PPP fast positioning method and system with additional slant path ionospheric information constraints

Abstract

The present invention provides a PPP fast positioning method and system with additional slant path ionospheric information constraints, comprising: step S1: a server side obtains ionospheric observation values ​​from a reference station; step S2: the server side constrains a user side through a direct but biased STEC or SDBS‑ION method based on the ionospheric observation values. The present invention adopts an inter-satellite single difference method to avoid parameterizing the inter-frequency deviation of the receiving instrument and eliminates the requirement for satellite common view, so as to realize fast positioning of PPP initialization and reinitialization with additional ionospheric information constraints.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation technology, and in particular to a PPP rapid positioning method and system with additional slant path ionospheric information constraints, and more particularly to a PPP rapid positioning method and system with additional slant path ionospheric information constraints that do not rely on satellite common view. Background Art

[0002] Currently, many ionospheric information constraints related to additional priors are used to constrain precise point positioning to achieve rapid positioning. However, since the slant path ionospheric information is often coupled with the receiver instrument bias, directly adding ionospheric prior information strictly requires that the ionospheric information comes from the same set of reference stations, that is, all reference stations continuously agree on the same set of satellites to ensure that the same receiver instrument inter-frequency bias is estimated. In actual operation, this requires abandoning or reselecting common-view satellites, which will lead to a waste of effective ionospheric information.

[0003] Patent document CN110286396A (application number: 201910417354.9) discloses a non-difference non-combined PPP positioning method based on dual constraints of ionospheric prior information and ionospheric spatiotemporal variation information. Based on the ionospheric spatial variation structure, that is, the statistics of ionospheric delay spatial correlation and variability information, a high-precision and high-resolution ionospheric grid is obtained through the Kriging spatial interpolation method, providing accurate ionospheric delay prior correction information, while adding appropriate time domain constraint information to perform non-difference non-combined PPP (IC-PPP) positioning solution. Summary of the invention

[0004] In view of the defects in the prior art, the object of the present invention is to provide a PPP rapid positioning method and system with additional slant path ionospheric information constraints.

[0005] According to the present invention, a PPP fast positioning method with additional slant path ionospheric information constraints is provided, comprising:

[0006] Step S1: The server obtains ionospheric observation values ​​from the reference station;

[0007] Step S2: The server constrains the user side based on ionospheric observations through a direct but biased STEC or SDBS-ION method.

[0008] Preferably, the step S2 adopts: the user end applies the constraint to the UPPP model through a direct but biased STEC or SDBS-ION method.

[0009] Preferably, the constraint comprises a deterministic part of the ionospheric constraint and an uncertain part of the ionospheric constraint.

[0010] Preferably, the deterministic part of the ionospheric constraint is to calculate the ionospheric correction using an inverse distance weighted method:

[0011]

[0012] Among them, x ion represents the interpolated ionospheric delay of the user station; w i represents the weight of each line-of-sight ionospheric observable; the subscript i represents the index of the relevant reference station; represents the external ionospheric constraint from the reference station; d i represents the distance between the mobile stations; Indicates the reference station DCB; I 1,i represents the unbiased ionospheric information; γ2 represents They represent the frequencies corresponding to the satellites respectively.

[0013] Preferably, the uncertainty of the ionospheric constraint is the variance of the ionospheric constraint:

[0014]

[0015] Among them, P ion represents the variance of the interpolation delay; represents the formal accuracy of the estimated ionospheric parameters; β is the empirical value; el represents the elevation; P 0,i Represents the ionospheric random error extracted by the reference station.

[0016] Preferably, the direct but biased STEC employs: position parameters with additional receiver DCB when direct ionospheric constraints are applied, including:

[0017]

[0018] in, Ionospheric parameters representing external ionospheric constraints, Receiver instrument bias parameters representing ionospheric constraints, Represents cdt r and c represents the speed of light; dt r Indicates the receiver clock; represents the receiver code bias of the ionosphere-free combination; T represents the tropospheric vertical delay; xyz represents the unknown coordinates; represents the floating point ambiguity, including the deviation of frequency j;

[0019] The SDBS-ION method includes: The constraints of SDBS-ION can be expressed as equation

[0020]

[0021] in, It represents the ionospheric observable values ​​of the reference satellite for a certain period, and the satellite with the highest altitude is selected as the reference; represents the ionospheric observable values ​​from other satellites; is the inter-satellite ionospheric residual; represents the DCB between the reference satellite and other satellites; ε represents the noise.

[0022] Preferably, the UPPP model adopts:

[0023]

[0024] Among them, P j and Φ j is the code and carrier phase measurement at frequency j, j = 1, 2; ρ represents the geometric distance between the receiver and the satellite; c represents the speed of light; the superscripts r and s refer to the receiver and the satellite respectively; dt r Indicates the receiver clock; dt s Indicates the satellite's clock; and denote the receiver and satellite code biases of the ionosphere-free combination, respectively; T denotes the tropospheric delay; represents the ionospheric delay at frequency m along the line of sight; denote the differential code bias associated with the receiver and the satellite, respectively; Respectively represent the frequencies corresponding to the satellites; ε P and ε Φ Contains multipath noise and measurement noise for code and carrier phase measurement respectively; λ j represents the wavelength at frequency j; represents the floating point ambiguity, including the deviation of frequency j;

[0025] The UPPP model considers the ionospheric delay as an unknown parameter

[0026]

[0027]

[0028] in, represents unknown parameters; xyz represents unknown coordinates; Also includes cdt r and T represents the tropospheric vertical delay; represents the ionospheric tilt parameter; ε represents the noise.

[0029] According to the present invention, a PPP rapid positioning system with additional slant path ionospheric information constraints is provided, comprising:

[0030] Module M1: The server obtains ionospheric observations from the reference station;

[0031] Module M2: The server constrains the user side based on ionospheric observations through a direct but biased STEC or SDBS-ION method.

[0032] Preferably, the module M2 adopts: the user end combines the constraint effect with the UPPP model through a direct but biased STEC or SDBS-ION method;

[0033] The constraint includes a deterministic part of the ionospheric constraint and an uncertain part of the ionospheric constraint;

[0034] The deterministic part of the ionospheric constraint is to compute the ionospheric correction using the inverse distance weighted method:

[0035]

[0036] Among them, x ion represents the interpolated ionospheric delay of the user station; w i represents the weight of each line-of-sight ionospheric observable; the subscript i represents the index of the relevant reference station; represents the external ionospheric constraint from the reference station; d i represents the distance between the mobile stations; Indicates the reference station DCB; I 1,i represents the unbiased ionospheric information; γ2 represents They represent the frequencies corresponding to the satellites respectively;

[0037] The uncertainty of the ionospheric constraint is the variance of the ionospheric constraint:

[0038]

[0039] Among them, P ion represents the variance of the interpolation delay; represents the formal accuracy of the estimated ionospheric parameters; β is the empirical value; el represents the elevation; P 0,i Represents the ionospheric random error extracted by the reference station.

[0040] Preferably, the direct but biased STEC employs: position parameters with additional receiver DCB when direct ionospheric constraints are applied, including:

[0041]

[0042] in, Ionospheric parameters representing external ionospheric constraints, Receiver instrument bias parameters representing ionospheric constraints, Represents cdt r and c represents the speed of light; dt r Indicates the receiver clock; represents the receiver code bias of the ionosphere-free combination; T represents the tropospheric vertical delay; xyz represents the unknown coordinates; represents the floating point ambiguity, including the deviation of frequency j;

[0043] The SDBS-ION method includes: The constraints of SDBS-ION can be expressed as equation

[0044]

[0045] in, It represents the ionospheric observable values ​​of the reference satellite for a certain period, and the satellite with the highest altitude is selected as the reference; represents the ionospheric observable values ​​from other satellites; is the inter-satellite ionospheric residual; represents the DCB between the reference satellite and other satellites; ε represents the noise;

[0046] The UPPP model adopts:

[0047]

[0048] Among them, P j and Φ j is the code and carrier phase measurement at frequency j, j = 1, 2; ρ represents the geometric distance between the receiver and the satellite; c represents the speed of light; the superscripts r and s refer to the receiver and the satellite respectively; dt r Indicates the receiver clock; dt s Indicates the satellite's clock; and denote the receiver and satellite code biases of the ionosphere-free combination, respectively; T denotes the tropospheric delay; represents the ionospheric delay at frequency m along the line of sight; denote the differential code bias associated with the receiver and the satellite, respectively; Respectively represent the frequencies corresponding to the satellites; ε P and ε Φ Contains multipath noise and measurement noise for code and carrier phase measurement respectively; λ j represents the wavelength at frequency j; represents the floating point ambiguity, including the deviation of frequency j;

[0049] The UPPP model considers the ionospheric delay as an unknown parameter

[0050]

[0051]

[0052] in, represents unknown parameters; xyz represents unknown coordinates; Also includes cdt r and T represents the tropospheric vertical delay; represents the ionospheric tilt parameter; ε represents the noise

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] 1. The present invention adopts the inter-satellite single difference method to avoid parameterization of the inter-frequency deviation of the receiving instrument and eliminate the requirement for satellite common view, so as to realize rapid positioning of PPP initialization and reinitialization with additional ionospheric information constraints;

[0055] 2. The traditional PPP method of additional ionospheric information constraint requires the ionospheric constraint benchmark to be consistent, and has high requirements for the ionospheric enhancement information of all reference stations. Once a reference station is unavailable, the ionospheric constraint of this epoch cannot be effective. However, the present invention can still be used when the additional ionospheric constraint benchmark is inconsistent through the inter-satellite single difference method. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0057] Figure 1 Flowchart of the PPP-RTK rapid positioning method constrained by ionospheric enhancement information.

[0058] Figure 2 Schematic diagram of the geographical distribution of all sites.

[0059] Fig. 3 shows the STD of the SDBS-ION method for each station as a function of the distance to station CIT1 and the geographical distribution of the STD of the single differences between satellites.

[0060] Figure 4 shows the time series of ionospheric observables and the corresponding formal accuracy estimated in the basic UPPP model.

[0061] Figure 5 Time series of horizontal, vertical and 3D accuracy position errors of CIT1 based on the UPPP basic model.

[0062] Figure 6 shows the time series of ionospheric observations and the corresponding formal precision estimated in the direct but biased ionospheric constrained UPPP model.

[0063] Figure 7 shows the receiver DCB and the corresponding formal accuracy estimated in the direct but biased ionospheric constrained UPPP model.

[0064] Figure 8 shows the time series of ionospheric observations and the corresponding forms estimated in SDBS-ION with precision constrained UPPP model. DETAILED DESCRIPTION

[0065] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0066] Example 1

[0067] Additional ionospheric prior information constrains precise point positioning (PPP) to achieve rapid positioning of PPP. When additional ionospheric prior information is added, the ionospheric parameters can be directly constrained, or inter-satellite difference can be performed on it. Since the additional ionospheric information and the receiver instrument inter-frequency deviation are coupled and difficult to separate, if the ionospheric parameters are directly constrained, considering that the receiver instrument inter-frequency deviation cannot be absorbed by the receiver clock error, it will affect the rapid convergence effect of PPP. Therefore, to directly constrain the ionospheric parameters, it is necessary to additionally parameterize the receiver instrument inter-frequency deviation, thereby reducing the error of the instrument inter-frequency deviation. However, for the oblique path ionospheric information, this method strictly requires that the ionospheric information comes from the same group of reference stations, that is, all reference stations continuously agree on the same group of satellites to ensure that the same receiver instrument inter-frequency deviation is estimated. The present invention will use the inter-satellite single difference method to eliminate the receiver instrument inter-frequency deviation, avoid estimating the receiver instrument inter-frequency deviation parameters, reduce the requirements for common view satellites, and at the same time, under the condition of fully considering the function and random model of ionospheric information, realize the rapid positioning of PPP initialization and reinitialization with additional ionospheric information constraint.

[0068] According to the invention, a PPP fast positioning method with additional slant path ionospheric information constraint is provided, as follows: Figure 1 As shown, including:

[0069] Step S1: The server obtains ionospheric observation values ​​from the reference station;

[0070] Step S2: The server constrains the user side through a direct but biased STEC or SDBS-ION method based on ionospheric observations. We apply ionospheric constraints to the user side to shorten the convergence time of PPP.

[0071] Specifically, the ionospheric error is space-dependent, and the error of the ionospheric constraint increases with the distance between the rover and the reference station.

[0072] Specifically, the step S2 adopts: Here we show two methods to apply ionospheric constraints as pseudo-measurements in the filter, the first is to apply direct but biased STEC, and the second is a single difference-ion between satellite ionospheric constraints (SDBS).

[0073] The user side incorporates constraints into the UPPP model through direct but biased STEC or SDBS-ION methods.

[0074] The constraints include a deterministic part of the ionospheric constraints and an uncertain part of the ionospheric constraints.

[0075] Specifically, the deterministic part of the ionospheric constraint is interpolated from the estimated ionospheric observables based on the reference station. Since the satellite DCB can be calibrated with an accuracy of 0.1ns (i.e. 3cm), the DCB product can be used to correct the satellite DCB in advance. After correcting the satellite DCB, the ionospheric correction can be calculated using the inverse distance weighted method when a nearby reference station is involved:

[0076]

[0077] Where i is the index of the relevant reference station; x ion represents the interpolated ionospheric delay of the user station; w i represents the weight of each line-of-sight ionospheric observable; the subscript i represents the index of the relevant reference station; represents the external ionospheric constraint from the reference station; d i represents the distance between the mobile stations; represents the reference station DCB; from the equation, it can be seen that DCB is an integral part of the ionospheric external constraints. 1,i represents the unbiased ionospheric information; γ2 represents Respectively represent the frequencies corresponding to the satellites.

[0078] Specifically, the uncertainty of the ionospheric constraint consists of two parts, one of which includes the formal accuracy, which depends on the measurement noise and multipath error. The other consists of interpolation errors. We assume that this uncertainty increases linearly with the distance between the user and the reference station. For example, in this case, with the empirical assumption that the ionospheric error is 0.61mm / km, the standard deviation of the reference station at 100km is 0.61*100mm, i.e. 0.061m. The variance of the ionospheric constraint is:

[0079]

[0080] Among them, P ion represents the variance of the interpolation delay; represents the formal accuracy of the estimated ionospheric parameters; β is the empirical value; el represents the elevation; P 0,i Represents the ionospheric random error extracted by the reference station.

[0081] Specifically, the direct but biased STEC adopts: Direct application of ionospheric observables from the network. When external ionospheric observations are directly applied to constrain the ionosphere at the user end, the receiver DCB in the ionospheric constraint becomes crucial, as shown in Figure 4, where different grayscales represent different satellites. The reason is that the receiver DCB has different effects on code and phase measurements and different frequencies. This shows that the receiver DCB cannot be completely absorbed by any other parameters. The receiver DCB requires an additional parameter. When direct ionospheric constraints are applied, the location parameters with additional receiver DCB include:

[0082]

[0083] in, Ionospheric parameters representing external ionospheric constraints, Receiver instrument bias parameters representing ionospheric constraints, Represents cdt r and c represents the speed of light; dt r Indicates the receiver clock; represents the receiver code bias of the ionosphere-free combination; T represents the tropospheric vertical delay; xyz represents the unknown coordinates; represents the floating point ambiguity, including the deviation of frequency j;

[0084] The SDBS-ION method includes: the SDBS-ION method eliminates the receiver DCB before applying the constraint, so the state vector will remain unchanged when using the SDBS-ION method. Compared with the first method requiring the same base station or the same reference station to have the same visibility, the use of SDBS-ION constraints is more flexible. The constraints of SDBS-ION can be expressed as equations, as shown in Figure 3, the ionospheric parameters (left) and corresponding accuracy (right) after the SDBS method adds ionospheric constraints, and different grayscales represent different satellites.

[0085]

[0086] in, It represents the ionospheric observable values ​​of the reference satellite for a certain period, and the satellite with the highest altitude is selected as the reference; represents the ionospheric observable values ​​from other satellites; is the inter-satellite ionospheric residual; Indicates the DCB between the reference satellite and other satellites.

[0087] Since the receiver DCB is mitigated by producing a single difference between satellites, what remains is the difference between the satellite ionospheric residual and the DCB. By calibration and assuming that the ionospheric constraints are independent of each other, we further express the ionospheric constraint as (8)

[0088]

[0089] The variance-covariance of the SDBS-ION method is, P SDBS-ION =D·P ion ·D T

[0090] This is the variance of the ionospheric observations estimated at each reference station.

[0091] in, and are the variances of the reference ionosphere and the estimated ionospheric observations from other satellites, respectively.

[0092] In summary, if the receiver DCBs are modeled as white noise, both methods will produce similar solutions. The direct but biased ionospheric constraint requires modeling multiple parameters of the receiver DCBs, while the SDBS-ION method sacrifices one constraint in forming a single difference between satellites. The advantage of the SDBS-ION method is that it is more flexible when ionospheric constraints for some reference stations are not available.

[0093] Specifically, unlike the traditional PPP method of formulating ionosphere-free combinations, the UPPP model treats the ionospheric delay as an unknown parameter. The advantage of the UPPP model is that the ionospheric parameters can be limited or corrected when external ionospheric information is available; the UPPP model adopts:

[0094]

[0095] Among them, P j and Φ j is the code and carrier phase measurement at frequency j, j = 1, 2; ρ represents the geometric distance between the receiver and the satellite; c represents the speed of light; the superscripts r and s refer to the receiver and the satellite respectively; dt r Indicates the receiver clock; dt s Indicates the satellite's clock; and denote the receiver and satellite code biases of the ionosphere-free combination, respectively; T denotes the tropospheric delay; represents the ionospheric delay at frequency m along the line of sight; denote the differential code bias associated with the receiver and the satellite, respectively; Respectively represent the frequencies corresponding to the satellites; ε P and ε Φ Contains multipath noise and measurement noise for code and carrier phase measurement respectively; λ j represents the wavelength at frequency j; represents a floating point ambiguity consisting of the bias in frequency j; other errors are corrected according to (Petit and Luzum 2010), such as phase wraparound, antenna corrections, Earth displacement, and relativistic effects.

[0096] The UPPP model considers the ionospheric delay as an unknown parameter

[0097]

[0098]

[0099] in, represents unknown parameters; xyz represents unknown coordinates; Also includes cdt r and T represents the tropospheric vertical delay; represents the ionospheric tilt parameter; ε represents the noise.

[0100] According to the present invention, a PPP rapid positioning system with additional slant path ionospheric information constraints is provided, comprising:

[0101] Module M1: The server obtains ionospheric observations from the reference station;

[0102] Module M2: The server side constrains the user side based on ionospheric observations through a direct but biased STEC or SDBS-ION method. We apply ionospheric constraints to the user side to shorten the convergence time of PPP.

[0103] Specifically, the ionospheric error is space-dependent, and the error of the ionospheric constraint increases with the distance between the rover and the reference station.

[0104] Specifically, the module M2 adopts: Here we show two methods to apply ionospheric constraints as pseudo-measurements in the filter, the first is to apply direct but biased STEC, and the second is a single difference-ion between satellite ionospheric constraints (SDBS).

[0105] The user side incorporates constraints into the UPPP model through direct but biased STEC or SDBS-ION methods.

[0106] The constraints include a deterministic part of the ionospheric constraints and an uncertain part of the ionospheric constraints.

[0107] Specifically, the deterministic part of the ionospheric constraint is interpolated from the estimated ionospheric observables based on the reference station. Since the satellite DCB can be calibrated with an accuracy of 0.1ns (i.e. 3cm), the DCB product can be used to correct the satellite DCB in advance. After correcting the satellite DCB, the ionospheric correction can be calculated using the inverse distance weighted method when a nearby reference station is involved:

[0108]

[0109] Where i is the index of the relevant reference station; x ion represents the interpolated ionospheric delay of the user station; w i represents the weight of each line-of-sight ionospheric observable; the subscript i represents the index of the relevant reference station; represents the external ionospheric constraint from the reference station; d i represents the distance between the mobile stations; represents the reference station DCB; from the equation, it can be seen that DCB is an integral part of the ionospheric external constraints. 1,i represents the unbiased ionospheric information; γ2 represents Respectively represent the frequencies corresponding to the satellites.

[0110] Specifically, the uncertainty of the ionospheric constraint consists of two parts, one of which includes the formal accuracy, which depends on the measurement noise and multipath error. The other consists of interpolation errors. We assume that this uncertainty increases linearly with the distance between the user and the reference station. For example, in this case, with the empirical assumption that the ionospheric error is 0.61mm / km, the standard deviation of the reference station at 100km is 0.61*100mm, i.e. 0.061m. The variance of the ionospheric constraint is:

[0111]

[0112] Among them, P ion represents the variance of the interpolation delay; represents the formal accuracy of the estimated ionospheric parameters; β is the empirical value; el represents the elevation; P 0,i Represents the ionospheric random error extracted by the reference station.

[0113] Specifically, the direct but biased STEC adopts: Direct application of ionospheric observables from the network. When external ionospheric observations are directly applied to constrain the ionosphere at the user end, the receiver DCB in the ionospheric constraint becomes crucial, as shown in Figure 4, where different grayscales represent different satellites. The reason is that the receiver DCB has different effects on code and phase measurements and different frequencies. This shows that the receiver DCB cannot be completely absorbed by any other parameters. The receiver DCB requires an additional parameter. When direct ionospheric constraints are applied, the location parameters with additional receiver DCB include:

[0114]

[0115] in, Ionospheric parameters representing external ionospheric constraints, Receiver instrument bias parameters representing ionospheric constraints, Represents cdt r and c represents the speed of light; dt r Indicates the receiver clock; represents the receiver code bias of the ionosphere-free combination; T represents the tropospheric vertical delay; xyz represents the unknown coordinates; represents the floating point ambiguity, including the deviation of frequency j;

[0116] The SDBS-ION method includes: the SDBS-ION method eliminates the receiver DCB before applying the constraint, so the state vector will remain unchanged when using the SDBS-ION method. Compared with the first method requiring the same base station or the same reference station to have the same visibility, the use of SDBS-ION constraints is more flexible. The constraints of SDBS-ION can be expressed as equations, as shown in Figure 3, the ionospheric parameters (left) and corresponding accuracy (right) after the SDBS method adds ionospheric constraints, and different grayscales represent different satellites.

[0117]

[0118] in, It represents the ionospheric observable values ​​of the reference satellite for a certain period, and the satellite with the highest altitude is selected as the reference; represents the ionospheric observable values ​​from other satellites; is the inter-satellite ionospheric residual; Indicates the DCB between the reference satellite and other satellites.

[0119] Since the receiver DCB is mitigated by producing a single difference between satellites, what remains is the difference between the satellite ionospheric residual and the DCB. By calibration and assuming that the ionospheric constraints are independent of each other, we further express the ionospheric constraint as (8)

[0120]

[0121] The variance-covariance of the SDBS-ION method is, P SDBS-ION =D·P ion ·D T

[0122] This is the variance of the ionospheric observations estimated at each reference station.

[0123] in, and are the variances of the reference ionosphere and the estimated ionospheric observations from other satellites, respectively.

[0124] In summary, if the receiver DCBs are modeled as white noise, both methods will produce similar solutions. The direct but biased ionospheric constraint requires modeling multiple parameters of the receiver DCBs, while the SDBS-ION method sacrifices one constraint in forming a single difference between satellites. The advantage of the SDBS-ION method is that it is more flexible when ionospheric constraints for some reference stations are not available.

[0125] Specifically, unlike the traditional PPP method of formulating ionosphere-free combinations, the UPPP model treats the ionospheric delay as an unknown parameter. The advantage of the UPPP model is that the ionospheric parameters can be limited or corrected when external ionospheric information is available; the UPPP model adopts:

[0126]

[0127] Among them, P j and Φ j is the code and carrier phase measurement at frequency j, j = 1, 2; ρ represents the geometric distance between the receiver and the satellite; c represents the speed of light; the superscripts r and s refer to the receiver and the satellite respectively; dt r Indicates the receiver clock; dt s Indicates the satellite's clock; and denote the receiver and satellite code biases of the ionosphere-free combination, respectively; T denotes the tropospheric delay; represents the ionospheric delay at frequency m along the line of sight; denote the differential code bias associated with the receiver and the satellite, respectively; Respectively represent the frequencies corresponding to the satellites; ε P and ε Φ Contains multipath noise and measurement noise for code and carrier phase measurement respectively; λ j represents the wavelength at frequency j; represents a floating point ambiguity consisting of the bias in frequency j; other errors are corrected according to (Petit and Luzum 2010), such as phase wraparound, antenna corrections, Earth displacement, and relativistic effects.

[0128] The UPPP model considers the ionospheric delay as an unknown parameter

[0129]

[0130]

[0131] in, represents unknown parameters; xyz represents unknown coordinates; Also includes cdt r and T represents the tropospheric vertical delay; represents the ionospheric tilt parameter; ε represents the noise.

[0132] Example 2

[0133] Embodiment 2 is a preferred embodiment of Embodiment 1

[0134] A preset number of reference stations are selected from the deployed continuously operating reference stations. A day with high solar activity and quiet weather is selected. One of the stations, CIT1, is selected as a test station or user station to evaluate the biased ionospheric constraints from other stations at different distances. The other stations are within 300 km of CIT1. The geographical distribution of all stations is as follows: Figure 2 As shown, circles represent selected other sites from different distances; triangles represent test sites;

[0135] When comparing direct ionospheric observables and constraints from the SDBS-ION approach, the parameters and settings remain unchanged.

[0136] The ionospheric constraints are estimated with high precision from UPPP, and we evaluate only the data after 4 hours of convergence to ensure that the ionospheric observables converge, i.e., 5:00-24:00 UTC. On the user side, CIT1 is initialized every hour. Therefore, there will be 20 sessions per day at each site. Further, since the study focuses on ionospheric effects, only ionospheric constraints are added, and no tropospheric constraints are applied. If tropospheric constraints are applied, especially in the vertical direction, the PPP performance will be further improved.

[0137] Selecting CIT1 as the user, we show the accuracy of the inter-satellite ionospheric residuals for a preset number of other stations. The STDs of the inter-satellite ionospheric residuals and the geographical distribution are shown in Figure 3. It can be seen that the STDs are highly correlated with the distance. This means that the distance is an important factor in the accuracy of STEC. As shown in Figure 3, the STD is linearly fitted as a function of distance. The inclination is 0.61 mm per kilometer. This empirical value will be used to calculate the uncertainty of the ionospheric correction. It is worth noting that the empirical value depends on various ionospheric conditions.

[0138] The estimated ionospheric parameters at CIT1 using the basic UPPP model without any constraints are given in Fig. 4. Each line represents each satellite. The ionospheric observables vary smoothly in the range of 2 to 10 m. Figure 4a The beginning of each ionospheric observable is noisier, and the beginning ionospheric observable is more obvious than the satellite that appears in the middle of reconvergence; Figure 4b The corresponding formal accuracy is shown, which decreases from one meter to centimeters. The noisier ionospheric observables at the beginning are also reflected in the formal accuracy of Jiaotong University. The formal accuracy of the satellites appearing in the middle is smaller starting from 0.5m than that starting from 1.5m.

[0139] Figure 5The position accuracy in horizontal two-dimensional, vertical and three-dimensional accuracy is given; the convergence time of 0.1m in the horizontal direction and 0.2m in the vertical direction is 30.7 and 13.7 minutes respectively; on average, the hourly position error of 2D and 3D basic PPP for one hour session is 0.224 and 0.368 meters respectively; the average position error and convergence time are used for comparison with the method proposed in the present invention.

[0140] We randomly select a station AZU1 at 21.3 km away to demonstrate the UPPP model with direct ionospheric constraints. Applying the constraints of ionospheric observables at AZU1, we Figure 5 The estimated ionospheric observables at CIT1 are shown in Fig. 4. The ionospheric observables range from -17.5 to -15 m, which differs from the basic UPP model which ranges from 2 to 10 m in Fig. 4. The difference is due to the ionospheric bias limit from the AZU1 station. Figure 6b It is obvious that the formal accuracy degrades faster than the basic UPPP model. However, we find that one of the satellites is not constrained; this satellite is at a low elevation angle of about 10 degrees and cannot obtain ionospheric observations from the reference station. In addition, the elevation of this satellite is shown in the cross bold line.

[0141] As described in the present invention section, the receiver DCB needs to be estimated correctly when applying direct but biased ionospheric constraints. Figure 7 shows the receiver DCB estimated in the constrained UPPP model. The receiver DCB is modeled as a random walk epoch of epochs. It can be noted that the range of the receiver DCB is about 14.8m. Figure 7b The formal accuracy of the estimated receiver DCB is shown. The formal accuracy of the receiver DCB is reduced from 0.4m to centimeter level.

[0142] Compared with the direct but biased ionospheric constrained UPPP model, we implemented the SDBS-ION constrained UPPP model. The ionospheric observables estimated using the proposed method are shown in Figure 8. Compared with the ionospheric observables in Figure 4, the scales of the ionospheric observables are similar, ranging from 2 meters to 10 meters. As mentioned earlier, this is because the SDBS-ION constraints are relative and do not introduce more bias. Figure 8b The formal accuracy of the corresponding ionospheric observables is shown. The formal accuracy is also improved compared to the basic UPPP model, but not as good as the direct constraint. We believe that the estimated receiver DCB in the direct constraint UPPP model absorbs the uncertainty.

[0143] Those skilled in the art know that, in addition to implementing the system, device and its various modules provided by the present invention in a purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, the system, device and its various modules provided by the present invention can be considered as a hardware component, and the modules included therein for implementing various programs can also be considered as structures within the hardware component; the modules for implementing various functions can also be considered as both software programs for implementing the method and structures within the hardware component.

[0144] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A PPP fast positioning method with additional slant path ionospheric information constraints, characterized in that: include: Step S1: The server obtains ionospheric observation values ​​from the reference station; Step S2: The server constrains the user side based on the ionospheric observations through a direct but biased STEC or SDBS-ION method; The step S2 adopts: the user end combines the constraint effect with the UPPP model through a direct but biased STEC or SDBS-ION method; The constraint includes a deterministic part of the ionospheric constraint and an uncertain part of the ionospheric constraint; The deterministic part of the ionospheric constraint is to compute the ionospheric correction using the inverse distance weighted method: Among them, x ion represents the interpolated ionospheric delay of the user station; w i represents the weight of each line-of-sight ionospheric observable; the subscript i represents the index of the relevant reference station; represents the external ionospheric constraint from the reference station; d i represents the distance between mobile stations; Indicates the reference station DCB; I 1,i represents the unbiased ionospheric information; γ2 represents They represent the frequencies corresponding to the satellites respectively; The uncertainty of the ionospheric constraint is the variance of the ionospheric constraint: Among them, P ion represents the variance of the interpolation delay; represents the formal accuracy of the estimated ionospheric parameters; β is the empirical value; el represents the elevation; P 0,i represents the ionospheric random error extracted by the reference station; The direct but biased STEC employs: location parameters with additional receiver DCBs when direct ionospheric constraints are applied, including: in, Ionospheric parameters representing external ionospheric constraints, Receiver instrument bias parameters representing ionospheric constraints, Represents cdt r and c represents the speed of light; dt r Indicates the receiver clock; represents the receiver code bias of the ionosphere-free combination; T represents the tropospheric vertical delay; xyz represents the unknown coordinates; represents the floating point ambiguity, including the deviation of frequency j; The SDBS-ION method includes: The constraints of SDBS-ION can be expressed as equation in, It represents the ionospheric observable values ​​of the reference satellite for a certain period, and the satellite with the highest altitude is selected as the reference; represents the ionospheric observables from other satellites; is the inter-satellite ionospheric residual; represents the DCB between the reference satellite and other satellites; ε represents the noise.

2. The additional slant path ionospheric information constraint PPP rapid positioning method according to claim 1, characterized in that: The UPPP model adopts: Among them, P j and Φ j is the code and carrier phase measurement at frequency j, j = 1, 2; ρ represents the geometric distance between the receiver and the satellite; c represents the speed of light; the superscripts r and s refer to the receiver and the satellite respectively; dt r Indicates the receiver clock; dt s Indicates the satellite's clock; and denote the receiver and satellite code biases of the ionosphere-free combination, respectively; T denotes the tropospheric delay; represents the ionospheric delay at frequency m along the line of sight; denote the differential code bias associated with the receiver and the satellite, respectively; Respectively represent the frequencies corresponding to the satellites; ε P and ε Φ Contains multipath noise and measurement noise for code and carrier phase measurement respectively; λ j represents the wavelength at frequency j; represents the floating point ambiguity, including the deviation of frequency j; The UPPP model considers the ionospheric delay as an unknown parameter in, represents unknown parameters; xyz represents unknown coordinates; Also includes cdt r and T represents the tropospheric vertical delay; represents the ionospheric tilt parameter; ε represents the noise.

3. A PPP rapid positioning system with additional slant path ionospheric information constraints, characterized in that: include: Module M1: The server obtains ionospheric observations from the reference station; Module M2: The server constrains the user side based on ionospheric observations through direct but biased STEC or SDBS-ION methods; The module M2 adopts: the user end combines the constraint effect with the UPPP model through a direct but biased STEC or SDBS-ION method; The constraint includes a deterministic part of the ionospheric constraint and an uncertain part of the ionospheric constraint; The deterministic part of the ionospheric constraint is to compute the ionospheric correction using the inverse distance weighted method: Among them, x ion represents the interpolated ionospheric delay of the user station; w i represents the weight of each line-of-sight ionospheric observable; the subscript i represents the index of the relevant reference station; represents the external ionospheric constraint from the reference station; d i represents the distance between mobile stations; Indicates the reference station DCB; I 1,i represents the unbiased ionospheric information; γ2 represents They represent the frequencies corresponding to the satellites respectively; The uncertainty of the ionospheric constraint is the variance of the ionospheric constraint: Among them, P ion represents the variance of the interpolation delay; represents the formal accuracy of the estimated ionospheric parameters; β is the empirical value; el represents the elevation; P 0,i represents the ionospheric random error extracted by the reference station; The direct but biased STEC employs: location parameters with additional receiver DCBs when direct ionospheric constraints are applied, including: in, Ionospheric parameters representing external ionospheric constraints, Receiver instrument bias parameters representing ionospheric constraints, Represents cdt r and c represents the speed of light; dt r Indicates the receiver clock; represents the receiver code bias of the ionosphere-free combination; T represents the tropospheric vertical delay; xyz represents the unknown coordinates; represents the floating point ambiguity, including the deviation of frequency j; The SDBS-ION method includes: The constraints of SDBS-ION can be expressed as equation in, It represents the ionospheric observable values ​​of the reference satellite for a certain period, and the satellite with the highest altitude is selected as the reference; represents the ionospheric observables from other satellites; is the inter-satellite ionospheric residual; represents the DCB between the reference satellite and other satellites; ε represents the noise.

4. The additional slant path ionospheric information constraint PPP rapid positioning system according to claim 3 is characterized in that: The UPPP model adopts: Among them, P j and Φ j is the code and carrier phase measurement at frequency j, j = 1, 2; ρ represents the geometric distance between the receiver and the satellite; c represents the speed of light; the superscripts r and s refer to the receiver and the satellite respectively; dt r Indicates the receiver clock; dt s Indicates the satellite's clock; and denote the receiver and satellite code biases of the ionosphere-free combination, respectively; T denotes the tropospheric delay; represents the ionospheric delay at frequency m along the line of sight; denote the differential code bias associated with the receiver and the satellite, respectively; Respectively represent the frequencies corresponding to the satellites; ε P and ε Φ Contains multipath noise and measurement noise for code and carrier phase measurement respectively; λ j represents the wavelength at frequency j; represents the floating point ambiguity, including the deviation of frequency j; The UPPP model considers the ionospheric delay as an unknown parameter in, represents unknown parameters; xyz represents unknown coordinates; Also includes cdt r and T represents the tropospheric vertical delay; represents the ionospheric tilt parameter; ε represents the noise.

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