WO2013011309A1

WO2013011309A1 - Satellite navigation system and method

Info

Publication number: WO2013011309A1
Application number: PCT/GB2012/051715
Authority: WO
Inventors: Marcio AQUINO; Biagio FORTE; Zeynep ELMAS; Sreeja VEETTIL; Joao Francisco Galera MONICO
Original assignee: The University Of Nottingham
Priority date: 2011-07-18
Filing date: 2012-07-18
Publication date: 2013-01-24
Also published as: GB201112336D0

Abstract

A method of improving the accuracy of a geographical position calculated by a GNSS device using signals received from a plurality of satellites is described. In the method,observations obtained from the received signals are weighted in the position calculation using In-phase (I) and/or Quadra-phase (Q) correlation samples derived from each received signal.A GNSS device operable to perform the method is also described.

Description

SATELLITE NAVIGATION SYSTEM AND METHOD

The present invention relates to satellite navigation systems, and particularly but not exclusively to Global Navigation Satellite Systems, commonly referred to by the acronym GNSS.

A satellite navigation system typically comprises a constellation of around 20 to 35 satellites in orbit around the Earth. The satellite orbits are arranged such that multiple satellites (usually at least four and preferably six or more) are simultaneously visible from any location in which the system is intended to be operable. The satellites each transmit information including data on their position and an accurate time. Transmitted information from multiple satellites can be used by a receiver to calculate its position. Examples of GNSSs include the Global Positioning System (GPS), Galileo and GLONASS.

A GNSS device is defined herein as any device that contains a GNSS receiver/processor capable of tracking GNSS satellites and estimating position. The position calculations performed by a GNSS device generally assume that the respective signals have travelled along a straight line (of sight) from a given satellite to the device at the speed of light (the signals being electromagnetic radiation, usually in the form of radio waves). The position of the GNSS device can be calculated from the time of flight of the signals in a known way.

Typically, satellite signals are detected at a GNSS device and interpreted in a process known as ' signal tracking' . This is achieved by two types of receiver tracking loops that are well known in the field.

The Delay Locked Loop (DLL) maintains an exact code phase alignment between the modulated code of the received signal and a locally generated modulated code. The output of the DLL is directly related to the accuracy of the signal travel time and therefore to the range measurements made by the GNSS device, which are used to calculate the position. These range measurements (also termed range Observations') are known in the field as 'pseudoranges' . The Phase Locked Loop (PLL) minimizes the error between the input phase of the signal and its estimated phase output measurement (also termed carrier phase Observation'), which feeds the GNSS receiver processor. The PLL remains in lock or not depending on the magnitude of this error.

The position calculation in a GNSS device is accomplished by a well known method called Least Squares adjustment, which takes into account the pseudoranges and/or carrier phase observations produced by the DLL and PLL, respectively, to estimate the best possible solution for position.

A fundamental threat to the reliable operation of a GNSS device is the variable propagation conditions encountered by GNSS signals as they pass through the Earth's upper atmosphere (the ionosphere). The ionosphere delays the signals causing a positioning error of up to tens of metres. Additionally, disturbances in the ionosphere can cause sudden rapid signal fading and operational outages.

The effect of the ionosphere on radio signals such as those transmitted by GNSS satellites is dependent on its Total Electron Content (TEC) - the integrated number of free electrons in the path between the satellite and the receiver. This can be modelled by making use of measurements made on two (or more) different frequencies that are usually transmitted by GNSS satellites.

The regular behaviour of the ionosphere, which is fundamental to accurately model its effects, is greatly influenced by solar activity. Significant disturbances in the ionosphere can take place usually, but not only, in years of high sunspot activity. One such effect, known as ionospheric scintillation, is more likely to occur in equatorial and auroral regions. Scintillations are phase and amplitude fluctuation in the signals transmitted by the GNSS satellites due to irregularities in the ionosphere, occurring typically, but not only, under high solar activity conditions. Whatever GNSS application is considered (e.g. navigation for marine, aviation or land applications, environmental monitoring, deformation analysis of civil engineering structures, etc.), this disturbance may become more significant closer to the peaks of the Solar Cycle. Conventional GNSS devices cannot mitigate these effects very accurately. We propose herein an alternative approach to mitigating ionospheric disturbances, scintillation in particular, in a GNSS position calculation.

According to a first aspect of the invention there is provided a method of improving the accuracy of a geographical position calculated by a GNSS device using signals received from a plurality of satellites, wherein one or more observations obtained from the received signals are weighted in the position calculation using In-phase (I) and/or Quadra-phase (Q) correlation samples derived from the received signals. As used herein Observations ' mean measurements obtained from the received signal by a GNSS device, for example based on the phase of the modulated code or of the carrier frequency. The observations may include one or more outputs produced by a DLL and/or a PLL of the GNSS device, such as, respectively, the pseudoranges and carrier phase observations mentioned above.

Observables' are described hereafter as observations of the same type, for instance of the pseudorange type or of the carrier phase type. More than one observable may be obtained from the signal received from each satellite. The In-phase (I) and/or Quadra-phase (Q) correlation samples used to weight the observations are derived from the received signals by the GNSS device. In a typical GNSS receiver, I and Q correlation samples are continuously generated (but not necessarily stored). However, they are used for a different purpose, and are not used to weight the observations.

Weighting the observations may comprise assigning an observation a lesser or greater 'importance' (weight) in the position calculation than another. Current art normally assigns equal weights to all observations of the same type, i.e. 'equal observables - equal weights' .

The method may comprise assigning different weights to different observations of the same type, (i.e. observables). One or more of the observations may have the same weight. All the observations may have different weights. The method may comprise using both the In-phase (I) and Quadra-phase (Q) correlation samples to weight the observations.

The I and Q correlation samples may be used to estimate a signal tracking error for a respective received satellite signal. The weights may be derived from the estimated satellite signal tracking error, and in particular from the variance of the estimated satellite signal tracking error.

The weights assigned to each observation may be given by the inverse of the variance of the respective satellite signal tracking error. The observations from all satellites being tracked and used in the solution may be weighted, including a plurality of frequencies, satellites and constellations.

The calculation of position may comprise a Least Squares estimation.

An important feature of the Least Squares estimation is known as the stochastic model, from which a Weight Matrix (W) is derived. The stochastic model defines the statistical properties of the observations and the Weight Matrix in particular provides the weights to be assigned to each observation to be taken into account in the Least Squares adjustment.

The method may comprise using a Weight Matrix (W) of the form:

where l/o_x' is the weight assigned to observation 'i' derived from the I and/or Q correlation samples derived from a signal received from a satellite 'i', where 'i = 1 , 2, ...n' ; and where 'x' denotes the type of observation.

The method may comprise using a Weight Matrix of the form set out above, wherein, in principle, ≠σ^ ≠ ...≠σ " . That is, the Weight Matrix may comprise a weight, which does not equal at least one other of the weights, l G_x ³ (where i, j = 1 , 2 ...n, and i≠ j).

.2

For an observation of type 'x' derived from satellite 'i', O_x may be the variance o the tracking error for that observation.

In the case of pseudorange observations, for satellite 'i' the variance of the DLL tracking error may be given by , and the Weight Matrix (W) may be written:

VDⁿLL

In principle, for each satellite i = 1 , 2, ...n, O _DLL ≠G_DLL ≠...≠G_L' In the case of observations of the carrier phase type, the variance of the PLL tracking error is used and, for satellite , is given by PLL , so that 1/c ' is replaced in the Weight Matrix (W) by the weight 1 / In principle, for each satellite i,

PLL PLL ≠...≠G_pLL .

More that one type of observation may be included in the Least Squares estimation. Both pseudorange (DLL) and carrier phase observations (PLL) may be included in the Least Squares estimation.

The weight matrix W is preferably a square matrix whose dimension depends on the number of observations to be taken into account, which in turn may depend on the number of satellites in view. Preferably, it is assumed that there is no correlation between observations, and that W is a diagonal matrix. The method may comprise discarding one of more of the observations from the position calculation. This may be the case if the weight of the observation falls below a predefined threshold. The method may comprise weighting the observations in real time (i.e. in the same time frame as the position calculation is performed). New weights may be calculated for the observations each time the position calculation is carried out.

According to a second aspect of the invention there is provided a GNSS device operable to establish a geographical position using a plurality of signals received from a plurality of satellites, wherein the GNSS device comprises a processor module operable to use observations derived from the received signals in a position calculation to establish a position, and wherein the device is operable to weight the observations in the position calculation using In-phase (I) and/or Quadra-phase (Q) correlation samples derived from the received signals.

The observations may be weighted as described above with reference to the first aspect of the invention. The observations may be weighted in a weighting module of the GNSS device. The weighting module may be operable to assign one observation from the received signals a lesser weight in the position calculation than another observation, possibly depending on the variance of their corresponding tracking errors. One or more observations may have the same weight. All the observations may have different weights.

The weighting module may be operable to discard one or more of the observations from the position calculation. That may be the case if the calculated weight of the observation falls below a certain threshold.

The weighted observations may be used in a Least Squares estimation, which may be as described above with respect to the first aspect of the invention.

The weighting module may be operable to weight the observations in real time, as described above. According to a further aspect of the invention there is provided a satellite navigation system including a GNSS device in accordance with the second aspect of the invention and/or operable to perform a method in accordance with the first aspect of the invention.

The invention will now be described in more detail, by way of example only, with reference to the accompanying Figures, in which: Figure 1 shows an example global navigation satellite system (GNSS) and an associated GNSS device;

Figure 2 shows the variation of the I and Q signal components observed under a simulated environment with different levels of scintillation implied by the scintillation amplitude index S4;

Figure 3 shows a simplified method of calculating a GNSS position; and

Figure 4 compares the errors in the height component of a real world GNSS positioning time series using (A) a conventional technique called Precise Point Positioning (PPP) and (B) the present invention.

The architecture of a GNSS receiver/processor is well known in the art and will not be described in detail herein. However, a very simplified high level example of a GNSS device 10 is shown in Figure 1.

The device 10 includes a module 12 operable to receive electromagnetic GNSS signals (typically in the range 1 100MHz to 1600MHz) from satellites 20 (e.g. SV16, or Space Vehicle 16). The GNSS device also includes a processor module 14. The device 10 might be any electronic device which requires knowledge of its position. For example, the device might be a dedicated satellite navigation device such as those used to provide a user with directions in a vehicle or on foot. Alternatively, the device might be a mobile phone or laptop computer with GNSS capacity. The device might be a scientific instrument requiring accurate position information. The exact nature of the device does not matter - the invention is applicable to any device operable to calculate a position using GNSS signals.

Together with a control centre (not shown) the satellites 20 each form part of one or more global navigation satellite systems (GNSS). Each satellite 20 continuously transmits GNSS signals encoded with data, including information on the position and orbit of the satellite, as well as accurate time information. The processor module 14 of device 10 is operable to use the encoded information to derive observations from the signals from each satellite (e.g. pseudoranges and phase observations, as explained above), which in turn are used to calculate the position of the GNSS device. GNSS position calculations typically make use of a Least Squares estimation, which is well known in the art, and so is not described herein.

One important factor intrinsic to GNSS position estimation is that it relies on a calculation of time of flight. A very accurate measure of the time of flight is necessary in order to determine the position of the GNSS device accurately. Even small errors in time of flight may translate to large errors in distance. It is a known problem that as electromagnetic signals pass through the ionosphere they are delayed. This delay alters the relationship between time of flight and distance travelled, and so introduces an error into the position calculation. This error can usually be modelled to a first order by appropriate manipulation of the observations that is well described in the art. However disturbances in the ionosphere may introduce significant errors in the observations which are not easily modelled and can propagate into the calculation of position, degrading its accuracy.

One problem with the way in which conventional GNSS receivers operate is that the calculations used by the processor assume that all of the signals of the same type received at the GNSS receiver are of the same 'quality', i.e. they are assigned the same weight in the Least Squares process. (Observations of the same type, also called Observables' in the art, herein are described, for instance, by ranges measured on the same modulated signal or carrier phase observations measured on the same carrier frequency). However, in practice this is not necessarily the case. Each satellite 20 is necessarily in a different location, and so each GNSS signal travels along a different path to reach the receiver. The effects of ionospheric disturbances are likely to be different on each transmitted signal, making some received signals less precise than others, and consequently leading to observations with different statistical properties, i. e. ultimately different precisions.

We have realised that it is desirable to weight each observation in accordance with the precision with which it was measured. We have realised that the signal itself comprises some information about the medium through which it has passed, and in particular about the ionosphere. We propose to use this information to produce a better estimate of position. In this way observations obtained from less precise GNSS signals can be given less importance (weight) in the position calculation.

One particularly useful measure of a signal' s precision can be determined by analysing the intensity and phase of the received signal, and in particular the phase error. A measure of the phase error is already determined in most conventional GNSS devices for a completely different purpose, as described in more detail below. We have found that these errors strongly correlate with disturbances in the ionosphere, scintillation in particular, as well as other factors that may be present in the particular satellite path to the receiver. For this reason we propose to use this error to weight observations in the Least Squares position estimation. To assist in the understanding of the invention, the operation of a typical GNSS device is briefly described below. In such a device, GNSS signals from all available satellites in view are received by the GNSS receiver, and then down-converted to an intermediate frequency (IF). An analog-to-digital conversion process occurs after the down conversion to the IF. The digitised IF signal is first stripped off the carrier by multiplying the signal with a carrier replica Next the PRN code (pseudo-random noise code), which modulates the signal carrier wave and distinguishes the signals received from different satellites, is removed from the signal. After correlation In-phase (I) and Quadra-phase (Q) correlation samples, which are phases 90° apart, are produced. Generally, the I sample is mostly thermal noise multiplied by the replica digital sine wave, whereas the Q sample is the product of the thermal noise and the replica digital cosine wave. Each of these I and Q correlation samples are then used by a PLL (also known in the field as a 'carrier tracking loop') to estimate the phase error in the PLL discriminator, and by a DLL (also known in the field as a 'code tracking loop') for normalizing the code discriminator. The output from the PLL also feeds the DLL. The outputs of the DLL and PLL are then used by the device to calculate an estimate of position. We have realised that, as the two output I and Q correlation values can be used to estimate the phase error, these samples, and in particular this estimated error, can also be used to weight the observations obtained from the received signal in the position calculation to produce a more accurate estimate of position. This weighting is not performed in current GNSS receivers.

Referring again to Figure 1 , a GNSS device 10 in accordance with the invention will now be described. As in the conventional GNSS device outlined above, the device comprises a receiver module 12 which digitises electromagnetic signals received from a plurality of satellites to produce I and Q correlation samples 16 for each satellite. The device also comprises a processor module 14 which uses observations made from the received signals in a position calculation carried out by an algorithm 18. The position calculation is in this example substantially a Least Squares calculation, but with an improved Weight Matrix as discussed below. The GNSS device 10, and in particular the processor module 14 of the GNSS device, includes a weighting module 22. The weighting module 22 uses the I and/or Q correlation samples 16 derived from the received signal to compute weights for each of the observations intended to be used in the calculation of position. For example, observations derived from low quality signals might be assigned a lesser weight when forming the Least Squares Weight Matrix, and might even be discarded if their weight falls below a defined threshold. In the example discussed below, the weighting module uses the I and Q correlation samples to produce weights which are based on the variances of the signal tracking errors calculated for each received signal. The position calculation is then carried out by the position calculation algorithm 18 using the calculated weights. Other observed information might be used to weight the observations as well or instead, e.g. the satellites elevation angle or other metric, if required.

A simplified flow diagram of the method is shown in Figure 3. The diagram shows that the GNSS device 10 first receives GNSS signals from a plurality of satellites, and then makes observations on those signals. The observations may be in the form of pseudoranges and phase observations, as discussed above. Weights are calculated for the observations which are to be used in the position calculation using the I and/or Q correlation samples, as appropriate. The calculated weights are then used to weight the observations and a position is calculated using the weighted observations.

The method is shown for one calculation, but it will be appreciated that typically multiple position calculations are performed by a GNSS device, and for every new position calculation new weights can be calculated according to the new observation data being used. Where observation data is gathered continuously, new weights and new positions may be calculated continuously, in real time.

It will be seen that the weighting of the observations in the present invention is based on data derived from observed signals, and in particular calculated from the values of the I and Q correlation samples for a given signal.

For the sake of simplification, we take as an example the typical GPS LI C/A code pseudorange single epoch point positioning case, for which the Least Squares model, for a receiver at station A tracking satellites 1, 2, ..., n, normally considers a '« x «' Weight matrix of the observations W, of the form:

Ι/σ '

0 1/σ -

W (1 )

0 1 /σ_Α"

In the above case only the pseudorange observable is used and it is assumed that there is no correlation between individual pseudorange observations; and that their variances are the same, i.e. W is a diagonal matrix where:

This allows the Weight matrix to be written as:

W = l/o ²(l) (3) where / is the identity matrix. This is not a realistic Weight matrix, especially under disturbed ionospheric conditions, where different satellite signals will be affected differently by these disturbances.

Our invention proposes to substitute the simplified and unrealistic Weight matrix given in (3) above by a Weight matrix where different weights l/c_x' are assigned to the observations (x) from different satellite links (i), based on the values of the I and/or Q correlation samples, for the different signals being used in the solution. This gives the least squares stochastic model used for position computation a more realistic representation, vis-a-vis the otherwise ' equal observables - equal weights' solution, normally applied in GNSS positioning. In the example given below, the I and Q correlation samples are used to calculated the estimated variances of the satellite tracking errors for each signal being considered, and these are used to form the weights. Because these variances can be estimated continuously our method can therefore be used in real time positioning.

In line with the example above we show the formula used for the calculation of the variances of the DLL tracking errors for the case of the GPS L I C/A code pseudorange observable:

In the formula DLL_bw is the DLL bandwidth, and the mean and standard deviation of the I component are estimated over the time interval between consecutive observations.

A more general

where d is a constant related with the correlator spacing. Once these variances are computed for all satellites being tracked the corresponding observations are then suitably weighted and the new Weight matrix is formed in the weighting module 22. In the case exemplified above (of GPS LI C/A pseudorange single epoch point positioning) the new Weight matrix would take the form:

Crucially, in the new Weight matrix all weights are in principle different, i.e. :

' DLL DLL ≠...≠σ DLL

Then the processing module uses the position calculation algorithm 18 to calculate a position for the device. The position calculation algorithm follows the well known Least Squares adjustment, the only difference being the new Weight matrix. This will significantly improve the accuracy of the calculated position.

It will be appreciated that the method can be used for all types of GNSS observations, i. e. for all GNSS observables, not only the GPS LI C/A pseudorange. For example if the GPS LI carrier phase observable is included in the solution, the formula used to estimate the variance of the PLL tracking error is given by: yl, _f » st iatani¾ : i0 (6)

Where the standard deviation of the value of atan(g/|/| ) is estimated over the time interval between consecutive observations.

Therefore this formula can equally be used to provide the weights for the GPS LI carrier phase observations. These formulas can also be used for all GNSS observables, including existing Galileo and GLONASS as well as new under development GNSS. Figure 2 shows how the I and Q components change during different levels of scintillation while the signal from a representative satellite SV16 is being tracked (see Figure 1 ). SV16 is a simulated GPS satellite which was modelled as having a start elevation of 60° and a final elevation of 90° and the signal being tracked is the GPS LI C/A. The simulated satellite was modelled over a 40 minute period, with the scintillation effects given by an amplitude scintillation index S4 that varies gradually between 0.3 and 1 (inclusive). It is generally accepted in the field that an S4 value of 0.3 refers to weak to moderate scintillation and a value of 1 is considered to indicate strong scintillation.

From Figure 2 it can be seen that during weak-to-moderate scintillation levels (0.3 < S₄ < 0.5), both I and Q components have values confined to smaller ranges showing less scattering (deviation), indicated by areas W and X in Figure 2. However, during strong levels of scintillation (0.6 < S₄ < 1 , indicated by areas Y and Z in Figure 2), both components reach greater values with more scattering (deviation) showing how different scintillation levels can drive the correlation outputs to greater ranges (less confined in magnitude).

Analysis of the I and Q correlation samples shows that the scattering as well as the magnitudes of the respective outputs change according to different levels of scintillation. This demonstrates that the I and Q values can be used to provide an indication of the actual scintillation level and hence an indication of the reliability of the received signal.

The present invention can be used to provide an accurate estimate of the position of a GNSS device even in adverse ionospheric conditions. The method described herein can be applied in real time using information that is available in any GNSS receiver.

The method is applicable at all levels of scintillation as long as the GNSS receiver can track the signals, but is particularly useful under strong scintillation where prior art devices are either unable to calculate a position or only able to provide a position with a degraded accuracy. Because the method described herein uses observed signal data, it takes into account the real time effects of a disturbed ionosphere on the transmitted signals, and not the effects based on models or predictions. We believe the described method also has the potential to correct for other signal propagation errors due to time of flight irregularities, such as signal reflections or multipath, occurring for instance in 'urban canyons' . It will be appreciated that the method and systems described herein are applicable to any satellite navigation system. The use throughout of the term 'GNSS ' is not intended to limit the invention to existing global navigation satellite systems only - it is also applicable to any new or under development systems. It will be further appreciated that the invention is applicable to other frequencies of signal - any frequency, in fact, at which a GNSS operates.

Figure 4 demonstrates the improvement achieved with the present invention. Figure 4 shows the errors in the height component of a real world GNSS positioning time series using a technique called Precise Point Positioning (PPP), which is well known in the field, as well as the errors in the height component when calculated using the present invention. The results represent the errors for a period of 6 hours during which the level of scintillation varies from strong to moderate as shown by the S4 index (represented by the line marked S₄). It is known in the field that S4 values over 0.6 represent strong scintillation. It is also well known in the field that the height component is the most affected by scintillation in GNSS positioning.

In Figure 4 the line marked A represents the errors in the conventional PPP solution, i. e. without applying the present invention, whereas the line marked B represents the errors when the invention is applied. It is known in the field that the PPP technique requires an initial convergence period for the solution to settle and this is shown in Figure 4. The table below shows the rms errors for the new PPP solution applying the present invention and the rms errors for the conventional PPP solution, as computed from the results shown in Figure 4.

RMS (m)

Invention Conventional Improvement

During convergence 0.41 0.59 29%

After convergence 0.18 0.52 65%

Claims

1. A method of improving the accuracy of a geographical position calculated by a GNSS device using signals received from a plurality of satellites, wherein observations obtained from the received signals are weighted in the position calculation using In-phase (I) and/or Quadra-phase (Q) correlation samples derived from each received signal.

2. The method of claim 1 , wherein weighting the observations comprises assigning an observation derived from one of the received signals a lesser or greater

'importance' (weight) in the position calculation than another observation, derived from a different received signal.

3. The method of claim 2, wherein all of the observations are assigned different weights.

4. The method of any preceding claim, wherein weights derived from the I and Q correlation samples are assigned to the observations.

5. The method of any preceding claim, wherein the I and/or Q correlation samples are used to estimate a signal tracking error for each observation, and wherein a weight is assigned to each observation using the respective satellite signal tracking error.

6. The method of claim 5, wherein the weight assigned to each observation is the inverse of the variance of the respective satellite signal tracking error.

7. The method of any preceding claim, wherein the calculation of position comprises a Least Squares estimation.

8. The method of claim 7, wherein the Least Squares estimation comprises a stochastic model from which a Weight Matrix (W) is derived, and wherein the Weight Matrix has the form:

where l/c_x' is the weight assigned to observation 'i' derived from the I and/or Q correlation samples derived from a signal received from a satellite 'i', where 'i = 1 , 2, ...n' ; and where 'x' denotes the type of observation.

9. The method of claim 8, wherein in the Weight Matrix at least one weight, l<3_x , does not equal at least one other weight, \/c_x (where i, j = 1 , 2, ...n and i≠ j).

10. The method of claim 8 or claim 9, wherein the observations comprises

■ 2 - 2

pseudoranges, and wherein the weights l/c_x' comprise l/c_D' _LL , where:

where d is a constant related with the correlator spacing.

1 1. The method of claim 8 or claim 9, wherein the observations comprise a phase

■ 2 - 2

observations, and wherein the weights l/c_x' comprise l/o_P'_LL , where:

&j_fLi ~ std(atan(Q :ii|)

12. The method of any preceding claim, wherein the method comprises weighting the observations in real time.

13. The method of any preceding claim, wherein weights are calculated for all observations to be used in the position calculation.

14. The method of any preceding claim, wherein the position calculation is repeated, and wherein new weights are calculated for the observations each time the position calculation is carried out.

15. A GNSS method substantially as described herein, with reference to the accompanying Figures.

16. A GNSS device operable to establish a geographical position using a plurality of signals received from a plurality of satellites, wherein the GNSS device comprises a processor module operable to use observations derived from the received signals in a position calculation to establish a position, and wherein the device is operable to weight the observations in the position calculation using In-phase (I) and/or Quadra- phase (Q) correlation samples derived from the received signals.

17. The GNSS device of claim 16, wherein the GNSS device is operable to perform the method of any one of claims 1 to 15.

18. A GNSS device substantially as described herein, with reference to the accompanying Figures.