Method and system to reduce convergence time of precise point positioning

Abstract

A method to reduce convergence time of Precise Point Positioning (PPP) uses triple-frequency signals from multiple Global Navigation Satellite System (GNSS) satellites that transmit ranging signals on three, four, or five frequencies. Satellites transmitting on three or more frequencies provide more choices for iono-free observables and allows for more robust adaptive algorithms. The method to reduce convergence time of Precise Point Positioning using triple-frequency signals from multiple GNSS constellations pertains to an algorithm for PPP.

Description

METHOD AND SYSTEM TO REDUCE CONVERGENCETIME OF PRECISE POINT POSITIONINGFIELD OF THE INVENTION

[0001] The present disclosure relates generally to global positioning, and more particularly to a method for a universal triple-frequency PPP -rover solution, compatible with a range of publicly available open-formatted PPP correction streams.BACKGROUND

[0002] Global Navigation Satellite Systems (GNSS), such as GPS (USA), GALILEO (EU), GLONASS (Russia), and BeiDou Navigation Satellite System (China) transmit radio signals that enable users to determine their position, velocity, and time (PVT). Since dispersive signal delays in the ionosphere are the greatest challenge and error source in accurate positioning, all GNSS were from inception designed to transmit on at least two frequencies (LI and L2) to mitigate those delays by using dual-frequency iono-free observables. Multi-frequency GNSS have become available to further enhance mitigation of dispersive signal delays in the ionosphere. Galileo currently transmits five signals and GPS has five fully capable triplefrequency satellites that are currently available, and more are planned to be launched. BeiDou operates more than 30 four-frequency satellites. The Russian GLONASS has three satellites transmitting triple-frequency CDMA signals. The current availability of triple-frequency signals is already sufficient for practical implementation of multi -frequency technologies.

[0003] Research to improve Precise point positioning ambiguity resolution (PPP AR) with the use of the 3rd frequency has been attempted in the past. The operation of PPP in known applications depends upon commercial networks of reference stations and the use of proprietary data streams. What is needed is a universal PPP-rover solution, compatible with a range of PPP correction providers.SUMMARY

[0004] A method for triple-frequency precise point positioning ambiguity resolution includes the steps of generating a Main Navigation Filter (MNF), processing IF code and IF phase with float ambiguities using the MNF until wide lane frequencies are resolved, and processing IFcode, by the MNF, using the best available unambiguous iono-free measurement combination after wide-lane frequencies are resolved. A precise point positioning ambiguity resolution (PPP AR) solution is generated in response to determining that LI has been resolved and a precise point positioning (PPP) float solution is generated in response to determining that LI has not been resolved. The method can further include the steps of generating an additional navigation filter for wide-lane ambiguities filtering and resolution using reference satellites different from reference satellites used by the MNF and processing IF code and Wide-Lane lono-Free (WLIF) phase with float ambiguities using the additional navigation filter (ANF). In one embodiment, the wide-lane ambiguities are resolved by the ANF and extra wide-lane ambiguities are resolved externally in response to the ANF failing or operating slower than necessary. In one embodiment, the extra wide-lane ambiguities are resolved by averaging the Melbourne-Wubbena combination. In one embodiment, the best available unambiguous iono- free measurement combination is selected by: selecting WLIF in the main navigation filter in response to determining that LI, L2, L3, Pl, and P2 are available and selecting a Minimal Code Noise-3 (MCN-3) in the MNF in response to determining that LI, L2, Pl, P2, and P3 are available, wherein an IF code is used in the MNF in response to determining that LI, L2, Pl, and P2 are available.

[0005] A method for using the best trio of signals includes the steps of selecting the best WLIF in response to determining that the best choice of LI, L2, and L3 are available, selecting a second-best WLIF in response to determining that the second-best choice of LI, L2, and L3 are available, selecting a third-best WLIF in response to determining that a third-best choice of LI, L2, and L3 are available, and selecting a different processing mode in response to determining that the best choice, the second-best choice, and the third-best choice of LI, L2, and L3 are not available.

[0006] A method for robust LI ambiguity resolution using a LAMBDA-based ambiguity resolution technique combining ‘fix-and-hold’ and ‘epoch-wise’ strategies includes the steps of fixing a subset of ambiguities to minimize error probability, generating an ambiguity set comprising a generic set of candidate integer ambiguities characterized by a rating and stored for further reuse, using stored ambiguity sets for epochs which do not allow ambiguity resolution with current epoch measurements, and using a multicriterial approach to reduce aset of several parameters to a single criterion to be a single measure of validity to facilitate easier comparison and ordering of entities.

[0007] An apparatus having memory storing computer program instructions and a computer readable medium storing instructions for a method for triple-frequency precise point positioning ambiguity resolution are also described herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1A shows a graph of IF code vs. WLIF, Galileo PRN 30, meters;

[0009] FIG. IB shows a graph of IF code vs. WLIF, Galileo PRN 15, meters;

[0010] FIG. 2A shows a graph of IF code vs. WLIF, GPS PRN 11, meters;

[0011] FIG. 2B shows a graph of IF code vs. WLIF, GPS PRN 32, meters;

[0012] FIG. 3 A shows a graph of IF code vs. WLIF, BDS PRN 19, meters;

[0013] FIG. 3B shows a graph of IF code vs. WLIF, BDS PRN 34, meters;

[0014] FIG. 4 shows a triple-frequency PPP-AR algorithm based on the use of WLIF according to one embodiment;

[0015] FIG. 5A shows IF code vs noise-optimal triple-frequency, GPS PRN 27, meters;

[0016] FIG. 5B shows IF code vs noise-optimal triple-frequency, GAL PRN 4, meters;

[0017] FIG. 6 shows IF code vs noise-optimal triple-frequency, BDS PRN 26, meters;

[0018] FIG. 7. shows a method for using optimal MNC LCs in both ANF and MNF according to one embodiment;

[0019] FIG. 8 shows a method for using the best trio of signals when available according to one embodiment;

[0020] FIG. 9 shows a method including an ambiguity-coasting (amb-coasting) mechanism according to one embodiment;

[0021] FIG. 10A shows a graph with traditional constraints and multiple constant thresholds according to one embodiment;

[0022] FIG. 10B shows a graph illustrating how multi -criteri al constraints can be reduced to a single circular threshold ; and

[0023] FIG. 11 shows a high-level schematic of a computer for implementing the methods described herein according to one embodiment.DETAILED DESCRIPTION

[0024] The methods (also referred to as algorithms) described herein offer a generic Precise Point Positioning (PPP) rover algorithm that is able to work with a wide range of open- formatted commercially available correction streams, for example, SSR-C, Terrastar, Starpoint, etc. Although some of the principles of Wide Lane lono-Free (WLIF)-based PPP AR have already been formulated, no practical industry-grade processing system based on these principles exists. The method described herein provides a universal PPP -rover solution, compatible with a range of high accuracy triple-frequency PPP corrections providers.

[0025] A method to reduce convergence time of Precise Point Positioning (PPP) using triplefrequency signals from multiple Global Navigation Satellite System (GNSS) satellites that transmit ranging signals on three, four, or five frequencies is described herein. Satellites transmitting on three or more frequencies afford more choices for iono-free observables and allow for more robust adaptive algorithms.

[0026] Demand for seamless cm-level global positioning service stimulated the development of PPP technology characterized by using a single global source of corrections broadcast via the Internet or satellites. One challenge of PPP is the need for protracted initialization which could reach 15-30 min, which is too long for many practical applications, particularly on land. The initialization of PPP is typically implemented via joint processing of iono-free (IF) phase (LI, L2) and iono-free (IF) code pseudoranges (Pl, P2), using the formulas:whereIFphase is iono-free phase combination of phases Li and L2 (all phases in meters);IF code is iono-free code combination of pseudoranges Pi and P2 (in meters); fi.f2 are carrier frequencies of signals LI and L2.

[0027] The initialization of PPP also depends upon the availability of externally provided corrections, such as precise orbits / clocks and code / phase biases. The duration of the initialization period depends upon the noise of IF code pseudoranges. The lower the noise,the shorter the initialization period. With more than two frequencies, multiple choices for IF code observables become available. With three frequencies (LI, L2, L3) two Wide-Lane (WL) phase observables can be formed: a usual WL with a wavelength about Im and an Extra-Wide Lane (EWL) formed of carrier waves L2, L3 with a wavelength of several meters. (It should be noted that in existing constellations, the trio of frequencies is not symmetrical: L2 is situated between LI and L3, but much closer to L3 than to LI.) The phase pseudoranges (L) for WL and EWL can each be calculated using the formulas:whereLWL is wide-lane phase pseudorange (unambiguous), derived from phases Li and L2 (all phases in meters);LEWIS' extra-wide lane phase pseudorange (unambiguous), derived from phases L2 andLs (all phases in meters);TVw / is wide-lane phase ambiguity in cycles;Wew / is extra- wide lane phase ambiguity in cycles; wide-lane wavelength in meters; z^n' / is extra-wide lane wavelength in meters; fi,f2,fs are carrier frequencies of signals LI, L2, L3.

[0028] A unique phase-only iono-free combination, referred to as Wide Lane lono-Free (WLIF) can be generated using the combination of WL and EWL phases (LWL and LEWL above) in the same manner as the usual IF phase is generated using raw phases LI and L2 using the formula:whereWLIF wide-lane iono-free phase combination (unambiguous, in meters).Multiple iono-free code combinations can be defined as well as linear combinations thatinclude phases and codes on multiple frequencies available from different positioning systems.

[0029] Joint processing of an optimal trio of signals at three frequencies can significantly help to accelerate convergence of PPP due to special properties of triple-frequency WLIF combination. However, the use of more than three signals results in little additional benefit. A suitable processing strategy for systems transmitting ranging signals on four or more frequencies (e. g., Galileo and BeiDou) would be to select most efficient trios of signals. The selection criteria are as follows: (1) the L1-L2 separation should be as narrow as possible in order to maximize the WL wavelength; (2) the WLIF noise amplification factor (Table 1 below, right-most column) should be as low as possible in order to optimize the performance of WLIF pseudoranges. Table 1 below contains the list of optimal trios of signals for Galileo and BeiDou. For GPS only one trio is available.Table 1.

[0030] In dual -frequency PPP, the main filter performs joint processing of IF code and IF phase. Due to high meter-level noise of IF code, the convergence of IF phase ambiguities is slow. Even with the use of multiple constellations it takes 5-10 minutes. If the IF code is replaced with a low-noise pseudorange observable, the filter converges faster. In one embodiment of the method described herein, the unambiguous WLIF observable is substituted for the IF code. Once both WL and EWL ambiguities are resolved and corrected, the WLIF combination can be used instead of the IF code. The WLIF combination with resolved ambiguities thus functions as pseudorange. Due to noise amplification factors the noise of WLIF is dm-level even though it is composed of phase measurements.

[0031] The comparison of noises of IF code and WLIF is presented in FIGS. 1-3 (described below). The noise of WLIF is represented by the time series of a difference (WLIF-IF phase) and the noise of IF code is similarly represented by a difference (IF code-IF phase). Because the noise of IF phase is much lower than the noises of both WLIF and IF code, comparing the time series of these two geometry-free differences is equivalent to comparing noise components of WLIF and IF code.

[0032] Although the noises of raw phases are generally smaller than the noises of raw code pseudoranges by a factor of about a 100, the noise of WLIF is amplified by factors of 50-100 (an order of magnitude of the coefficients of WLIF linear combination) relative to the noise of raw phase measurements, such that it becomes dm-level. Observed differences of behavior between WLIF and IF code can be explained by physical differences between code and phase multipath and tracking noise. The WLIF curves are visibly smoother, especially for Galileo and BDS, due to the relatively low noise amplification factors compared to GPS. For GPS only the newest Block III satellites can currently be included in WLIF processing due to the well-known L5 clock anomaly affecting older L5-enabled satellites. With regards to BeiDou, it should be noted that some BDS satellites exhibit code biases. For such satellites, the benefit of replacing IF code with WLIF could be even more significant.

[0033] The graphs presented in FIGS. 1-3 are obtained with the use of an NG5 receiver and PGF1 antenna. This type of antenna is typically used in precise industrial applications, such as precise agriculture, construction, or machine control. The ratio of code / phase noises is antenna-dependent, hence for other antennas (geodetic or mass market - smartphones, automotive etc.) the plots will look different.

[0034] FIGS. 1A and IB show a noise comparison of IF code and WLIF pseudoranges for Galileo. FIG. 1A shows a graph of IF code vs. WLIF for Galileo PRN 30 whereas FIG. IB shows a graph of IF code vs. WLIF for Galileo PRN 15. Both FIG. 1A and FIG. IB are graphs showing meters on the Y axis and 10A4 seconds in day on the X-axis. Both graphs are based on the data collected on an NG5 receiver on 08.06.2024.

[0035] FIGS. 2A and 2B show a noise comparison of IF code and WLIF pseudoranges for GPS. FIG. 2A shows a graph of IF code vs. WLIF for GPS PRN 11 and is an example of a Block III satellite (fully modernized), whereas FIG. 2B shows a graph of IF code vs. WLIF for GPS PRN 32 and is an example of a Block IIF satellite (affected by the L5 anomaly). BothFIG. 2A and FIG. 2B are graphs showing meters on the Y axis and 10A4 seconds in day on the X-axis. Both graphs are based on the data collected on an NG5 receiver on 08.06.2024.

[0036] FIGS. 3A and 3B show a noise comparison of IF code and WLIF pseudoranges for BeiDou. FIG. 3 A shows a graph of IF code vs. WLIF for BDS PRN 19 whereas FIG. 3B shows a graph of IF code vs. WLIF for BDS PRN 34 and is an example of a satellite affected by variable code biases. Both FIG. 3A and FIG. 3B are graphs showing meters on the Y axis and 10A4 seconds in day on the X-axis. Both graphs are based on the data collected on an NG5 receiver on 08.06.2024.

[0037] FIG. 4 shows a flow-chart of method 400 for a cascading ambiguity resolution process starting at start 402. The method begins simultaneously at three entry-points where 3 fdters are initialized: Melboume-Wubbena Filter-init (MWF-init) at step 406, ANF-init at step 410, and MNF-init at step 404. Each of the three fdters results in the resolution of respective ambiguities and passes the resolved ambiguities to the next level of the fixing cascade. The filters run epoch-wise and every time it is checked whether the resolution was successful. The resolution of EWL(MW) is the simplest and is normally the fastest. Once it is done (step 408), the EWL ambiguities are passed to the ANF (step 410) and attempts to resolve WL will begin. It should be noted that a rapid fixing of WL with ANF is possible only in triple-frequency PPP; if triple-frequency processing is impossible for any reason, WL can be resolved in a usual way via a Melboume-Wubbena Filter (MWF). Once WL ambiguities are resolved (set 412), both WL and EWL ambiguities are passed to the WLIF-substitution module (step 414) and MNF switches from the joint processing of IF code / IF phase to the joint processing WLIF / IF phase. The MNF is used to fix LI ambiguities and produce a PPP solution (either float or fixed). At step 416, it is determined whether LI ambiguities have been resolved. LI ambiguity resolution goes as follows: once IF float ambiguities are sufficiently converged, an attempt can be made to extract float estimates of LI ambiguities together with their covariances and employ a standard fixing procedure to resolve LI (see FIG. 9). An effective wavelength in this process is about half of the wavelength of LI (e g., 0.109 m for Galileo). If LI has been resolved, a PPP AR solution is generated at step 418. If LI has not been resolved, a PPP float solution is generated at step 420.

[0038] While in dual-frequency PPP there is only one way to construct IF LCs, with three frequencies we have a one-parameter family of LCs from which LCs with optimal qualitiescan be identified. It is possible to select the Minimal Code Noise (MCN) IF code LC. The optimal LC would have a general form:In one embodiment, the optimal (minimum -noise) coefficients are shown in table 2:Table 2.

[0039] The gain that can be achieved with the use of a 3rdfrequency is shown in FIGS. 5 and 6.

[0040] FIGS. 5A and 5B show a comparison of triple-frequency MCN and dual -frequency standard IF codes for GPS, shown in FIG. 5A, and Galileo, shown in FIG. 5B. FIG. 5A shows IF code vs noise-optimal triple-frequency linear combination (LC-optimal) for GPS PRN 27 whereas FIG. 5B shows IF code vs noise-optimal triple-frequency for GAL PRN 4. Both graphs are based on the data collected with an NG5 receiver on 08.06.2024. FIG. 6 shows IF code vs noise-optimal triple-frequency for BDS PRN 26 which illustrates a comparison of triple-frequency MCN with dual -frequency standard IF code for BDS. The graph is based on the data collected with an NG5 receiver on 08.06.2024.

[0041] In one embodiment, optimal MNC LCs are used instead of standard IF codes in both ANF and MNF. The logic of switching from standard IF codes to MNC LCs is shown and described in connection with FIG. 7 (described below).

[0042] In one embodiment, methods described herein are designed to optimize performance by automatically selecting the best combinations of available GNSS observations and using them in the most efficient way. In contrast, traditional rigidly structured algorithms are programmed to use fixed combinations of a-priori prescribed signals. These traditional algorithms will fail if some of the required observations are not available due to any reason, such as: selective interference, hardware limitations, restrictions of network corrections, or just random tracking outages in challenging environments, such as under foliage or in urban canyons. In one embodiment, the methods described herein will also use most performativecombinations of observations when they are available. However, when the desired set of signals is lost, the methods described herein revert to the next-in-line and the nearest in quality set of signals with minimal drop in performance.

[0043] The operation of the methods described herein is achieved using substantial logical sophistication of the associated algorithm. The following two examples illustrate this approach. First, the diversity of the MNF processing modes is described, and second, how the method described herein chooses between not-the-best trios of signals.

[0044] Depending on the availability of measurements, the MNF could run in different modes as shown in method 700 of FIG. 7. The method begins at start 702 and proceeds to step 704 where it is determined if LI, L2, L3, Pl, and P2 are available. If LI, L2, L3, Pl, and P2 are available, the method proceeds to step 706 and the WLIF is used in the MNF. If LI, L2, L3, Pl, and P2 are not available the method proceeds to step 708 where it is determined if LI, L2, Pl, P2, and P3 are available. If LI, L2, Pl, P2, and P3 are available, the method proceeds to step 710 and MCN-3 is used in the MNF. If LI, L2, Pl, P2, and P3 are not available, the method proceeds to step 712 where it is determined if LI, L2, Pl, and P2 are available. If LI, L2, Pl, and P2 are available, the method proceeds to step 714 and IF code is used in MNF (dual frequency PPP). If LI, L2, Pl, and P2 are not available the method proceeds to step 716 because no triple-frequency PPP is available and ordinary dual-frequency PPP is used. As shown in method 700 of FIG. 7, in the best-case scenario, if L3 phase is available, WLIF is formed and is used in MNF. In this case availability of P3 is not important (in reality, the code pseudorange P3 is always available if phase on L3 is available). The inverse is more realistic in that it is possible to have no L3 phase, but only P3 code. In this case processing on MNF can be optimized using MCN triple-frequency combinations (MCN-3).

[0045] In one embodiment, the method allows for the use of suboptimal trios of signals in cases when some signals (typically, the third frequency) are not available. Such an option would be needed only for satellites transmitting on more than three frequencies. Table 3 below shows Galileo’s available trios of signals.Table 3.

[0046] As shown in the table above, for Galileo, three possible trios of signals can be used. The best trio and second-best trio include E6, while this signal is somewhat uncommon and some receivers, particularly old ones, might not track E6, or some correction streams might not include this signal. The same is true of E5a / E5b: because these signals are similar, for some older receivers E5a-only or E5b-only signal tracking options were foreseen.

[0047] FIG. 8 shows method 800 according to one embodiment in which the best trio of signals is selected when available, otherwise the method falls back to the second-best and the third-best in sequence. This method is applicable to both Galileo and BeiDou. Method 800 begins at start 802 and proceeds to step 804 where it is determined if the best choice of LI, L2, and L3, is available. If the best choice of LI, L2, and L3 is available, the method proceeds to step 806 and the best WLIF is selected for use in MNF. If the best choice of LI, L2, and L3 is not available the method proceeds to step 808 where it is determined if the second-best choice of LI, L2, and L3 is available. If the second-best choice of LI, L2, and L3 is available, the method proceeds to step 810 and the second best WLIF is selected for use in MNF. If the second-best choice of LI, L2, and L3 is not available, the method proceeds to step 812 where it is determined if the third-best choice for LI, L2, and L3 is available. If the third-best choice for LI, L2, and L3 is available, the method proceeds to step 814 and the third-best WLIF is selected for use in WLIF. If the third-best choice for LI, L2, and L3 is not available, the method proceeds to step 816 because the WLIF is not usable and another mode should be selected.

[0048] With respect to ambiguity resolution, two strategies are used, namely, fix-and-hold and epoch-wise fixing. Both strategies begin with the navigation filter estimating float ambiguities. The two strategies differ after a first fix. In the fix-and-hold paradigm all fixed ambiguities in the PPP filter are set to their integer values and are treated as resolved. Un-fixed ambiguities remain float ambiguities, and the filter becomes a mixed fixed-and-float filter, which, in one embodiment, is the only filter used in this strategy.

[0049] In the epoch-wise approach, the MNF runs with float ambiguities independently of the fixing process which occurs anew in each epoch in a separate filter. For each epoch, the data and status parameters of the main filter are copied to a one-epoch ‘fixing filter’ where fixing attempts occur. If enough ambiguities are resolved, a ‘fixed’ positioning solution is produced.

[0050] Each of the two strategies has its benefits and drawbacks. With the fix-and-hold approach, fixing is more random chance: once a choice is made it stays forever and wrong fixes are notoriously hard to detect. Because the price of an error is so high, fixing criteria must be strict and first fixes are inevitably delayed. The epoch-wise strategy is repeatedly verifying itself, hence an occasional wrong fix is more likely to be replaced with a good fix automatically. On the other hand, this strategy takes no advantage of the fundamental property of integer ambiguities, namely their constancy. Fixing an ambiguity just one time must be enough, assuming that the fix is correct.

[0051] A mixed strategy has been designed based on the concept of an ambiguity set (ambset). An ambset is any, possibly incomplete, set of integer ambiguities. The two-filter architecture of an epoch-wise method is retained but previously fixed ambiguities are stored in an ambset storage allowing their reuse at future epochs. Ambset objects contain not only ambiguities themselves but also related information items which are used to assess their chances of being correct (referred to as “rating”). In this way we mitigate the inherent instability of the epochwise approach, its tendency to jump out of a good fix for short periods of time or to have short no-fix intervals.

[0052] For example, assume that at a certain epoch there are 12 good satellites, and ambiguities are resolved. Also assume, that at the next epoch, due to changing satellite visibility on the rover side, only 5 satellites would remain, and fixing would become impossible. In such a situation, an epoch-wise algorithm would report a ‘no-fix’, but fix-and- hold algorithms would have no problems at all using previously fixed ambiguities. In one embodiment, an algorithm handles such cases through a mechanism of ‘amb-coasting’, which includes storage and reuse of previously fixed ambiguities.

[0053] In one embodiment, a method includes the mechanism of LI ambiguity resolution optimized for robust fixing in diverse application environments. At entry, a set of float LIambiguities together with their covariance matrix are produced (this is a normal epoch-wise output of the MNF). At the first step of AR, these float ambiguities are passed to a standard LAMBDA module, and a resolution attempt is made and validated by a customary combination of norm-tests and ratio-tests augmented by an additional condition constraining the difference between float and PPP AR solutions. If the first candidate set of LI ambiguities is rejected, best subsets are picked out in sequence. LAMBDA-resolution is repeated with each of the subsets, the total number of attempts not exceeding MAX SUBSETS. If the first LAMBDA-candidate and all its subset-candidates fail to pass validation, the AR-algorithm turns to amb-coasting as shown in FIG. 9.

[0054] FIG. 9 shows method 900 including amb-coasting mechanism 902. The definitions of terms used in FIG. 9 are as follows. Amb-coasting is a method of storage and reuse of successful ambiguity sets. Float amb set, a target of fixing is a set of float LI ambiguities which are derived from float iono-free ambiguities sufficiently converged in the MNF such that a fixing (i. e., ‘collective rounding’) attempt can be undertaken. |Float-fix| test is an empirical test used to validate sets of ambiguity candidates. In order to pass a test, the geometric distance between the position of the float solution and a fixed solution to be tested cannot exceed the threshold value of MAXFLTminFIX. LAMBDA is a well-known method of integer least-squares adjustment. LAMBDA begins with a vector of LSQ-optimal float ambiguities and a var-covar matrix produced in the MNF filter. In a sequence of decorrelation steps LAMBDA transforms the var-covar matrix to a more spherical form and thus simplifies the search of candidates with minimal norm values. MAXFLTminFIX is a threshold value of the |Float-fix| test. MINposStdFxd is the minimal standard deviation of calculated position to be fixed. MINtropoStdFxd is the minimal standard deviation of the unmodeled residual zenith wet troposphere delay, which is treated in PPP as an unknown value. MNF is the Main Navigation Filter, the principal filter that processes iono-free code and phases and where float ambiguities converge. Norm test is a well-known empirical test used to validate sets of integer ambiguity candidates. The basic norm value is the Mahalanobis distance between an LSQ-optimal set of float ambiguities and a set of integer candidates. In an ideal case norm=0, hence the valid value of a successful norm test must be smaller than the norm test threshold. Ns is a counter of best sets of ambiguity candidates obtained in the procedure of partial fixing. Pos. std. is an a-priori (i.e., theoretical) estimation of the expected 3D standard deviation ofthe calculated position. At step 908 a Pos. std. is used as an indicator of convergence of the float solution in the MNF. At the onset of the MNF, the Pos. std is initialized to a large value, gradually decreasing with convergence. When the Pos. std gets smaller than the threshold value of MINposStdFxd, (and when a similar condition also holds for the Tropo. std.) the float solution is considered sufficiently converged to begin fixing attempts. Tropo std. is an a- priori (theoretical) estimation of the expected standard deviation of the unmodeled residual zenith wet tropospheric delay, which is treated in PPP as an unknown value. At the initialization of the MNF, the Tropo, std. is set to a relatively large value, gradually decreasing with convergence. When the Tropo. std gets smaller than the threshold value of MINtropoStdFxd, (and when a similar condition also holds for the Pos. std.) the float solution is considered sufficiently converged to begin fixing attempts. PPP AR solution is a PPP solution with resolved integer phase ambiguities, which are said to be ‘fixed’. PPP float solution is a positional solution based on float ambiguities. Such a solution is outputted when fixing fails or is impossible. Ratio test is a well-known empirical test used to validate sets of ambiguity candidates. The basic ratio value is the ratio of the norm of the best candidate to the norm of the second-best candidate. In order to pass, the ratio test value must be higher than the threshold, see also Norm test.

[0055] In one embodiment, method 900 consists of four algorithmic modules: (Module 1, steps 906-912) identifies the target set of float ambiguities and assesses ‘maturity’ of convergence; (Module 2, steps 916, 918, 920, 924) performs LAMBDA fixing attempt and validation; (Module 3, steps 914, 922) performs partial fixing; (Module 4, steps 928-924) performs Amb-coasting: if a new fix is invalid or impossible, the module checks if a previously stored ambiguity set can be reused. Note that method 900 outputs either a PPP AR solution (‘fixed PPP’) or a PPP float solution. Detailed descriptions of how the modules function are as follows. Module 1 identifies a set of float LI ambiguities produced by the MNF filter as a target for fixing and checks whether the filter has enough converged to attempt fixing. Module 2, using LAMBDA version of integer LSQ, searches for a number of integer candidates, nearest to target float values in a sense of a ‘norm test’ (Mahalanobis distance); candidates have to pass three validation tests to be accepted. With respect to module 3, there is a chance that the LAMBDA-best candidate would not pass validation because one or two target ambiguities are estimated with a bias while others are fine. In this case partial fixingmight work, if satellites which block fixing would be removed while those likely to be easily fixed would be retained. With respect to module 4, if all fixing attempts with float ambiguities of the current epoch would fail, the module resorts to stored ambiguities paying particular attention to possible losses of lock.

[0056] Method 900 pertains to the fixing process and its detailed description is as follows. Method 900 begins at start 904 and proceeds to its first operation at step 906 where a set of MNF float ambiguities, a target of this fixing process is identified. It proceeds further to steps 908 and 912 where it is determined whether the filtering process of the MNF is sufficiently converged to begin fixing. Two parameters are chosen as indicators of convergence: Pos. std and Tropo. std, which both decrease with convergence. The accuracy of calculated position improves with time, hence position std is decreasing. Tropo std refers to the tropospheric residual zenith delay estimated by the float filter and is also decreasing with convergence. Method 900 will proceed to fixing if both std’s shall get lower than their defined thresholds MinposStdFxd and MintropoStdFxd. At the start-up of the filter both std’s are large values and they exceed the thresholds, hence the positional output will always begin with a few epochs of the float solution. If both Pos. std and Tropo. std drop to the levels lower than their respective thresholds, fixing might be attempted and the processing proceeds to Module 2. Passing over the data administration step 914 we enter the LAMBDA rectangle (step 916) which contains all there is to fixing in a proper sense. LAMBDA is a classical technique which allows to de-correlate the variance-covariance matrix of float ambiguities in order to accelerate the search process which would deliver a set of best (nearest to the target set of float candidates in the sense of Mahalanobis distance) integer fix candidates which are characterized by the so-called ‘norm’, derived from the Mahalonobis distance. The best candidate, having the smallest norm, must satisfy three empirical criteria. The first one is the norm test (step 918): the value of the norm must be lower than the threshold (if the estimation of the float ambiguities were ideal, the norm would be zero). The second is a ratio test (step 920): it would reject the best candidate if it were too close to its second-best (this would mean that the process is unable to distinguish two best ambiguity sets). The third test (step 924) verifies that fixed and float positional solutions are sufficiently close to each other in terms of geometric distance. The three validation tests work together as a single validation module: if they all succeed, the fixed PPP solution is outputted (step 926). If at least one of them fails,the best candidate is declared invalid, and the partial fixing loop gets control. The main body of the loop is the same LAMBDA joined with the same three validation criteria. But the integer ambiguity candidates would now contain incomplete sets of integer ambiguities, such that some ambiguities would remain float. The execution of the loop is controlled by the counter Ns which is initialized to 0 at the start of fixing. The counter is incremented at each execution of the loop in step 922 but not more than MAX_SUBSETS times. Once Ns++ exceeds MAX_SUBSETS, the loop exits w / o success, and the Amb-coasting module gets control (step 928). The purpose of Amb-coasting is to use previously validated ambiguities deemed reliable enough for reuse at a later epoch. In any case, before we accept a stored set of ambiguities it must pass again the |Float-fix| test.

[0057] It should be noted that amb-coasting mechanism 902 requires that sufficiently reliable ambiguity sets (ambsets) are stored and available for reuse unless a loss-of-lock or any other event invalidating previous ambiguities would occur. If no ambsets are stored, or if those available did not pass validation, the failure of fixing is reported.

[0058] Amb-coasting mechanism 902 stores current ambiguities, but only those which themselves are fixed by LAMBDA and not those retrieved from the coasting storage. This means that the ambset storage of the coasting mechanism always contains the latest LAMBDA fix. Each stored ambset has a rating which is obtained by a multi criteri al formula, of the kind described in the following section. Validity criteria of stored ambsets are as follows:

[0060] In one embodiment, a method for multi-frequency precise point positioning ambiguity resolution begins with generating a main navigation filter. IF code and IF phase with float ambiguities are processed using the main navigation filter until wide lane frequencies are resolved. IF code is processed by the main navigation filter using the best available unambiguous iono-free measurement combination after wide-lane frequencies are resolved.Then, a precise point positioning ambiguity resolution solution is generated in response to determining that LI has been resolved. A precise point positioning float resolution solution is generated in response to determining that LI has not been resolved. In one embodiment, the method can further include the steps of generating an additional navigation fdter for wide- lane ambiguities filtering and resolution using reference satellites different from reference satellites used by the main navigation filter and processing IF code and Wide-Lane lono-Free (WLIF) phase with float ambiguities using the additional navigation filter. In one embodiment, the wide-lane ambiguities are resolved by the additional navigation filter and extra wide-lane ambiguities are resolved externally in response to the additional navigation filter failing or operating slower than necessary. In one embodiment, the extra wide-lane ambiguities are resolved by averaging the Melbourne-Wubbena combination. In one embodiment, the best available unambiguous iono-free measurement combination is selected by: selecting WLIF in the main navigation filter in response to determining that LI, L2, L3, Pl, and P2 are available and selecting an MCN-3 in the main navigation filter in response to determining that LI, L2, Pl, P2, and P3 are available, wherein an IF code is used in the main navigation filter in response to determining that LI, L2, Pl, and P2 are available.

[0061] A method for using a best trio of signals includes the steps of selecting a best WLIF in response to determining that a best choice of LI, L2, and L3 are available, selecting a second-best WLIF in response to determining that a second-best choice of LI, L2, and L3 are available, selecting a third-best WLIF in response to determining that a third best choice of LI, L2, and L3 are available, and selecting a different processing mode in response to determining that the best choice, second best choice, and third best choice of LI, L2, and L3 are not available.

[0062] A method for robust LI ambiguity resolution using a LAMBDA-based ambiguity resolution technique combining ‘fix-and-hold’ and ‘epoch-wise’ strategies includes the steps of fixing a subset of ambiguities to minimize error probability, generating an ambiguity set comprising a generic set of candidate integer ambiguities characterized by a rating and stored for further reuse, using stored ambiguity sets for epochs which do not allow ambiguity resolution with current epoch measurements, and using a multicriterial approach to reduce a set of several parameters to a single criterion to be a single measure of validity to facilitate easier comparison and ordering of entities.

[0063] In one embodiment, a method uses a generalized multi criteri al approach to validate ambiguity sets and constrain other processes that can be characterized by parameters with a few empirically optimizable thresholds. The multicriterial approach reduces a set of several parameters to a single parameter, which is referred to as a rating and is meant to be a single measure of validity allowing for easier comparison and ordering of entities in accordance with certain validity criteria. As an example, consider a case with two parameters x and y having positive values with a range of validity between 0 and 1, where 0 is its ideal value and 1 is its validity threshold. This is sufficiently general because any other validity range can be scaled to [0; 1] by a linear transformation. It can be assumed that the two criteria x and y are uncorrelated. In this case the statistical ‘cloud’ of sample points is likely to exhibit radial symmetry. Hence the traditional two-dimensional validation scheme with two logically ANDed constant thresholds will be useable but sub-optimal. As an example, consider the three pairs [1; 1], [0; 1] and [1; 0], They all belong to the same boundary defined by two equal thresholds x<l AND y<I, while it is intuitively clear that a pair [1; 1] is more likely to be invalid that pairs [0; 1] or [1; 0], It is intuitively clear that the validity figure of a square can be ‘optimized’ by changing its shape by ‘cutting off a corner at the vertex [1; 1] and ‘smoothing out’ the corners at [0; 1] and [1; 0], To avoid discontinuity, it is simpler to replace a validity square with a validity circle. In this way, there is one radial threshold instead of a set of two constant linear thresholds. FIGS. 10A and 10B shows a reduction of bi-criterial set of thresholds to a singular circular (or ellipsoidal) rating. FIG. 10A shows graph 1000 having traditional constraints with multiple constant thresholds while FIG. 10B. shows graph 1002 having multi-criterial constraints with a single circular threshold.

[0064] Using a more formal statistical language, FIGS. 10A and 10B show a multivariate normal distribution of validity criteria that can be constrained with a single threshold value for a Mahalanobis distance directly linked to the overall error probability. Such statistical models for validity criteria can also accommodate inter-correlation between the criteria, if the need arises.

[0065] The methods described herein can be implemented using a computer. A high-level block diagram of such a computer is illustrated in FIG. 11. Computer 1102 contains a processor 1104 which controls the overall operation of the computer 1102 by executing computer program instructions which define such operation. The computer programinstructions may be stored in a storage device 1112, or other computer readable medium (e.g., magnetic disk, CD ROM, etc.), and loaded into memory 1110 when execution of the computer program instructions is desired. Thus, the method steps of FIGS. 4, 7, 8, and 9, as well as other methods and algorithms described herein, can be defined by the computer program instructions stored in the memory 1110 and / or storage 1112 and controlled by the processor 1104 executing the computer program instructions. For example, the computer program instructions can be implemented as computer executable code programmed by one skilled in the art to perform an algorithm defined by the method steps of FIGS. 4, 7, 8, and 9, as well as other methods and algorithms described herein. Accordingly, by executing the computer program instructions, the processor 1104 executes an algorithm defined by the method steps of FIGS. 4, 7, 8, and 9 or other methods and algorithms described herein. The computer 1102 also includes one or more network interfaces 1106 for communicating with other devices via a network. The computer 1102 also includes input / output devices 1108 that enable user interaction with the computer 1102 (e.g., display, keyboard, mouse, speakers, buttons, etc.) One skilled in the art will recognize that an implementation of an actual computer could contain other components as well, and that FIG. 11 is a high-level representation of some of the components of such a computer for illustrative purposes.

[0066] The foregoing Detailed Description is to be understood as being in every respect illustrative and exemplary, but not restrictive, and the scope of the inventive concept disclosed herein is not to be determined from the Detailed Description, but rather from the claims as interpreted according to the full breadth permitted by the patent laws. It is to be understood that the embodiments shown and described herein are only illustrative of the principles of the inventive concept and that various modifications may be implemented by those skilled in the art without departing from the scope and spirit of the inventive concept. Those skilled in the art could implement various other feature combinations without departing from the scope and spirit of the inventive concept.

Claims

CLAIMS:

1. A method for triple-frequency precise point positioning ambiguity resolution, the method comprising: generating a main navigation filter; processing IF code and IF phase with float ambiguities using the main navigation filter until wide-lane frequencies are resolved; processing IF code, by the main navigation filter, using the best available unambiguous iono-free measurement combination after wide-lane frequencies are resolved; generating a precise point positioning ambiguity resolution solution in response to determining that LI has been resolved; and generating a precise point positioning float resolution solution in response to determining that LI has not been resolved.

2. The method of claim 1, further comprising: generating an additional navigation filter for wide-lane ambiguities filtering and resolution using reference satellites different from reference satellites used by the main navigation filter; and processing IF code and Wide-Lane lono-Free (WLIF) phase with float ambiguities using the additional navigation filter.

3. The method of claim 2, wherein the wide-lane ambiguities are resolved by the additional navigation filter and extra wide-lane ambiguities are resolved externally in response to the additional navigation filter failing or operating slower than necessary.

4. The method of claim 3, wherein the extra wide-lane ambiguities are resolved by averaging the Melboume-Wubbena combination.

5. The method of claim 1, wherein the best available unambiguous iono-free measurement combination is selected by: selecting WLIF in the main navigation filter in response to determining that LI, L2, L3, Pl, and P2 are available; andselecting an MCN-3 in the main navigation filter in response to determining that LI, L2, Pl, P2, and P3 are available, wherein an IF code is used in the main navigation filter in response to determining that LI, L2, Pl, and P2 are available.

6. A method for using a best trio of signals comprising: selecting a best WLIF in response to determining that a best choice of LI, L2, and L3 are available; selecting a second-best WLIF in response to determining that a second-best choice of LI, L2, and L3 are available; selecting a third-best WLIF in response to determining that a third best choice of LI, L2, and L3 are available; and selecting a different processing mode in response to determining that the best choice, second best choice, and third best choice of LI, L2, and L3 are not available.

7. A method for robust LI ambiguity resolution using a LAMBDA-based ambiguity resolution technique combining ‘fix-and-hold’ and ‘epoch-wise’ strategies, the method comprising: fixing a subset of ambiguities to minimize error probability; generating an ambiguity set comprising a generic set of candidate integer ambiguities characterized by a rating and stored for further reuse; using stored ambiguity sets for epochs which do not allow ambiguity resolution with current epoch measurements; and using a multicriterial approach to reduce a set of several parameters to a single criterion to be a single measure of validity to facilitate easier comparison and ordering of entities.

8. An apparatus for triple-frequency precise point positioning ambiguity resolution, the apparatus comprising: a processor; and a memory to store computer program instructions, the computer program instructions, which, when executed on the processor cause the processor to perform operations comprising:generating a main navigation filter; processing IF code and IF phase with float ambiguities using the main navigation filter until wide-lane frequencies are resolved; processing IF code, by the main navigation filter, using the best available unambiguous iono-free measurement combination after wide-lane frequencies are resolved; generating a precise point positioning ambiguity resolution solution in response to determining that LI has been resolved; and generating a precise point positioning float resolution solution in response to determining that LI has not been resolved.

9. The apparatus of claim 8, the operations further comprising: generating an additional navigation filter for wide-lane ambiguities filtering and resolution using reference satellites different from reference satellites used by the main navigation filter; and processing IF code and Wide-Lane lono-Free (WLIF) phase with float ambiguities using the additional navigation filter.

10. The apparatus of claim 9, wherein the wide-lane ambiguities are resolved by the additional navigation filter and extra wide-lane ambiguities are resolved externally in response to the additional navigation filter failing or operating slower than necessary.

11. The apparatus of claim 10, wherein the extra wide-lane ambiguities are resolved by averaging the Melbourne-Wubbena combination.

12. The apparatus of claim 8, wherein the best available unambiguous iono-free measurement combination is selected by: selecting WLIF in the main navigation filter in response to determining that LI, L2, L3, Pl, and P2 are available; and selecting an MCN-3 in the main navigation filter in response to determining that LI, L2, Pl, P2, and P3 are available, wherein an IF code is used in the main navigation filter in response to determining that LI, L2, Pl, and P2 are available.

13. A computer readable medium storing computer program instructions for triplefrequency precise point positioning ambiguity resolution, which, when executed on a processor, cause the processor to perform operations comprising: generating a main navigation filter; processing IF code and IF phase with float ambiguities using the main navigation filter until wide lane frequencies are resolved; processing IF code, by the main navigation filter, using the best available unambiguous iono-free measurement combination after wide-lane frequencies are resolved; generating a precise point positioning ambiguity resolution solution in response to determining that LI has been resolved; and generating a precise point positioning float resolution solution in response to determining that LI has not been resolved.

14. The computer readable medium of claim 13, the operations further comprising: generating an additional navigation filter for wide-lane ambiguities filtering and resolution using reference satellites different from reference satellites used by the main navigation filter; and processing IF code and Wide-Lane lono-Free (WLIF) phase with float ambiguities using the additional navigation filter.

15. The computer readable medium of claim 14, wherein the wide-lane ambiguities are resolved by the additional navigation filter and extra wide-lane ambiguities are resolved externally in response to the additional navigation filter failing or operating slower than necessary.

16. The computer readable medium of claim 15, wherein the extra wide-lane ambiguities are resolved by averaging the Melbourne-Wubbena combination.

17. The computer readable medium of claim 13, wherein the best available unambiguous iono-free measurement combination is selected by:selecting WLIF in the main navigation filter in response to determining that LI, L2, L3, Pl, and P2 are available; and selecting an MCN-3 in the main navigation filter in response to determining that LI, L2, Pl, P2, and P3 are available, wherein an IF code is used in the main navigation filter in response to determining that LI, L2, Pl, and P2 are available.

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