Galileo five-frequency weak ionosphere PPP single-epoch wide-lane positioning method

Abstract

The application discloses a Galileo five-frequency weak-ionosphere PPP single-epoch wide-lane positioning method, which comprises the following steps: considering wavelength, noise and ionospheric amplification factor, determining a weak-ionosphere combination suitable for PPP single-epoch wide-lane positioning; smoothing multi-frequency weak-ionosphere observation values by using double-frequency ionosphere-free combination observation values with smaller noise, and improving the precision of the multi-frequency weak-ionosphere observation values; establishing two single-epoch positioning models of ionospheric float and ionospheric fixed according to whether ionospheric parameters are considered; fixing the float ambiguity estimated by the model by using an integer ambiguity search method, and obtaining a fixed solution of coordinate parameters. Compared with the traditional wide-lane positioning method which needs to fix wide-lane and super-wide-lane ambiguities step by step, the method only needs to directly fix weak-ionosphere ambiguity in one step, and the precision is equivalent, single-epoch PPP decimeter-level positioning is realized, and the operation load caused by multi-step ambiguity search can be avoided to a certain extent.

Description

Technical Field

[0001] This invention belongs to the field of GNSS (Global Navigation Satellite System) positioning and navigation technology, and relates to GNSS precise single-point positioning technology, specifically to a Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method. Background Technology

[0002] Precise Point Positioning (PPP) technology can provide high-precision navigation, positioning, and timing services globally. However, traditional PPP typically requires a convergence time of tens of minutes, which limits its application in high real-time scenarios. With the development of multi-frequency GNSS, ultra-wide lane and wide lane combinations, due to their longer wavelengths, can achieve reliable fixation in a single epoch, greatly improving the real-time performance of PPP. At the same time, multi-frequency PPP single-epoch wide lane decimeter-level positioning has become a positioning mode with great application prospects.

[0003] Currently, there are two main PPP wide-lane positioning methods: one is based on AFIF (ambiguity-fixed isosphere-free) observations, and the other is based on multi-frequency uncombined PPP sequential ambiguity fixing. The overall positioning performance of these two methods is comparable, typically achieving decimeter-level horizontal positioning globally. Regardless of whether the wide-lane positioning method is based on AFIF or uncombined PPP, its implementation often requires two steps of ambiguity fixing: ultra-wide-lane ambiguity and wide-lane ambiguity. Only when both are successfully fixed simultaneously can reliable decimeter-level positioning be achieved.

[0004] Unlike existing methods, this invention discloses a Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method to simplify the positioning process. It makes full use of the advantages of multi-frequency combined observations and achieves reliable decimeter-level positioning by directly fixing the weak ionospheric ambiguity in one step, instead of the traditional two-step ambiguity fixing in the ultra-wide lane and wide lane. The positioning process is simplified, and at the same time, the computational load introduced by multi-step ambiguity search can be avoided to a certain extent. Summary of the Invention

[0005] To address the aforementioned issues, this invention discloses a Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method. Utilizing the advantages of multi-frequency weak ionospheric combinations, it achieves decimeter-level positioning accuracy through a single step of ambiguity fixation.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method includes the following steps:

[0008] (1) Based on the theory of multi-frequency observation combination, the Galileo five-frequency weak ionospheric combination suitable for non-differential PPP solution is determined;

[0009] (2) Use dual-frequency ionospheric observations with lower noise to smooth multi-frequency weak ionospheric observations and improve their ranging accuracy;

[0010] (3) Based on whether the influence of ionospheric parameters is considered, two weak ionospheric PPP single-epoch solution models are established: ionospheric floating point and ionospheric fixed point.

[0011] (4) The integer fuzzy search method is used to fix the weak ionospheric combination fuzziness obtained by model estimation and obtain the corresponding fixed solution of coordinate parameters.

[0012] Furthermore: In step (1), the process of determining the Galileo five-frequency weak ionospheric PPP observation combination includes:

[0013] First, for the Galileo five-frequency signal, namely E1, E5a, E6, E5b, and E5ab, based on the multi-frequency observation combination theory, the carrier observation equation is established as shown in equation (1).

[0014]

[0015] Where, subscript i k (k = 1, 2, ..., 5) are the combination coefficients corresponding to the five frequencies, and all of them are integers; For combined carrier observations; ρ is the station-to-satellite distance; c is the speed of light; t r and t s These represent the clock biases of the receiver and the satellite, respectively; T represents the tropospheric delay; and I1 represents the ionospheric delay corresponding to the first frequency. This is the ionospheric amplification factor corresponding to the combined observations; The wavelength corresponding to the combined observations; The integer ambiguity of the combined observations; and These represent the receiver and satellite phase deviations included in the combined observations; ε is the noise amplification factor for the combined observations. j This is the observation noise of the base carrier. In equation (1) The specific expression is shown in equation (2).

[0016]

[0017] Among them, f i (i = 1, 2, ..., 5) correspond to the five frequencies of Galileo; The frequencies corresponding to the combined observations are shown in equation (3).

[0018]

[0019] It is important to note that This usually only reflects the impact of the residual ionosphere on ranging accuracy. To further analyze the impact of the ionosphere on ambiguity resolution, it needs to be transformed into the following form.

[0020]

[0021] For the combination coefficient i k (k=1,2,…,5), various combinations are traversed within the interval [-10,10]. Taking into account factors such as wavelength of combined observations, ionospheric amplification factor, and noise level, three combinations suitable for Galileo five-frequency weak ionospheric PPP single-epoch positioning are determined, as shown in Table 1.

[0022] Table 1 Galileo Five-Frequency Weak Ionospheric Combination Coefficients

[0023]

[0024] Further: In step (2), the process of smoothing the multi-frequency weak ionospheric observations using dual-frequency non-ionospheric observations includes:

[0025] Although the three weak ionospheric combinations have relatively long wavelengths and can theoretically be reliably fixed at a single epoch, their observation noise is amplified by 65.961, 72.656, and 95.407 times, respectively. To reduce this noise and improve observation accuracy, a combination with lower observation noise can be used for smoothing. In practical applications, to avoid ionospheric accumulation during the smoothing process, dual-frequency ionospheric observations of E1 and E5a are used for smoothing, while a suitable smoothing window (e.g., 20 epochs) is determined. Since the noise amplification factor of the dual-frequency ionospheric observations of E1 and E5a is only 2.588, which is much smaller than the noise of the weak ionospheric combination, it theoretically effectively smooths the noise.

[0026] For observations of different frequencies, they are generally considered to have equal precision and be uncorrelated, given an epoch t. i (i = 1, 2, ..., k), corresponding to the variance of carrier observations It can be represented by a sine function related to the elevation angle.

[0027]

[0028] Where a and b are generally both 0.003m; E(t) i ) represents the epoch t i The corresponding satellite elevation angle.

[0029] Meanwhile, for ease of description, the epoch t will be... i Unsmoothed observations and their corresponding variances are denoted as and Let the smoothed observations and their corresponding variances be denoted as... and The combined observations of the E1 and E5a dual-frequency ionospheric aneuploidy and their corresponding variances are denoted as L. IF (t i )and

[0030] For the first epoch t1, the smoothed combined observations With corresponding variance Equal to the unsmoothed observations and variance, according to the law of error propagation, it can be expressed in the following form:

[0031]

[0032] For the subsequent continuously smoothed k-th epoch t k Smoothed observations With corresponding variance It can be obtained using the following recursive method.

[0033]

[0034] Furthermore: In step (3), the process of constructing two positioning models, namely the floating-point ionospheric model and the fixed ionospheric model, includes:

[0035] Depending on whether the influence of ionospheric parameters is considered, the positioning model can be divided into two types: ionospheric floating-point model and ionospheric fixed model. The ionospheric floating-point model considers ionospheric parameters, while the ionospheric fixed model directly ignores ionospheric parameters.

[0036] First, an ionospheric floating-point model is constructed. Considering that satellite precision clock errors are usually based on two specific frequencies (e.g., E1 and E5a for Galileo), to avoid additional hardware bias corrections introduced by multi-frequency pseudorange observations, only the original pseudorange observations of E1 and E5a are used, instead of multi-frequency combined pseudorange observations. By combining the dual-frequency pseudorange with the weak ionospheric carrier observations in formula (1), and after appropriate parameter renormalization and simplification, the ionospheric floating-point positioning model can be obtained as follows.

[0037]

[0038] Where P1 and P2 are the original pseudoranges of the dual frequencies corresponding to E1 and E5a, respectively; e1 and e2 are the noise of the dual-frequency pseudorange observations; t r,IF and These are the receiver clock bias and satellite clock bias after parameter realignment, respectively; These are the ionospheric parameters after parameter reforming; This is the floating-point ambiguity after parameter renormalization, which incorporates pseudorange and phase hardware bias.

[0039] Based on the above model, if the influence of the ionosphere is small enough, the ionospheric parameters can be directly ignored, thereby improving the model redundancy. Since the ionospheric parameters are ignored, the dual-frequency pseudorange is combined into an ionosphere-free form to participate in the solution based on formula (8), as follows:

[0040]

[0041] Among them, P IF and e IF These are the pseudorange observations without ionosphere and their observation noise, respectively.

[0042] Further: In step (4), the process of fixing the combined ambiguity of the weak ionosphere using the integer ambiguity search method includes:

[0043] First, receiver-side hardware bias is eliminated using inter-satellite single-difference. Then, satellite-side hardware bias is corrected to restore the integer characteristics of weak ionospheric ambiguity. Finally, an integer ambiguity search algorithm is used to determine the optimal integer solution. Simultaneously, a strategy of partially fixing ambiguities can be employed to improve the search success rate. Because weak ionospheric ambiguities have a long wavelength, they can usually be fixed successfully in a single epoch. Considering their noise amplification level, theoretically, decimeter-level positioning accuracy can be guaranteed.

[0044] The beneficial effects of this invention include:

[0045] This invention proposes a Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method, which utilizes the advantages of multi-frequency weak ionospheric combination wavelengths being longer, ionospheric insensitivity, and integer solvability of combined ambiguities. By directly fixing the ambiguity of the weak ionospheric ultra-wide lane, reliable single-epoch decimeter-level positioning can be achieved. Compared to conventional PPP wide-lane positioning methods, which typically require a two-step ambiguity fixing process—fixing the ultra-wide lane and wide lane ambiguities separately—reliable decimeter-level positioning can only be achieved when both ambiguities are successfully fixed simultaneously, this invention requires only one ambiguity fixing step to achieve similar positioning results. This simplifies the positioning process and also avoids the computational burden of multi-step ambiguity searches to some extent. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the implementation of the Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method of the present invention.

[0047] Figure 2To correspond to the weak ionospheric combination 3, the positioning deviation of the KAT1 site ionospheric fixed model in the north, east, and sky directions;

[0048] Figure 3 This is a comparison of the horizontal positioning accuracy of two models corresponding to three combinations of weak ionospheres: floating point ionosphere for all stations and fixed ionosphere.

[0049] Figure 4 This corresponds to the weak ionosphere combination 1, and the statistics of horizontal and vertical positioning accuracy before and after smoothing of the ionosphere floating-point model. Detailed Implementation

[0050] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0051] like Figure 1 As shown in the figure, this embodiment discloses a Galileo five-frequency weak ionospheric combination PPP single-epoch wide-lane positioning method, the specific steps of which are as follows:

[0052] In step (1): Based on the theory of multi-frequency combined observations, the combination suitable for Galileo five-frequency weak ionospheric PPP single-epoch positioning is determined.

[0053] First, for the Galileo five-frequency signal, namely E1, E5a, E6, E5b, and E5ab, based on the multi-frequency observation combination theory, the carrier observation equation is established as shown in equation (1).

[0054]

[0055] Where, subscript i k (k = 1, 2, ..., 5) are the combination coefficients corresponding to the five frequencies, and all of them are integers; For combined carrier observations; ρ is the station-to-satellite distance; c is the speed of light; t r and t s These represent the clock biases of the receiver and the satellite, respectively; T represents the tropospheric delay; and I1 represents the ionospheric delay corresponding to the first frequency. This is the ionospheric amplification factor corresponding to the combined observations; The wavelength corresponding to the combined observations; The integer ambiguity of the combined observations; and These represent the receiver and satellite phase deviations included in the combined observations; ε is the noise amplification factor for the combined observations. j This is the observation noise of the base carrier. In equation (1) The specific expression is shown in equation (2).

[0056]

[0057] Among them, f i (i = 1, 2, ..., 5) correspond to the five frequencies of Galileo; The frequencies corresponding to the combined observations are shown in equation (3).

[0058]

[0059] It is important to note that This usually only reflects the impact of the residual ionosphere on ranging accuracy. To further analyze the impact of the ionosphere on ambiguity resolution, it needs to be transformed into the following form.

[0060]

[0061] For the combination coefficient i k (k=1,2,…,5), various combinations are traversed within the interval [-10,10]. Taking into account factors such as wavelength of combined observations, ionospheric amplification factor, and noise level, three combinations suitable for Galileo five-frequency weak ionospheric PPP single-epoch positioning are determined, as shown in Table 1.

[0062] Table 1 Galileo's Five-Frequency Weak Ionospheric Combination Coefficients

[0063]

[0064] In step (2): the noise of the multi-frequency weak ionospheric observations is smoothed using dual-frequency non-ionospheric observations.

[0065] Although the three weak ionospheric combinations have relatively long wavelengths and can theoretically be reliably fixed at a single epoch, their observation noise is amplified by 65.961, 72.656, and 95.407 times, respectively. To reduce this noise and improve observation accuracy, a combination with lower observation noise can be used for smoothing. In practical applications, to avoid ionospheric accumulation during the smoothing process, dual-frequency ionospheric observations of E1 and E5a are used for smoothing, while a suitable smoothing window (e.g., 20 epochs) is determined. Since the noise amplification factor of the dual-frequency ionospheric observations of E1 and E5a is only 2.588, which is much smaller than the noise of the weak ionospheric combination, it theoretically effectively smooths the noise.

[0066] For observations of different frequencies, they are generally considered to have equal precision and be uncorrelated, given an epoch t. i (i = 1, 2, ..., k), corresponding to the variance of carrier observations It can be represented by a sine function related to the elevation angle.

[0067]

[0068] Where a and b are generally both 0.003m; E(t) i ) represents the epoch t i The corresponding satellite elevation angle.

[0069] Meanwhile, for ease of description, the epoch t will be... i Unsmoothed observations and their corresponding variances are denoted as and Let the smoothed observations and their corresponding variances be denoted as... and The combined observations of the E1 and E5a dual-frequency ionospheric aneuploidy and their corresponding variances are denoted as L. IF (t i )and

[0070] For the first epoch t1, the smoothed combined observations With corresponding variance Equal to the unsmoothed observations and variance, according to the law of error propagation, it can be expressed in the following form:

[0071]

[0072] For the subsequent continuously smoothed k-th epoch t k Smoothed observations With corresponding variance It can be obtained using the following recursive method.

[0073]

[0074] Step (3): Establish the Galileo five-frequency weak ionospheric PPP single-epoch localization model

[0075] Depending on whether the influence of ionospheric parameters is considered, the positioning model can be divided into two types: ionospheric floating-point model and ionospheric fixed model. The ionospheric floating-point model considers ionospheric parameters, while the ionospheric fixed model directly ignores ionospheric parameters.

[0076] First, an ionospheric floating-point model is constructed. Considering that satellite precision clock errors are usually based on two specific frequencies (e.g., E1 and E5a for Galileo), to avoid additional hardware bias corrections introduced by multi-frequency pseudorange observations, only the original pseudorange observations of E1 and E5a are used, instead of multi-frequency combined pseudorange observations. By combining the dual-frequency pseudorange with the weak ionospheric carrier observations in formula (1), and after appropriate parameter renormalization and simplification, the ionospheric floating-point positioning model can be obtained as follows.

[0077]

[0078] Where P1 and P2 are the original pseudoranges of the dual frequencies corresponding to E1 and E5a, respectively; e1 and e2 are the noise of the dual-frequency pseudorange observations; t r,IF and These are the receiver clock bias and satellite clock bias after parameter realignment, respectively; These are the ionospheric parameters after parameter reforming; This is the floating-point ambiguity after parameter renormalization, which incorporates pseudorange and phase hardware bias.

[0079] Based on the above model, if the influence of the ionosphere is small enough, the ionospheric parameters can be directly ignored, thereby improving the model redundancy. Since the ionospheric parameters are ignored, the dual-frequency pseudorange is combined into an ionosphere-free form to participate in the solution based on formula (8), as follows:

[0080]

[0081] Among them, P IF and e IF These are the pseudorange observations without ionosphere and their observation noise, respectively.

[0082] Step (4): Use the integer fuzziness search method to fix the weak ionospheric fuzziness and obtain a fixed solution.

[0083] First, receiver-side hardware bias is eliminated using inter-satellite single-difference. Then, satellite-side hardware bias is corrected to restore the integer characteristics of weak ionospheric ambiguity. Finally, an integer ambiguity search algorithm is used to determine the optimal integer solution. Simultaneously, a strategy of partially fixing ambiguities can be employed to improve the search success rate. Because weak ionospheric ambiguities have a long wavelength, they can usually be fixed successfully in a single epoch. Considering their noise amplification level, theoretically, decimeter-level positioning accuracy can be guaranteed.

[0084] Figure 2 To correspond to the weak ionospheric combination 3, the positioning deviations of the KAT1 site ionospheric fixed model in the north, east, and sky directions are as follows: the positioning accuracy in the east and north directions is 0.120m and 0.103m, respectively, and the positioning accuracy in the sky direction is 0.379m.

[0085] Figure 3 This is a comparison of the horizontal positioning accuracy of the floating-point ionospheric model and the fixed ionospheric model for all stations, corresponding to three weak ionospheric combinations. As shown in the figure, in the weak ionospheric combination, the horizontal positioning accuracy of the floating-point ionospheric model and the fixed ionospheric model is basically the same. The horizontal positioning accuracy of the PPP single epoch for all three weak ionospheric combinations is at the decimeter level, about 0.15m.

[0086] Figure 4This corresponds to the weak ionospheric combination 1. The statistics of horizontal and vertical positioning accuracy before and after smoothing the floating-point model of the ionospheric region show that the observation accuracy is improved because the noise of the weak ionospheric observation values ​​is reduced after smoothing. Both horizontal and vertical accuracy are improved to varying degrees after smoothing. The average accuracy of the horizontal and vertical regions is improved from 0.131m and 0.380m to 0.098m and 0.339m, respectively, which are improvements of 25.6% and 11.0%.

[0087] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method, characterized in that, Includes the following steps: (1) Based on the theory of multi-frequency observation combination, the Galileo five-frequency weak ionospheric combination suitable for non-differential PPP solution is determined; (2) Use low-noise dual-frequency ionospheric observations to smooth multi-frequency weak ionospheric observations to improve their ranging accuracy; (3) Based on whether the influence of ionospheric parameters is considered, two weak ionospheric PPP single-epoch solution models are established: one with floating ionospheric parameters and the other with fixed ionospheric parameters. (4) The integer fuzzy search method is used to fix the weak ionospheric combination fuzziness obtained by model estimation and obtain the corresponding fixed solution of coordinate parameters; In step (1), the process of determining the Galileo five-frequency weak ionospheric PPP observation combination includes: First, for the Galileo five-frequency signal, namely E1, E5a, E6, E5b, and E5ab, based on the multi-frequency observation combination theory, the carrier observation equation is established as shown in equation (1). （1） Among them, subscript These are the combination coefficients corresponding to the five frequencies, and all are integers; These are combined carrier observations; The distance between the station and the star; The speed of light; and These are the clock biases for the receiver and the satellite, respectively. For tropospheric delay; The ionospheric delay corresponds to the first frequency; This is the ionospheric amplification factor corresponding to the combined observations; The wavelength corresponding to the combined observations; The integer ambiguity of the combined observations; and These represent the receiver and satellite phase deviations included in the combined observations; This is the noise amplification factor for the combined observations; The base carrier observation noise; in equation (1) , , The specific expression is shown in equation (2). （2） in, These correspond to the five frequencies of Galileo; The frequencies corresponding to the combined observations are shown in equation (3). （3） It is important to note that This usually only reflects the impact of the residual ionosphere on ranging accuracy. To further analyze the impact of the ionosphere on ambiguity resolution, it needs to be transformed into the following form. （4） For combination coefficients By traversing various combinations within the interval [-10, 10] and comprehensively considering factors such as the wavelength of the combined observations, the ionospheric amplification factor, and the noise level, three combinations suitable for Galileo five-frequency weak ionospheric PPP single-epoch localization were determined, namely combination 1, combination 2, and combination 3, as shown below: Combination 1: =1, =2, =-3, =-1, =1, =3.907m, =-0.0192, =-0.0049, =65.961; Combination 2: =1, =3, =-3, =0, =-1, =3.907m, =-0.0102, =-0.0026, =72.656; Combination 3: =1, =4, =-3, =1, =-3, =3.907m, =-0.0012, =-0.0003, =95.

407.

2. The Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method according to claim 1, characterized in that: In step (2), the process of smoothing multi-frequency weak ionospheric observations using dual-frequency non-ionospheric observations includes: Although the three weak ionospheric combinations have long wavelengths and can theoretically be reliably fixed in a single epoch, their observation noise is amplified by 65.961, 72.656, and 95.407 times, respectively. To reduce the noise and improve observation accuracy, a combination with low observation noise can be used for smoothing. In practical applications, to avoid ionospheric accumulation during the smoothing process, E1 and E5a dual-frequency ionospheric-free observations are used for smoothing, while a suitable smoothing window is determined. Since the noise amplification factor of the E1 and E5a dual-frequency ionospheric-free observations is only 2.588, which is much smaller than the noise of the weak ionospheric combination, it is theoretically effective in smoothing the noise. For observations of different frequencies, assuming they have equal precision and are uncorrelated, given an epoch... Variance of corresponding carrier observations It can be represented by a sine function related to the altitude angle. （5） in, and The value is generally 0.003m; For the calendar The corresponding satellite elevation angle; Meanwhile, for ease of description, the epoch will be... Unsmoothed observations and their corresponding variances are denoted as... and The smoothed observations and their corresponding variances are denoted as... and The combined observations of the E1 and E5a frequency ionospheric combinations and their corresponding variances are denoted as... and ; For the first epoch Smoothed combined observations With corresponding variance Equal to the unsmoothed observations and variance, according to the law of error propagation, it can be expressed in the following form: （6） For the kth epoch of subsequent continuous smoothing Smoothed observations With corresponding variance It can be obtained using the following recursive method, （7）。 3. The Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method according to claim 1, characterized in that: In step (3), the process of constructing two positioning models, namely floating-point ionospheric model and fixed ionospheric model, includes: Depending on whether the influence of ionospheric parameters is considered, the positioning model can be divided into two types: ionospheric floating-point model and ionospheric fixed model. The ionospheric floating-point model considers ionospheric parameters, while the ionospheric fixed model directly ignores ionospheric parameters. First, an ionospheric floating-point model is constructed. Considering that satellite precision clock errors are usually based on two specific frequencies, in order to avoid additional hardware bias corrections introduced by multi-frequency pseudorange observations, only the original pseudorange observations of E1 and E5a are used, instead of multi-frequency combined pseudorange observations. By combining the dual-frequency pseudorange with the weak ionospheric carrier observations in formula (1), and after appropriate parameter renormalization and simplification, the following ionospheric floating-point positioning model can be obtained. （8） in, and These are the original pseudoranges of the dual frequencies corresponding to E1 and E5a, respectively. and These represent the noise levels of the dual-frequency pseudorange observations; and These are the receiver clock bias and satellite clock bias after parameter realignment, respectively; These are the ionospheric parameters after parameter reforming; This is the floating-point ambiguity after parameter renormalization, which incorporates pseudorange and phase hardware bias. Based on the above model, if the influence of the ionosphere is small enough, the ionospheric parameters can be directly ignored, thereby improving the model redundancy. Since the ionospheric parameters are ignored, based on formula (8), the dual-frequency pseudorange is combined into an ionosphere-free form to participate in the solution, as follows. （9） in, and These are the pseudorange observations without ionosphere and their observation noise, respectively.

4. The Galileo five-frequency weak ionospheric PPP single-epoch wide-lane positioning method according to claim 1, characterized in that: In step (4), the process of fixing the combined ambiguity of the weak ionosphere using the integer ambiguity search method includes: First, the hardware deviation at the receiver end is eliminated by inter-satellite single-difference. Then, the hardware deviation at the satellite end is corrected to restore the integer characteristics of the weak ionospheric ambiguity. Finally, an integer ambiguity search algorithm is used to determine the optimal integer solution. At the same time, a strategy of fixing some ambiguities can be used to improve the success rate of the search. Since the wavelength of the weak ionospheric ambiguity is long, it can usually be fixed successfully in a single epoch. Considering its noise amplification level, theoretically, it can guarantee a positioning accuracy of decimeter level.

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