A PPP-RTK ionospheric slant delay fusion optimization method and device

Abstract

The present application relates to a PPP-RTK ionospheric slant delay fusion optimization method and device. The method comprises: receiving observation values and SSR products; obtaining the predicted ionospheric slant delay of the terminal user at the current moment through polynomial fitting prediction and inverse distance interpolation; constructing an observation equation containing ionospheric slant delay parameters and a corresponding state equation according to the cycle slip state and the number of frequency points of the observation value and performing extended Kalman filter solution; performing fusion constraint update on the ionospheric slant delay of the terminal user at the current moment obtained by the extended Kalman filter solution and the predicted ionospheric slant delay to obtain the optimized ionospheric slant delay of the terminal user at the current moment, and performing PPP-RTK positioning solution based on the optimized ionospheric slant delay, and outputting the optimized terminal user position information. This method can optimize the ionospheric slant delay of the terminal user and improve the real-time positioning accuracy.

Description

Technical Field

[0001] The present application relates to the field of PPP-RTK positioning technology, and in particular to a PPP-RTK ionospheric slant delay fusion optimization method and device. Background Art

[0002] PPP-RTK (Precise Point Positioning and Real-Time Kinematic) terminal rapid positioning uses state-space representation (SSR) corrections, including real-time precise satellite orbits, precise clock errors, phase decimal deviations, and regional atmospheric products, broadcast by satellites or networks. This corrects various terminal error terms to accelerate ambiguity parameter searches and achieve centimeter-level high-precision positioning within 1 minute.

[0003] PPP-RTK terminal users must be able to receive SSR data broadcast from the server in real time and continuously. However, the server takes a certain amount of time to receive, solve, generate, and broadcast the data, resulting in a delay in the SSR received by the terminal. Furthermore, as the server's solution delay and network transmission delay increase, this may lead to failures in server ionospheric modeling and incomplete ionospheric data received by the terminal (due to data loss from a certain satellite). In this case, the terminal ionospheric slant delay (Slant Electron Content, STEC) calculated using the SSR ionospheric product will differ significantly from the actual STEC of the terminal user, affecting the convergence of various parameters and the fixation of ambiguities, ultimately resulting in poor positioning accuracy.

[0004] The existing technical solution for obtaining high-precision STEC at PPP-RTK terminals is as follows (see application CN116203608A): After the user calculates STEC using SSR ionospheric products, if the user uses single-frequency or dual-frequency observations and a cycle slip occurs, a polynomial fitting is used to predict the ionospheric residuals at grid points adjacent to the user's location. The historical ionospheric products at the user's location are then compensated using inverse distance weighting to obtain the current STEC. If the user uses dual-frequency observations and no cycle slips occur, or if the conditions for polynomial fitting are unavailable, the ionospheric residuals are combined to calculate the inter-epoch ionospheric difference and compensate for the historical STEC to obtain the current STEC. This method primarily relies on the SSR ionospheric product and its corresponding STEC accuracy information to calculate the user's STEC. A significant discrepancy between this STEC and the actual STEC at the user's location can degrade positioning accuracy. In this case, the longer the delay in the server broadcasting the ionospheric product, the lower the forecast accuracy. Therefore, the existing method can only provide short-term, high-precision ionospheric forecasts. Summary of the Invention

[0005] Based on this, it is necessary to provide a PPP-RTK ionospheric slant delay fusion optimization method and device to address the above technical problems. While using the server-side ionospheric product for real-time forecasting, it is proposed to combine the terminal real-time observation values to construct an observation equation related to the ionosphere. By extending the Kalman filter fusion weighting, a more accurate terminal STEC is obtained, thereby improving the PPP-RTK real-time positioning accuracy.

[0006] A PPP-RTK ionospheric slant delay fusion optimization method, the method comprising:

[0007] Receive GNSS observations and SSR products broadcast by the PPP-RTK server;

[0008] The polynomial fitting forecast is performed based on the SSR products of the historical epochs to obtain the predicted ionospheric residual of the ionospheric grid points near the end user's location, and the residual is compensated by inverse range interpolation to obtain the predicted ionospheric slant delay at the end user's current moment;

[0009] Based on the cycle slip state and frequency number of the observation value, the observation equation containing the ionospheric slant delay parameter and the corresponding state equation are constructed and the extended Kalman filter solution is performed. Among them, for the observation value with cycle slips, the Doppler velocity measurement is used to determine the position parameters of the terminal user, and the ordinary ionospheric observation equation and the corresponding state equation are constructed. For the single-frequency observation value without cycle slips, the pseudo-range carrier combination observation equation and the corresponding state equation are constructed. For the dual-frequency or multi-frequency observation value without cycle slips, the geometry-free combination observation equation and the corresponding state equation are constructed.

[0010] The ionospheric slant delay of the terminal user at the current moment obtained by the extended Kalman filter solution is fused with the predicted ionospheric slant delay to obtain the optimized ionospheric slant delay of the terminal user at the current moment. PPP-RTK positioning solution is performed based on the optimized ionospheric slant delay, and the optimized terminal user position information is output.

[0011] In one embodiment, receiving GNSS observations and SSR products broadcast by a PPP-RTK server includes:

[0012] End users receive GNSS observations and SSR products broadcast by the PPP-RTK server. SSR products include precise orbits, precise clock errors, fractional phase deviations, tropospheric products, and ionospheric products.

[0013] Determine whether the current moment is the first epoch. If so, directly perform PPP-RTK positioning solution, output the terminal user's position information, extract the current moment's observation value, the solved position information, the ambiguity and the troposphere to pass to the next moment; otherwise, enter the ionospheric slant delay fusion optimization process.

[0014] In one embodiment, a polynomial fitting forecast is performed based on the SSR products of the historical epochs to obtain the predicted ionospheric residual of the ionospheric grid point near the terminal user location, including:

[0015] The end user receives the polynomial coefficients in the ionospheric product and the longitude and latitude of the regional grid modeling center point, and uses the polynomial model and the ionospheric grid residual to obtain the grid points at The ionospheric slant delay at time , is expressed as:

[0016] ;

[0017] in, is Time grid k Ionospheric slant delay to satellite s, 、 、 and are the polynomial coefficients, are the longitude and latitude of the regional grid center coordinates, are the longitude and latitude of the end user respectively;

[0018] According to the grid points The calculation formula of the ionospheric slant delay at the moment is obtained. The ionospheric slant delay of each grid point in the epoch ionospheric grid is formed to form the historical epoch ionospheric slant delay data series and perform polynomial fitting; the polynomial fitting model is:

[0019] ;

[0020] in, , and Respectively represent the starting time and ending time of the fitting window, for Time grid k To Satellite s The ionospheric slant delay fitting value is are the polynomial fitting coefficients, n represents the fitting order;

[0021] Before selection The grid historical ionospheric slant delay of the epoch is fitted to the above polynomial fitting model, and the polynomial fitting coefficients are obtained, and then the polynomial fitting coefficients are calculated. Time grid k To Satellite s The ionospheric slant delay fitting value of , ionospheric grid fitting residuals and ionospheric grid fitting accuracy ;in, and Respectively expressed as:

[0022] ;

[0023] ;

[0024] And according to the following prediction, we can get Time grid k To Satellite s The ionospheric slant delay fitting value of , expressed as:

[0025] ;

[0026] And according to the following prediction Time grid k To Satellite s Ionospheric slant delay accuracy , expressed as:

[0027] ;

[0028] in, is the ionospheric product delay, and is the product delay threshold;

[0029] And according to Calculated Time grid k To Satellite s The predicted ionospheric residual , expressed as:

[0030] .

[0031] In one embodiment, performing residual compensation by inverse range interpolation to obtain the predicted ionospheric slant delay of the terminal user at the current moment includes:

[0032] according to The predicted ionospheric residuals of the four grid points near the terminal user at the moment are interpolated by inverse range to obtain Moment end user rTo Satellite s Predicted ionospheric slant delay , expressed as:

[0033] ;

[0034] in, is based on Perform inverse distance interpolation Moment end user r To Satellite s The predicted ionospheric residual is expressed as:

[0035] ;

[0036] in, From the end user location to the grid k The geometric distance;

[0037] And calculated according to the following formula Moment end user r To Satellite s The accuracy of the predicted ionospheric slant delay , expressed as:

[0038] ;

[0039] in, express Moment end user r To Satellite s The ionospheric slant delay accuracy is given by the ionospheric product; and After that, further obtain Moment end user r The predicted ionospheric slant delay to all available satellites and the predicted ionospheric slant delay accuracy are combined into the predicted ionospheric slant delay vector and the predicted ionospheric slant delay accuracy vector , and use these two vectors as constraints for subsequent fusion filter measurement updates; where, and The subscript 1 indicates the first frequency.

[0040] In one embodiment, before constructing an observation equation containing ionospheric slant delay parameters and a corresponding state equation based on the cycle slip state and the number of frequency points of the observation value and performing an extended Kalman filter solution, the method further includes:

[0041] Construct the original observation equation, expressed as:

[0042] ;

[0043] in, 、 and Respectively represent the satellite's PRN number, the end user's receiver ID, and the signal frequency; and Represent pseudorange and carrier phase observation values, respectively, in meters; for The carrier phase wavelength is in meters per cycle; is the geometric distance between the end user and the satellite. This is the position parameter to be estimated, in meters. 、 Represent the receiver clock error and satellite clock error respectively, in seconds, where It is called the receiver clock error parameter to be estimated. Calculated from the precise ephemeris broadcast by the server; 、 They represent the tropospheric slant delay and the ionospheric slant delay respectively, in meters. Eliminate through server-side products, real Obtained through subsequent estimation; Indicates the carrier phase integer ambiguity, in units of weeks, It is called the ambiguity parameter to be estimated. If there is no cycle slip between the previous and next epochs, the ambiguity is considered unchanged. 、 are the frequency-dependent receiver and satellite pseudorange hardware delays in meters, Eliminate the inter-satellite single difference in the PPP-RTK positioning solution algorithm. Eliminate through server-side products; 、 are the frequency-dependent receiver and satellite phase hardware delays in weeks, respectively, where The same is done by eliminating the inter-satellite single difference. Eliminate through server-side products; 、 are the sum of pseudorange and carrier observation noise, multipath effects and other unmodeled errors, respectively, in meters;

[0044] According to the cycle slip state and frequency number of the observed value, the purpose of constructing the observation equation containing the ionospheric slant delay parameter and the corresponding state equation is to remove the original observation equation. All parameters except the parameter become known.

[0045] In one embodiment, for observations with cycle slips, Doppler velocity measurement is used to determine the terminal user's position parameters, and a common ionospheric observation equation and a corresponding state equation are constructed, including:

[0046] For single-frequency observations with cycle slips, Doppler velocity measurement is used to obtain the position increment of the terminal user at the current moment relative to the previous moment. ,Will Add to the end user position calculated at the last moment Get the current location of the terminal user , further combined with and the current satellite position Sure , thus eliminating the position parameters to be estimated; among them, and Respectively expressed as:

[0047] ;

[0048] ;

[0049] set up Denotes the first frequency, and constructs the general ionospheric state equation, which is expressed as:

[0050] ;

[0051] in, is the system state vector at the current moment, and ; The estimated parameters of ionospheric slant delay of all available satellites at the current moment; for The parameter to be estimated is the rate of change of ionospheric slant delay drift; represents the ambiguity parameter to be estimated for the satellite that experiences a cycle slip, The dimension of the matrix is Row 1 column, m is the number of available satellites;

[0052] is the state transition matrix, is the process noise vector, which is set by empirical value and satisfies , for The covariance matrix of and Specifically expressed as:

[0053] ;

[0054] ;

[0055] In the above formula It is a diagonal matrix composed of scalar 1, and the number of diagonal rows and columns are m , is all scalar 0 mdimensional square matrix, The diagonal is The diagonal matrix of represents the sampling interval; express The error drift noise matrix; express process noise; express The process noise matrix of T represents transpose;

[0056] Construct the general ionospheric observation equation, which is expressed as:

[0057] ;

[0058] in, is the observation vector at the current moment, is the observation matrix at the current moment, is the observation noise at the current moment; and Specifically expressed as:

[0059] ;

[0060] ;

[0061] For dual-frequency or multi-frequency observations with cycle slips, the ordinary ionospheric observation equation and the corresponding state equation constructed based on single-frequency observations are expanded according to the number of frequency points to obtain the ordinary ionospheric observation equation and the corresponding state equation based on dual-frequency or multi-frequency observations.

[0062] In one embodiment, for a single-frequency observation value without a cycle slip, constructing a pseudorange-carrier combined observation equation and a corresponding state equation includes:

[0063] For single-frequency observations without cycle slips, the system state vector in the constructed pseudorange-carrier combination state equation is , state transfer matrix and the process noise vector Respectively expressed as:

[0064] ;

[0065] ;

[0066] ;

[0067] The observation vector in the constructed pseudorange-carrier combined observation equation is and the observation matrix Respectively expressed as:

[0068] ;

[0069] ;

[0070] in, express The identity matrix of order.

[0071] In one embodiment, for dual-frequency or multi-frequency observations without cycle slips, constructing a geometry-free combined observation equation and a corresponding state equation includes:

[0072] For dual-frequency or multi-frequency observations without cycle slips, the system state vector in the constructed geometry-free combined state equation is , state transfer matrix and the process noise vector Respectively expressed as:

[0073] ;

[0074] ;

[0075] ;

[0076] For dual-frequency observations without cycle slips, the observation vector in the constructed geometry-free combined observation equation is and the observation matrix Respectively expressed as:

[0077] ;

[0078] ;

[0079] For multi-frequency observations without cycle slips, the observation vector in the constructed geometry-free combined observation equation is and the observation matrix Respectively expressed as:

[0080] ;

[0081] ;

[0082] in, express m The identity matrix of order, p is the number of received signal frequencies.

[0083] In one embodiment, the steps of the extended Kalman filter solution are the same whether the observation value has a cycle slip or not, including:

[0084] Prediction steps:

[0085] ;

[0086] Update steps:

[0087] ;

[0088] in, is the predicted value of the parameter to be estimated, is the system state vector at the previous moment, is the state transition matrix, is the process noise vector of the previous moment; is the predicted state covariance, is the state covariance at the previous moment, is the covariance matrix of the process noise vector; is the Kalman gain for the end-user ionospheric slant delay; is the observation matrix at the current moment; is the observation noise covariance matrix, which is given based on experience and altitude angle weighting strategy; is the state estimate after end-user ionosphere update; is the observation vector at the current moment; is the updated covariance; is the unit diagonal matrix; superscript T Indicates transpose.

[0089] In one embodiment, the ionospheric slant delay of the terminal user at the current moment obtained by the extended Kalman filter solution is fused with the predicted ionospheric slant delay to perform constraint update to obtain the optimized ionospheric slant delay of the terminal user at the current moment, including:

[0090] Fusion constraint step: After the extended Kalman filter update is completed, Get the estimated parameters of ionospheric slant delay of all available satellites at the current moment , the predicted ionospheric slant delay vector and the predicted ionospheric slant delay accuracy vector As a constraint, external ionospheric constraints are imposed on the ionospheric parameters of the observation equation, and a virtual observation equation is constructed, which is expressed as:

[0091] ;

[0092] in, Satellites predicted by the server at the current moment s The ionospheric slant delay, is the satellite obtained by extending Kalman filter at the current moment s The ionospheric slant delay, for The corresponding measurement noise;

[0093] The observation vector and observation matrix of the constructed virtual observation equation are expressed as follows:

[0094] ;

[0095] ;

[0096] in, is the number of available satellites;

[0097] Update steps:

[0098] ;

[0099] in, is the Kalman gain of the server-side predicted ionospheric slant delay; The updated filter Contains only The variance-covariance part of for Contains only The estimated parameter part of is The diagonal matrix is formed; thus, the optimized ionospheric slant delay of the terminal user at the current moment is obtained and its state covariance matrix and use Synchronous Update The state covariance value corresponding to the ionospheric slant delay of the terminal user is used for the extended Kalman filter solution at the next moment.

[0100] A PPP-RTK ionospheric slant delay fusion optimization device, comprising:

[0101] Data receiving module, used to receive GNSS observation values and SSR products broadcast by PPP-RTK server;

[0102] The polynomial fitting prediction module is used to perform polynomial fitting prediction based on the SSR products of historical epochs to obtain the predicted ionospheric residual of the ionospheric grid points near the end user's location, and to compensate for the residual by inverse range interpolation to obtain the predicted ionospheric slant delay at the end user's current moment;

[0103] The Kalman filter solution module is used to construct an observation equation containing ionospheric slant delay parameters and the corresponding state equation based on the cycle slip state and frequency number of the observation value, and perform extended Kalman filter solution. Specifically, for observation values with cycle slips, Doppler velocity measurement is used to determine the terminal user's position parameters, and a normal ionospheric observation equation and the corresponding state equation are constructed. For single-frequency observation values without cycle slips, a pseudorange-carrier combination observation equation and the corresponding state equation are constructed. For dual-frequency or multi-frequency observation values without cycle slips, a geometry-free combination observation equation and the corresponding state equation are constructed.

[0104] The fusion constraint update module is used to perform fusion constraint update on the terminal user's current ionospheric slant delay obtained by the extended Kalman filter solution and the predicted ionospheric slant delay to obtain the optimized ionospheric slant delay of the terminal user at the current moment, perform PPP-RTK positioning solution based on the optimized ionospheric slant delay, and output the optimized terminal user position information.

[0105] The above-mentioned PPP-RTK ionospheric slant delay fusion optimization method and device, while using the server-side ionospheric product for real-time forecasting, proposes to construct an observation equation related to the ionosphere in combination with the real-time observation values of the end user. By extending the Kalman filter fusion weighting, a more accurate ionospheric slant delay can be obtained, thereby improving the PPP-RTK real-time positioning accuracy. Compared with the existing technology, this application has the following advantages:

[0106] (1) Real-time dynamic update: The integration of end-user observation data improves the ionospheric slant delay correction capability in dynamic environments.

[0107] (2) Adaptive adjustment: If the end-user observation data is more accurate, the Kalman filter weight will be automatically increased to optimize the ionospheric correction.

[0108] (3) Taking into account both long-term trends (service side) and short-term fluctuations (end users), the accuracy of ionospheric correction is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 1 is a flow chart of a PPP-RTK ionospheric slant delay fusion optimization method in one embodiment;

[0110] Figure 2 Schematic diagram of implementation steps of a PPP-RTK ionospheric slant delay fusion optimization method in one embodiment;

[0111] Figure 3 Schematic diagram of the construction process of observation equations and corresponding state equations under different observation values in one embodiment;

[0112] Figure 4Schematic diagram of the architecture of a PPP-RTK ionospheric slant delay fusion optimization device in one embodiment. DETAILED DESCRIPTION

[0113] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0114] In one embodiment, Figure 1 As shown, a PPP-RTK ionospheric slant delay fusion optimization method is provided, comprising the following steps:

[0115] Step 1: Receive GNSS (Global Navigation Satellite System) observations and SSR products broadcast by the PPP-RTK server.

[0116] Specifically, the end user receives GNSS observations and SSR products broadcast by the PPP-RTK server; among them, SSR products include precise orbits, precise clock errors, phase fractional deviation products, tropospheric products, and ionospheric products. Figure 2 As shown in the figure, after receiving the observation value and SSR product, it is first determined whether the current moment is the first epoch. If so, the PPP-RTK positioning solution is directly performed, the terminal user's position information is output, and the observation value at the current moment, the calculated position information, ambiguity and tropospheric parameter information are extracted and passed to the next moment; otherwise, the ionospheric slant delay fusion optimization process is entered.

[0117] Step 2: Perform polynomial fitting forecast based on the SSR products of historical epochs to obtain the predicted ionospheric residual of the ionospheric grid points near the end user's location, and compensate the residual through inverse range interpolation to obtain the predicted ionospheric slant delay at the end user's current moment.

[0118] Specifically, the implementation process of step 2 includes:

[0119] Step 2.1: The end user receives the polynomial coefficients in the ionospheric product and the latitude and longitude of the regional grid modeling center point, and uses the polynomial model and the ionospheric grid residual to obtain the grid points at The ionospheric slant delay at time , is expressed as:

[0120] (1)

[0121] in, is Time grid k Ionospheric slant delay to satellite s, 、 、 and are the polynomial coefficients, are the longitude and latitude of the regional grid center coordinates, are the longitude and latitude of the end user respectively;

[0122] According to formula (1), each grid point is The calculation formula of the ionospheric slant delay at the moment is obtained. The ionospheric slant delay of each grid point in the epoch ionospheric grid is formed to form the historical epoch ionospheric slant delay data series and perform polynomial fitting; the polynomial fitting model is:

[0123] (2)

[0124] in, , and Respectively represent the starting time and ending time of the fitting window, for Time grid k To Satellite s The ionospheric slant delay fitting value is are the polynomial fitting coefficients, n Indicates the fitting order.

[0125] Step 2.2, select the front The grid historical ionospheric slant delay of the epoch is fitted to the polynomial fitting model of Equation (2), and the polynomial fitting coefficients are obtained, and then the polynomial fitting coefficients are calculated. Time grid k To Satellite s The ionospheric slant delay fitting value of , ionospheric grid fitting residuals and ionospheric grid fitting accuracy ;in, and Respectively expressed as:

[0126] (3)

[0127] (4)

[0128] Step 2.3, according to the following formula (5), we can get Time grid k To Satellite s The ionospheric slant delay fitting value of , expressed as:

[0129] (5)

[0130] And according to the following formula (6), we can get Time grid k To Satellite s Ionospheric slant delay accuracy , expressed as:

[0131] (6)

[0132] in, is the ionospheric product delay, and The product latency threshold.

[0133] Step 2.4, according to Calculated Time grid k To Satellite s The predicted ionospheric residual , expressed as:

[0134] (7)

[0135] Step 2.5, according to The predicted ionospheric residuals of the four grid points near the terminal user at the moment are interpolated by inverse range to obtain Moment end user r To Satellite s Predicted ionospheric slant delay , expressed as:

[0136] (8)

[0137] in, is based on Perform inverse distance interpolation Moment end user r To Satellite s The predicted ionospheric residual is expressed as:

[0138] (9)

[0139] in, From the end user location to the grid k The geometric distance.

[0140] In step 2.6, according to the error propagation law, the ionospheric delay accuracy of the final user terminal position prediction takes into account the interpolation accuracy of the grid point prediction ionospheric residual and the ionospheric accuracy of the user terminal itself, and is calculated according to formula (10) Moment end user r To Satellite s The accuracy of the predicted ionospheric slant delay , expressed as:

[0141] (10)

[0142] in, express The ionospheric slant delay accuracy from the terminal user r to the satellite s at the moment is given by the ionospheric product; and After that, further obtain Moment end user r The predicted ionospheric slant delay to all available satellites and the predicted ionospheric slant delay accuracy are combined into the predicted ionospheric slant delay vector and the predicted ionospheric slant delay accuracy vector , and use these two vectors as constraints for subsequent fusion filter measurement updates; where, and The subscript 1 indicates the first frequency.

[0143] Step 3: Based on the cycle slip state and frequency number of the observation value, the observation equation containing the ionospheric slant delay parameter and the corresponding state equation are constructed and the extended Kalman filter is solved; wherein, for the observation value with cycle slips, the Doppler velocity measurement is used to determine the position parameters of the terminal user, and the ordinary ionospheric observation equation and the corresponding state equation are constructed; for the single-frequency observation value without cycle slips, the pseudo-range carrier combination observation equation and the corresponding state equation are constructed; for the dual-frequency or multi-frequency observation value without cycle slips, the geometry-free combination observation equation and the corresponding state equation are constructed.

[0144] The construction process of observation equation and corresponding state equation under different observation values is as follows: Figure 3 Specifically, the implementation process of step 3 includes:

[0145] Step 3.1: In order to construct the spatiotemporal relationship between the current epoch observations and the ionospheric parameters, the original observation equation is constructed, which is expressed as:

[0146] (11)

[0147] in, 、 and Respectively represent the satellite's PRN (pseudo-random noise) number, the end user's receiver ID, and the signal frequency; and Represent pseudorange and carrier phase observation values, respectively, in meters; for The carrier phase wavelength is in meters per cycle; is the geometric distance between the end user and the satellite. This is the position parameter to be estimated, in meters. 、 Represent the receiver clock error and satellite clock error respectively, in seconds, where It is called the receiver clock error parameter to be estimated. Calculated from the precise ephemeris broadcast by the server; 、 They represent the tropospheric slant delay and the ionospheric slant delay respectively, in meters. Eliminate through server-side products, real Obtained through subsequent estimation; Indicates the carrier phase integer ambiguity, in units of weeks, It is called the ambiguity parameter to be estimated. If there is no cycle slip between the previous and next epochs, the ambiguity is considered unchanged. 、 are the frequency-dependent receiver and satellite pseudorange hardware delays in meters, Eliminate the inter-satellite single difference in the PPP-RTK positioning solution algorithm. Eliminate through server-side products; 、 are the frequency-dependent receiver and satellite phase hardware delays in weeks, respectively, where The same is done by eliminating the inter-satellite single difference. Eliminate through server-side products; 、 are the sum of pseudorange and carrier observation noise, multipath effects and other unmodeled errors, respectively, in meters;

[0148] According to the cycle slip state and frequency number of the observed value, the purpose of constructing the observation equation containing the ionospheric slant delay parameter and the corresponding state equation is to remove the original observation equation. All parameters except the parameter become known;

[0149] Among them, when there is a cycle slip in the observation value, Doppler velocity measurement is used to obtain the position increment of the terminal user at the current moment relative to the previous moment ,Will Add to the end user position calculated at the last moment Get the current location of the terminal user , further combined with and the current satellite position Sure , thus eliminating the position parameters to be estimated; among them, and Respectively expressed as:

[0150] (12)

[0151] (13)

[0152] When there is no cycle slip in the observation value, different combinations of pseudorange and carrier phase are used to eliminate the ambiguity parameters and receiver clock error parameters according to the number of received frequency points, and the corresponding observation equation is constructed in different cases.

[0153] Step 3.2: Cycle slips in the observations. To clarify the derivation process, this step uses single-frequency observations as an example to illustrate the process of calculating the current terminal user's ionospheric slant delay using an extended Kalman filter when cycle slips are present. The solution for dual-frequency and multi-frequency conditions can be derived by simply expanding on the single-frequency derivation in this step. This step specifically includes:

[0154] Step 3.2.1, determine the parameters to be estimated:

[0155] Doppler velocity measurement is used to calculate velocity information. The observation equation is as follows:

[0156] (14)

[0157] in,

[0158] (15)

[0159] (16)

[0160] in, represents the Doppler observation value; represents the pseudorange rate; Represents the receiver clock error change rate; represents the satellite clock error change rate; represents the rate of change of tropospheric delay; represents the rate of change of ionospheric delay; and are the satellite position and velocity vectors calculated based on the precise ephemeris; is the receiver position vector, which can be obtained through PPP (Precise Point Positioning) floating point solution; is the receiver velocity vector; is the direction cosine vector from the receiver to the satellite; is the Doppler observation noise. Since the velocity measurement is completed in a very short time, the influence of the ionosphere and troposphere delay variation rate on the velocity measurement can be ignored.

[0161] The receiver clock error change rate in equation (14) can be calculated using least squares: and the three-dimensional velocity in Eq. (15) , and then according to the relationship between speed and time, the position increment is obtained:

[0162] (17)

[0163] in, Indicates the sampling interval.

[0164] Step 3.2.2, general ionospheric observation equation and corresponding state equation:

[0165] Assume that the received signal frequency in equation (11) is the first frequency, that is, , when the observation value has a cycle slip, in formula (11) Need to be re-estimated, and the combined observation equation cannot be formed at this time, so it is necessary to estimate ,consider The short-term changes are small, so the previous moment can be used. is a required parameter, so the parameters to be estimated are: 、 、 , then the system state vector for:

[0166] (18)

[0167] in, The estimated parameters of ionospheric slant delay of all available satellites at the current moment; for The estimated parameter of the ionospheric slant delay drift change rate can reflect the time-varying characteristics of the ionosphere and conform to the state space model of the dynamic system, which is convenient for state prediction and improves real-time performance and accuracy. represents the ambiguity parameter to be estimated for the satellite that experiences a cycle slip, The dimension of the matrix is 3 m +1 row and 1 column, m is the number of available satellites.

[0168] The general ionospheric state equation can be expressed as:

[0169] (19)

[0170] Where, represent The error drift noise, 、 Respectively and The process noise is:

[0171] (20)

[0172] In the above formula, is the state transition matrix, is the process noise vector, which is set by empirical value to satisfy , for The covariance matrix of . According to formula (19), it can be expressed as:

[0173] (twenty one)

[0174] (twenty two)

[0175] It should be noted that in the above formula It is a diagonal matrix composed of scalar 1, and the number of diagonal rows and columns are m , is all scalar 0 m dimensional square matrix, The diagonal is The diagonal matrix of represents the sampling interval; express The error drift noise matrix; express process noise; express The process noise matrix of T Indicates transpose.

[0176] According to equations (11), (18) and their explanations, shifting the known quantities to the left, we obtain the following general ionospheric observation equation:

[0177] (twenty three)

[0178] The above formula can be simplified as:

[0179] (twenty four)

[0180] in, is the observation vector at the current moment, is the observation matrix at the current moment, is the observation noise at the current moment; and Specifically expressed as:

[0181] (25)

[0182] (26)

[0183] If a cycle slip occurs for the received dual-frequency or multi-frequency observation value, the number of received signal frequencies is p , then the ordinary ionospheric observation equation based on single frequency in equation (23) is expanded to obtain the ordinary ionospheric observation equation based on dual frequency or multi-frequency, as shown in equation (27):

[0184] (27)

[0185] Corresponding to the observation equation (27), on a single-frequency basis 、 、 Expand accordingly, to be estimated Need to increase Parameters, and expand according to the observation value of the increased frequency and , obtaining the general ionospheric equation of state based on dual-frequency or multi-frequency. Using more received signal frequencies is conducive to obtaining better STEC estimation accuracy, but the computational complexity will also increase simultaneously.

[0186] Step 3.2.3, Extended Kalman filter prediction and update:

[0187] According to equations (20) and (24), the Kalman filtering process can be performed. The specific steps are as follows:

[0188] Prediction steps:

[0189] (28)

[0190] Update steps:

[0191] (29)

[0192] in, is the predicted value of the parameter to be estimated, is the system state vector at the previous moment, is the state transition matrix, is the process noise vector of the previous moment; is the predicted state covariance, is the state covariance at the previous moment, is the covariance matrix of the process noise vector; is the Kalman gain for the end-user ionospheric slant delay; is the observation matrix at the current moment; is the observation noise covariance matrix, which is given based on experience and altitude angle weighting strategy; is the state estimate after end-user ionosphere update; is the observation vector at the current moment; is the updated covariance; is the unit diagonal matrix; superscript T Indicates transpose.

[0193] In formula (29):

[0194] (30)

[0195] in, Expressed as altitude angle function, For the The altitude angle of the satellite is given by an empirical expression:

[0196] (31)

[0197] Where a and b are constants. Similarly, when using multi-frequency observations, taking dual-frequency as an example, it is necessary to Adding a second frequency point on the diagonal ,at this time It becomes a 2m-order matrix.

[0198] In step 3.3, there are no cycle slips in the observed values.

[0199] Step 3.3.1: For single-frequency observations without cycle slips, construct the pseudorange-carrier combined observation equation and the corresponding state equation. The specific steps are:

[0200] For single-frequency users, when there is no cycle slip, a pseudo-range-minus-carrier combination can be constructed. 、 Eliminate in the process of making a difference, You can continue to use the previous epoch, is a required parameter, so the parameters to be estimated are: , then the system state vector for:

[0201] (32)

[0202] The pseudorange-carrier combination state equation is:

[0203] (33)

[0204] The above formula can be expressed as formula (20), where:

[0205] (34)

[0206] (35)

[0207] According to equations (11), (32) and their explanations, the following pseudorange-carrier combined observation equation is obtained:

[0208] (36)

[0209] Shift the known quantity to the left:

[0210] (37)

[0211] Simplifying the above formula into the form of formula (24), where:

[0212] (38)

[0213] (39)

[0214] In formula (39), express The identity matrix of order.

[0215] At this point, the extended Kalman filter prediction and update steps are the same as in step 3.2.3.

[0216] Step 3.3.2: For dual-frequency or multi-frequency observations without cycle slips, construct the geometry-free combined observation equation and the corresponding state equation. The specific steps are:

[0217] For dual-frequency and multi-frequency users, when there is no cycle slip, a geometry-free (GF) combined observation is constructed. 、 Eliminate in the process of making a difference, You can continue to use the previous epoch, is a required parameter, so the parameters to be estimated are: , then the system state vector for:

[0218] (40)

[0219] The equations of state without geometric combinations are:

[0220] (41)

[0221] The above formula can be expressed as formula (20), where:

[0222] (42)

[0223] (43)

[0224] According to Equation (11), Equation (40) and their explanations, for dual-frequency observations without cycle slips, the following geometry-free combination observation equation can be obtained:

[0225] (44)

[0226] Shift the known quantity to the left:

[0227] (45)

[0228] Simplifying the above formula into the form of formula (24), where:

[0229] (46)

[0230] (47)

[0231] For multi-frequency observations without cycle slips, the equations (46) and (47) can be expanded. When the number of received signal frequency points is p hour ， It has the following representation:

[0232] (48)

[0233] (49)

[0234] When there is no cycle slip in the observation value, the extended Kalman filter prediction and update steps are consistent with step 3.2.3.

[0235] Step 4: The ionospheric slant delay of the terminal user at the current moment obtained by the extended Kalman filter solution is fused with the predicted ionospheric slant delay to obtain the optimized ionospheric slant delay of the terminal user at the current moment, and PPP-RTK positioning solution is performed based on the optimized ionospheric slant delay to output the optimized terminal user position information.

[0236] Specifically, the implementation process of step 4 includes:

[0237] Step 4.1, after the extended Kalman filter update is completed, Get the estimated parameters of ionospheric slant delay of all available satellites at the current moment , the predicted ionospheric slant delay vector and the predicted ionospheric slant delay accuracy vector As a constraint, external ionospheric constraints are imposed on the ionospheric parameters of the observation equation, and a virtual observation equation is constructed, which is expressed as:

[0238] (50)

[0239] in, Satellites predicted by the server at the current moment s The ionospheric slant delay, is the satellite obtained by extending Kalman filter at the current moment s The ionospheric slant delay, for The corresponding measurement noise.

[0240] Convert Equation (50) into Equation (24), where:

[0241] (51)

[0242] (52)

[0243] Step 4.2, the update step is similar to Equation (28), as follows:

[0244] (53)

[0245] in, is the Kalman gain of the server-side predicted ionospheric slant delay; The updated filter Contains only The variance-covariance part of for Contains only The estimated parameter part of is The diagonal matrix is formed; thus, the optimized ionospheric slant delay of the terminal user at the current moment is obtained and its state covariance matrix and use Synchronous Update The state covariance value corresponding to the ionospheric slant delay of the terminal user is used for the extended Kalman filter solution at the next moment.

[0246] Step 4.3: According to the above steps, PPP-RTK positioning solution is performed using the optimized ionospheric slant delay to output the optimized terminal user position information.

[0247] In summary, the present application provides a PPP-RTK ionospheric slant delay fusion optimization method. While using the server-side ionospheric product for real-time forecasting, it proposes to construct an observation equation related to the ionosphere in combination with the terminal real-time observation value. By extending the Kalman filter fusion weighting, a more accurate terminal STEC is obtained, thereby improving the PPP-RTK real-time positioning accuracy.

[0248] In one embodiment, Figure 4 As shown, a PPP-RTK ionospheric slant delay fusion optimization device is provided, comprising:

[0249] The data receiving module 401 is used to receive GNSS observation values and SSR products broadcast by the PPP-RTK server.

[0250] The polynomial fitting prediction module 402 is used to perform polynomial fitting prediction based on the SSR products of the historical epochs to obtain the predicted ionospheric residual of the ionospheric grid points near the terminal user's location, and to compensate for the residual by inverse range interpolation to obtain the predicted ionospheric slant delay at the terminal user's current moment.

[0251] The Kalman filter solution module 403 is used to construct an observation equation containing ionospheric slant delay parameters and a corresponding state equation based on the cycle slip state and frequency number of the observation value, and perform an extended Kalman filter solution. Specifically, for observation values with cycle slips, Doppler velocity measurement is used to determine the terminal user's position parameters, and a conventional ionospheric observation equation and a corresponding state equation are constructed. For single-frequency observation values without cycle slips, a pseudorange-carrier combination observation equation and a corresponding state equation are constructed. For dual-frequency or multi-frequency observation values without cycle slips, a geometry-free combination observation equation and a corresponding state equation are constructed.

[0252] The fusion constraint update module 404 is used to perform a fusion constraint update on the terminal user's current ionospheric slant delay obtained by the extended Kalman filter solution and the predicted ionospheric slant delay to obtain the optimized ionospheric slant delay of the terminal user at the current moment, perform PPP-RTK positioning solution based on the optimized ionospheric slant delay, and output the optimized terminal user position information.

[0253] Regarding the specific definition of a PPP-RTK ionospheric slant delay fusion optimization device, please refer to the definition of a PPP-RTK ionospheric slant delay fusion optimization method above, which will not be repeated here. The various modules in the above-mentioned PPP-RTK ionospheric slant delay fusion optimization device can be implemented in whole or in part by software, hardware, and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0254] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0255] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A PPP-RTK ionospheric slant delay fusion optimization method, characterized in that: The method comprises: Receive GNSS observations and SSR products broadcast by the PPP-RTK server; The polynomial fitting forecast is performed based on the SSR products of the historical epochs to obtain the predicted ionospheric residual of the ionospheric grid points near the end user's location, and the residual is compensated by inverse range interpolation to obtain the predicted ionospheric slant delay at the end user's current moment; Based on the cycle slip state and frequency number of the observation value, the observation equation containing the ionospheric slant delay parameter and the corresponding state equation are constructed and the extended Kalman filter solution is performed. Among them, for the observation value with cycle slips, the Doppler velocity measurement is used to determine the position parameters of the terminal user, and the ordinary ionospheric observation equation and the corresponding state equation are constructed. For the single-frequency observation value without cycle slips, the pseudo-range carrier combination observation equation and the corresponding state equation are constructed. For the dual-frequency or multi-frequency observation value without cycle slips, the geometry-free combination observation equation and the corresponding state equation are constructed. The ionospheric slant delay of the terminal user at the current moment obtained by the extended Kalman filter solution is fused with the predicted ionospheric slant delay to obtain the optimized ionospheric slant delay of the terminal user at the current moment. PPP-RTK positioning solution is performed based on the optimized ionospheric slant delay, and the optimized terminal user position information is output.

2. The method according to claim 1, characterized in that Receive GNSS observations and SSR products broadcast by the PPP-RTK server, including: End users receive GNSS observations and SSR products broadcast by the PPP-RTK server; the SSR products include precise orbits, precise clock errors, fractional phase deviation products, tropospheric products, and ionospheric products. Determine whether the current moment is the first epoch. If so, directly perform PPP-RTK positioning solution, output the terminal user's position information, extract the current moment's observation value, the solved position information, the ambiguity and the troposphere to pass to the next moment; otherwise, enter the ionospheric slant delay fusion optimization process.

3. The method according to claim 2, characterized in that Based on the SSR products of historical epochs, a polynomial fitting forecast is performed to obtain the predicted ionospheric residuals of the ionospheric grid points near the end user location, including: The end user receives the polynomial coefficients in the ionospheric product and the longitude and latitude of the regional grid modeling center point, and uses the polynomial model and the ionospheric grid residual to obtain the grid points at The ionospheric slant delay at time , is expressed as: ； in, is Time grid k Ionospheric slant delay to satellite s, 、 、 and are the polynomial coefficients, are the longitude and latitude of the regional grid center coordinates, are the longitude and latitude of the end user respectively; According to the grid points The calculation formula of the ionospheric slant delay at the moment is obtained. The ionospheric slant delay of each grid point in the epoch ionospheric grid is formed to form the historical epoch ionospheric slant delay data series and perform polynomial fitting; the polynomial fitting model is: ； in, , and Respectively represent the starting time and ending time of the fitting window, for Time grid k To Satellite s The ionospheric slant delay fitting value is are the polynomial fitting coefficients, n represents the fitting order; Before selection The grid historical ionospheric slant delay of the epoch is fitted to the above polynomial fitting model, and the polynomial fitting coefficients are obtained, and then the polynomial fitting coefficients are calculated. Time grid k To Satellite s The ionospheric slant delay fitting value of , ionospheric grid fitting residuals and ionospheric grid fitting accuracy ;in, and Respectively expressed as: ； ； And according to the following prediction, we can get Time grid k To Satellite s The ionospheric slant delay fitting value of , expressed as: ； And according to the following prediction Time grid k To Satellite s Ionospheric slant delay accuracy , expressed as: ； in, is the ionospheric product delay, and is the product delay threshold; And according to Calculated Time grid k To Satellite s The predicted ionospheric residual , expressed as: 。 4. The method according to claim 3, characterized in that The residual compensation is performed by inverse range interpolation to obtain the predicted ionospheric slant delay of the end user at the current moment, including: according to The predicted ionospheric residuals of the four grid points near the terminal user at the moment are interpolated by inverse range to obtain Moment end user r To Satellite s Predicted ionospheric slant delay , expressed as: ； in, is based on Perform inverse distance interpolation Moment end user r To Satellite s The predicted ionospheric residual is expressed as: ； in, From the end user location to the grid k The geometric distance; And calculated according to the following formula Moment end user r To Satellite s The accuracy of the predicted ionospheric slant delay , expressed as: ； in, express Moment end user r To Satellite s The ionospheric slant delay accuracy is given by the ionospheric product; and After that, further obtain Moment end user r The predicted ionospheric slant delay to all available satellites and the predicted ionospheric slant delay accuracy are combined into the predicted ionospheric slant delay vector and the predicted ionospheric slant delay accuracy vector , and use these two vectors as constraints for subsequent fusion filter measurement updates; where, and The subscript 1 indicates the first frequency.

5. The method according to claim 1, wherein Before constructing the observation equation containing the ionospheric slant delay parameter and the corresponding state equation based on the cycle slip state and frequency number of the observation value and performing the extended Kalman filter solution, the following steps are also included: Construct the original observation equation, expressed as: ； in, 、 and Respectively represent the satellite's PRN number, the end user's receiver ID, and the signal frequency; and Represent pseudorange and carrier phase observation values, respectively, in meters; for The carrier phase wavelength is in meters per cycle; is the geometric distance between the end user and the satellite. This is the position parameter to be estimated, in meters. 、 Represent the receiver clock error and satellite clock error respectively, in seconds, where It is called the receiver clock error parameter to be estimated. Calculated from the precise ephemeris broadcast by the server; 、 They represent the tropospheric slant delay and the ionospheric slant delay respectively, in meters. Eliminate through server-side products, real Obtained through subsequent estimation; Indicates the carrier phase integer ambiguity, in units of weeks, It is called the ambiguity parameter to be estimated. If there is no cycle slip between the previous and next epochs, the ambiguity is considered unchanged. 、 are the frequency-dependent receiver and satellite pseudorange hardware delays in meters, Eliminate the inter-satellite single difference in the PPP-RTK positioning solution algorithm. Eliminate through server-side products; 、 are the frequency-dependent receiver and satellite phase hardware delays in weeks, respectively, where The same is done by eliminating the inter-satellite single difference. Eliminate through server-side products; 、 are the sum of pseudorange and carrier observation noise, multipath effects and other unmodeled errors, respectively, in meters; According to the cycle slip state and frequency number of the observed value, the purpose of constructing the observation equation containing the ionospheric slant delay parameter and the corresponding state equation is to remove the original observation equation. All parameters except the parameter become known.

6. The method according to claim 5, characterized in that For observations with cycle slips, Doppler velocity measurement is used to determine the terminal user's position parameters, and the general ionospheric observation equation and the corresponding state equation are constructed, including: For single-frequency observations with cycle slips, Doppler velocity measurement is used to obtain the position increment of the terminal user at the current moment relative to the previous moment. ,Will Add to the end user position calculated at the last moment Get the current location of the terminal user , further combined with and the current satellite position Sure , thus eliminating the position parameters to be estimated; among them, and Respectively expressed as: ； ； set up Denotes the first frequency, and constructs the general ionospheric state equation, which is expressed as: ； in, is the system state vector at the current moment, and ; The estimated parameters of ionospheric slant delay of all available satellites at the current moment; for The parameter to be estimated is the rate of change of ionospheric slant delay drift; represents the ambiguity parameter to be estimated for the satellite that experiences a cycle slip, The dimension of the matrix is Row 1 column, is the number of available satellites; is the state transition matrix, is the process noise vector, which is set by empirical value and satisfies , for The covariance matrix of and Specifically expressed as: ； ； In the above formula It is a diagonal matrix composed of scalar 1, and the number of diagonal rows and columns are m , is all scalar 0 dimensional square matrix, The diagonal is The diagonal matrix of represents the sampling interval; express The error drift noise matrix; express process noise; express The process noise matrix of represents transpose; Construct the general ionospheric observation equation, which is expressed as: ； in, is the observation vector at the current moment, is the observation matrix at the current moment, is the observation noise at the current moment; and Specifically expressed as: ； ； For dual-frequency or multi-frequency observations with cycle slips, the ordinary ionospheric observation equation and the corresponding state equation constructed based on single-frequency observations are expanded according to the number of frequency points to obtain the ordinary ionospheric observation equation and the corresponding state equation based on dual-frequency or multi-frequency observations.

7. The method according to claim 6, characterized in that For single-frequency observations without cycle slips, the pseudorange-carrier combined observation equation and the corresponding state equation are constructed, including: For single-frequency observations without cycle slips, the system state vector in the constructed pseudorange-carrier combination state equation is , state transfer matrix and the process noise vector Respectively expressed as: ； ； ； The observation vector in the constructed pseudorange-carrier combined observation equation is and the observation matrix Respectively expressed as: ； ； in, express m The identity matrix of order.

8. The method according to claim 6, characterized in that For dual-frequency or multi-frequency observations without cycle slips, the geometry-free combined observation equation and the corresponding state equation are constructed, including: For dual-frequency or multi-frequency observations without cycle slips, the system state vector in the constructed geometry-free combined state equation is , state transfer matrix and the process noise vector Respectively expressed as: ； ； ； For dual-frequency observations without cycle slips, the observation vector in the constructed geometry-free combined observation equation is and the observation matrix Respectively expressed as: ； ； For multi-frequency observations without cycle slips, the observation vector in the constructed geometry-free combined observation equation is and the observation matrix Respectively expressed as: ； ； in, express m The identity matrix of order, p is the number of received signal frequencies.

9. The method according to claim 1, characterized in that The steps for solving the extended Kalman filter are the same whether the observations have cycle slips or not, including: Prediction steps: ； Update steps: ； in, is the predicted value of the parameter to be estimated, is the system state vector at the previous moment, is the state transition matrix, is the process noise vector of the previous moment; is the predicted state covariance, is the state covariance at the previous moment, is the covariance matrix of the process noise vector; is the Kalman gain for the end-user ionospheric slant delay; is the observation matrix at the current moment; is the observation noise covariance matrix, which is given based on experience and altitude angle weighting strategy; is the state estimate after end-user ionosphere update; is the observation vector at the current moment; is the updated covariance; is the unit diagonal matrix; superscript Indicates transpose.

10. The method according to claim 9, characterized in that The ionospheric slant delay of the terminal user at the current moment obtained by the extended Kalman filter is integrated with the predicted ionospheric slant delay to obtain the optimized ionospheric slant delay of the terminal user at the current moment, including: Fusion constraint step: After the extended Kalman filter update is completed, Get the estimated parameters of ionospheric slant delay of all available satellites at the current moment , the predicted ionospheric slant delay vector and the predicted ionospheric slant delay accuracy vector As a constraint, external ionospheric constraints are imposed on the ionospheric parameters of the observation equation, and a virtual observation equation is constructed, which is expressed as: ； in, Satellites predicted by the server at the current moment s The ionospheric slant delay, is the satellite obtained by extending Kalman filter at the current moment s The ionospheric slant delay, for The corresponding measurement noise; The observation vector and observation matrix of the constructed virtual observation equation are expressed as follows: ； ； in, is the number of available satellites; Update steps: ； in, is the Kalman gain of the server-side predicted ionospheric slant delay; The updated filter Contains only The variance-covariance part of for Contains only The estimated parameter part of is The diagonal matrix is formed; thus, the optimized ionospheric slant delay of the terminal user at the current moment is obtained and its state covariance matrix and use Synchronous Update The state covariance value corresponding to the ionospheric slant delay of the terminal user is used for the extended Kalman filter solution at the next moment.

11. A PPP-RTK ionospheric slant delay fusion optimization device, characterized in that: The device comprises: Data receiving module, used to receive GNSS observation values and SSR products broadcast by PPP-RTK server; The polynomial fitting prediction module is used to perform polynomial fitting prediction based on the SSR products of historical epochs to obtain the predicted ionospheric residual of the ionospheric grid points near the end user's location, and to compensate for the residual by inverse range interpolation to obtain the predicted ionospheric slant delay at the end user's current moment; The Kalman filter solution module is used to construct an observation equation containing ionospheric slant delay parameters and the corresponding state equation based on the cycle slip state and frequency number of the observation value, and perform extended Kalman filter solution. Specifically, for observation values with cycle slips, Doppler velocity measurement is used to determine the terminal user's position parameters, and a normal ionospheric observation equation and the corresponding state equation are constructed. For single-frequency observation values without cycle slips, a pseudorange-carrier combination observation equation and the corresponding state equation are constructed. For dual-frequency or multi-frequency observation values without cycle slips, a geometry-free combination observation equation and the corresponding state equation are constructed. The fusion constraint update module is used to perform fusion constraint update on the terminal user's current ionospheric slant delay obtained by the extended Kalman filter solution and the predicted ionospheric slant delay to obtain the optimized ionospheric slant delay of the terminal user at the current moment, perform PPP-RTK positioning solution based on the optimized ionospheric slant delay, and output the optimized terminal user position information.

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