Time sequence RTK / INS (Real Time Kinematic / Inertial Navigation System) integrated navigation method based on double difference between GNSS epochs

Abstract

The invention relates to a time sequence RTK / INS (Real Time Kinematic / Inertial Navigation System) integrated navigation method based on double differences between GNSS epochs, and belongs to the technical field of navigation positioning and integrated navigation. The method comprises the following steps: performing single-point positioning and error correction on GNSS original observation data, and constructing an inter-epoch double-difference observation value; carrying out Lie group / manifold space pre-integration on IMU data, estimating a carrier state and assisting cycle slip detection; and finally, based on a factor graph optimization framework, fusing various constraint factors for modeling and solving, checking fixed integer ambiguity through an LAMBDA method and Ratio, and performing feedback optimization. According to the invention, centimeter-level high-precision relative positioning can be realized, and the continuity, robustness and calculation precision of positioning in a complex environment can be improved.

Description

Technical Field

[0001] This invention relates to a time-series RTK / INS integrated navigation method based on GNSS epoch-difference, belonging to the field of navigation, positioning and integrated navigation technology. Background Technology

[0002] In modern autonomous driving, automatic driving, and intelligent transportation systems, Global Navigation Satellite Systems (GNSS) and Inertial Navigation Systems (INS) are the core sensors for achieving high-precision positioning and navigation. They are highly complementary: GNSS provides high-precision position in a global coordinate system, but its sampling rate is low and its signal is susceptible to environmental interference; INS provides high-sampling-rate data and is not limited by the environment, but errors accumulate over long-term operation. To obtain environmentally robust, high-precision, high-sampling-rate integrated navigation results, GNSS / INS integrated navigation technology has been widely researched and applied.

[0003] GNSS technology is mainly divided into two categories: Precise Point Positioning (PPP) and Real-Time Kinematic (RTK). The corresponding integrated navigation methods have significant drawbacks: PPP / INS integrated navigation requires only one GNSS receiver, resulting in lower cost, but static PPP convergence to centimeter-level accuracy takes more than half an hour, and dynamic PPP convergence takes even longer or fails altogether, leading to a long convergence time for integrated navigation. RTK / INS integrated navigation converges quickly, achieving centimeter-level accuracy rapidly, but requires the deployment of additional base stations near the rover for simultaneous observation, resulting in high cost and limited application scenarios. Furthermore, both PPP / INS and RTK / INS integrated navigation often employ the Extended Kalman Filter (EKF) method, neglecting the epochal correlation of GNSS observations. When GNSS signals are missing, the long INS recursion time leads to error accumulation, and the system still requires time to reconverge after the GNSS signal is restored.

[0004] While existing GNSS epoch-difference RTK positioning can provide high planar accuracy, its stability and continuity are poor in signal obstruction or dynamic environments; while INS, although it has short-term autonomous navigation capabilities, suffers from cumulative errors. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a time-series RTK / INS integrated navigation method based on GNSS epoch-difference. This invention can achieve centimeter-level high-precision relative positioning and improve the continuity, robustness, and solution accuracy of positioning in complex environments.

[0006] To achieve the above objectives, the technical solution provided by this invention is a time-series RTK / INS integrated navigation method based on GNSS epoch-difference, comprising the following steps:

[0007] S1. GNSS Data Preprocessing and Construction of Inter-Epoch Double-Difference Observations: Single-point positioning is performed on the received raw GNSS observation data to obtain the initial position, clock error, and initial values ​​of tropospheric delay; observation quality control is performed based on the initial solution to determine the satellite; ionospheric, tropospheric, antenna phase center, and relative clock error model corrections are performed on the determined satellite; inter-epoch double-difference GNSS observations are calculated and constructed on the time series to form the relative constraint factor;

[0008] S2, IMU pre-integration and auxiliary cycle slip detection: The accelerometer and gyroscope data of the IMU are pre-integrated in the Lie group / manifold space to obtain the relative motion constraint factor between epochs and estimate the carrier state at any time; the estimated carrier state is used to predict the satellite geometric distance, construct cycle slip decision variables, assist GNSS observation cycle slip detection and provide initial values;

[0009] S3. Factor Graph Optimization and Ambiguity Fixation: Based on the factor graph optimization framework, the GNSS epoch-difference observation factor, IMU pre-integration factor, prior factor, tropospheric relative constraint factor, and GNSS carrier and pseudorange absolute constraint factor are uniformly modeled to construct a time-series RTK / INS integrated navigation factor graph. The integrated navigation state is solved using nonlinear least squares or incremental optimization algorithms. A partial ambiguity analysis method based on least squares ambiguity decorrelation adjustment is adopted, and robust integer ambiguity solutions are selected by combining the Ratio test. Integer ambiguities are fed back to the factor graph as strong constraints to update the navigation state and improve the solution accuracy and stability.

[0010] The further improvement to the above technical solution is as follows:

[0011] The specific steps for GNSS data preprocessing and inter-epoch double-difference observation construction in step S1 are as follows:

[0012] The GNSS observation equation is:

[0013] ;

[0014] In the formula, superscript Represents satellite, subscript Representing a moment; Indicates the geometric distance from the satellite to the receiver; This represents the speed of light in a vacuum. and These represent the receiver clock bias and the satellite clock bias, respectively. Indicates satellite orbital error; Indicates tropospheric delay; Indicates ionospheric delay; Other correction terms include at least phase loop effect, antenna phase center offset and phase center change, as well as relativistic effects and Earth rotation effects; and These represent the sum of measurement noise and multipath error for pseudorange and carrier phase, respectively; Represents pseudorange observations; Indicates the wavelength of the carrier phase observation; Represents the carrier phase observation value; Indicates carrier phase ambiguity;

[0015] GNSS-related status for:

[0016]

[0017] in, It is the receiver location. It is the receiver clock bias. It is a tropospheric delay. It is the carrier phase ambiguity of each satellite. Each satellite corresponds to a cycle slip;

[0018] Single-point positioning is performed using GNSS observation data to obtain receiver position, clock error, and initial tropospheric delay. Then, based on the relative constraints of receiver position, clock error, and initial tropospheric delay, the following factors are constructed:

[0019] ;

[0020] in, As a priori factor, For tropospheric stochastic process factors; These are the initial values ​​of the observation data for the GNSS observation equations;

[0021] Simultaneously, pseudorange and carrier phase absolute constraint factors, which are used in traditional precise single-point positioning, are introduced:

[0022] ;

[0023] in, and These are pseudorange and carrier phase absolute observation factors, respectively. and These are the pseudorange and carrier phase residual functions of the original observations, respectively, derived from the GNSS observation equations; This is the corresponding Jacobian matrix;

[0024] Based on the dual-difference mode of base station-mobile station in real-time dynamic positioning technology, at different times , The double difference expression is as follows:

[0025] ;

[0026] ;

[0027] In the formula, It is the double difference operator, superscript. and They represent the first and satellite; subscript and Representing time respectively and ; Represents pseudorange observations; Represents the carrier phase observation value; Indicates carrier phase ambiguity; This represents double-difference noise;

[0028] After double-difference processing, receiver-side errors, satellite-side errors, and atmospheric delays are eliminated, leaving only the double-difference satellite-to-ground distance, double-difference ambiguity, and double-difference noise terms. Based on these terms, the inter-epoch double-difference relative constraint factor is formed.

[0029] ;

[0030] In the formula, and These are, respectively, double differential pseudorange and carrier factor; and These are the pseudorange and carrier phase residual functions of the double-difference method, respectively. This is the corresponding Jacobian matrix.

[0031] The specific steps for IMU pre-integration and auxiliary cycle slip detection in step S2 are as follows:

[0032] (1) IMU pre-integration

[0033] Assume IMU is The measured value at time is angular velocity. acceleration From adjacent time , The pre-integral calculation between them is as follows:

[0034] ;

[0035] In the formula, , , These represent the rotation, velocity, and position changes between adjacent epochs calculated by pre-integration, respectively. and Zero bias on the gyroscope and zero bias on the accelerometer, respectively; for , At any time between, for , The change in velocity between them; for , The time interval;

[0036] Status related to IMU include:

[0037] ;

[0038] in, For location, For speed, For attitude angle, Zero bias on the gyroscope and zero bias on the accelerometer, respectively;

[0039] The IMU connects two state variables. , The IMU pre-integration factor is expressed as:

[0040] ;

[0041] In the formula, , Representing the Earth coordinate system and the IMU body coordinate system respectively, with The system is an inertial frame of reference. , They represent and B-series time; The vector of gravitational acceleration in the E frame; and They are respectively The gyroscope and accelerometer are both at zero bias. , They are respectively The gyroscope and accelerometer are both at zero bias.

[0042] (2) IMU-assisted GNSS cycle slip detection

[0043] Assume satellite Observations were conducted at three consecutive time points, denoted as follows: , and Construct the following double-difference observations:

[0044] ;

[0045] In the formula, and They represent the first , The and the first , Time Satellite The difference in geometric distance to the receiver; and They represent , Cycle slips at two points in time; , and They represent the first , , Time Satellite Carrier phase observations; This represents the noise in the double-difference carrier phase observation;

[0046] Using the position information from inertial navigation, the distance between the user receiver and the base station between two consecutive epochs is calculated using the following formula:

[0047] ;

[0048] In the formula, This represents the distance between the user receiver and the base station between two consecutive epochs. , This represents the difference in geometric distance between the satellite and the receiver calculated using the receiver position estimated through IMU pre-integration. This represents the noise in the carrier phase observation calculated using IMU pre-integration;

[0049] The cycle slip decision variables are constructed as follows:

[0050] ;

[0051] In the formula, Represents the cycle jump decision variable;

[0052] Weekly jump decision variables Used to detect the generation and number of cycle slips.

[0053] The specific steps for factor graph optimization and ambiguity fixing in step S3 are as follows:

[0054] (1) Factor graph structure

[0055] (1) Factor graph structure

[0056] GNSS status With IMU status After merging, the overall state is:

[0057] ;

[0058] in, , These represent dynamic and static states, respectively.

[0059] The factors in the factor graph structure include prior factors, tropospheric relative constraint factors, GNSS carrier and pseudorange absolute constraint factors, GNSS carrier and pseudorange epoch double difference factors, and IMU pre-integration factors. The overall optimization function is:

[0060] ;

[0061] (2) Fixed fuzziness constraint

[0062] After obtaining the floating-point ambiguity estimate through FGO, a partial ambiguity resolution method based on least squares ambiguity decorrelation adjustment is adopted to improve the ambiguity solution performance and fixation rate; then, the searched integer ambiguity resolution is checked through the Ratio test.

[0063] When the ambiguity is solved using the least squares ambiguity decorrelation adjustment method, an integer ambiguity constraint is generated. This integer ambiguity constraint is then applied to the floating-point estimate, i.e.:

[0064] ;

[0065] In the formula, It is the ambiguity factor. Let be the integer ambiguity to be determined. The floating-point ambiguity obtained through FGO;

[0066] Integer ambiguity The constraints are incorporated into the estimator to update each state and obtain a high-precision solution with carrier phase ambiguity resolution.

[0067] The fixed condition for integer ambiguity in step S3 is as follows: when the floating-point ambiguity resolves to the same integer within 5 consecutive periods, it is determined to be the correctly resolved ambiguity and is incorporated into the estimator as an integer ambiguity constraint.

[0068] As can be seen from the above technical solution, the present invention provides a time-series RTK / INS integrated navigation method based on GNSS epoch-difference double difference. This method constructs epoch-difference double difference observations by performing single-point positioning and error correction on raw GNSS observation data; then, it performs Lie group / manifold space pre-integration on IMU data to estimate the vehicle state and assist in cycle slip detection; finally, based on a factor graph optimization framework, it integrates multiple constraint factors for modeling and solving, and uses the LAMBDA method and Ratio to verify fixed integer ambiguities and provide feedback optimization. The present invention has the following advantages over existing technologies:

[0069] (1) The technical solution adopted in this invention introduces the double difference between GNSS epochs, which eliminates the need for additional reference stations. The fixed solution of the double difference between epochs can be obtained by a single GNSS receiver, which greatly reduces the system deployment cost and overcomes the limitations of traditional RTK scenarios.

[0070] (2) The technical solution adopted in this invention constructs a hybrid span factor graph optimization framework, integrates multiple constraint factors, fully explores the correlation between GNSS epochs, effectively suppresses some epoch gross errors, and improves the robustness of navigation solution.

[0071] (3) The technical solution adopted in this invention uses the IMU pre-integrated relative distance prediction value to assist cycle slip detection, and combines the batch processing characteristics of factor graph optimization to realize online cycle slip estimation, which significantly improves the ability to identify anomalies and ensures the continuity of positioning in complex environments.

[0072] (4) The technical solution adopted in this invention achieves robust integer ambiguity fixation through the LAMBDA method and Ratio test, and sets up a consistency verification mechanism for five consecutive periods, feeding the ambiguity as a strong constraint back to the factor graph to achieve centimeter-level high-precision positioning, taking into account both accuracy and reliability. Attached Figure Description

[0073] Figure 1 Flowchart of the method of this invention;

[0074] Figure 2 Flowchart of GNSS timing RTK / INS integrated navigation solution;

[0075] Figure 3 Schematic diagram of factor graph structure. Detailed Implementation

[0076] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited to the following embodiments.

[0077] The flowchart of a time-series RTK / INS integrated navigation method based on GNSS epoch-difference double difference provided in this invention is as follows. Figure 1 As shown, it includes the following steps:

[0078] S1. GNSS Data Preprocessing and Construction of Inter-Epoch Double-Difference Observations: Single-point positioning is performed on the received raw GNSS observation data to obtain the initial position, clock error, and initial values ​​of tropospheric delay; observation quality control is performed based on the initial solution to determine the satellite; ionospheric, tropospheric, antenna phase center, and relative clock error model corrections are performed on the determined satellite; inter-epoch double-difference GNSS observations are calculated and constructed on the time series to form the relative constraint factor;

[0079] according to Figure 2 The specific steps for GNSS data preprocessing and the construction of inter-epoch double-difference observations are as follows:

[0080] The GNSS observation equation is:

[0081] ;

[0082] In the formula, superscript Represents satellite, subscript Representing a moment; Indicates the geometric distance from the satellite to the receiver; This represents the speed of light in a vacuum. and These represent the receiver clock bias and the satellite clock bias, respectively. Indicates satellite orbital error; Indicates tropospheric delay; Indicates ionospheric delay; Other correction terms include at least phase loop effect, antenna phase center offset and phase center change, as well as relativistic effects and Earth rotation effects; and These represent the sum of measurement noise and multipath error for pseudorange and carrier phase, respectively; Represents pseudorange observations; Indicates the wavelength of the carrier phase observation; Represents the carrier phase observation value; Indicates carrier phase ambiguity;

[0083] GNSS-related status for:

[0084]

[0085] in, It is the receiver location. It is the receiver clock bias. It is a tropospheric delay. It is the carrier phase ambiguity of each satellite. Each satellite corresponds to a cycle slip;

[0086] Single-point positioning is performed using GNSS observation data to obtain receiver position, clock error, and initial tropospheric delay. Then, based on the relative constraints of receiver position, clock error, and initial tropospheric delay, the following factors are constructed:

[0087] ;

[0088] in, As a priori factor, For tropospheric stochastic process factors; These are the initial values ​​of the observation data for the GNSS observation equations;

[0089] Simultaneously, pseudorange and carrier phase absolute constraint factors, which are used in traditional precise single-point positioning, are introduced:

[0090] ;

[0091] in, and These are pseudorange and carrier phase absolute observation factors, respectively. and These are the pseudorange and carrier phase residual functions of the original observations, respectively, derived from the GNSS observation equations; This is the corresponding Jacobian matrix;

[0092] Based on the dual-difference mode of base station-mobile station in real-time dynamic positioning technology, at different times , The double difference expression is as follows:

[0093] ;

[0094] ;

[0095] In the formula, It is the double difference operator, superscript. and They represent the first and satellite; subscript and Representing time respectively and ; Represents pseudorange observations; Represents the carrier phase observation value; Indicates carrier phase ambiguity; This represents double-difference noise;

[0096] After double-difference processing, receiver-side errors, satellite-side errors, and atmospheric delays are eliminated, leaving only the double-difference satellite-to-ground distance, double-difference ambiguity, and double-difference noise terms. Based on these terms, the inter-epoch double-difference relative constraint factor is formed.

[0097] ;

[0098] In the formula, and These are, respectively, dual differential pseudorange and carrier factor; and These are the pseudorange and carrier phase residual functions of the double-difference method, respectively. This is the corresponding Jacobian matrix.

[0099] S2, IMU pre-integration and auxiliary cycle slip detection: The accelerometer and gyroscope data of the IMU are pre-integrated in the Lie group / manifold space to obtain the relative motion constraint factor between epochs and estimate the carrier state at any time; the estimated carrier state is used to predict the satellite geometric distance, construct cycle slip decision variables, assist GNSS observation cycle slip detection and provide initial values;

[0100] according to Figure 2 The specific steps of IMU pre-integration and auxiliary cycle slip detection are as follows:

[0101] (1) IMU pre-integration

[0102] Assume IMU is The measured value at time is angular velocity. acceleration From adjacent time , The pre-integral calculation between them is as follows:

[0103] ;

[0104] In the formula, , , These represent the rotation, velocity, and position changes between adjacent epochs calculated by pre-integration, respectively. and Zero bias on the gyroscope and zero bias on the accelerometer, respectively; for , At any time between, for , The change in velocity between them; for , The time interval;

[0105] Status related to IMU include:

[0106] ;

[0107] in, For location, For speed, For attitude angle, Zero bias on the gyroscope and zero bias on the accelerometer, respectively;

[0108] The IMU connects two state variables. , The IMU pre-integration factor is expressed as:

[0109] ;

[0110] In the formula, , Representing the Earth coordinate system and the IMU body coordinate system respectively, with The system is an inertial frame of reference. , They represent and B-series time; The vector of gravitational acceleration in the E frame; and They are respectively The gyroscope and accelerometer are both at zero bias. , They are respectively The gyroscope and accelerometer are both at zero bias.

[0111] Assume satellite Observations were conducted at three consecutive time points, denoted as follows: , and Construct the following double-difference observations:

[0112] ;

[0113] In the formula, and They represent the first , The and the first , Time Satellite The difference in geometric distance to the receiver; and They represent , Cycle slips at two points in time; , and They represent the first , , Time Satellite Carrier phase observations; This represents the noise in the double-difference carrier phase observation;

[0114] In this embodiment, when no cycle slip occurs and All are 0; when a cycle slip occurs, and Combination and Make judgments separately;

[0115] ;

[0116] In the formula, This represents the distance between the user receiver and the base station between two consecutive epochs. , This represents the difference in geometric distance between the satellite and the receiver calculated using the receiver position estimated through IMU pre-integration. This represents the noise in the carrier phase observation calculated using IMU pre-integration;

[0117] The cycle slip decision variables are constructed as follows:

[0118] ;

[0119] In the formula, Represents the cycle jump decision variable;

[0120] Weekly jump decision variables Used to detect the generation and number of cycle slips.

[0121] S3. Factor Graph Optimization and Ambiguity Fixation: Based on the factor graph optimization framework, the GNSS epoch-difference observation factor, IMU pre-integration factor, prior factor, tropospheric relative constraint factor, and GNSS carrier and pseudorange absolute constraint factor are uniformly modeled to construct a time-series RTK / INS integrated navigation factor graph. The integrated navigation state is solved using nonlinear least squares or incremental optimization algorithms. A partial ambiguity analysis method based on least squares ambiguity decorrelation adjustment is adopted, and robust integer ambiguity solutions are selected by combining the Ratio test. Integer ambiguities are fed back to the factor graph as strong constraints to update the navigation state and improve the solution accuracy and stability.

[0122] according to Figure 2 As can be seen, the specific steps for factor graph optimization and ambiguity fixation are as follows:

[0123] (1) Factor graph structure

[0124] GNSS status With IMU status After merging, the overall state is:

[0125] ;

[0126] in, , These represent dynamic and static states, respectively.

[0127] The factors in the factor graph structure include prior factors, tropospheric relative constraint factors, GNSS carrier and pseudorange absolute constraint factors, GNSS carrier and pseudorange epoch double difference factors, and IMU pre-integration factors. The overall optimization function is:

[0128] ;

[0129] (2) Fixed fuzziness constraint

[0130] After obtaining the floating-point ambiguity estimate through FGO, a partial ambiguity resolution method based on least squares ambiguity decorrelation adjustment is adopted to improve the ambiguity solution performance and fixation rate; then, the searched integer ambiguity resolution is checked through the Ratio test.

[0131] When resolving ambiguities using the least squares ambiguity decorrelation adjustment method, an integer ambiguity constraint is generated. This integer ambiguity (IA) constraint is then applied to the floating-point estimate, i.e.:

[0132] ;

[0133] In the formula, It is the ambiguity factor. Let be the integer ambiguity to be determined. The floating-point ambiguity obtained through FGO;

[0134] Integer ambiguity The constraints are incorporated into the estimator to update each state and obtain a high-precision solution with carrier phase ambiguity resolution.

[0135] In this embodiment, the weight of the integer fuzziness constraint is The fixed condition for integer ambiguity is that when the floating-point ambiguity resolves to the same integer within 5 consecutive periods, it is determined to be the correctly resolved ambiguity and is incorporated into the estimator as an integer ambiguity constraint.

[0136] In summary, this invention can achieve centimeter-level high-precision relative positioning without external reference stations by integrating only a single GNSS receiver and IMU. This significantly reduces system deployment costs and scenario limitations. Furthermore, it can fully exploit the correlation between GNSS epochs and improve the continuity, robustness, and solution accuracy of positioning in complex environments through IMU-assisted cycle slip detection and factor graph optimization framework. This effectively overcomes the shortcomings of traditional integrated navigation, such as slow convergence, weak anti-interference capability, and error accumulation.

Claims

1. A time-series RTK / INS integrated navigation method based on GNSS epoch-difference dual differences, characterized in that, Includes the following steps: S1. GNSS Data Preprocessing and Construction of Inter-Epoch Double-Difference Observations: Single-point positioning is performed on the received raw GNSS observation data to obtain the initial position, clock error, and initial values ​​of tropospheric delay; observation quality control is performed based on the initial solution to determine the satellite; ionospheric, tropospheric, antenna phase center, and relative clock error model corrections are performed on the determined satellite; inter-epoch double-difference GNSS observations are calculated and constructed on the time series to form the relative constraint factor; S2, IMU pre-integration and auxiliary cycle slip detection: The accelerometer and gyroscope data of the IMU are pre-integrated in the Lie group / manifold space to obtain the relative motion constraint factor between epochs and estimate the carrier state at any time. The estimated carrier state is used to predict the satellite geometric distance, construct cycle slip decision variables, assist GNSS observation cycle slip detection and provide initial values; S3. Factor Graph Optimization and Ambiguity Fixation: Based on the factor graph optimization framework, the GNSS epoch-difference observation factor, IMU pre-integration factor, prior factor, tropospheric relative constraint factor, and GNSS carrier and pseudorange absolute constraint factor are uniformly modeled to construct a time-series RTK / INS integrated navigation factor graph. The integrated navigation state is solved using nonlinear least squares or incremental optimization algorithms. A partial ambiguity analysis method based on least squares ambiguity decorrelation adjustment is adopted, and robust integer ambiguity solutions are selected by combining the Ratio test. Integer ambiguities are fed back to the factor graph as strong constraints to update the navigation state and improve the solution accuracy and stability.

2. The time-series RTK / INS integrated navigation method based on GNSS epoch-difference double difference as described in claim 1, characterized in that, The specific steps for GNSS data preprocessing and inter-epoch double-difference observation construction in step S1 are as follows: The GNSS observation equation is: ； In the formula, superscript Represents satellite, subscript Representing a moment; Indicates the geometric distance from the satellite to the receiver; This represents the speed of light in a vacuum. and These represent the receiver clock bias and the satellite clock bias, respectively. Indicates satellite orbital error; Indicates tropospheric delay; Indicates ionospheric delay; Other correction terms include at least phase loop effect, antenna phase center offset and phase center change, as well as relativistic effects and Earth rotation effects; and These represent the sum of measurement noise and multipath error for pseudorange and carrier phase, respectively; Indicates pseudorange observations; Indicates the wavelength of the carrier phase observation; Represents the carrier phase observation value; Indicates carrier phase ambiguity; GNSS-related status for: in, It is the receiver location. It is the receiver clock bias. It is a tropospheric delay. It is the carrier phase ambiguity of each satellite. Each satellite corresponds to a cycle slip; Single-point positioning is performed using GNSS observation data to obtain receiver position, clock error, and initial tropospheric delay. Then, based on the relative constraints of receiver position, clock error, and initial tropospheric delay, the following factors are constructed: ； in, As a priori factor, For tropospheric stochastic process factors; These are the initial values ​​of the observation data for the GNSS observation equations; Simultaneously, pseudorange and carrier phase absolute constraint factors, which are used in traditional precise single-point positioning, are introduced: ； in, and These are pseudorange and carrier phase absolute observation factors, respectively. and These are the pseudorange and carrier phase residual functions of the original observations, respectively, derived from the GNSS observation equations; This is the corresponding Jacobian matrix; Based on the dual-difference mode of base station-mobile station in real-time dynamic positioning technology, at different times , The double difference expression is as follows: ； ； In the formula, It is the double difference operator, superscript. and They represent the first and satellite; subscript and Representing time respectively and ; Indicates pseudorange observations; Represents the carrier phase observation value; Indicates carrier phase ambiguity; This represents double-difference noise; After double-difference processing, receiver-side errors, satellite-side errors, and atmospheric delays are eliminated, leaving only the double-difference satellite-to-ground distance, double-difference ambiguity, and double-difference noise terms. Based on these terms, the inter-epoch double-difference relative constraint factor is formed. ； In the formula, and These are, respectively, dual differential pseudorange and carrier factor; and These are the pseudorange and carrier phase residual functions of the double-difference method, respectively. This is the corresponding Jacobian matrix.

3. The time-series RTK / INS integrated navigation method based on GNSS epoch-difference double difference as described in claim 1, characterized in that, The specific steps for IMU pre-integration and auxiliary cycle slip detection in step S2 are as follows: (1) IMU pre-integration Assume IMU is The measured value at time is angular velocity. acceleration From adjacent time , The pre-integral calculation between them is as follows: ； In the formula, , , These represent the rotation, velocity, and position changes between adjacent epochs calculated by pre-integration, respectively. and Zero bias on the gyroscope and zero bias on the accelerometer, respectively; for , At any time between, for , The change in velocity between them; for , The time interval; Status related to IMU include: ； in, For location, For speed, For attitude angle, Zero bias on the gyroscope and zero bias on the accelerometer, respectively; The IMU connects two state variables. , The IMU pre-integration factor is expressed as: ； In the formula, , Representing the Earth coordinate system and the IMU body coordinate system respectively, with The system is an inertial frame of reference. , They represent and B-series time; The vector of gravitational acceleration in the E frame; and They are respectively The gyroscope and accelerometer are both zero biased. , They are respectively The gyroscope and accelerometer are both zero biased. (2) IMU-assisted GNSS cycle slip detection Assume satellite Observations were conducted at three consecutive time points, denoted as follows: , and Construct the following double-difference observations: ； In the formula, and They represent the first , The and the first , Time Satellite The difference in geometric distance to the receiver; and They represent , Cycle slips at two points in time; , and They represent the first , , Time Satellite Carrier phase observations; This represents the noise in the double-difference carrier phase observation; Using the position information from inertial navigation, the distance between the user receiver and the base station between two consecutive epochs is calculated using the following formula: ； In the formula, This represents the distance between the user receiver and the base station between two consecutive epochs. , This represents the difference in geometric distance between the satellite and the receiver calculated using the receiver position estimated by IMU pre-integration. This represents the noise in the carrier phase observation calculated using IMU pre-integration; The cycle slip decision variables are constructed as follows: ； In the formula, Represents the cycle jump decision variable; Weekly jump decision variables Used to detect the generation and number of cycle slips.

4. The time-series RTK / INS integrated navigation method based on GNSS epoch-difference double difference as described in claim 1, characterized in that, The specific steps for factor graph optimization and ambiguity fixing in step S3 are as follows: (1) Factor graph structure GNSS status With IMU status After merging, the overall state is: ； in, , These represent dynamic and static states, respectively. The factors in the factor graph structure include prior factors, tropospheric relative constraint factors, GNSS carrier and pseudorange absolute constraint factors, GNSS carrier and pseudorange epoch double difference factors, and IMU pre-integration factors. The overall optimization function is: ； (2) Fixed fuzziness constraint After obtaining the floating-point ambiguity estimate through FGO, a partial ambiguity resolution method based on least squares ambiguity decorrelation adjustment is adopted to improve the ambiguity solution performance and fixation rate; then, the searched integer ambiguity resolution is checked through the Ratio test. When the ambiguity is solved using the least squares ambiguity decorrelation adjustment method, an integer ambiguity constraint is generated. This integer ambiguity constraint is then applied to the floating-point estimate, i.e.: ； In the formula, It is the ambiguity factor. Let be the integer ambiguity to be determined. The floating-point ambiguity obtained through FGO; Integer ambiguity The constraints are incorporated into the estimator to update each state and obtain a high-precision solution with carrier phase ambiguity resolution.

5. The time-series RTK / INS integrated navigation method based on GNSS epoch-difference double difference as described in claim 1, characterized in that, The fixed condition for integer ambiguity in step S3 is as follows: when the floating-point ambiguity resolves to the same integer within 5 consecutive periods, it is determined to be the correctly resolved ambiguity and is incorporated into the estimator as an integer ambiguity constraint.

Images