L1 C/A observations and for the GPS L1 C/A observations of the COTS receiver, it is important to note that the number of processed observations, and then the GDOP are not the only difference. Indeed, the tracking code loop and the tracking carrier loop characteristics assumed to carry out the results of Section 5.1 may not correspond to the ones of the COTS receiver, and then also different

Fig. 5:3. GDOP for the COTS receiver during the three days of the defined GEO.

GDOP as effect of a reduced availability, results to be larger compared to the one of Fig. 3:12. Fig. 5:5 shows the Radial, In-track and Cross-track components of the single-epoch least-squares solution error and of the filtered solution error. In addition, the norm of single-epoch least-squares solution error

Fig. 5:4. Number of satellites (or PRNs) available for the COTS receiver during the three days of the defined GEO.

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Fig. 5:5. Radial, In-track, Cross-track components of the single-epoch least squares solution error (LS) and of the filtered solution error (OF), for the COTS GPS L1 receiver, during three days of the defined GEO. The position error is illustrated on the left while the velocity on the right.

Fig. 5:6. Norm of the COTS GPS L1 receiver – based single-epoch least squares solution error (LS) and filtered solution error (OF) for three days of the defined GEO. The position error is illustrated at the top while the velocity at the bottom.

few mm/s in velocity estimation. In particular, when using only one frequency from the same GNSS satellite (i.e. in the two considered GPS L1 C/A and GPS L5-Galileo E5 signals combinations), in order to prevent the processing of any signal delayed by the atmosphere, we discarded the signals crossing the ionosphere and the troposphere layers. While we considered also the observations from the signal crossing the ionosphere, when making use of a second frequency from the same satellite (i.e. in the considered signals combination GPS L1 C/ A- L5Q - Galileo E1c-E5aQ +E5bQ). The tests results show that although the use of two signals with different frequencies from the same GNSS satellite can be used to provide a iono-free pseudorange estimate, enabling the processing also of the signals crossing the ionosphere (and then improving the availability), however, the achievable gain in accuracy is smaller than the error introduced by the combination of the L1/E1 band pseudoranges (characterized by larger code tracking thermal noise) with the L5/E5 band pseudoranges. Thus, among the considered signals combinations, the one GPS L5-Galileo E5 seems to be the most efficient. Finally, both estimators were also validated with realistic observations provided by a GPS L1 C/A COTS receiver, when connected to our Spirent simulator to process realistic hardware-in-the-loop RF signals for the considered GEO. In this case we could not process all the available signals as done when processing modelled observations, but only the 12 strongest ones, as our simulator could only generate maximum 12 signals simultaneously. Indeed, the achievable single-

receiver noise have to be considered in the range and range rate estimation accuracy. 6. Conclusions In this research work, firstly we motivated the preselection of different GNSS signals and of combinations of them. In order to provide the requirements for a GNSS receiver for GEO missions, for each signal, the power received at the receiver position, the Doppler shifts and Doppler rates affecting its carrier were investigated, assuming a receiver antenna specifically designed for GNSS signals reception in GEO. Accordingly, for three different combinations of the considered signals the availability and the GDOP were analyzed. We summarized the main characteristics of our orbital filter that adaptively fuses GNSS observations with a model of the spacecraft dynamics, in order to improve position and velocity estimations. Finally we showed the navigation performance obtained processing the modelled observations for the three different signals combinations considered, when using a single-epoch least-squares estimator and when using the described orbital filter, assuming a 20 dB-Hz receiver sensitivity. First of all, in both cases, processing signals from more than one constellation (i.e. Galileo as well as GPS) brings a remarkable improvements in accuracy. In addition, as expected, the filtered solution significantly improves the navigation performance, achieving respectively an accuracy better than half-meter in positioning and of a 340

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