PPP-RTK time delay processing method and device in conversion from SSR to OSR

Abstract

The invention discloses a PPP-RTK time delay processing method and device in conversion from SSR to OSR, and relates to the technical field of global navigation satellite system positioning, and the method comprises the steps: converting orbit, clock error, ionosphere and troposphere delay SSR parameters provided by a server into OSR virtual observation values through geometric distance calculation and projection function mapping; based on a constant velocity model and a static random process, predicting a correction amount of a future moment, and correcting an OSR virtual observation value through state transition matrix compensation time delay; combining server side parameters and user side observation data, recursively generating an error covariance matrix, dynamically adjusting a state prediction weight, and obtaining covariance information through adaptive filtering optimization positioning calculation; and realizing ambiguity rapid fixation and centimeter-level positioning by using the corrected OSR observation value and covariance information. According to the method, real-time centimeter-level positioning in a high-delay scene is realized through a dynamic correction value prediction method and a recursive covariance estimation method.

Description

Technical Field

[0001] The present invention relates to the field of global navigation satellite system positioning technology, and specifically to a PPP-RTK time delay processing method and device in SSR to OSR conversion, especially the conversion of state space representation (SSR) to observable space representation (OSR) in Precise Point Positioning-Real-Time Kinematic (PPP-RTK) technology, and the correction processing of time delay in traditional PPP-RTK correction value transmission. Background Art

[0002] With the rapid evolution of Global Navigation Satellite System (GNSS) technology and the growing demand for high-precision positioning, traditional single-mode augmentation systems are struggling to meet the technical challenges of multi-scenario applications. Against this backdrop, the Integrated Satellite-Terrestrial Augmentation System (ISTAS) has become a research hotspot. This system uses a ground-based augmentation network to calculate satellite orbit, clock, and atmospheric delay corrections in real time. It then broadcasts state-space representation (SSR) corrections from geostationary orbit (GEO) satellites, providing wide-area satellite-based augmentation services. Simultaneously, the ground-based system uses a state-to-observation domain conversion algorithm (SSR2OSR) to map SSR parameters into observation-space representation (OSR) corrections, enhancing compatibility with ground-based real-time kinematic (RTK) systems. This technical approach has two advantages: first, by standardizing the observation domain parameter output, it avoids the heterogeneous errors of the terminal-server solution model; second, based on a unified ambiguity reference maintenance strategy, it can effectively suppress the whole-cycle jump caused by reference station switching and support seamless switching between RTK and Precise Point Positioning (PPP) modes in scenarios without network coverage, significantly improving positioning continuity in complex environments (Wang et al., 2019).

[0003] The BeiDou-3 global system completed constellation deployment in 2020. Its augmentation service system will be implemented in two phases. The first phase will provide free decimeter-level services to China and surrounding areas via the PPP-B2b signals from three GEO satellites, with a typical convergence time of 30 minutes and a broadcast rate of 500 bits per second. The second phase plans to introduce Q-branch signals, further improving positioning accuracy to centimeter-level and reducing convergence time to less than 10 minutes through multi-frequency and multi-mode fusion processing. This will also expand service coverage globally to meet the stringent precision requirements of areas such as land surveying and mapping, precision agriculture, and marine resource development (China Satellite Navigation System Administration Office, 2020). Within this framework, PPP-RTK technology, due to its efficient data transmission, has become the preferred solution for satellite-based augmentation services. Its core mechanism leverages the temporal correlation of SSR correction parameters (such as the slow variation of orbit error and the rapid variation of clock error) to dynamically adjust the broadcast frequency of each parameter, thereby reducing data bandwidth requirements by 60%-80%. However, down-converting transmission will lead to the attenuation of the correction timeliness, and the user end needs to perform time domain extrapolation of the received SSR parameters to compensate for the signal transmission and processing delays.

[0004] Therefore, developing a PPP-RTK time delay processing technology has important practical significance. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to solve the deficiencies in the prior art and design a PPP-RTK time delay processing method and device in SSR to OSR conversion to achieve real-time centimeter-level positioning in high-delay scenarios and improve the success rate of ambiguity fixation.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] In a first aspect, the present invention provides a PPP-RTK time delay processing method in SSR to OSR conversion, comprising:

[0008] The orbit, clock error, ionospheric and tropospheric delay SSR parameters provided by the server are converted into OSR virtual observation values through geometric distance calculation and projection function mapping;

[0009] The correction amount at future moments is predicted based on the constant velocity model and static random process, and the OSR virtual observation value is corrected by compensating the time delay through the state transfer matrix;

[0010] Combining server-side parameters with user-side observation data, the error covariance matrix is recursively generated, the state prediction weight is dynamically adjusted, and the covariance information is obtained through adaptive filtering and optimization positioning solution;

[0011] The corrected OSR observations and covariance information are used to achieve rapid ambiguity fixation and centimeter-level positioning.

[0012] As a further technical solution of the present invention, the orbit, clock error, ionospheric and tropospheric delay SSR parameters provided by the server are converted into OSR virtual observation values through geometric distance calculation and projection function mapping; specifically, the method comprises: using a fusion processing method of ground-based augmented network RTK and satellite-based augmented PPP technology, and using the base station network to calculate the obtained orbit products, clock error products, phase deviation products, and atmospheric products; and converting them into OSR correction numbers on the server through the SSR2OSR algorithm. The basic formula is:

[0013]

[0014] In the formula are pseudorange and phase virtual observation values; is the geometric distance between satellite s and the virtual reference station calculated using orbit products; t s is the clock error calculated from the clock error product; T z is the high-precision tropospheric delay correction value calculated for the tropospheric product, is the corresponding tropospheric projection function; is the high-precision ionospheric delay correction value calculated from the ionospheric product. is the corresponding ionospheric projection function; b s,f is the satellite pseudorange deviation correction value; λ is the carrier wavelength corresponding to the frequency f, is the phase deviation correction value at frequency f;

[0015] At this time, the single-difference observation equation between the user and the virtual reference station is:

[0016]

[0017] Where, is the single-difference pseudorange observation value, is the single-difference carrier observation value, b u,f is the user hardware delay; λ is the carrier wavelength corresponding to frequency f; Single-difference Earth-satellite geometric distance, t u,sys is the receiver clock error, is a floating-point deambiguation parameter, ε p and ε Φ are pseudorange and phase observation noise, respectively;

[0018] At this time, the parameters to be estimated include ambiguity parameters, tropospheric wet delay, ionospheric delay residual error, coordinate parameters and receiver clock error, and its random model is:

[0019]

[0020] Where, The satellite's ambiguity parameters at frequency f, In actual data processing, the ambiguity parameter is usually estimated as a constant, so The value is usually set to a small value. T is the tropospheric parameter, is the tropospheric variance. In actual data processing, only the wet delay part is usually estimated, and it is usually estimated as random noise. is the ionospheric residual error, is the corresponding variance information, which is obtained from the virtual observation accuracy information; X, t r,sys 、 They are coordinate parameters, receiver clock error, coordinate variance and receiver clock error variance respectively.

[0021] As a further technical solution of the present invention, the ambiguity parameter is processed as follows:

[0022] The ambiguity parameters are transferred to wide lane and narrow lane for processing. At this time, the wide lane single difference ambiguity is expressed as:

[0023]

[0024] is the single-difference wide-lane ambiguity; is the first frequency wide-lane phase deviation; is the first frequency wide-lane ambiguity, is the first frequency wide-lane phase deviation; is the second frequency wide-lane ambiguity; is the reference star width lane phase deviation; is the non-reference star wide lane ambiguity; is the non-reference star wide lane phase deviation;

[0025] On this basis, we further select the reference star and make the secondary difference between the non-reference star and the reference star to obtain the wide lane double difference ambiguity.

[0026]

[0027] Fixing it can obtain the wide lane double difference ambiguity fixed solution is the user non-reference star wide lane ambiguity; is the non-reference star wide lane phase deviation; is the reference star wide lane ambiguity; is the reference star width lane phase deviation;

[0028] Get the narrow lane single-difference ambiguity:

[0029]

[0030] Where, is the narrow lane single difference ambiguity, First frequency single-difference wide-lane ambiguity, is the second frequency single-difference wide-lane ambiguity, is the reference satellite narrow lane phase deviation; the narrow lane double difference ambiguity is obtained by inter-satellite single difference Fix the integers to get the narrow lane double difference fixed solution

[0031] As a further technical solution of the present invention, the correction amount at a future moment is predicted based on the constant velocity model and the static random process, and the OSR virtual observation value is corrected by compensating the time delay through the state transfer matrix; specifically, it includes:

[0032] The process of selecting a steady state models the temporal behavior of ionospheric delay, ambiguity, pseudorange, and carrier phase bias:

[0033] α(i)=α(i-1)+n α (i),i=2,…,k; (7)

[0034] At the same time, a constant speed process is selected to describe the temporal behavior of the satellite clock:

[0035]

[0036] where α and β represent parameters whose temporal behaviors are modeled by constant state and constant velocity processes, respectively; is the time first derivative of β, i, k and Δt represent epoch, total number of epochs and sampling period respectively; n α 、n β and They represent the system noise with zero mean.

[0037] As a further technical solution of the present invention, the server-side parameters and user-side observation data are combined to recursively generate an error covariance matrix, dynamically adjust the state prediction weight, and obtain covariance information through adaptive filtering optimization positioning solution; specifically including:

[0038] The state space equations are established using Khodabandeh's full-rank model;

[0039] Establish a variance-covariance matrix based on the random model of carrier and pseudorange;

[0040] Predict the correction time of the user's positioning time;

[0041] Build the variance-covariance matrix of the user phase and code measurements.

[0042] As a further technical solution of the present invention, the state space equation is established by using Khodabandeh's full rank model; specifically comprising:

[0043] Using Khodabandeh's full-rank model, the state space equation is expressed as follows:

[0044]

[0045] Where, and is the observation value of satellite s (s = 1, ..., m) at frequency j (j = 1, ..., f) collected by reference station r without combining phase and pseudorange observation equations; is the expectation operator, where m and f represent the number of satellites and frequency respectively; the commonly used receiver and satellite clock parameters are dt r and dt s After removing the prior value, the zenith tropospheric delay (ZTD) of the receiver r and its mapping function to the receiver r and satellite s are represented by τ r and The first-order slant ionospheric delay experienced by the receiver r and the satellite s at the first frequency is expressed as It is related to the observation through the wavelength-dependent coefficient Completed, λ j .δ r,j and represent the phase deviations of the receiver and satellite respectively, and d r,j and They represent the phase deviation of the coded observation respectively; the integer phase ambiguity is represented by a r ,j s .remove and a r ,j s Except for the period, all other parameters are expressed in distance units; I is the measurement model, and II is the dynamic model;

[0046] In the formula is the receiver clock error,

[0047] is the satellite clock error,

[0048] is the ionospheric delay, is the receiver phase deviation,

[0049] is the satellite phase deviation,

[0050] is the receiver pseudorange bias, is the satellite pseudorange bias, is the satellite clock speed, dt r (1),d r,j(1),δ r,j (1), dt r (2) basic parameters;

[0051] in Represents its system noise, with a mean of 0;

[0052] In the dynamic model, due to the introduction of satellite clock number parameters The rank deficiency of the equation is caused by This constraint causes the receiver clock error, satellite clock error, and their clock rate to be systematically correlated with the reference parameter, so two epochs of data are required to initialize the filter.

[0053] As a further technical solution of the present invention, the variance-covariance matrix is established according to the random model of the carrier and the pseudorange; specifically comprising:

[0054] The variance-covariance matrix of the random model of carrier and pseudorange is as follows:

[0055]

[0056] Where, They represent the carrier measurement vector and pseudorange measurement vector from the receiver to the satellite at the i-th epoch, respectively. The carrier measurement vector Pseudorange measurement vector Δp r (i) Similar to the carrier measurement vector; f×f matrix C φφ and C pp Represents the variance-covariance matrix of the carrier and pseudorange respectively; m×m matrix represents the weight of the intersatellite vector of each station in the i-th epoch; represents the dispersion operator, is the Kronecker product. The symbols diag and blkdiag represent "diagonal" and "block diagonal" matrices respectively;

[0057] In the dynamic model, the receiver and satellite biases are assumed to be constant in time, so their system noise is set to zero; the temporal behavior of the satellite clock and the slant ionospheric delay are modeled by a constant velocity process and a constant state process, respectively; therefore, the covariance matrix S of their associated system noise is:

[0058]

[0059] Among them, the covariance matrix S is used to connect the parameters of two consecutive epochs, and They represent the spectral density of clock and ionospheric velocity parameters, in m2 / s, respectively.m is the m×m identity matrix.

[0060] As a further technical solution of the present invention, the correction time of the user positioning time is predicted; specifically comprising:

[0061] Assuming that all PPP-RTK correction parameters are provided at the same epoch k, the correction time of the user positioning time is predicted as follows:

[0062]

[0063] Where [lk]Δt is the delay time, and the corrections for k epochs are collected on the vector: and their corresponding variance matrices

[0064] Assuming that the change of the correction value over time follows the constant velocity model, constructing the state transfer matrix will generate the correction value at time k Predict the user receiving time l:

[0065]

[0066] Among them, Φ l|k The state transition includes time delay, and the correction amount includes satellite clock error, ionospheric delay, and phase deviation.

[0067] As a further technical solution of the present invention, establishing a variance-covariance matrix of user phase and code measurements specifically includes:

[0068] Covariance matrix of the correction Propagate to the delay time l through the state transfer matrix and superimpose the system noise S l :

[0069]

[0070] Among them, S l is the system noise variance matrix, obtained by replacing Δt with [lk]Δt; Φ l|k is the state transition matrix:

[0071]

[0072] The supplier's dynamic model parameters are made available to the user via a real-time interface or an offline database; the user can then obtain the combined PPP-RTK corrections The specific form is:

[0073]

[0074] in,

[0075]

[0076] Where Λ is an f×f diagonal matrix whose elements store frequency-specific wavelengths;

[0077] μ is an f-dimensional vector containing ionospheric coefficients;

[0078] E f is the f×f identity matrix with the first two columns removed;

[0079] The single epoch, corrected phase and code observation equations are expressed as follows:

[0080]

[0081] Where, Receiver clock error,

[0082] is the ionospheric delay,

[0083] is the receiver phase deviation, j>2 is the receiver pseudorange deviation, s≠1 is the fuzziness parameter;

[0084] in,

[0085] The variance-covariance matrix of the user phase and code measurements is defined as:

[0086]

[0087] Among them, Δφ u (l) and Δp u (l) are the user segment carrier measurement vector and pseudorange measurement vector of the lth epoch respectively; the carrier covariance matrix C φφ and the pseudorange covariance matrix C pp On the server side and the user side it depends on the receiver used.

[0088] In a second aspect, the present invention further provides a PPP-RTK time delay processing device in SSR to OSR conversion, comprising:

[0089] The OSR virtual observation unit converts the orbit, clock error, ionospheric and tropospheric delay SSR parameters provided by the server into OSR virtual observation values through geometric distance calculation and projection function mapping;

[0090] The correction unit predicts the correction amount at future moments based on the constant velocity model and static random process, and compensates for the time delay through the state transfer matrix

[0091] The covariance estimation unit combines server-side parameters with user-side observation data to recursively generate the error covariance matrix, dynamically adjust the state prediction weights, and optimize the positioning solution through adaptive filtering;

[0092] The positioning unit is optimized and the corrected OSR observations and covariance information are used to achieve rapid ambiguity fixation and centimeter-level positioning.

[0093] Compared with the prior art, the present invention has the following beneficial effects:

[0094] 1. The present invention converts SSR information into virtual observation values of ORS. At the same time, when time delay occurs, a dynamic prediction correction method and a recursive covariance estimation method are used, combined with the fusion processing of satellite-based augmentation and ground-based augmentation, to obtain a combined PPP-RTK correction, thereby achieving real-time centimeter-level positioning in high-delay scenarios.

[0095] 2. This invention addresses the non-stationary characteristics of satellite clock errors by using a constant velocity model to model their dynamic noise. For the slowly varying characteristics of short-term (<30 seconds) ionospheric delays, a static random process model is used. Time domain extrapolation is used to compensate for signal transmission and processing delays, reducing the impact of correction timeliness decay.

[0096] 3. The present invention adopts recursive covariance estimation: combining the dynamic parameters of the server and the real-time observation data of the user, jointly solving and generating a complete error covariance matrix; introducing an adaptive factor to dynamically adjust the state prediction weight, and using sliding window least squares to assist observation update and suppress the propagation of delay errors;

[0097] 4. The present invention uses the covariance propagation mechanism to transmit the uncertainty of the correction amount to the user end, thereby optimizing the random model of the positioning solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 This is a flow chart of a PPP-RTK time delay processing method in SSR to OSR conversion proposed by the present invention;

[0099] Figure 2 Schematic diagram of the process of converting SSR to OSR proposed in the present invention;

[0100] Figure 3 A schematic diagram of a process for recursive covariance estimation according to an embodiment of the present invention;

[0101] Figure 4 This is a structural diagram of the PPP-RTK time delay processing device in SSR to OSR conversion proposed by the present invention. DETAILED DESCRIPTION

[0102] The specific implementation of the present invention is described below with reference to the accompanying drawings and embodiments:

[0103] It should be noted that the structures, colors, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the efficacy and purpose that can be achieved by the present invention.

[0104] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" quoted in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0105] like Figure 1 As shown, the present invention provides a PPP-RTK time delay processing method in SSR->OSR conversion, comprising:

[0106] Step 101: The orbit, clock error, ionospheric and tropospheric delay SSR parameters provided by the server are converted into OSR virtual observation values through geometric distance calculation and projection function mapping;

[0107] Step 102: Predict the correction amount at the future time based on the constant velocity model and the static random process, and correct the OSR virtual observation value by compensating the time delay through the state transfer matrix;

[0108] Step 103: Recursively generate an error covariance matrix by combining the server-side parameters and the user-side observation data, dynamically adjust the state prediction weight, and obtain covariance information through adaptive filtering optimization positioning solution;

[0109] Step 104: Use the corrected OSR observations and covariance information to achieve rapid ambiguity fixation and centimeter-level positioning.

[0110] The overall technical process of this invention involves predicting future satellite clock errors, ionospheric delays, and receiver biases using a state transition model. This is combined with dynamic server-side parameters and real-time user-side observation data to generate a complete error covariance matrix for optimal positioning. By constructing a time-varying noise covariance matrix to quantify prediction uncertainty, employing adaptive factors to dynamically adjust state prediction weights, and introducing a sliding window least squares algorithm to aid observation updates, this method effectively suppresses delay error propagation and ensures stable positioning accuracy at the decimeter to centimeter level.

[0111] In step 101, the orbit, clock, ionospheric and tropospheric delay SSR parameters provided by the server are converted into OSR virtual observation values through geometric distance calculation and projection function mapping. Specifically, the process includes: using the fusion processing method of ground-based augmented network RTK and satellite-based augmented PPP technology, and using the base station network to calculate the orbit product, clock product, phase deviation product, and atmospheric product; and then using the SSR2OSR algorithm on the server to convert them into OSR corrections. The basic formula is:

[0112]

[0113] In the formula are pseudorange and phase virtual observation values; is the geometric distance between satellite s and the virtual reference station calculated using orbit products; t s is the clock error calculated from the clock error product; T z is the high-precision tropospheric delay correction value calculated for the tropospheric product, is the corresponding tropospheric projection function; is the high-precision ionospheric delay correction value calculated from the ionospheric product. is the corresponding ionospheric projection function; b s,f is the satellite pseudorange deviation correction value; λ is the carrier wavelength corresponding to the frequency f, is the phase deviation correction value at frequency f;

[0114] At this time, the single-difference observation equation between the user and the virtual reference station is:

[0115]

[0116] Where, is the single-difference pseudorange observation value, is the single-difference carrier observation value, b u,f is the user hardware delay; λ is the carrier wavelength corresponding to frequency f; Single-difference Earth-satellite geometric distance, t u,sys is the receiver clock error, is a floating-point deambiguation parameter, ε p and ε Φ are pseudorange and phase observation noise, respectively;

[0117] At this time, the parameters to be estimated include ambiguity parameters, tropospheric wet delay, ionospheric delay residual error, coordinate parameters and receiver clock error, and its random model is:

[0118]

[0119] Where, The satellite's ambiguity parameters at frequency f, In actual data processing, the ambiguity parameter is usually estimated as a constant, so The value is usually set to a small value. T is the tropospheric parameter, is the tropospheric variance. In actual data processing, only the wet delay part is usually estimated, and it is usually estimated as random noise. is the ionospheric residual error, is the corresponding variance information, which is obtained from the virtual observation accuracy information; X, t r,sys 、 They are coordinate parameters, receiver clock error, coordinate variance and receiver clock error variance respectively.

[0120] In this embodiment of the present invention, in order to keep the terminal PPP and RTK models consistent, the ambiguity parameters are transferred to wide lane and narrow lane for processing. In this case, the wide lane single difference ambiguity is expressed as:

[0121]

[0122] Where, is the single-difference wide-lane ambiguity; is the first frequency wide-lane phase deviation; is the first frequency wide-lane ambiguity, is the first frequency wide-lane phase deviation; is the second frequency wide-lane ambiguity; is the reference star width lane phase deviation; is the non-reference star wide lane ambiguity; is the non-reference star width lane phase deviation.

[0123] On this basis, we further select the reference star and make the secondary difference between the non-reference star and the reference star to obtain the wide lane double difference ambiguity.

[0124]

[0125] Fixing it can obtain the wide lane double difference ambiguity fixed solution is the user non-reference star wide lane ambiguity; is the non-reference star wide lane phase deviation; is the reference star wide lane ambiguity; is the reference star wide lane phase deviation and the narrow lane single difference ambiguity can be further obtained:

[0126]

[0127] Where, is the narrow lane single difference ambiguity, First frequency single-difference wide-lane ambiguity, is the second frequency single-difference wide-lane ambiguity, is the reference satellite narrow lane phase deviation. On this basis, the narrow lane double difference ambiguity can be obtained by further inter-satellite single difference Fixing the integers can get the narrow lane double difference fixed solution The SSR2OSR algorithm is used to convert SSR products into OSR products. During terminal positioning, satellite-based augmentation and ground-based augmentation use a unified ambiguity benchmark. Therefore, no cycle slips will occur when switching reference stations. In addition, PPP and RTK can be switched freely even without a network connection, meeting positioning requirements in some specific scenarios.

[0128] The SSR2OSR algorithm is used to convert SSR products into OSR products. During terminal positioning, satellite-based augmentation and ground-based augmentation use a unified ambiguity benchmark. Therefore, no cycle slips will occur when switching reference stations. In addition, PPP and RTK can be switched freely even without a network connection, meeting positioning requirements in some specific scenarios.

[0129] See also Figure 2 The dynamic prediction and correction method provided by the present invention includes: inputting SSR correction parameters; selecting a prediction model, constant speed / random walk; calculating a state transfer matrix; predicting a correction amount; calculating a correction amount covariance; and outputting a predicted SSR correction amount.

[0130] The SSR2OSR algorithm is used to convert SSR products into OSR products. During terminal positioning, satellite-based augmentation and ground-based augmentation use a unified ambiguity benchmark. Therefore, no cycle slips will occur when switching reference stations. In addition, PPP and RTK can be switched freely even without a network connection, meeting positioning requirements in some specific scenarios.

[0131] In some cases, the receiver is often unable to obtain real-time enhancement information, resulting in PPP-RTK only being able to achieve the positioning level of SPP. The present invention proposes to predict the correction amount at future time based on the constant velocity model and static random process, and to correct the OSR virtual observation value by compensating the time delay through the state transfer matrix. Specifically, it includes:

[0132] The process of selecting a steady state models the temporal behavior of ionospheric delay, ambiguity, pseudorange, and carrier phase bias:

[0133] α(i)=α(i-1)+n α (i),i=2,…,k; (7)

[0134] At the same time, a constant speed process is selected to describe the temporal behavior of the satellite clock:

[0135]

[0136] where α and β represent parameters, and their temporal behaviors are modeled by a steady state (random walk) and a constant velocity process, respectively; is the time first derivative of β, i, k and Δt represent epoch, total number of epochs and sampling period respectively; n α 、n β and They represent the system noise with zero mean.

[0137] The construction of the GNSS parameter time evolution model in the present invention is based on the following: the whole-cycle ambiguity parameters have time-invariant characteristics under the condition that no cycle slip occurs, and the receiver hardware bias and ranging signal delay show significant time stability during the observation period. The system noise covariance matrix based on these two parameters is assigned a zero matrix. For the ionospheric delay component, its short-term (<30 seconds) change magnitude is lower than the observation noise level, and its timing characteristics can be effectively characterized by a static random process. However, the satellite clock error parameters are affected by the atomic frequency standard phase noise, and show significant non-stationary characteristics at the sub-millisecond level, and need to be modeled using a dynamic noise-enhanced random walk model. The receiver clock error is described by a white noise process, and its inter-epoch correlation is decoupled by the zero element configuration of the state transfer matrix. This parameterization scheme effectively controls the dimensionality expansion problem of the state vector while ensuring the accuracy of the model.

[0138] See also Figure 3 , a flow chart of the recursive covariance estimation provided by an embodiment of the present application. The recursive covariance estimation method includes the following: inputting server-side SSR data and user-side data, calculating virtual observation values, generating observation equations, calculating the error covariance matrix, recursively updating the state estimate, and outputting the optimized PPP-RTK settlement result.

[0139] In step 103, the server-side parameters and user-side observation data are combined to recursively generate an error covariance matrix, dynamically adjust the state prediction weight, and obtain covariance information through adaptive filtering optimization positioning solution. Specifically, the following steps are included:

[0140] The state space equations are established using Khodabandeh's full-rank model;

[0141] Establish a variance-covariance matrix based on the random model of carrier and pseudorange;

[0142] Predict the correction time of the user's positioning time;

[0143] Build the variance-covariance matrix of the user phase and code measurements.

[0144] In the embodiment of the present invention, the full-rank model proposed by Khodabandeh is used to establish the state space equation; specifically, the following steps are performed:

[0145] Using the full-rank model proposed by Khodabandeh, the state space equation is expressed as follows:

[0146]

[0147] Where, and is the observation value of satellite s (s = 1, ..., m) at frequency j (j = 1, ..., f) collected by the reference station r without combining the phase and pseudorange observation equations. is the expectation operator, where m and f represent the number of satellites and frequency respectively. Common receiver and satellite clock parameters are denoted by dt r and dt s After removing the prior value, the zenith tropospheric delay (ZTD) of the receiver r and its mapping function to the receiver r and satellite s are represented by τ r and The first-order slant ionospheric delay experienced by the receiver r and the satellite s at the first frequency is expressed as It is related to the observation through the wavelength-dependent coefficient Completed, λ j .δ r,j and represent the phase deviations of the receiver and satellite respectively, and d r,j and They represent the phase deviation of the coded observation respectively. The integer phase ambiguity is expressed as a r ,j s .Divide δ r,j , and a r ,j s Except for the period, all other parameters are expressed in distance. I is the measurement model and II is the dynamic model. is the receiver clock error, is the satellite clock error, is the ionospheric delay, is the receiver phase deviation, is the satellite phase deviation, is the receiver pseudorange bias, is the satellite pseudorange bias, is the satellite clock speed, dt r (1),d r,j (1),δ r,j (1), dt r (2) is the basic parameter.

[0148] in Represents its system noise, with a mean of 0.

[0149] In the dynamic model, due to the introduction of satellite clock number parameters The rank deficiency of the equation is caused by This constraint causes the receiver clock error, satellite clock error, and their clock rate to be systematically correlated with the reference parameter, so two epochs of data are required to initialize the filter.

[0150] In the embodiment of the present invention, a variance-covariance matrix is established according to a random model of the carrier and the pseudorange; specifically, the variance-covariance matrix of the random model of the carrier and the pseudorange is:

[0151]

[0152] Where, They represent the carrier measurement vector and pseudorange measurement vector from the receiver to the satellite at the i-th epoch, respectively. The carrier measurement vector Pseudorange measurement vector Δp r (i) Similar to the carrier measurement vector; f×f matrix C φφ and C pp Represents the variance-covariance matrix of the carrier and pseudorange respectively; m×m matrix represents the weight of the intersatellite vector of each station in the i-th epoch; represents the dispersion operator, is the Kronecker product. The symbols diag and blkdiag denote “diagonal” and “block diagonal” matrices, respectively.

[0153] In the dynamic model, the receiver and satellite biases are assumed to be constant in time, so their systematic noise is set to zero. The temporal behavior of the satellite clock and the slant ionospheric delay are modeled by constant velocity and constant state processes, respectively. Therefore, the covariance matrix S of their associated systematic noise (the parameter used to connect two consecutive epochs) is:

[0154]

[0155] in, and They represent the spectral density of clock and ionospheric velocity parameters, in m2 / s, respectively. m is the m×m identity matrix.

[0156] In the embodiment of the present invention, assuming that the correction generation time k is different from the user positioning time l (l>k), the user needs to use a single correction and Time prediction of PPP-RTK corrections. Although satellite code bias and phase bias have higher time stability than other parameters (allowing for lower transmission rates), for the sake of symbol consistency, it is assumed that all PPP-RTK correction parameters are provided at the same epoch k. The corrected time prediction of the user positioning time is as follows:

[0157]

[0158] Where [lk]Δt is the delay time. The corrections for k epochs are collected on the vector, and their corresponding variance matrices

[0159] Assuming that the correction value (such as satellite clock error, ionospheric delay, phase deviation) changes with time and obeys the constant velocity model, constructing the state transfer matrix will generate the correction value at time k Predict the user receiving time l:

[0160]

[0161] Among them, Φ l|k Contains state transitions related to time delays (such as the constant velocity term of the satellite clock).

[0162] In an embodiment of the present invention, establishing a variance-covariance matrix of user phase and code measurements specifically includes:

[0163] Covariance matrix of the correction Propagate to the delay time l through the state transfer matrix and superimpose the system noise S l :

[0164]

[0165] Among them, S l is the system noise variance matrix, obtained by replacing Δt with [lk]Δt; Φ l|k is the state transition matrix:

[0166]

[0167] The supplier's dynamic model parameters are made available to the user via a real-time interface or an offline database; the user can then obtain the combined PPP-RTK corrections The specific form is:

[0168]

[0169] in,

[0170]

[0171] Where Λ is an f×f diagonal matrix whose elements store frequency-specific wavelengths;

[0172] μ is an f-dimensional vector containing ionospheric coefficients;

[0173] E f is the f×f identity matrix with the first two columns removed;

[0174] The single epoch, corrected phase and code observation equations are expressed as follows:

[0175]

[0176] Where, Receiver clock error; is the ionospheric delay; is the receiver phase deviation; j>2 is the receiver pseudorange bias; s≠1 is the fuzziness parameter;

[0177] in,

[0178] Similar to the vendor's random model, the variance-covariance matrix of the user's phase and code measurements is defined as:

[0179]

[0180] Among them, Δφ u (l) and Δp u (l) are the user segment carrier measurement vector and pseudorange measurement vector of the lth epoch respectively; the carrier covariance matrix C φφ and the pseudorange covariance matrix C pp The uncertainty of the time-predicted PPP-RTK corrections is taken into account on both the server and user sides. The user-side measurement covariance matrix accounts for the uncertainty of the time-predicted PPP-RTK corrections. This factor is often overlooked in most PPP-RTK studies, as these studies assume that the calibrations are sufficiently accurate to be considered deterministic. Another reason is that the server needs to transmit the correction estimates and their associated covariance matrix, but the large amount of matrix information required not only contradicts the overall goal of state-space representation (SSR) but also neglects its core design purpose.

[0181] Furthermore, the recursive covariance estimation algorithm specifically includes: inputting server-side SSR data + user-side data; calculating virtual observation values; generating observation equations and calculating error covariance matrices; recursively updating state estimates and outputting optimized PPP-RTX solution results.

[0182] The present invention converts SSR information to obtain virtual observation values of ORS. At the same time, when time delay occurs, a dynamic prediction correction method and a recursive covariance estimation method are used, combined with the fusion processing of satellite-based augmentation and ground-based augmentation, to obtain a combined PPP-RTK correction, thereby achieving real-time centimeter-level positioning in high-delay scenarios.

[0183] The present invention adopts dynamic prediction correction to predict satellite clock error, ionospheric delay and receiver bias at future moments based on the state transition model;

[0184] The present invention uses a constant velocity model to model the dynamic noise of the non-stationary characteristics of satellite clock errors. The slow-varying characteristics of short-term (<30 seconds) ionospheric delays are modeled using a static random process. Time domain extrapolation is used to compensate for signal transmission and processing delays, reducing the impact of correction timeliness attenuation.

[0185] The present invention adopts recursive covariance estimation: combining the dynamic parameters of the server and the real-time observation data of the user end, jointly solving and generating a complete error covariance matrix; introducing an adaptive factor to dynamically adjust the state prediction weight, and using sliding window least squares to assist observation update to suppress the transmission of delay errors;

[0186] The present invention utilizes the covariance propagation mechanism to transmit the uncertainty of the correction amount to the user end, thereby optimizing the random model of the positioning solution.

[0187] See also Figure 4 The present invention also provides a PPP-RTK time delay processing device in SSR to OSR conversion, comprising:

[0188] The OSR virtual observation unit 201 converts the orbit, clock error, ionospheric and tropospheric delay SSR parameters provided by the server into OSR virtual observation values through geometric distance calculation and projection function mapping;

[0189] Correction unit 202 predicts the correction amount at the future time based on the constant velocity model and static random process, and compensates for the time delay through the state transfer matrix

[0190] The covariance estimation unit 203 combines the server-side parameters and the user-side observation data to recursively generate the error covariance matrix, dynamically adjust the state prediction weights, and optimize the positioning solution through adaptive filtering;

[0191] The optimized positioning unit 204 uses the corrected OSR observations and covariance information to achieve rapid ambiguity fixation and centimeter-level positioning.

[0192] The various variations and specific examples of the PPP-RTK time delay processing method in an SSR to OSR conversion in the aforementioned embodiment are also applicable to a PPP-RTK time delay processing device in an SSR to OSR conversion in this embodiment. Through the aforementioned detailed description of the PPP-RTK time delay processing method in an SSR to OSR conversion, those skilled in the art can clearly understand the PPP-RTK time delay processing device in an SSR to OSR conversion in this embodiment, so for the sake of brevity of the specification, it will not be described in detail here.

[0193] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the modules is merely a logical function division. In actual implementation, there may be other division methods, such as multiple modules or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0194] If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0195] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0196] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A PPP-RTK time delay processing method in SSR to OSR conversion, characterized in that: include: The orbit, clock error, ionospheric and tropospheric delay SSR parameters provided by the server are converted into OSR virtual observation values through geometric distance calculation and projection function mapping; The correction amount at future moments is predicted based on the constant velocity model and static random process, and the OSR virtual observation value is corrected by compensating the time delay through the state transfer matrix; Combining server-side parameters with user-side observation data, the error covariance matrix is recursively generated, the state prediction weight is dynamically adjusted, and the covariance information is obtained through adaptive filtering and optimization positioning solution; The corrected OSR observations and covariance information are used to achieve rapid ambiguity fixation and centimeter-level positioning.

2. The PPP-RTK time delay processing method in SSR to OSR conversion according to claim 1, characterized in that: The orbit, clock error, ionospheric and tropospheric delay SSR parameters provided by the server are converted into OSR virtual observation values through geometric distance calculation and projection function mapping. Specifically, the process includes: using a fusion processing method of ground-based augmented network RTK and satellite-based augmented PPP technology, and using the base station network to calculate the obtained orbit products, clock error products, phase deviation products, and atmospheric products; and converting them into OSR correction numbers through the SSR2OSR algorithm on the server. The basic formula is: In the formula are pseudorange and phase virtual observation values; is the geometric distance between satellite s and the virtual reference station calculated using orbit products; t s is the clock error calculated from the clock error product; T z is the high-precision tropospheric delay correction value calculated for the tropospheric product, is the corresponding tropospheric projection function; is the high-precision ionospheric delay correction value calculated from the ionospheric product. is the corresponding ionospheric projection function; b s,f is the satellite pseudorange deviation correction value; λ is the carrier wavelength corresponding to the frequency f, is the phase deviation correction value at frequency f; At this time, the single-difference observation equation between the user and the virtual reference station is: Where, is the single-difference pseudorange observation value, is the single-difference carrier observation value, b u,f is the user hardware delay; λ is the carrier wavelength corresponding to frequency f; Single-difference Earth-satellite geometric distance, t u,sys is the receiver clock error, is a floating-point deambiguation parameter, ε p and ε Φ are pseudorange and phase observation noise, respectively; At this time, the parameters to be estimated include ambiguity parameters, tropospheric wet delay, ionospheric delay residual error, coordinate parameters and receiver clock error, and its random model is: Where, The satellite's ambiguity parameters at frequency f, is the ambiguity parameter of its corresponding variance in the actual data processing process; T is the tropospheric parameter, is the tropospheric variance. In actual data processing, only the wet delay part is usually estimated, and it is usually estimated as random noise. is the ionospheric residual error, is the corresponding variance information, which is obtained from the virtual observation accuracy information; X, t r，sys 、 They are coordinate parameters, receiver clock error, coordinate variance and receiver clock error variance respectively.

3. The PPP-RTK time delay processing method in SSR to OSR conversion according to claim 2, characterized in that: The ambiguity parameters are processed as follows: The ambiguity parameters are transferred to wide lane and narrow lane for processing. At this time, the wide lane single difference ambiguity is expressed as: is the single-difference wide-lane ambiguity; is the first frequency wide-lane phase deviation; is the first frequency wide-lane ambiguity, is the first frequency wide-lane phase deviation; is the second frequency wide-lane ambiguity; is the reference star width lane phase deviation; is the non-reference star wide lane ambiguity; is the non-reference star wide lane phase deviation; On this basis, we further select the reference star and make the secondary difference between the non-reference star and the reference star to obtain the wide lane double difference ambiguity. Fixing it can obtain the wide lane double difference ambiguity fixed solution is the user non-reference star wide lane ambiguity; is the non-reference star wide lane phase deviation; is the reference star wide lane ambiguity; is the reference star width lane phase deviation; Get the narrow lane single-difference ambiguity: Where, is the narrow lane single difference ambiguity, First frequency single-difference wide-lane ambiguity, is the second frequency single-difference wide-lane ambiguity, is the reference satellite narrow lane phase deviation; the narrow lane double difference ambiguity is obtained by inter-satellite single difference Fix the integers to get the narrow lane double difference fixed solution 4. The PPP-RTK time delay processing method in SSR to OSR conversion according to claim 1, characterized in that: The method predicts the correction amount at the future moment based on the constant velocity model and the static random process, and corrects the OSR virtual observation value by compensating the time delay through the state transfer matrix; specifically includes: The process of selecting a steady state models the temporal behavior of ionospheric delay, ambiguity, pseudorange, and carrier phase bias: α(i)=α(i-1)+n α (i),i=2,...,k; (7) At the same time, a constant speed process is selected to describe the temporal behavior of the satellite clock: where α and β represent parameters whose temporal behaviors are modeled by constant state and constant velocity processes, respectively; is the time first derivative of β, i, k and Δt represent epoch, total number of epochs and sampling period respectively; n α 、n β and They represent the system noise with zero mean.

5. The PPP-RTK time delay processing method in SSR to OSR conversion according to claim 1, characterized in that: The method combines the server-side parameters with the user-side observation data, recursively generates the error covariance matrix, dynamically adjusts the state prediction weight, and obtains the covariance information through adaptive filtering optimization positioning solution; specifically includes: The state space equations are established using Khodabandeh's full-rank model; Establish a variance-covariance matrix based on the random model of carrier and pseudorange; Predict the correction time of the user's positioning time; Build the variance-covariance matrix of the user phase and code measurements.

6. The PPP-RTK time delay processing method in SSR to OSR conversion according to claim 5, characterized in that: The state space equation is established by using Khodabandeh's full rank model; specifically including: Using Khodabandeh's full-rank model, the state space equation is expressed as follows: Where, and is the observation value of satellite s (s = 1, ..., m) at frequency j (j = 1, ..., f) collected by reference station r without combining the phase and pseudorange observation equations; is the expectation operator, where m and f represent the number of satellites and frequency respectively; the commonly used receiver and satellite clock parameters are dt r and dt s After removing the prior value, the zenith tropospheric delay (ZTD) of the receiver r and its mapping function to the receiver r and satellite s are represented by τ r and The first-order slant ionospheric delay experienced by the receiver r and the satellite s at the first frequency is expressed as It is related to the observation through the wavelength-dependent coefficient Completed, λ j .δ r，j and represent the phase deviations of the receiver and satellite respectively, and d r，j and They represent the phase deviation of the coded observation respectively; the integer phase ambiguity is represented by a r ,j s ·remove and a r ,j s Except for the period, all other parameters are expressed in distance units; I is the measurement model, and II is the dynamic model; In the formula is the receiver clock error, is the satellite clock error, is the ionospheric delay, is the receiver phase deviation, is the satellite phase deviation, is the receiver pseudorange bias, is the satellite pseudorange bias, is the satellite clock speed, dt r (1),d r,j (1),δ r,j (1), is the basic parameter; in Represents its system noise, with a mean of 0; In the dynamic model, due to the introduction of satellite clock number parameters The rank deficiency of the equation is caused by This constraint causes the receiver clock error, satellite clock error, and their clock rate to be systematically correlated with the reference parameter, so two epochs of data are required to initialize the filter.

7. The PPP-RTK time delay processing method in SSR to OSR conversion according to claim 5, characterized in that: The variance-covariance matrix is established according to the random model of the carrier and the pseudorange; specifically comprising: The variance-covariance matrix of the random model of carrier and pseudorange is as follows: Where, They represent the carrier measurement vector and pseudorange measurement vector from the receiver to the satellite at the i-th epoch, respectively. The carrier measurement vector Pseudorange measurement vector Δp r (i) Similar to the carrier measurement vector; f×f matrix C φφ and C pp Represents the variance-covariance matrix of the carrier and pseudorange respectively; m×m matrix represents the weight of the intersatellite vector of each station in the i-th epoch; represents the dispersion operator, is the Kronecker product, and the symbols diag and blkdiag represent "diagonal" and "block diagonal" matrices respectively; In the dynamic model, the receiver and satellite biases are assumed to be constant in time, so their system noise is set to zero; the temporal behavior of the satellite clock and the slant ionospheric delay are modeled by a constant velocity process and a constant state process, respectively; therefore, the covariance matrix S of their associated system noise is: Among them, the covariance matrix S is used to connect the parameters of two consecutive epochs, and They represent the spectral density of clock and ionospheric velocity parameters, in m2 / s, respectively. m is the m×m identity matrix.

8. The PPP-RTK time delay processing method in SSR to OSR conversion according to claim 5, characterized in that: The method of predicting the correction time of the user positioning time specifically includes: Assuming that all PPP-RTK correction parameters are provided at the same epoch k, the correction time of the user positioning time is predicted as follows: Where [lk]Δt is the delay time, and the corrections for k epochs are collected on the vector: and their corresponding variance matrices Assuming that the change of the correction value over time follows the constant velocity model, constructing the state transfer matrix will generate the correction value at time k Predict the user receiving time l: Among them, Φ l|k The state transition includes time delay, and the correction amount includes satellite clock error, ionospheric delay, and phase deviation.

9. The PPP-RTK time delay processing method in SSR to OSR conversion according to claim 5, characterized in that: The establishment of the variance-covariance matrix of user phase and code measurements specifically includes: Covariance matrix of the correction Propagate to the delay time l through the state transfer matrix and superimpose the system noise S l : Among them, S l is the system noise variance matrix, obtained by replacing Δt with [lk]Δt; Φ l|k is the state transition matrix: The supplier's dynamic model parameters are made available to the user via a real-time interface or an offline database; the user can then obtain the combined PPP-RTK corrections The specific form is: in, Where Λ is an f×f diagonal matrix whose elements store frequency-specific wavelengths; μ is an f-dimensional vector containing ionospheric coefficients; E f is the f×f identity matrix with the first two columns removed; The single epoch, corrected phase and code observation equations are expressed as follows: Where, Receiver clock error, is the ionospheric delay, is the receiver phase deviation, j>2 is the receiver pseudorange deviation, s≠1 is the fuzziness parameter; in, The variance-covariance matrix of the user phase and code measurements is defined as: Among them, Δφ u (l) and Δp u (l) are the user segment carrier measurement vector and pseudorange measurement vector of the lth epoch respectively; the carrier covariance matrix C φφ and the pseudorange covariance matrix C pp On the server side and the user side it depends on the receiver used.

10. A PPP-RTK time delay processing device in SSR to OSR conversion, characterized in that: A PPP-RTK time delay processing method in SSR to OSR conversion according to any one of claims 1 to 9 is adopted, comprising: The OSR virtual observation unit converts the orbit, clock error, ionospheric and tropospheric delay SSR parameters provided by the server into OSR virtual observation values through geometric distance calculation and projection function mapping; The correction unit predicts the correction amount at future moments based on the constant velocity model and static random process, and compensates for the time delay through the state transfer matrix; The covariance estimation unit combines server-side parameters with user-side observation data to recursively generate the error covariance matrix, dynamically adjust the state prediction weights, and optimize the positioning solution through adaptive filtering; The positioning unit is optimized and the corrected OSR observations and covariance information are used to achieve rapid ambiguity fixation and centimeter-level positioning.

Images