GLOBAL NAVIGATION SATELLITE SYSTEMS

Field of the Invention

The present invention relates to a method of analysing multiple signals transmitted by discrete global navigation satellite systems.

More particularly, the present invention relates to a method of analysing multiple signals transmitted by discrete global navigation satellite system (GNSS) for identifying information to be combined and delivered to a single receiver for use in an application.

Background of the invention In precise point positioning (PPP) a user employs a single global navigation satellite system receiver that collects carrier-phase and code (pseudo-range) observations from a signal transmitted by a satellite to determine the position of the receiver with centimetre to decimetre accuracy. The positioning accuracy that can be achieved with PPP strongly depends on the observation time over which the signal is accumulated by the receiver.

Single-frequency GNSS PPP, which relies on the availability of ionospheric corrections

(obtained from e.g. Global Ionospheric Maps), has a positioning accuracy which is typically at decimetre level after about 15 minutes. In the absence of such ionospheric corrections, but based on the ionosphere-free combination of dual-frequency observations, the accuracy of GNSS PPP can reach centimetre level, but this requires a much longer signal observation time span, e.g. at least one hour. Although PPP is based on the very precise carrier-phase data, this high precision cannot be exploited as ambiguities in the carrier-phase data are not estimable as integers.

PPP-RTK is integer ambiguity resolution-enabled precise point positioning. It extends PPP by providing single-receiver users information about satellite phase biases. PPP-RTK has the potential of benefiting enormously from the integration of multiple GNSS/RNSS systems. However, since unaccounted inter-system biases (ISBs) have a direct impact on the integer ambiguity resolution performance, the PPP-RTK network and user models need to be sufficiently flexible to accommodate the occurrence of system-specific receiver biases. The basic principle of GNSS-based positioning is to measure the distance between a specific position point and satellites whose position and biases in their signal transmission time are known through published orbits/clocks. The positioning measurement setup is structured by the code observables and\or by the carrier-phase observables. While the code observables (of decimetre level precision) can be used to determine the position of a single receiver user in a real-time manner, the very precise carrier-phase observables (of millimetre level precision) cannot take a truly active part in determining the single receiver user's position, unless a rather long observational time takes place. This is due to the nature of the carrier- phase observables, as they are biased by time-constant ambiguous cycles, the so-called ambiguities. The ambiguities are composed of two parts: 1 ) the integer part that relates to the channel between the transmitting satellite and the user receiver, and 2) the non-integer part that captures the receiver and satellite instrumental delays. By correcting the non- integer part, the remaining integer-recovered ambiguities can be resolved through an application of the integer ambiguity resolution methods, of which the LAMBDA method is the de facto standard. The ambiguity-resolved carrier-phase observables would then act as very precise code observables, thereby realizing fast precise positioning with mm-cm level of accuracy.

In order to correct the non-integer part, use must be made of external corrections obtained by a network of GNSS receivers. Several methods have been proposed to determine such network-derived corrections, but all these methods are designed for a single satellite system. When dealing with multiple satellite systems, the strategy applied is to analyse and to determine the corrections separately on a system-by-system basis. On the one hand, treating each satellite system in a standalone manner leads to loss of possible information existing between the corrections of the satellite systems. This is the case when, for instance, the corrections are attributed to instrumental delays that are imposed by satellites of two distinct systems, but then sharing signals with one common overlapped frequency. On the other hand, ignoring the presence of any misalignments between the satellite systems and treating the satellite systems as one single system may result in a catastrophic failure of integer ambiguity resolution. Knowledge of such between-system information is therefore essential to efficiently combine the multi-system corrections as it enables the signals of multiple satellite systems to be combined into a unitary system. Summary of the Invention

According to one aspect, there is provided a method of analysing multiple signals transmitted by multiple discrete global navigation satellite systems for identifying information to be combined and delivered to a single-receiver user for use in an application, the method comprising the steps of:

a) analysing each of the signals to identify observed quantities of the signal, wherein the observed quantities comprise information tracked by a network of receivers or by a single receiver;

b) formulating full-rank observation equations from the observed quantities;

c) determining inter-system biases existing between the discrete satellite systems; d) incorporating the inter-system biases (ISB) into the full-rank observation equations to yield ISB-corrected observation equations, thereby allowing the multiple discrete global navigation satellite systems to be represented as a single global navigation satellite system; and

e) delivering the ISB-corrected observation equations to the single-receiver user.

Each of the signals may be a single frequency signal. Each of the signals may be a multiple frequency signal.

The signals may be transmitted by at least one of the GPS, Galileo, BeiDou, QZSS, IRNSS and GLONASS systems. The observation equations may comprise carrier-phase and code (pseudo range) observed quantities.

The observed quantities may include geometric range data, tropospheric delays, receiver clock offsets, receiver phase biases, receiver code biases, satellite clock offsets, satellite phase biases, satellite code biases, and ionospheric delays. The method may further comprise deriving a five-fold functionality within the observation equations enabling single-receiver integer ambiguity resolution to be performed. The method may comprise selecting one of the multiple discrete global navigation satellite systems as a reference system and determining the inter-system biases with respect to that reference system.

Step (c) may comprise constructing a reference table including all the inter-system biases existing between the multiple discrete global navigation satellite systems.

The multiple discrete global navigation satellite systems may comprise network receivers wherein the inter-system biases are grouped into clusters according to network receivers of similar type.

The application may comprise determining location parameters for use in determining a location of the receiver.

The application may comprise determining atmospheric parameters for use in weather forecasting.

The application may comprise determining the offset between the coordinated universal time and the reference time of the multi global navigation satellite systems. The application may comprise determining receiver and satellite instrumental biases attributed to each of the global navigation satellite systems.

Step (b) may further comprise the steps of:

identifying rank deficiencies within initial observation equations through use of S- system theory;

forming system-specific estimable parameters as functions of original GNSS parameters; and

parameterizing offsets between the system-specific receiver instrumental biases as estimable functions of the inter-system biases.

In the specification hereinafter and above, reference is made to S-system theory as described in Teunissen, "Generalised inverses, adjustment, the datum problem and

S-Transformations", Springer- Verlag, pp 1 1 -55, 1985 Brief Description of the Figures

The present invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

Figure 1 shows an embodiment of a receiver and satellite system for use with the method of the present invention;

Figure 2 shows a table providing estimable parameters for use in the method, wherein the estimable parameters represent interpretations of multi-system parameters, system- specific parameters (indicated by the asterisk), and corresponding network S-basis parameters chosen;

Figure 3 shows a table characterizing five-fold functionality of the network-derived corrections upon which single-receiver integer ambiguity resolution becomes feasible;

Figure 4 shows schematic construction of the user estimable parameters that are formed by the five-fold functionality of the corrections being linked to the choice of the network's S-basis;

Figure 5 shows a table providing estimable ISBs as a function of the GNSS system- specific parameters;

Figure 6 shows a table presenting single-epoch, multi-frequency, multi-system network model's redundancy, together with the number of observations and estimable parameters as functions of the number of frequencies f, number of receivers n, number of satellites M, number of systems S, wherein υ is the dimension of position vector;

Figure 7 shows a table presenting the increase in the network/user model's redundancy by switching from the ISB-unknown model to the ISB-known model, whereby the increase in the user model's redundancy follows by setting n = 2 ;

Figure 8 shows schematic presentation of a network ISB look-up table in conjunction with network-derived corrections; and

Figure 9 shows a partitioning of the network receivers into multiple clusters based on their types.

Detailed Description of Specific Embodiments

The present disclosure now is described more fully hereinafter with reference to the accompanying figures. The present disclosure provides a method to align multi-system network-derived corrections through processing multi-GNSS, multi-frequency carrier-phase and code data that are tracked by a network of receivers or by a single receiver. Provided with such aligned multi-system corrections, a single-receiver user would be in a position to correct his/her own multi-GNSS data and integrate his/her multi-system measurement setup into a super high-precision single-system setup enabling integer ambiguity resolution. The corresponding ambiguity-resolved multi-GNSS data would then serve as input to a wide range of GNSS applications including, precise point postioning real time kinematic (PPP- RTK), GNSS atmospheric sensing, and instrumental bias calibration.

1. Multi-GNSS observation equations.

In the present disclosure we apply the S-system theory to the undifferenced, multi-GNSS, multi-frequency observation equations to formulate full-rank multi-system models for a network of receivers and/or a single receiver tracking code division multiple access (CDMA) signals such as those transmitted by GPS, Galileo, BeiDou, QZSS, IRNSS, and the modernised GLONASS. The general form of the rank-deficient multi-system GNSS observation equations can be expressed as

The description of the subscripts, superscripts and indices in the GNSS observation equations is provided as follows. The asterisk-symbol * indicates the corresponding system of satellites. It ranges within the multiple systems * = G, J, ... , E. The number of receivers, visible satellites of system * and frequencies are denoted by n, m, and / ^" , respectively. The receiver, satellite and frequency indices are denoted by r = 1, ... , n; s _* = 1, ... , m _* ; and j = 1, ... , / ^" ; respectively. The delta-symbol Δ indicates the increments of the quantities, as a- priori values can be subtracted from the quantities.

The description of the measurements in the GNSS observation equations is provided as follows. The carrier-phase and the code (pseudo-range) observations are denoted by Αφ^ and pr , respectively. The description of the unknown parameters in the GNSS observation equations is provided as follows. First, there is the increment of the geometric range, lumped with that of the tropospheric delays, denoted by Δ ^ ^* . The stated increment can be further parameterized into position coordinates (3 per receiver) and a zenith tropospheric delay (ZTD; 1 per receiver) through the parameterization App = g _r ^s "Ax _r . This zenith tropospheric delay is the result of the mapping of the slant tropospheric delays for one receiver to the local zenith of that receiver. For notational convenience, these are combined for one receiver in a

4-dimensional vector, denoted as Ax _r . Their coefficients, i.e. the receiver-satellite

line-of-sight vector for the position and the tropospheric mapping function for the ZTD, are stored in 4-dimensional vector ^ ^* . For the application of this disclosure, it is assumed that the position of the satellites are known (computed from either the satellite's navigation message, or externally provided e.g. by the International GNSS Service) and thus do not appear as unknown parameters. The second type of parameters are the receiver-dependent parameters: a receiver clock offset denoted as dt _r , a receiver phase bias (per frequency, per system) denoted as 5 ^* ₇ , and a receiver code bias (per frequency, per system) denoted as d ^* _j . The third type of parameters are the satellite-dependent parameters. These are very similar to the receiver-dependent parameters: a satellite clock offset (per system) denoted as dt ^s a satellite phase bias (per frequency, per system) denoted as S , and a satellite code bias (per frequency, per system) denoted as d ^s . The fourth type of parameters are the slant ionospheric delays, denoted as i . Because of the dispersive character of the ionosphere, the ionospheric delays for all frequencies are mapped to the ionospheric delay of the first frequency. The frequency-ionospheric coefficient is denoted and defined as μ ₇ = , with the signal's wavelength denoted as A, . The fifth type of parameters only apply to the carrier-phase measurements: these are the integer parts of the ambiguities (per frequency, per system), denoted as z ^* - .

All observables and parameters are expressed in units of range, except for the carrier-phase unique parameters, i.e. receiver/satellite phase bias and ambiguities, which are expressed in cycles (one cycle corresponds to one wavelength).

2. System-specific full-rank models.

After applying S-system theory to the observation equations of the network-component as illustrated in Figure 1 , the full-rank network multi-system model reads

Δρ^ - Δ ρ + dt; - dt* ^> 4- _μ μρ + ¾ - ¾

The tilde-symbol 7 is used to discriminate the estimable parameters from their original counterparts. The interpretations of the network-derived estimable parameters are provided in Figure 2. As shown, the estimable receiver clocks dt _r ^* are combinations of the between- station original receiver clocks dt _r and the ionosphere-free (IF) component of the system- specific receiver code biases d _r ^* _] . Therefore, due to the "system-dependency" of the receiver biases, each system has its own estimable receiver clock dt;, receiver phase biases 5 ^* ₇ , and receiver code biases d _r ^* _j . According to the interpretation of the estimable ambiguities z _r ^s* it is necessary to select one pivot satellite for each system to form the estimable ambiguities. 3. Five-fold functionality of the correction-component.

The network-derived corrections (shown in Figure 1 ) realising single-receiver integer ambiguity resolutions are presented in combined-form as follows

The combined corrections that need to be added to the user carrier-phase and code data are, respectively, denoted by and c^. They are linear combinations of the estimable satellite clocks dt ^s satellite phase biases S , and satellite code biases d ^s . With the aid of the interpretations given in Figure 2, the five-fold functionality of the correction-component is derived and presented in Figure 3. It shows that next to the primary function of the corrections, which is the removal of satellite clocks and satellite phase/code biases from the user observation equations, the corrections also establish an additional four S-basis dependent links between network and user. After applying the network-derived corrections, the full-rank multi-system user model follows as

The description of the user's measurements and the estimable unknown parameters follows from those of the network by replacing the receiver index r with the user index u. As illustrated in Figure 4, the five-fold functionality of the correction component directly makes clear how the estimability of the user parameters is linked to the estimability of the network parameters. As with the multi-system network model, the user must also take one pivot satellite per system to form the estimable ambiguities. Likewise, the user must estimate different receiver clocks and phase/code biases for each system.

4. Aligning the multi-system signals through determining the estimable ISBs Going from a single-system GNSS measurement setup to its multi-system counterpart is very beneficial in the sense of significantly increasing the number of available satellites, thus the number of observations. While an increase in the number of observations strengthen the underlying measurement model, essential care must be taken regarding the increase in the corresponding unknown parameters. Apart from the satellite-dependent parameters, the multi-system setup introduces extra unknown parameters per additional system *≠ G, that is

= (n - i ) _i = ( ; - 1) ₅ ^ = ( - 2)(« - I)

user :

# ₍ ¾ = 1. #¾ = . #¾ = (/ - 2) where # indicates the number of parameters. The presence of these extra unknowns is due to the "system-dependency" of the original receiver biases 5 ^* ₇ and d _r ^* _j . One may parameterize the full-rank multi-system models by capturing the inter-system biases with respect to one system chosen as reference, say system G. One would then be working with the differences where S _r = <¾? ₇ - and d _r = d^ . The parameters and d£ ^* are referred to as the phase and code inter system biases (ISBs), respectively. Using the above definitions, together with the interpretations given in Figure 2, the estimable parameters dt ^* , S ^* _j and d _r ^* _] are linked to their counterparts of the system G through

<K - dt _r -

u

r,3 in which d^ ^* _1F , d^ ^* and are estimable ISBs. Their interpretations are provided in Figure 5. Substitution of the above ISB-link into our earlier full-rank multi-system models gives:

• The ISB-unknown full-rank network model

• The ISB-unknown full-rank user model

-.

The above ISB-unknown models explicitly link the unknown estimable ISBs to the

observations, thus modelling one common receiver clocks and biases for the systems involved in the measurement setup, thereby aligning the multi-system signals.

5. Strengthening the multi-system network model by correcting the estimable ISBs Given the explicit formulation of the ISBs and their temporal stability, one would be in a position to a-priori determine the estimable ISBs and correct the multi-system models for these unknowns. Figure 6 provides the number of observations, number of unknown estimable parameters and the model's redundancy for a single measurement epoch. The term "redundancy" refers to the number of redundant observations, that is, the number of observations minus the number of estimable unknown parameters. The larger the redundancy is the stronger the model will be. By a-priori correcting the estimable ISBs, the model's redundancy increases, thereby strengthening the underlying model. Figure 7 provides the increase in the network model's redundancy through a-priori correcting the estimable ISBs. The increase in the user model's redundancy follows by setting n = 2.

The ISB-corrected full-rank network model reads

Comparison with the corresponding ISB-unknown model shows that non-integer phase ISB S ^* and the estimable ambiguities z* ^* . are replaced by the integer-valued ambiguities This replacement reveals that only one pivot satellite, i.e. the first satellite of the reference system G, is required to form the new estimable ambiguities Thus by correcting the estimable ISBs, the multi-system network setup can be treated as if a single-system network setup is utilised.

6. Strengthening the multi-system user model by application of ISB look-up table We now focus our attention on the multi-system user model. As with the network, the goal is to a-priori correct the ISB-unknown user model for the estimable ISBs. As shown in Figure 5 however, the interpretations of the estimable ISBs are of a between-station difference nature. Therefore, single-receiver users cannot correct their model for ISBs in as straightforward a manner as that of the network receivers. In order for the user to benefit from the network- derived estimable ISBs, we make use of the basic property of the ISBs stating that receivers of the same type (i.e. make, type, firmware) experience the same ISBs. This enables the construction of an ISB reference look-up table consisting of the network-derived ISB solutions d£/F _> ^ANCL ^r ( ^{r = 1} _> - _> ⁿ )- As the ISBs may be considered stable in time, the look-up table will be made up of accurately calibrated estimable ISBs having a low refreshment rate. The user can then search the table for a network receiver of the same type (i.e. receiver r = q) and pick up the corresponding ISBs c¾ _F , and 8 * . The concept of the ISB look-up table is illustrated in Figure 8. After applying the network-derived ISBs, the ISB-corrected full-rank user model reads

' b i"lu,3 ^: '·< · ./ - ^: ·

if

As with the network, the new integer-valued parameters take the role of the user estimable ambiguities, meaning that only one satellite, i.e. the first satellite of the reference system G, is required to be chosen as the pivot satellite. Thus the ISB-corrected model acts as if a single-system measurement setup is considered, with a difference, that the number of visible satellites can then be much larger than that of the single-system setup. 7. Cluster-based ISB-unknown network model

In constructing the aforementioned look-up table, the following two issues must be recognized:

• The inclusion of extra unknowns C¾?/F _> ^ANC ' ^r f° ^{r a} " ^tne network receivers

(r = 2, ... , n), thus considerably weakening the strength of the network model as compared to the ISB-corrected model.

• In case the number of network receivers is large, a large amount of ISB-data needs to be stored in the stated look-up table. For instance, for a network of size n = 100 tracking dual-frequency data, the number of the estimable ISBs becomes (cf. Figure 7)

(2/— l ) (n— i) ^J ~ ^" 297 per additional system

Fortunately, the above issues can be properly handled by considering the fact that the network receivers are confined to a limited number of types. In the earlier formulation, the estimable ISB parameters d^ _I ^* _F , d^ ^* and were considered to be different from receiver to receiver. The more practical scenario is the case where the network of mixed-receiver types is partitioned into h clusters. The concept is illustrated in Figure 9 where each cluster contains receivers of the same or similar type. Upon such clustering, the number estimable ISB considerably reduces. For a network of size n = 100 tracking dual-frequency data, but then clustered by h = 8 receiver types, the number of the estimable ISBs reduces from 297 to f=2

(2/— l){ h,— 1 ) ^' =~ 21 per additional system

The foregoing is illustrative of the present invention and is not to be construed as limiting thereof. Although a few exemplary embodiments of this invention have been described, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the claims. In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the word "comprise" or variations such as "comprises" or "comprising" is used in an inclusive sense, i.e. to specify the presence of the stated features but not to preclude the presence or addition of further features in various embodiments of the invention. It is to be understood that, if any prior art publication is referred to herein, such reference does not constitute an admission that the publication forms a part of the common general knowledge in the art in any country. List of abbreviations:

GNSS = Global Navigation Satellite Systems

ISB = Inter System Bias

GPS = Global Positioning System

QZSS = Quasi-Zenith Satellite System

IRNSS = Indian Regional Navigation Satellite System PPP = Precise Point Positioning

RTK = Real-Time Kinematic

PPP-RTK = Precise Point Positioning Real-Time Kinematic ZTD = Zenith Troposp eric Delay

IF = Ionosphere-free