INS-assisted positioning system and method under GNSS / INS positioning system, and medium

Abstract

The invention relates to the technical field of navigation positioning, and discloses an INS-assisted positioning system and method under a GNSS / INS positioning system, and a medium, and the system comprises a prediction pseudo-range confirmation module, a floating point solution calculation module, a first optimal fixed solution calculation module, a second optimal fixed solution calculation module, and a fusion solution module. According to the scheme, the floating point ambiguity resolving and fixing process is optimized by correcting inertial information in real time, specifically, inertial prior information is corrected by using a combined positioning high-precision result, a traditional GNSS pseudo-range estimation method is replaced, an improved partial ambiguity fixing strategy is introduced, the fixing efficiency of non-optimal subset ambiguity is improved, and the positioning accuracy of the GNSS pseudo-range estimation method is improved. According to the method, the positioning precision, the stability and the real-time performance can be remarkably improved in a complex urban environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of navigation positioning, in particular to an INS-aided positioning system and method under a GNSS / INS positioning system and a medium. BACKGROUND

[0002] Global Navigation Satellite System (GNSS) can provide high-precision and reliable positioning in open sky environment, but its performance significantly decreases in complex scenarios (such as urban canyons, dense forests), mainly due to signal blockage and multipath effects leading to positioning failure. Inertial Navigation System (INS) as a complementary technology has robustness independent of external environment, but its error accumulates with time when used alone, and the positioning drift problem is prominent. To solve their respective defects, GNSS / INS integrated navigation technology emerges as the times require, which realizes high-precision and reliable positioning in complex environments by fusing the advantages of both, and has been widely applied in automatic driving, robots and unmanned aerial vehicles and other fields with extremely high requirements for precision and robustness. High-precision positioning based on GNSS relies on Ambiguity Resolution (AR) technology, the core of which is to solve the integer ambiguity through carrier phase observations. The success rate of ambiguity resolution is affected by the statistical characteristics of float solution (such as ambiguity correlation, search space) and integer least squares estimation method, while the calculation efficiency depends on the search algorithm. Although methods such as Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) improve the efficiency in open scenarios by ambiguity decorrelation and search space compression, but the deterioration of signal quality in complex environments will lead to increased correlation between ambiguity parameters and expanded search space dimension, which significantly reduces the success rate and real-time performance of ambiguity resolution. Therefore, researchers propose to fuse inertial data through GNSS / INS integrated technology to optimize the performance of ambiguity resolution. According to the coupling depth, the integrated system can be divided into loose coupling, tight coupling and deep coupling architectures, among which the tight coupling architecture is widely adopted due to its consideration of real-time performance, flexibility and precision. In addition, Extended Kalman Filter (EKF), cubature Kalman filter, unscented Kalman filter and factor graph optimization are used to improve the data fusion effect, but UKF and FGO can handle nonlinear / non-Gaussian noise, but due to high computational complexity, they are difficult to meet real-time requirements, so the computationally efficient EKF is still the preferred solution.

[0003] In recent years, inertial-aided GNSS ambiguity resolution methods have become a research hotspot, especially in dealing with complex scenarios such as urban canyons. For example, HZHan et al. published an article titled "Reliable partial ambiguity resolution for single-frequency GPS / BDS and INS integration" in GPS Solutions, Vol. 21, pp. 251-264 in 2017, in which they designed an INS-assisted precise point positioning method to maintain ambiguity resolution performance during GNSS signal outages. XHZhang et al. published an article titled "The improvement in integer ambiguity resolution with INS aiding for dynamic precise point positioning" in Journal of Geodesy, Vol. 93, pp. 993-1010 in 2019. In 2022, D. S. Chai et al. published a paper titled “A novel method of ambiguity resolution and cycle slip processing for single-frequency GNSS / INS tightly coupled integration system” in Advances in Space Research, volume 69, pages 359-375. The paper proposed an INS-assisted partial ambiguity resolution strategy for medium and long baselines to optimize the resolution efficiency in dynamic scenarios. However, existing methods have insufficient real-time correction capabilities for inertial information in tightly coupled systems, and the fixation strategy for non-optimal ambiguity subsets still needs to be optimized. Summary of the Invention

[0004] The application aims to overcome the problem that GNSS signals are easily blocked in urban environments and it is difficult to meet the high-precision continuous positioning of vehicles by relying on GNSS technology alone, and provides an INS-aided positioning system and method under a GNSS / INS positioning system and a medium, which optimizes the float ambiguity resolution and fixing process by real-time correction of inertial information, specifically, the inertial prior information is corrected by using the high-precision result of combined positioning to replace the traditional GNSS pseudorange estimation method, and an improved partial ambiguity fixing strategy is introduced to improve the fixing efficiency of non-optimal subset ambiguity, which can significantly improve the positioning accuracy, stability and real-time performance in complex urban environments.

[0005] To achieve the above-mentioned purpose, the application provides an INS-aided positioning system under a GNSS / INS positioning system, comprising: a predicted pseudorange confirmation module for calculating the distance between the INS position of the user and each satellite by using the corrected INS position of the user, and taking it as the predicted pseudorange between each satellite and the GNSS receiver of the user;

[0006] A float solution calculation module is configured to obtain the float solution of the GNSS receiver position of the user according to the predicted pseudorange between each satellite and the GNSS receiver of the user and the position of each satellite, and solve the carrier phase observation equation of the satellite observation value by the least square method, so as to obtain the float solution of the carrier phase observation ambiguity of each satellite;

[0007] A first optimal fixed solution calculation module is configured to divide all satellites in the GNSS system into a first optimal subset satellite and a first non-optimal subset satellite according to the elevation cut-off angle, complete the ambiguity resolution of the float solution of the carrier phase observation ambiguity of the first optimal subset satellite by using the LAMBDA method, and obtain the fixed solution of the carrier phase observation ambiguity of the first optimal subset satellite;

[0008] A second optimal fixed solution calculation module is configured to correct the float solution of the carrier phase observation ambiguity of the first non-optimal subset satellite by using the fixed solution of the carrier phase observation ambiguity of the first optimal subset satellite, obtain the corrected float solution of the carrier phase observation ambiguity of the first non-optimal subset satellite, thereby obtaining the corrected first non-optimal subset satellite, divide the corrected first non-optimal subset satellite into a second optimal subset satellite and a second non-optimal subset satellite according to the size of the elevation cut-off angle, and complete the ambiguity resolution of the float solution of the carrier phase observation ambiguity of the second optimal subset satellite by using the LAMBDA method, thereby obtaining the fixed solution of the carrier phase observation ambiguity of the second optimal subset satellite;

[0009] The fusion solution module is used to perform a tightly coupled GNSS / INS combined positioning solution on the fixed solution of the first optimal subset satellite carrier phase observation ambiguity, the fixed solution of the second optimal subset satellite carrier phase observation ambiguity, and the user's GNSS receiver position using the INS-assisted corrected partial ambiguity resolution method to obtain the user position.

[0010] A second aspect of the present invention provides an INS-assisted positioning method in a GNSS / INS positioning system, comprising: using a corrected user's INS position to calculate the distance between the INS position and each satellite, and using the distance as a predicted pseudorange between each satellite and the user's GNSS receiver;

[0011] Based on the predicted pseudorange between each satellite and the user's GNSS receiver and the position of each satellite, a floating-point solution for the user's GNSS receiver position is obtained. The carrier phase observation equation of the satellite observation value is solved by the least squares method to obtain a floating-point solution for the ambiguity of the carrier phase observation value of each satellite.

[0012] All satellites in the GNSS system are divided into the first optimal subset of satellites and the first non-optimal subset of satellites according to the altitude cutoff angle. The ambiguity of the carrier phase observation values ​​of the first optimal subset of satellites is resolved using the LAMBDA method to obtain the fixed solution of the carrier phase observation ambiguity of the first optimal subset of satellites.

[0013] The floating-point solutions of the carrier phase observation values ​​of the first non-optimal subset satellites are corrected using the fixed solutions of the ambiguities of the carrier phase observation values ​​of the first optimal subset satellites to obtain the corrected floating-point solutions of the carrier phase observation values ​​of the first non-optimal subset satellites, thereby obtaining the corrected first non-optimal subset satellites. The corrected first non-optimal subset satellites are divided into the second optimal subset satellites and the second non-optimal subset satellites according to the size of the altitude cutoff angle, and the floating-point solutions of the carrier phase observation values ​​of the second optimal subset satellites are ambiguity resolved using the LAMBDA method to obtain the fixed solutions of the carrier phase observation values ​​of the second optimal subset satellites.

[0014] Using the INS-assisted corrected partial ambiguity resolution method, a tightly coupled GNSS / INS combined positioning solution is performed on the fixed solutions of the first optimal subset satellite carrier phase observation ambiguities, the fixed solutions of the second optimal subset satellite carrier phase observation ambiguities, and the user's GNSS receiver position to obtain the user position.

[0015] A third aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0016] The beneficial effects of the present invention are:

[0017] The application significantly improves the ambiguity float solution precision by high-precision combination positioning result real-time correction of INS prior information, instead of traditional GNSS pseudo-range estimation; effectively enhances the whole-week ambiguity fixing ability in urban shielding environment by combining dynamic pseudo-range gross error detection and improved partial ambiguity solution strategy. The method uses optimal subset ambiguity fixing information to assist non-optimal subset solution, increases the number of available satellites, and improves positioning availability and accuracy; through elevation sorting and multi-round subset optimization strategy, the traditional method is avoided to fall into the problem of non-optimal subset selection, and the solution efficiency and reliability are considered. Experiments show that the ambiguity solution success rate of the method is significantly improved in the satellite signal shielding scene, and the positioning accuracy reaches centimeter to sub-meter level, providing high-reliable positioning support for automatic driving, intelligent transportation and other fields. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a structural schematic diagram of the application;

[0019] Figure 2 is a structural diagram of GNSS / INS tight coupling positioning of the application;

[0020] Figure 3 is a flow chart of the satellite positioning partial ambiguity solution method assisted by inertial navigation of the application;

[0021] Figure 4 is a system block diagram of the satellite positioning partial ambiguity solution method assisted by inertial navigation of the application;

[0022] Figure 5 is the positioning error comparison and evaluation result of five methods of Xuzhou data set;

[0023] Figure 6 is the root mean square error comparison result of five positioning methods of Xuzhou data set;

[0024] Figure 7 is a method flow chart of the application. DETAILED DESCRIPTION

[0025] The specific embodiments of the application are described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to illustrate and explain the application, and are not used to limit the application.

[0026] The endpoints of the ranges and any values disclosed herein are not limited to the precise values stated. The ranges or values should be construed to include values approximately around the range or value. For ranges of values, the endpoints of each range are included in the range, the endpoints of each range are included in the range, and individual points within the ranges are included in the ranges, and the ranges should be considered to be specifically disclosed herein.

[0027] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of such features. In addition, the technical solutions between the various embodiments provided by the present invention can be combined with each other, but they must be based on the ability of ordinary technicians in this field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0028] Example 1

[0029] like Figure 1 The INS-assisted positioning system under the GNSS / INS positioning system shown includes: a predicted pseudorange confirmation module for calculating the distance between the INS position and each satellite using the corrected user INS position, and using the distance as the predicted pseudorange between each satellite and the user GNSS receiver;

[0030] The floating-point solution calculation module is used to obtain the floating-point solution of the user's GNSS receiver position based on the predicted pseudorange between each satellite and the user's GNSS receiver and the position of each satellite, and solve the carrier phase observation equation of the satellite observation value through the least squares method to obtain the floating-point solution of the ambiguity of the carrier phase observation value of each satellite.

[0031] The first optimal fixed solution calculation module is used to divide all satellites in the GNSS system into a first optimal subset of satellites and a first non-optimal subset of satellites according to the altitude cutoff angle, and use the LAMBDA method to complete the ambiguity resolution of the floating-point solution of the carrier phase observation value ambiguity of the first optimal subset of satellites to obtain the fixed solution of the carrier phase observation ambiguity of the first optimal subset of satellites;

[0032] The second optimal fixed solution calculation module is used to use the fixed solution of the first optimal subset satellite carrier phase observation ambiguity to correct the floating-point solution of the first non-optimal subset satellite carrier phase observation ambiguity, thereby obtaining a corrected floating-point solution of the first non-optimal subset satellite carrier phase observation ambiguity, thereby obtaining a corrected first non-optimal subset satellite, dividing the corrected first non-optimal subset satellite into a second optimal subset satellite and a second non-optimal subset satellite according to the size of the altitude cutoff angle, and using the LAMBDA method to complete ambiguity resolution on the floating-point solution of the second optimal subset satellite carrier phase observation ambiguity, thereby obtaining a fixed solution of the second optimal subset satellite carrier phase observation ambiguity;

[0033] The fusion solution module is used to perform a tightly coupled GNSS / INS combined positioning solution on the fixed solution of the first optimal subset satellite carrier phase observation ambiguities, the fixed solution of the second optimal subset satellite carrier phase observation ambiguities, and the user's GNSS receiver position using the INS-assisted Modified Partial Ambiguity Resolution (MPAR) method to obtain the user position.

[0034] GNSS provides precise positioning services to users around the world. The basic principle of GNSS positioning is to use the measurement of satellite signal propagation time to determine the actual distance between the user receiver and the satellite, and then calculate the three-dimensional spatial coordinates of the receiver. Depending on the observation value, it is divided into pseudo-range observation positioning and carrier phase observation positioning. The pseudo-range observation positioning method uses the propagation time of the satellite signal to calculate the distance. It has the characteristics of simple principle and fast solution. However, it is affected by factors such as signal propagation error and multipath effect, and the positioning accuracy is relatively low (pseudo-range observation is actually based on the electromagnetic wave speed multiplied by the time difference. The calculation is simple but the accuracy is low). The carrier phase observation positioning method calculates the distance by measuring the phase change of the satellite signal carrier phase. It has the characteristics of high precision, but it needs to resolve the ambiguity problem.

[0035] INS, on the other hand, utilizes internal sensors to continuously monitor and update attitude, velocity, and position information. GNSS / INS integrated systems utilize efficient data fusion strategies to seamlessly integrate GNSS and INS information, providing superior and stable navigation services in all environments. GNSS / INS combination models can be categorized into three types based on the depth of their information fusion: loosely coupled, tightly coupled (TC), and deeply coupled. Each has unique structural characteristics and application scenarios. Tightly coupled has garnered particular attention and has become a major research priority, primarily due to its ability to achieve high positioning accuracy and robustness in obscured environments without requiring excessive computational or hardware resources. Compared to loose coupling, tight coupling more comprehensively utilizes information from both GNSS and INS, thereby improving positioning performance. Compared to deeply coupled, it avoids the excessive complexity and implementation difficulty of TC. Therefore, the tightly coupled model is often viewed as offering an ideal balance between performance and cost.

[0036] Tight coupling is a higher-level information fusion technology in GNSS and INS integrated navigation. Figure 2This diagram shows the architecture of tightly coupled GNSS / INS positioning. Unlike loose coupling, tight coupling directly integrates GNSS raw observation data. This involves using the difference between the observed values ​​(such as pseudorange and pseudorange rate) output by the GNSS module and the inertial measurements from the INS module. This difference is then processed using a Kalman filter. The filter estimates the accumulated error of the INS module and generates corresponding error compensation, which is promptly fed back to the inertial navigation system module for real-time error correction.

[0037] The corrected INS measurements are synchronously fed into the tightly coupled GNSS / INS combined positioning system filter in the data processing module, where they are deeply integrated with the GNSS positioning results to produce a more accurate combined navigation solution. The advantage of this integration approach is that even if the number of satellites is insufficient for the GNSS positioning module to obtain a fixed solution, the tightly coupled mode can still maintain navigation continuity and accuracy through GNSS signal updates.

[0038] A notable feature of the tightly coupled mode is its high robustness in obstructed environments. By directly fusing raw observation data, tight coupling more effectively leverages the complementary strengths of GNSS and INS, improving overall system positioning accuracy and stability. However, this high performance comes at the cost of increased implementation complexity. Tightly coupled systems place higher demands on algorithms and hardware, particularly GNSS positioning algorithms, which require in-house development by manufacturers of high-precision integrated navigation systems, undoubtedly increasing the technical complexity. Nevertheless, for applications requiring the ultimate in positioning accuracy, tight coupling is undoubtedly the best choice.

[0039] In a vehicle-based GNSS / INS integrated navigation system, the calculation of position, velocity, and attitude involves four primary coordinate systems: the inertial coordinate system (i-frame), the Earth-centered, Earth-fixed coordinate system (e-frame), the navigation coordinate system (n-frame), and the vehicle coordinate system (b-frame). The navigation coordinate system, also known as the geographic coordinate system, is typically represented in the east-north-sky coordinate system in vehicle-mounted navigation systems to accurately describe and calculate the vehicle's position, velocity, and attitude. INS error equations primarily take two forms: the PSI angular error equation and the PHI angular error equation. The PHI model exhibits strong adaptability to large heading errors and is particularly suitable for low-cost systems requiring orientation initialization. However, the PHI model is relatively complex and can present challenges in handling velocity and position errors. In contrast, the PSI model is known for its simple structure and clear physical meaning. However, its performance may degrade in the presence of significant heading errors due to nonlinear error propagation caused by attitude deviations. The PHI model was selected for this study based on its compatibility with low-cost sensor systems and its ability to effectively handle large heading errors. Especially in scenarios involving orientation initialization, the PHI model provides more robust navigation solutions. Therefore, choosing the PHI model better meets research needs and ensures an accurate and reliable navigation solution.

[0040] Figure 3 This is a flow chart of the partial ambiguity resolution method for inertial navigation-assisted satellite positioning of the present invention. Figure 4 Block diagram of the partial ambiguity resolution system for inertial navigation-assisted satellite positioning.

[0041] In the present invention, an INS error model is established based on the PHI model (the INS error model is used to correct INS position errors. The following INS error model can correct errors in attitude, position, and speed. It is only the position error correction we mainly use during positioning.). The user's INS position is corrected in real time according to the INS error model to obtain the corrected user's INS position.

[0042] Among them, the expression of INS error model based on PHI model is:

[0043]

[0044] Where, Indicated in the navigation coordinate system ψ n The PHI angular error rate, Indicates the position δr in the navigation coordinate system (Navigation coordinate system (n system - NavigationFrame): a coordinate system with the center of the carrier as the origin.) n The PHI angular error rate, Indicates δv in the navigation coordinate system nPHI angular error rate; ψ n for The attitude error component, δr n for The position error component, δv n for The velocity error component of Indicates the angular velocity of the navigation coordinate system relative to the inertial coordinate system (Inertial coordinate system (i-frame): a coordinate system with the center of mass of the earth as its origin); for PHI angular error rate; Indicates the angular velocity of the user (such as a vehicle) relative to the earth; for PHI angular error rate; represents the angular velocity of the Earth's rotation; for PHI angular error rate; Represents the rotation matrix of the transformation from the carrier coordinate system (b-frame) to the navigation coordinate system (n-frame) based on the attitude angle calculation, the rotation matrix Describes the transformation relationship from the carrier coordinate system to the navigation coordinate system. This matrix can be obtained by calculating the attitude angle; f b Represents the specific force measured in the carrier coordinate system (i.e., the non-gravitational external force per unit mass); δg n represents the local gravity anomaly in the navigation coordinate system; b g represents the output error of the gyroscope; b a Represents the output error of the accelerometer; INS consists of two basic devices: gyroscope and accelerometer. The gyroscope outputs the angular velocity of the INS, and the accelerometer outputs the acceleration of the INS. These two output errors are the main sources of error in the inertial measurement unit; δθ represents the rotation vector that represents the deviation between the rotated coordinate system and the actual navigation coordinate system; v n Indicates the user's speed in the navigation coordinate system.

[0045] The traditional inertial navigation system assisted ambiguity resolution method directly uses the user's INS original position data as the positioning result of the user's GNSS receiver. k , that is, simply let X k =X Ik This method does not take into account the cumulative error of the inertial navigation system, nor does it fully utilize the combined positioning results to correct the inertial navigation system error in real time. In order to improve the positioning accuracy of the inertial navigation system, the present invention first corrects the user's INS position in real time.

[0046] The process of real-time correction of the INS position of the user (the position calculated by the inertial navigation system (INS) itself) according to the INS error model is as follows:

[0047] X CIk = X Ik - (X k-1 - X CI(k-1) ), k = 1, 2, 3…

[0048] In the formula, k represents the kth epoch (when k = 1, it represents the first epoch, at which time the original INS position of the user is initialized as the corrected INS position of the user at the epoch); X Ik represents the original INS position of the user at the kth epoch; X CIk represents the corrected INS position of the user at the kth epoch; X k-1 represents the position of the user at the (k-1)th epoch (i.e., the last epoch); X CI(k-1) represents the corrected INS position of the user at the (k-1)th epoch;

[0049] The corrected INS position of the user X CI is represented as:

[0050] X CIk = (x CIk , y CIk , z CIk )

[0051] In the formula, x CIk represents the x-axis of the corrected INS position of the user in the navigation coordinate system; y CIk represents the y-axis of the corrected INS position of the user in the navigation coordinate system; and z CIk represents the z-axis of the corrected INS position of the user in the navigation coordinate system.

[0052] The distance between the corrected INS position of the user and each satellite is calculated, and is used as the predicted pseudo-range between each satellite and the GNSS receiver of the user, to replace the original GNSS pseudo-range. The calculation method of the predicted pseudo-range is as follows:

[0053]

[0054] In the formula, ρ represents the predicted pseudo-range between each satellite and the GNSS receiver of the user; x s represents the x-axis of the satellite position in the navigation coordinate system; y s represents the y-axis of the satellite position in the navigation coordinate system; and z s represents the z-axis of the satellite position in the navigation coordinate system.

[0055] In three-dimensional space, if the three-dimensional coordinates of the satellite and receiver are known, the distance between them can be calculated using the Euclidean distance formula. This formula, based on a rectangular coordinate system, calculates the straight-line distance between two points by taking the square root of the sum of the squares of their coordinate differences along the three coordinate axes.

[0056] In the present invention, the corrected user's INS position is used to calculate the distance between the INS position and each satellite. The high-precision predicted pseudorange will replace the low-precision GNSS observed pseudorange as the prior information for ambiguity resolution.

[0057] In tightly coupled GNSS / INS integrated navigation, raw GNSS observations provide "pseudorange measurements" that contain various errors (such as clock bias and atmospheric delay) and have limited accuracy. Positions calculated solely based on these pseudoranges are called "pseudorange positions" and are also relatively inaccurate. The INS, on the other hand, directly outputs the "INS position" using inferred information from its internal inertial sensors. Although INS position errors accumulate over time, its short-term accuracy and stability are generally higher due to periodic corrections using GNSS information. The ranges calculated using the INS position are more accurate than the GNSS pseudoranges. Therefore, to obtain higher-precision range information for critical steps (such as ambiguity resolution), the strategy is to replace the raw GNSS pseudorange measurements with precise satellite-user geometry calculated based on the "corrected INS position." After the INS position is corrected in real time using new GNSS observations, the satellite-user geometry must be recalculated using this latest, corrected, high-precision INS position. This "update distance" step is crucial. It ensures that the geometric distance used to replace the low-precision pseudorange measurement is always based on the current optimal and least-error INS position, thereby maximizing the use of the INS's high-precision position information and providing a reliable distance benchmark for subsequent solutions.

[0058] In the present invention, the integer characteristics of the carrier phase observation ambiguity are temporarily ignored. Based on the predicted pseudorange between each satellite and the user's GNSS receiver and the position of each satellite, a floating-point solution of the user's GNSS receiver position is obtained. By directly applying the least squares method (Least-Squares, LS) to the carrier phase observation equation of the satellite observation value (carrier phase observation equation: refers to the equation for calculating the GNSS receiver coordinates using satellite carrier phase observation values ​​(satellite observation values ​​include pseudorange observation values ​​and carrier phase observation values. This equation refers to the known satellite coordinates and the distance obtained based on the carrier phase observation value, and the receiver coordinates are calculated)), a higher-precision floating-point solution to the ambiguity of the carrier phase observation value of each satellite can be obtained. The specific method includes:

[0059] The carrier phase observation equation is expressed as:

[0060] φ=λ -1 (ρ-I+T)+f(δt-δt s )+N+ε

[0061] Where:

[0062]

[0063] Where φ represents the carrier phase observation value at frequency f; λ represents the carrier signal wavelength at frequency f; ρ represents the actual geometric distance between the user's GNSS receiver and the satellite; I represents the ionospheric delay at frequency f; T represents the tropospheric delay; δt represents the user's GNSS receiver clock error; δt s represents the clock error of satellite s; N represents the ambiguity vector of the carrier phase observation value; ε represents the observation noise of the carrier phase value; c represents the speed of signal propagation;

[0064] Before searching and fixing the ambiguity, we first need to ignore the integer characteristics of the ambiguity and solve the floating-point solution of the parameter to be estimated and its covariance matrix. In order to simplify the expression, we need to linearize the carrier phase observation equation, ignore the explicit modeling of errors such as the troposphere and ionosphere, merge it with the clock error term into a parameter vector X, and treat the ambiguity vector N as an independent parameter to obtain the linearized observation equation as shown below:

[0065]

[0066] Where V is the residual vector; A represents the coefficient matrix of the parameter vector X to be estimated (such as position, velocity, attitude clock error, etc.); B represents the coefficient matrix of the ambiguity vector N; C is the free term vector;

[0067] According to the least squares criterion, we have:

[0068] (AX+BN+C)P(AX+BN+C)=min

[0069] Where P is the weight matrix of the observation value; min means minimization, that is, finding the parameters that make the objective function reach the minimum value;

[0070] The corresponding normal equation is:

[0071]

[0072] Simplified to:

[0073]

[0074] Where, represents the floating-point solution of the parameter vector X to be estimated; represents the floating point solution of the ambiguity vector N; T is the transposed sign; where N 11 Representative A T PA, N 12 Representative A T PB, N 21 Representative B T PA, N 22 Representative B T PB, U1 represents -A T PC, U2 represents -B T PA.

[0075] Solving the simplified normal equation above can obtain floating-point solutions for X and N respectively. as well as and The corresponding covariance matrix and and The cross-covariance matrix The corresponding results are as follows:

[0076]

[0077] By applying the above methods, the non-difference method is able to fully preserve the observations.

[0078] In the present invention, all satellites in the GNSS system are divided into a first optimal subset of satellites and a first non-optimal subset of satellites according to an altitude cutoff angle. The floating-point solution of the carrier phase observation ambiguity of the first optimal subset of satellites is resolved using the LAMBDA method, and rounded based on the sequential rounding method. The specific method for obtaining the fixed solution of the carrier phase observation ambiguity of the first optimal subset of satellites includes:

[0079] First, arrange all satellites in the GNSS system in order from low to high according to the altitude cutoff angle. Assume that the initial altitude cutoff angle is A en =A e1 (A e1After all satellites are arranged in order from low to high according to the altitude cutoff angle, the lowest altitude cutoff angle is used to determine the initial first optimal subset satellite, that is, the satellite with the lowest altitude cutoff angle is divided into the first non-optimal subset satellite, and the satellite with an altitude cutoff angle greater than the lowest altitude cutoff angle is divided into the first optimal subset satellite. At this time, the floating-point solution of the ambiguity of the carrier phase observation value of the first optimal subset satellite is efficiently searched and resolved using the LAMBDA method, and rounded based on the sequential rounding method (Bootstrapping) to obtain the fixed solution of the ambiguity of the carrier phase observation value of the first optimal subset satellite. Then, the fixed solution of the ambiguity of the carrier phase observation value of the first optimal subset satellite is tested to determine whether to accept or reject the solution. When the Bootstrapping rounding success rate P is met at the same time, s Exceeds the preset threshold P0, and the reliability test index Ratio is higher than the set threshold R thres And the number of satellites in the first optimal subset shall not be less than the set minimum number of satellites n min When , the division is considered successful, and the fixed solution of the carrier phase observation value ambiguity of the first optimal subset satellite is accepted, and the fixed solutions of the carrier phase observation value ambiguity of the first optimal subset satellite, the first non-optimal subset satellite, and the first optimal subset satellite are obtained;

[0080] Otherwise (i.e., the Bootstrapping rounding success rate P is not satisfied at the same time s Exceeds the preset threshold P0, and the reliability test index Ratio is higher than the set threshold R thres And the number of satellites in the first optimal subset shall not be less than the set minimum number of satellites n min When the first non-optimal subset satellites and the first optimal subset satellites need to be re-divided, the satellites with an altitude cut-off angle greater than the second lowest altitude cut-off angle are divided into the first optimal subset satellites (i.e., set A en =A e2 ), the satellites with an altitude cutoff angle less than or equal to the second-to-last lowest altitude cutoff angle are divided into the first non-optimal subset satellites, and the floating-point solution of the carrier phase observation value ambiguity of the first optimal subset satellites divided at this time is efficiently searched using the LAMBDA method to complete the ambiguity resolution, and rounded based on the sequential rounding method to obtain the fixed solution of the carrier phase observation value ambiguity of the first optimal subset satellites at this time, and then the fixed solution of the carrier phase observation value ambiguity of the first optimal subset satellites at this time is tested to determine whether the above conditions are met at the same time (Bootstrapping rounding success rate P s Exceeds the preset threshold P0, and the reliability test index Ratio is higher than the set threshold R thres And the number of satellites in the first optimal subset shall not be less than the set minimum number of satellites n min) to determine whether to accept or reject the solution, and so on, until all conditions are met (Bootstrapping rounding success rate P s Exceeds the preset threshold P0, and the reliability test index Ratio is higher than the set threshold R thres And the number of satellites in the first optimal subset shall not be less than the set minimum number of satellites n min ) of the first optimal subset of satellites, the first non-optimal subset of satellites, and the fixed solution of the carrier phase observation ambiguities of the first optimal subset of satellites.

[0081] Integer-cycle ambiguity is one of the core challenges of carrier phase observation in satellite navigation positioning. When a receiver measures the carrier phase of a continuous cosine wave carrier signal transmitted by a satellite, the signal itself lacks a period marker. Therefore, during the initial observation, it is impossible to accurately determine which complete carrier cycle the current carrier phase belongs to. This uncertainty arises from integer-cycle ambiguity. Technically, integer-cycle ambiguity is represented by an integer offset superimposed on the cumulative carrier phase change observed by the receiver from the first observation to the current moment. This integer offset remains constant across observations, but it significantly affects the absolute accuracy of the carrier phase observation. To achieve centimeter-level or even millimeter-level positioning accuracy, effective methods must be implemented to accurately estimate and eliminate the impact of integer-cycle ambiguity. When a satellite signal is first acquired, the received signal contains a fractional fraction of a whole cycle and an unknown integer-cycle ambiguity. Subsequently, if the receiver continues to receive satellite signals, at the kth observation epoch, its carrier phase observation will contain the integer-cycle change relative to the first observation, the fractional fraction of a whole cycle, and the persistent unknown integer-cycle ambiguity. Currently, methods for resolving integer ambiguities can be categorized into four main categories. Among them, the LAMBDA method, based on integer least squares estimation within the ambiguity domain, is the most classic. It excels in both efficiency and reliability, making it a widely adopted ambiguity resolution method.

[0082] While traditional ambiguity resolution methods, such as the LAMBDA method, perform well in most situations, their efficiency is significantly limited when processing increasingly complex, multi-frequency, multi-system, high-dimensional data, making it difficult to meet the demands of real-time positioning. Furthermore, partial ambiguity resolution methods improve processing speed and the success rate of ambiguity fixation by only resolving ambiguities for an optimal subset of satellites. However, in obscured environments, the optimal subset may contain insufficient satellites, preventing full utilization of non-optimal subset satellites for positioning. Therefore, the present invention further utilizes this fixed ambiguity information to assist in resolving ambiguities for satellites in the non-optimal subset. This approach effectively increases the number of satellites with successfully fixed ambiguities, thereby improving system availability and positioning accuracy.

[0083] Among them, ambiguity resolution uses the LAMBDA method of ambiguity search within the ambiguity domain. This method has excellent performance in both solution efficiency and solution reliability. The LAMBDA method uses the integer ambiguity covariance matrix to perform Gaussian transformation, combined with Z transform technology, to reduce the correlation between ambiguity parameters, effectively reducing the search space, thereby significantly improving the accuracy and efficiency of the solution. The LAMBDA method performs well in solution efficiency and reliability, making full use of the satellite's double-difference observation information and geometric constraints. Ambiguity resolution based on the LAMBDA method usually includes five steps:

[0084] (1) Ignore the integer nature of the ambiguity and find the floating-point solution of the estimated parameter and its covariance;

[0085] (2) Perform ambiguity down-correlation processing. Considering the floating-point solution of the ambiguity and its covariance matrix, the GNSS double-difference ambiguity is estimated using the least squares method;

[0086] (3) Performing a discrete ambiguity search process. After the correlation reduction process, the covariance matrix is ​​subjected to Cholesky decomposition, followed by an ambiguity search.

[0087] (4) Ambiguity reliability test (reliability test is performed after the ambiguity search to obtain the candidate value closest to the ambiguity integer solution, and the ambiguity is fixed to an integer only after it meets the conditions).

[0088] (5) Convert the corresponding floating-point solution into an integer solution. After passing the ambiguity test, a reverse conversion is required to restore the original integer value of the ambiguity. The floating-point solution of the estimated parameter (user coordinate) is updated to a fixed integer solution using the fixed integer ambiguity (initially, the ambiguity characteristics are ignored. Now that the ambiguity fixed integer solution is obtained, the position fixed integer solution can be obtained as the final positioning to replace the initial position floating-point solution obtained by ignoring the ambiguity integer characteristics).

[0089] Based on this, the ambiguity of the floating-point solution of the first optimal subset satellite carrier phase observation value is resolved using the LAMBDA method, and the fixed solution of the ambiguity of the first optimal subset satellite carrier phase observation value is obtained by rounding based on the sequential rounding method. The specific method includes:

[0090] Ignoring the integer nature of the ambiguity, solve the parameter vector to be estimated and its covariance matrix:

[0091] By directly applying the least squares method (LS) to solve the carrier phase observation equation, we can obtain the floating-point solution of the parameters to be estimated (position, ambiguity), and calculate their corresponding covariance matrix, which can be expressed as:

[0092]

[0093] Perform ambiguity reduction processing:

[0094] At this stage, the least squares method is mainly used to accurately estimate the double-difference ambiguity of the GNSS system. This process is based on the floating-point solution of the ambiguity and its corresponding covariance matrix, which ensures that the estimation results are close to reality while maintaining the accuracy and efficiency of the calculation. The application of the ILS method aims to obtain the optimal ambiguity solution by minimizing the sum of squares of the ambiguity residuals. This lays a solid foundation for further processing of ambiguities and prepares for reducing errors and improving overall positioning accuracy in subsequent steps. In this process, it is necessary to fully consider the characteristics of the whole-cycle ambiguity itself and its relationship with other variables in order to achieve a more comprehensive de-correlation processing. Therefore, based on the principle of minimizing the sum of squared residuals, the ambiguity objective function is defined as follows:

[0095]

[0096] Where, represents the fixed solution of the ambiguity vector N; Z represents the matrix of descending correlation transformation;

[0097] The Z transform is expressed as:

[0098]

[0099] Where z represents the ambiguity vector after Z transformation; Represents the ambiguity floating point solution vector after Z transformation; express covariance matrix of ; Note that if N is an integer vector, then z must also be an integer vector.

[0100] The original least squares problem is transformed into the following new least squares problem by descending correlation:

[0101]

[0102] Where, represents the fixed solution for the ambiguity vector z after the Z-transform. During this process, the ambiguity is first transformed to reduce its correlation with other variables, which is crucial for improving the efficiency and accuracy of the problem solution. This transformation simplifies the originally complex ambiguity estimation problem, making the subsequent integer least squares solution more direct and efficient. The properties of integer vectors ensure the accuracy of information during the transformation process, making the final solution more reliable.

[0103] The search space after descending correlation is expressed as:

[0104]

[0105] Where, γ 2 is the search space threshold; f(z) represents the search space of the ambiguity vector z after down-correlation; Z n represents the n-dimensional Z matrix, where n is the total number of satellites;

[0106] Perform a discrete search of the ambiguity:

[0107] After the reduction in correlation is completed, the covariance matrix is ​​further subjected to the key Cholesky decomposition, and then the ambiguity search is carried out. Cholesky decomposition plays a core role in this step. It transforms the original covariance matrix into a more easily handled form, laying a solid foundation for the subsequent discrete search. This transformation not only significantly improves the search efficiency, but also greatly enhances the accuracy of the search results. As a decisive link in the entire method, the quality of the ambiguity search is directly related to the accuracy of the final solution. Through decomposition, the structure of the covariance matrix is ​​clarified, which provides strong support for more accurate determination and selection of appropriate ambiguity values. The search algorithm efficiently searches for the best matching ambiguity value in the optimized search space, ensuring the high accuracy and high reliability of the final solution. Therefore, it can be said that Cholesky decomposition plays an indispensable bridging role in the entire process of ambiguity processing.

[0108] Covariance matrix after descending correlation Perform Cholesky decomposition, and the covariance matrix after decomposition for:

[0109]

[0110] Where:

[0111] D=diag(d1,d2,…,d n )

[0112]

[0113] Where L represents the lower triangular matrix; D is the diagonal matrix obtained after Cholesky decomposition; d n is the nth diagonal element in the diagonal matrix D; l n1 represents the element in the nth row and the first column of the lower triangular matrix L; l n2 Represents the element in the nth row and second column of the lower triangular matrix L;

[0114] The decomposed covariance matrix Bringing it into the search space after descending correlation, the corresponding search space is updated as follows:

[0115]

[0116] Where z i represents the ambiguity of the i-th satellite after Z transformation; represents the floating point solution of the ambiguity of the i-th satellite after Z transformation; z j represents the ambiguity of the jth satellite after Z transformation; represents the floating point solution of the ambiguity of the jth satellite after Z transformation; l ji represents the lower triangular element with subscript ji in the lower triangular matrix L; d i is the i-th diagonal element in the diagonal matrix D;

[0117] set up is the conditional valuation, which means is Determine the valuation under the conditions and set Is the conditional variance, then the conditional valuation is:

[0118]

[0119] The search space is simplified to:

[0120]

[0121] The sequential rounding method is used in the ambiguity search. First, the ambiguity value of the previous level is determined. Then, it is used as a benchmark to construct the search range of the next level of ambiguity. In this process, the search range of the n-th satellite ambiguity is first determined, then the search range of the next level of ambiguity is determined in sequence, and finally the search range of the ambiguity of the first satellite is determined. And so on. The boundaries of each level of ambiguity search are determined as follows:

[0122]

[0123] Where, represents the ambiguity conditional variance of the last satellite; represents the ambiguity conditional variance of the j-th satellite; represents the ambiguity conditional variance of the i-th satellite; represents the ambiguity conditional variance of the first satellite; z n Indicates the ambiguity of the last satellite after Z transformation; It represents the floating point solution of the ambiguity of the last satellite after Z transformation; z1 represents the ambiguity of the first satellite after Z transformation; Represents the floating-point solution of the ambiguity of the first satellite after Z transformation;

[0124] To quantify reliability, the present invention uses a Ratio test for reliability verification. This test is performed by calculating the ratio of the residual sum of squares of the suboptimal integer solution to the residual sum of squares of the optimal integer solution. This test assesses the closeness of the floating-point solution to the optimal solution, thereby accurately evaluating the quality of the rounded ambiguity. If this ratio is sufficiently small, it means that the optimal solution sought is very close to the true value, that is, the solution has a high reliability. This test is crucial to ensuring the overall performance of the method. It not only helps identify the optimal ambiguity resolution solution, but also ensures the reliability and stability of this solution in practical applications. Therefore, the Ratio test is an indispensable part of the entire ambiguity processing process.

[0125] Ratio detection is expressed as:

[0126]

[0127] Where Ratio is a value greater than 1. is closest Candidate values ​​for This time close Candidate value of; empirical threshold R thres Generally, it is set to 1.5, 2 and 3. When the Ratio value exceeds the set threshold R thres When , it indicates that the obtained optimal solution has high reliability. Therefore, the optimal solution is considered to be the correct solution.

[0128] The reliability test of fuzziness is a key step to ensure the accuracy of solution. Among them, Ratio test plays an important role as a quantitative evaluation method. The core of this method is to calculate the suboptimal integer solution. The residual sum of squares and the optimal integer solution The ratio of the residual sum of squares is used to evaluate the closeness between the suboptimal solution and the optimal solution, thereby reflecting the quality of the rounded integer ambiguity.

[0129] After the ambiguity test, an inverse transform is performed to recover the ambiguity fixed solution of the non-Z-transformed carrier phase observation value. The inverse transform process is:

[0130]

[0131] Once the integer ambiguity is resolved, the floating point solution of the parameter to be estimated needs to be updated to a fixed integer solution. and its covariance matrix Expressed as:

[0132]

[0133] Bootstrapping rounding success rate P sThe calculation method is:

[0134]

[0135] Where, is the floating point solution (real number solution) of the i-th ambiguity parameter; is the real integer value of the i-th ambiguity parameter; Indicates the floating point solution of the i-th ambiguity parameter The variance of (diagonal elements of the covariance matrix); Φ(·) represents the cumulative distribution function of the standard normal distribution, which represents the probability that the error is less than a certain threshold.

[0136] In a specific implementation manner, the preset threshold value P0 is set to 99.9% in the embodiment of the present invention, and R thres is 3.0, n min 4 (at least four satellites are needed to accurately calculate the three-dimensional coordinates of the satellite).

[0137] Furthermore, the present invention proposes a modified partial ambiguity resolution method for satellite positioning, aiming to more fully utilize observation data from all available satellites. This strategy first uses the PAR method to determine an optimal subset of satellites and successfully fix their ambiguities. Subsequently, this fixed ambiguity information is used to assist in resolving ambiguities for satellites in the non-optimal subset, effectively increasing the number of satellites with successfully fixed ambiguities, thereby improving system availability and positioning accuracy. Specifically, this strategy enhances the ability to resolve ambiguities for satellites in the non-optimal subset by introducing additional observation information and constraints. This not only allows for the effective utilization of observation values ​​from more satellites, but also further enhances overall positioning performance.

[0138] At the same time, a floating-point solution is proposed to use the fixed ambiguity information of the first optimal subset of satellites to assist the ambiguity of the carrier phase observation value of the first non-optimal subset of satellites. and its covariance matrix This method helps more satellite ambiguities be successfully fixed to integers. It performs partial ambiguity resolution on a non-optimal subset and applies specific criteria to verify the correctness of the integer ambiguities. The resulting integer ambiguity fixation solution is then achieved.

[0139] Therefore, specifically, in the present invention, the floating-point solution of the first non-optimal subset satellite ambiguity is corrected using the fixed solution of the first optimal subset satellite carrier phase observation ambiguity (the correction is intended to enable more satellite carrier phase observation ambiguities to be successfully fixed to integers). The specific process of obtaining the corrected floating-point solution of the first non-optimal subset satellite ambiguity includes:

[0140]

[0141] Where, represents the floating-point solution to the ambiguity of the first non-optimal subset of satellite carrier phase observations; yes The covariance matrix of represents the floating-point solution to the ambiguity of the first best subset of satellite carrier phase observations; represents the fixed solution of the ambiguity of the first optimal subset of satellite carrier phase observations; express and The cross-covariance matrix of ; Indicates The covariance matrix of express The covariance matrix of represents the float solution of the corrected ambiguity of the first non-optimal subset of satellite carrier phase observations; express The covariance matrix of

[0142] After obtaining the floating-point solution of the corrected first non-optimal subset satellite carrier phase observation ambiguity through the above formula, the LAMBDA method is used to perform partial ambiguity resolution on the floating-point solution of the carrier phase observation ambiguity of this part of the carrier phase observation, and verify whether the integer ambiguity is correct, and obtain the fixed solution of the carrier phase observation ambiguity of the second optimal subset satellite. Finally, the fixed solution of the carrier phase observation ambiguity of the first optimal subset satellite is combined with the fixed solution of the carrier phase observation ambiguity of the first optimal subset satellite. The fixed solution to the ambiguity of the entire set of carrier phase observations is obtained as:

[0143]

[0144] Where, represents the ambiguity fixed solution of the carrier phase observations of the second optimal subset obtained by partial ambiguity resolution of the modified first non-optimal subset;

[0145] Update using the above formula and Will Updated to Get the final and its covariance matrix Expressed as:

[0146]

[0147] Since the appropriate first non-optimal subset satellites and first optimal subset satellites have been successfully divided in the previous steps, the altitude cutoff angles of the two subset satellites have been arranged in order of size, and the divided first optimal subset satellites have also been tested and meet the requirements. The revised first non-optimal subset satellites can be further divided into the second optimal subset satellites and the second non-optimal subset satellites can be directly divided according to the size of the altitude cutoff angle. Preferably, the altitude cutoff angle for division is set to 20-30°. Among the revised first non-optimal subset satellites, those with an altitude cutoff angle greater than this benchmark are divided into the second optimal subset satellites, and those less than or equal to this benchmark are divided into the second non-optimal subset satellites.

[0148] In a specific embodiment of the present invention, the altitude cutoff angle for division is set to 30°. Among the corrected first non-optimal subset satellites, those with an altitude cutoff angle greater than 30° are divided into the second optimal subset satellites, and those with an altitude cutoff angle less than or equal to 30° are divided into the second non-optimal subset satellites.

[0149] The ambiguity of the floating-point solution of the second-best subset satellite carrier phase observation value is resolved using the LAMBDA method, and rounded based on the sequential rounding method to obtain the fixed solution of the ambiguity of the second-best subset satellite carrier phase observation value. The specific process includes:

[0150] Perform down-correlation processing on the ambiguity of the second optimal subset satellite carrier phase observation value:

[0151] Based on the principle of minimum residual sum of squares, the fuzzy objective function is defined as follows:

[0152]

[0153] Where N 2P represents the ambiguity vector after correction of the first non-optimal subset satellite; Z 2P A matrix representing the descending correlation transformation of the second best subset of satellites;

[0154] The Z transform is expressed as:

[0155]

[0156] Where z 2P represents the ambiguity after the ambiguity conversion of the second best subset satellite carrier phase observation value; represents the floating-point solution to the ambiguity of the second best subset of satellite carrier phase observations; express The covariance matrix of express The covariance matrix of

[0157] After decorrelation processing, the original least square problem is converted to the following new least square problem:

[0158]

[0159] wherein, represents the fixed ambiguity vector of the second optimal subset satellite after Z transformation;

[0160] The search space after decorrelation is represented as:

[0161]

[0162] wherein, f(z 2P ) represents the search space of the ambiguity vector z of the second optimal subset satellite after decorrelation; represents the n 2P -dimensional Z 2P matrix, wherein n 2P represents the total number of the second optimal subset satellites;

[0163] The discrete search process of the ambiguity is performed as follows:

[0164] The covariance matrix of the float solution of the ambiguity of the carrier phase observation of the second optimal subset satellite is subjected to Cholesky decomposition, and the decomposed carrier phase observation ambiguity covariance matrix of the second optimal subset satellite is:

[0165]

[0166] wherein:

[0167]

[0168] wherein, is the nth 2P diagonal element in the decomposed diagonal matrix D 2P of the second optimal subset satellite; represents the element in the 1st column of the nth 2P row in the lower triangular matrix L 2P of the second optimal subset satellite; represents the element in the 2nd column of the nth 2P row in the lower triangular matrix L 2Pi of the second optimal subset satellite;

[0169] The decomposed carrier phase observation ambiguity covariance matrix of the second optimal subset satellite is brought into the search space after decorrelation, and the corresponding search space is updated as:

[0170]

[0171] Where, d 2Pi is a diagonal matrix D 2P The 2Pith diagonal element in z 2Pi represents the ambiguity of the 2Pi satellite in the second best subset of satellites after Z transformation, represents the floating point solution of the ambiguity of the 2Pi satellite in the second best subset of satellites after Z transformation; l 2Pji The lower triangular matrix L represents the second best subset of satellites 2P The lower triangular elements with subscript ji; z 2Pj represents the ambiguity of the 2Pjth satellite in the second best subset of satellites after Z transformation, represents the floating-point solution of the ambiguity of the 2Pjth satellite in the second best subset of satellites after Z transformation;

[0172] set up is the conditional estimate of the second best subset of satellites, indicating is Determine the valuation under the conditions and set Is the conditional variance, then the conditional valuation is:

[0173]

[0174] The search space is simplified to:

[0175]

[0176] In the fuzzy search, the sequential rounding method is used. First, the fuzzy value of the previous level is determined, and then the search range of the next level of fuzzy is constructed based on this value. In this process, the nth level is first determined. 2P The search range of the satellite ambiguity is determined first, and then the search range of the next level of ambiguity is determined in turn. Finally, the search range of the ambiguity of the first satellite is determined, and so on. The boundaries of each level of ambiguity search are determined as follows:

[0177]

[0178] Where, represents the ambiguity conditional variance of the last satellite in the second best subset of satellites; represents the ambiguity conditional variance of the i-th satellite in the second optimal subset of satellites; represents the ambiguity conditional variance of the jth satellite in the second optimal subset of satellites; represents the ambiguity conditional variance of the first satellite in the second optimal subset of satellites; represents the ambiguity of the last satellite in the second best subset of satellites after Z transformation; represents the floating point solution of the ambiguity of the last satellite in the second best subset of satellites after Z transformation; 2P1 represents the ambiguity of the first satellite in the second best subset of satellites after Z transformation; It represents the floating point solution of the ambiguity of the first satellite in the second best subset of satellites after Z transformation;

[0179] Ratio detection is used to test the reliability of fuzziness:

[0180] Ratio detection is expressed as:

[0181]

[0182] Where, is the closest Candidate values ​​for This time close candidate value of .

[0183] After the fuzziness test, the reverse transformation is performed to restore the original value of the fuzziness. The restoration process is:

[0184]

[0185] In obscured environments, the accuracy of floating-point ambiguity solutions and observations is a key factor limiting improvements in ambiguity resolution performance. This method uses high-precision combined positioning to correct INS errors in real time. The corrected user INS position is used as a priori information to obtain floating-point ambiguity solutions, replacing the pseudorange positions of the original observations. This method improves the accuracy of floating-point ambiguity solutions and ensures system reliability in obscured environments. Furthermore, the proposed modified partial ambiguity resolution method aims to more fully utilize observation data from all available satellites. This strategy first uses the partial ambiguity resolution method to identify an optimal subset of satellites and successfully fix their ambiguities. This fixed ambiguity information is then used to assist in resolving ambiguities for satellites in the non-optimal subset. This method effectively increases the number of satellites with successfully fixed ambiguities, thereby improving system availability and positioning accuracy. Specifically, this strategy enhances the ambiguity resolution capability for satellites in the non-optimal subset by introducing additional observation information and constraints. This not only enables the effective utilization of observations from more satellites but also further improves overall positioning performance. This method increases the number of satellites with successfully fixed ambiguities, thereby improving positioning accuracy.

[0186] The realization of INS-assisted floating-point solutions to satellite ambiguity depends on the deep fusion of GNSS and INS data. Through methods such as the extended Kalman filter, the information from the two navigation systems can be effectively integrated, thereby improving the accuracy and stability of the floating-point solutions. The auxiliary role of INS becomes particularly important when GNSS signals are blocked or interrupted, ensuring navigation continuity and accuracy. This is particularly true in urban environments with multiple obstructions. This fusion method has significant research significance and application value for achieving fast, high-precision positioning.

[0187] In GNSS / INS integrated navigation, the EKF (Extended Kernel Calculation) (EKF) is highly favored for its simplicity, ease of implementation, and low computational complexity. In GNSS / INS integrated navigation, the standard EKF is typically used to fuse observation data from satellite navigation systems and inertial sensors to provide continuous and accurate navigation information. Specifically, the standard EKF's nonlinear discrete dynamic system state model consists of observation equations and state transition equations.

[0188] Preferably, the INS-assisted modified partial ambiguity resolution method is used to perform a tightly coupled GNSS / INS combined positioning solution on the fixed solution of the first optimal subset satellite carrier phase observation ambiguity, the fixed solution of the second optimal subset satellite carrier phase observation ambiguity, and the user's GNSS receiver position. The specific process of obtaining the user position includes:

[0189] In the GNSS / INS combined system, the nonlinear discrete model of the extended Kalman filter method is:

[0190]

[0191] Where, X k represents the parameter vector to be estimated at the kth epoch of the dynamic system, X k-1 represents the parameter vector to be estimated at the k-1th epoch of the dynamic system; F k / k-1 Refers to the discrete-time state transfer matrix of the kth epoch; Z k represents the noise observation vector of the kth epoch; H k It's X k-1 The measurement transfer matrix; w k-1 represents the k-1th epoch motion noise sequence with zero mean; ε k represents the observation noise sequence with zero mean at the kth epoch;

[0192] For the nonlinear system outlined in the above equation, state prediction and measurement update are two key steps. The standard extended Kalman filter method follows the following processing sequence:

[0193] initialization:

[0194] Initial state estimate of the filtering process and its corresponding covariance for:

[0195]

[0196] Where X0 represents the initial state value of the filtering process; E[X0] represents the covariance operation of X0; express Covariance operation of ;

[0197] Status prediction:

[0198]

[0199] Where, Represents X k-1 The predicted value of P k-1 Represents X k-1 The system covariance matrix of represents the predicted state vector; Represents the predicted state vector The covariance of Q k-1 represents the motion noise covariance of the k-1th epoch;

[0200] Measurement Update:

[0201] The calculation for making observation predictions in a nonlinear measurement model is as follows:

[0202]

[0203] Where, represents observation prediction;

[0204] represents the noise observation vector Z k The innovation vector of the difference between the measured value and its predicted value in the nonlinear measurement model and its covariance matrix Updated to:

[0205]

[0206] Where R k Represents ε k The covariance matrix of

[0207] Filter gain update:

[0208] The filter gain is mathematically defined as follows:

[0209]

[0210] Where K k represents the filter gain; express The inverse matrix of

[0211] The user's location estimate is obtained through the following process

[0212]

[0213] Each sample was processed according to the above process.

[0214] The final user position obtained by the above operation is the precise positioning of the user in the current epoch. When determining the user position of the next epoch, the user position of the current epoch is taken as the position in the navigation coordinate system and entered into the INS error model, and the calculation is performed cyclically according to the solution of the present invention.

[0215] In the technical solution of the present invention, the implementation of INS-assisted acquisition of satellite ambiguity floating-point solutions relies on the deep fusion of GNSS and INS data. By using methods such as extended Kalman filtering, the information of the two navigation systems can be effectively fused, thereby improving the accuracy and stability of the ambiguity floating-point solution. When the GNSS signal is blocked or interrupted, the auxiliary role of INS becomes particularly important. It can ensure the continuity and accuracy of navigation, especially in urban environments with multiple obstructions. This fusion method has significant research significance and application value for achieving fast and high-precision positioning.

[0216] Figure 5 This comparative evaluation of positioning errors among five methods on the Xuzhou dataset comprehensively demonstrates the position error comparisons of the five GNSS / INS integrated positioning ambiguity resolution methods in the east, north, and up directions on the Xuzhou dataset. In-depth analysis shows that the EKF CIA-MPAR method demonstrates significant advantages in all directions, with minimal error fluctuation and the highest positioning accuracy and stability. In the east and north directions, this method maintains an error within 0.2 meters for the majority of the time, with much less fluctuation than the other methods. In contrast, the FGO PAR and EKF TIA-PAR methods exhibit larger error fluctuations during certain periods, indicating lower positioning accuracy in certain situations. Despite a slightly larger overall error in the up direction, the EKF CIA-MPAR method also achieves the lowest error in this direction, remaining within 0.1 meters for the majority of the time, further demonstrating its high-precision performance in all directions. Overall, the EKF CIA-MPAR method achieves the lowest positioning error in all directions on the Xuzhou dataset, demonstrating the best overall performance.

[0217] Figure 6This figure compares the root mean square error (RMSE) of five positioning methods in the Xuzhou dataset, analyzing the positioning results in the east, north, and up directions for the five GNSS / INS integrated positioning methods in the Xuzhou dataset. In the east direction, the RMSE of all methods is within 5 cm, with the EKF CIA-MPAR method performing particularly well, achieving the lowest RMSE value, demonstrating high accuracy and good stability in this direction. In the north direction, while the RMSE is generally higher than in the east direction, the EKF CIA-MPAR and EKF CIA-PAR methods still exhibit low error levels, further validating their excellent performance. Other methods, particularly FGO PAR, exhibit relatively high RMSE in the north direction, reflecting their limitations in north-direction positioning. In the up direction, the overall RMSE of all methods is high, but the EKF CIA-MPAR method maintains the lowest RMSE, significantly outperforming the other methods, further demonstrating its high-precision positioning capability in all directions. In summary, the EKF CIA-MPAR method shows the best overall performance on the Xuzhou dataset.

[0218] The ambiguity resolution performance of five positioning methods for the Xuzhou dataset is evaluated. The positioning performance evaluation results for 784 epochs in the dataset are presented. As shown in Table 1, when using GNSS alone, 765 epochs were successfully positioned. Using an integrated GNSS / INS system significantly improved positioning performance, increasing the number of successfully positioned epochs to 782, with only two remaining unpositioned epochs. This demonstrates that the GNSS / INS system offers a significant positioning advantage over GNSS alone in open urban environments. Further analysis of the data in Table 1 shows that all GNSS / INS integrated methods achieved near-perfect positioning success rates, with nearly all epochs successfully positioned, strongly validating the effectiveness of the integrated system. Specifically, the CIA-PAR and CIA-MPAR methods achieved fix success rates of 99.6% and 99.9%, respectively, significantly outperforming the other methods. These two methods demonstrate significant advantages in positioning accuracy, stability, and reliability. In terms of solution time, the INS-assisted TIA-PAR, CIA-PAR, and CIA-MPAR methods demonstrate higher efficiency, showing some advantages over the EKF PAR and FGO PAR methods. Although the efficiency differences between the various INS-assisted methods are subtle, they are still crucial for practical applications.

[0219] Table 1

[0220]

[0221] The present invention uses the combined positioning results of the tightly coupled GNSS / INS system to correct INS errors in real time, dynamically detects and eliminates pseudorange outliers based on residual analysis, and adopts a preferred fixing strategy for non-optimal ambiguity subsets. This solves the problems of low accuracy of ambiguity floating-point solutions, insufficient success rate of integer ambiguity fixation, and decreased positioning accuracy caused by unstable GNSS signals in urban occlusion environments, thereby achieving high-precision positioning from centimeter to sub-meter levels.

[0222] Traditional methods rely on pseudorange observations to obtain floating-point ambiguity solutions. Their accuracy is limited by pseudorange noise and multipath effects, and the success rate of ambiguity fixation is significantly reduced when satellite signals are partially obscured. This method uses high-precision tightly coupled GNSS / INS positioning results to correct INS errors in real time. The corrected INS positions are used to calculate the distances between the satellite and the user, replacing the GNSS pseudoranges, significantly improving the accuracy of floating-point ambiguity solutions. Furthermore, an improved partial ambiguity resolution strategy is proposed. This strategy selects an optimal subset of satellites to fix integer ambiguities and uses the resulting resolution to assist a suboptimal subset, expanding the number of satellites for which ambiguities can be fixed. Furthermore, by combining the residual information between the INS predicted pseudoranges and the GNSS observed pseudoranges, a dynamic gross error detection and rejection mechanism is designed to effectively eliminate the interference of anomalous observations on the solution process. Experimental results show that this method improves the success rate of ambiguity fixation by over 30% in scenarios with insufficient satellites or intermittent signal obstruction. The three-dimensional positioning accuracy of the GNSS / INS combined system is better than 3 cm, and the solution efficiency is 40% higher than that of the traditional LAMBDA algorithm. This method is suitable for fields such as autonomous driving, drone navigation and urban mobile mapping, and has the characteristics of strong robustness and high real-time performance.

[0223] Furthermore, the potential for integrating emerging technologies such as visual sensors, lidar, high-precision maps, and ultra-wideband with GNSS / INS is gradually emerging, enabling environmental awareness in complex scenarios. This invention, combined with multi-sensor fusion, could further overcome positioning bottlenecks in extreme scenarios like urban canyons and high-rise building clusters, driving the development of high-precision navigation towards multi-source collaboration.

[0224] Example 2

[0225] like Figure 7 The INS-assisted positioning method in the GNSS / INS positioning system shown includes: using the corrected user INS position to calculate the distance between the INS position and each satellite, and using the distance as the predicted pseudorange between each satellite and the user GNSS receiver;

[0226] Based on the predicted pseudorange between each satellite and the user's GNSS receiver and the position of each satellite, a floating-point solution for the user's GNSS receiver position is obtained. The carrier phase observation equation of the satellite observation value is solved by the least squares method to obtain a floating-point solution for the ambiguity of the carrier phase observation value of each satellite.

[0227] All satellites in the GNSS system are divided into the first optimal subset of satellites and the first non-optimal subset of satellites according to the altitude cutoff angle. The ambiguity of the carrier phase observation values ​​of the first optimal subset of satellites is resolved using the LAMBDA method to obtain the fixed solution of the carrier phase observation ambiguity of the first optimal subset of satellites.

[0228] The floating-point solutions of the carrier phase observation values ​​of the first non-optimal subset satellites are corrected using the fixed solutions of the ambiguities of the carrier phase observation values ​​of the first optimal subset satellites to obtain the corrected floating-point solutions of the carrier phase observation values ​​of the first non-optimal subset satellites, thereby obtaining the corrected first non-optimal subset satellites. The corrected first non-optimal subset satellites are divided into the second optimal subset satellites and the second non-optimal subset satellites according to the size of the altitude cutoff angle, and the floating-point solutions of the carrier phase observation values ​​of the second optimal subset satellites are ambiguity resolved using the LAMBDA method to obtain the fixed solutions of the carrier phase observation values ​​of the second optimal subset satellites.

[0229] Using the INS-assisted corrected partial ambiguity resolution method, a tightly coupled GNSS / INS combined positioning solution is performed on the fixed solutions of the first optimal subset satellite carrier phase observation ambiguities, the fixed solutions of the second optimal subset satellite carrier phase observation ambiguities, and the user's GNSS receiver position to obtain the user position.

[0230] Example 3

[0231] A computer-readable storage medium stores a computer program, wherein the computer program implements the steps of the method in Example 2 when executed by a processor.

[0232] It should be understood that parts not elaborated in detail in this specification belong to the prior art.

[0233] The preferred embodiments of the present invention have been described in detail above, but the present invention is not limited thereto. Within the technical concept of the present invention, various simple variations of the technical solution of the present invention may be made, including combining the various technical features in any other appropriate manner. These simple variations and combinations should also be regarded as disclosed in the present invention and fall within the scope of protection of the present invention.

Claims

1. An INS-assisted positioning system under a GNSS / INS positioning system, characterized in that: include: The predicted pseudorange confirmation module is used to calculate the distance between the INS position and each satellite using the corrected user's INS position, and use it as the predicted pseudorange between each satellite and the user's GNSS receiver; The floating-point solution calculation module is used to obtain the floating-point solution of the user's GNSS receiver position based on the predicted pseudorange between each satellite and the user's GNSS receiver and the position of each satellite, and solve the carrier phase observation equation of the satellite observation value by the least squares method to obtain the floating-point solution of the ambiguity of the carrier phase observation value of each satellite; The first optimal fixed solution calculation module is used to divide all satellites in the GNSS system into a first optimal subset of satellites and a first non-optimal subset of satellites according to the altitude cutoff angle, and use the LAMBDA method to complete the ambiguity resolution of the floating-point solution of the carrier phase observation value ambiguity of the first optimal subset of satellites to obtain the fixed solution of the carrier phase observation ambiguity of the first optimal subset of satellites; The second optimal fixed solution calculation module is used to use the fixed solution of the first optimal subset satellite carrier phase observation ambiguity to correct the floating-point solution of the first non-optimal subset satellite carrier phase observation ambiguity, thereby obtaining a corrected floating-point solution of the first non-optimal subset satellite carrier phase observation ambiguity, thereby obtaining a corrected first non-optimal subset satellite, dividing the corrected first non-optimal subset satellite into a second optimal subset satellite and a second non-optimal subset satellite according to the size of the altitude cutoff angle, and using the LAMBDA method to complete ambiguity resolution on the floating-point solution of the second optimal subset satellite carrier phase observation ambiguity, thereby obtaining a fixed solution of the second optimal subset satellite carrier phase observation ambiguity; The fusion solution module is used to perform a tightly coupled GNSS / INS combined positioning solution on the fixed solution of the first optimal subset satellite carrier phase observation ambiguity, the fixed solution of the second optimal subset satellite carrier phase observation ambiguity, and the user's GNSS receiver position using the INS-assisted corrected partial ambiguity resolution method to obtain the user position.

2. The INS-assisted positioning system under the GNSS / INS positioning system according to claim 1, characterized in that: An INS error model is established based on the PHI model, and the user's INS position is corrected in real time according to the INS error model to obtain the corrected user's INS position; The expression of INS error model based on PHI model is: Where, Indicated in the navigation coordinate system ψ n PHI angular error rate; Represents the position δr in the navigation coordinate system n PHI angular error rate; Indicates δv in the navigation coordinate system n PHI angular error rate; ψ n for The attitude error component of δr n for Position error component; δv n for The velocity error component of Represents the angular velocity of the navigation coordinate system relative to the inertial coordinate system; for PHI angular error rate; represents the user's angular velocity relative to the Earth, for PHI angular error rate; represents the angular velocity of the Earth's rotation, for PHI angular error rate; represents the rotation matrix; f b represents the specific force measured in the carrier coordinate system; δg n Represents the local gravity anomaly in the navigation coordinate system; b g represents the output error of the gyroscope; b a represents the output error of the accelerometer; δθ represents the rotation vector representing the deviation between the rotated coordinate system and the actual navigation coordinate system; v n Indicates the user speed in the navigation coordinate system; The process of real-time correction of the user's INS position according to the INS error model is as follows: X CIk =X Ik -(X k-1 -X CI(k-1) ),k=1,2,3… Where k represents the kth epoch; X Ik represents the original INS position of the user in the kth epoch; X CIk represents the corrected user's INS position in the kth epoch; X k-1 represents the user position in the k-1th epoch; X CI(k-1) represents the corrected user's INS position in the k-1th epoch; The corrected user's INS position X in the kth epoch CIk is represented as: X CIk =(x CIk ,y CIk ,z CIk ) Where x CIk The x-axis represents the user's INS position after correction in the navigation coordinate system; y CIk The y-axis represents the user's INS position after correction in the navigation coordinate system; z CIk The z-axis represents the user's INS position after correction in the navigation coordinate system; The distance between the INS position and each satellite is calculated using the corrected user INS position, and is used as the predicted pseudorange between each satellite and the user GNSS receiver to replace the original GNSS pseudorange. The predicted pseudorange is calculated as follows: Where, represents the predicted pseudorange between each satellite and the user's GNSS receiver; x s The x-axis represents the satellite position in the navigation coordinate system; the y-axis represents the satellite position in the navigation coordinate system; s The y-axis represents the satellite position in the navigation coordinate system; z s Indicates the z-axis of the satellite position in the navigation coordinate system.

3. The INS-assisted positioning system under the GNSS / INS positioning system according to claim 1 or 2, characterized in that: Based on the predicted pseudorange between each satellite and the user's GNSS receiver and the position of each satellite, a floating-point solution for the user's GNSS receiver position is obtained. The carrier phase observation equation of the satellite observation value is solved by the least squares method to obtain a floating-point solution for the ambiguity of the carrier phase observation value of each satellite. The specific method includes: The carrier phase observation equation is expressed as: f = l -1 (ρ-I+T)+f(δt-δt s )+N+e Where: Where φ represents the carrier phase observation value at frequency f; λ represents the carrier signal wavelength at frequency f; ρ represents the actual geometric distance between the user's GNSS receiver and the satellite; I represents the ionospheric delay at frequency f; T represents the tropospheric delay; δt represents the user's GNSS receiver clock error; δt s represents the clock error of satellite s; N represents the ambiguity vector of the carrier phase observation value; ε represents the observation noise of the carrier phase value; c represents the speed of signal propagation; Before searching and fixing the ambiguity, we first need to ignore the integer characteristics of the ambiguity and solve the floating-point solution of the parameter to be estimated and its covariance matrix. In order to simplify the expression, we need to linearize the carrier phase observation equation to obtain the linearized observation equation as shown below: Where V is the residual vector; A represents the coefficient matrix of the estimated parameter vector X; B represents the coefficient matrix of the ambiguity vector N; C is the free term vector; According to the least squares criterion, we have: (AX+BN+C)P(AX+BN+C)=min Where P is the weight matrix of the observation value; min means minimization; The corresponding normal equation is: Simplified to: Where, represents the floating-point solution of the parameter vector X to be estimated; represents the floating-point solution of the ambiguity vector N; T is the transposed sign; Solving the simplified normal equation above can obtain floating-point solutions for X and N respectively. as well as and The corresponding covariance matrix and and The cross-covariance matrix The corresponding results are as follows:

4. The INS-assisted positioning system under the GNSS / INS positioning system according to claim 1, characterized in that: All satellites in the GNSS system are divided into the first optimal subset satellites and the first non-optimal subset satellites according to the altitude cutoff angle. The ambiguity of the floating-point solution of the carrier phase observation value of the first optimal subset satellites is resolved using the LAMBDA method. The ambiguity is then rounded based on the sequential rounding method. The specific method for obtaining the fixed solution of the ambiguity of the carrier phase observation value of the first optimal subset satellites includes the following: First, all satellites in the GNSS system are arranged in order from low to high according to the altitude cut-off angle. The satellite with the lowest altitude cut-off angle is divided into the first non-optimal subset satellite, and the satellite with an altitude cut-off angle greater than the lowest altitude cut-off angle is divided into the first optimal subset satellite. At this time, the ambiguity of the floating-point solution of the carrier phase observation value of the first optimal subset satellite is resolved using the LAMBDA method, and rounded based on the sequential rounding method to obtain the fixed solution of the ambiguity of the carrier phase observation value of the first optimal subset satellite. Then, the fixed solution of the carrier phase observation value ambiguity of the first optimal subset satellite is tested. When the Bootstrapping rounding success rate P is met at the same time, the fixed solution of the carrier phase observation value ambiguity of the first optimal subset satellite is tested. s Exceeds the preset threshold P0, and the reliability test index Ratio is higher than the set threshold R thres And the number of satellites in the first optimal subset is not less than the set minimum number of satellites n min When , the division is considered successful, and the fixed solutions of the carrier phase observation ambiguities of the first optimal subset satellites, the first non-optimal subset satellites, and the first optimal subset satellites are obtained. Otherwise, the satellites with an altitude cutoff angle greater than the second-to-last lowest altitude cutoff angle are divided into the first optimal subset satellites, and the satellites with an altitude cutoff angle less than or equal to the second-to-last lowest altitude cutoff angle are divided into the first non-optimal subset satellites. The LAMBDA method is continued to be used to complete the ambiguity resolution of the floating-point solution of the carrier phase observation ambiguity of the first optimal subset satellites at this time, and rounded based on the sequential rounding method to obtain the fixed solution of the carrier phase observation ambiguity of the first optimal subset satellites at this time. The fixed solution of the carrier phase observation ambiguity of the first optimal subset satellites at this time is then tested to determine whether the above conditions are met at the same time. This is deduced again until the fixed solutions of the carrier phase observation ambiguities of the first optimal subset satellites, the first non-optimal subset satellites, and the first optimal subset satellites that meet the conditions are obtained.

5. The INS-assisted positioning system under the GNSS / INS positioning system according to claim 4, characterized in that: The ambiguity of the floating-point solution of the first optimal subset satellite carrier phase observation value is resolved using the LAMBDA method, and the fixed solution of the ambiguity of the first optimal subset satellite carrier phase observation value is obtained by rounding based on the sequential rounding method. The specific method includes: Ignoring the integer nature of the ambiguity, solve the parameter vector to be estimated and its covariance matrix: Perform ambiguity down-correlation processing: Based on the principle of minimum residual sum of squares, the fuzzy objective function is defined as follows: Where, represents the fixed solution of the ambiguity vector N; Z represents the matrix of descending correlation transformation; The Z transform is expressed as: z=Z T N Where z represents the ambiguity vector after Z transformation; Represents the ambiguity floating point solution vector after Z transformation; express The covariance matrix of The original least squares problem is transformed into the following new least squares problem by descending correlation: Where, represents the fixed solution of the ambiguity vector z after Z transformation; The search space after descending correlation is expressed as: Where, γ 2 is the search space threshold; f(z) represents the search space of the ambiguity vector z after down-correlation; Z n represents the n-dimensional Z matrix, where n is the total number of satellites; Perform a discrete search of the ambiguity: Covariance matrix after descending correlation Perform Cholesky decomposition, and the covariance matrix after decomposition for: Where: D=diag(d1,d2,…,d n ) Where L represents the lower triangular matrix; D is the diagonal matrix obtained after Cholesky decomposition; d n is the nth diagonal element in the diagonal matrix D; l n1 represents the element in the nth row and the first column of the lower triangular matrix L; l n2 Represents the element in the nth row and second column of the lower triangular matrix L; The decomposed covariance matrix Bringing it into the search space after descending correlation, the corresponding search space is updated as follows: Where z i represents the ambiguity of the i-th satellite after Z transformation; represents the floating point solution of the ambiguity of the i-th satellite after Z transformation; z j represents the ambiguity of the jth satellite after Z transformation; represents the floating point solution of the ambiguity of the jth satellite after Z transformation; l ji represents the lower triangular element with subscript ji in the lower triangular matrix L; d i is the i-th diagonal element in the diagonal matrix D; set up is the conditional valuation, which means is Determine the valuation under the conditions and set Is the conditional variance, then the conditional valuation is: The search space is simplified to: The sequential rounding method is used in the ambiguity search. First, the ambiguity value of the previous level is determined. Then, it is used as a benchmark to construct the search range of the next level of ambiguity. In this process, the search range of the n-th satellite ambiguity is first determined, then the search range of the next level of ambiguity is determined in sequence, and finally the search range of the ambiguity of the first satellite is determined. And so on. The boundaries of each level of ambiguity search are determined as follows: Where, represents the ambiguity conditional variance of the last satellite; represents the ambiguity conditional variance of the j-th satellite; represents the ambiguity conditional variance of the i-th satellite; represents the ambiguity conditional variance of the first satellite; z n Indicates the ambiguity of the last satellite after Z transformation; It represents the floating point solution of the ambiguity of the last satellite after Z transformation; z1 represents the ambiguity of the first satellite after Z transformation; Represents the floating-point solution of the ambiguity of the first satellite after Z transformation; Ratio detection is used to test the reliability of fuzziness: Ratio detection is expressed as: Where Ratio is a value greater than 1. is closest Candidate values ​​for This time close Candidate values ​​for After the ambiguity test, an inverse transform is performed to recover the ambiguity fixed solution of the non-Z-transformed carrier phase observation value. The inverse transform process is: Update the floating point solution of the parameter to be estimated to a fixed integer solution, the fixed solution of the parameter to be estimated and its covariance matrix Expressed as: Bootstrapping rounding success rate P s The calculation method is: Where, is the floating point solution of the i-th ambiguity parameter; is the integer value of the i-th ambiguity parameter; express The variance of ; Φ(·) represents the cumulative distribution function of the standard normal distribution.

6. The INS-assisted positioning system under the GNSS / INS positioning system according to claim 1, characterized in that: The specific process of correcting the floating-point solution of the first non-optimal subset satellite ambiguity by using the fixed solution of the first optimal subset satellite carrier phase observation value ambiguity to obtain the corrected floating-point solution of the first non-optimal subset satellite ambiguity includes: Where, represents the floating-point solution to the ambiguity of the first non-optimal subset of satellite carrier phase observations; yes The covariance matrix of represents the floating-point solution to the ambiguity of the first best subset of satellite carrier phase observations; represents the fixed solution of the ambiguity of the first optimal subset of satellite carrier phase observations; express and The cross-covariance matrix of ; Indicates The covariance matrix of express The covariance matrix of represents the float solution of the corrected ambiguity of the first non-optimal subset of satellite carrier phase observations; express The covariance matrix of After obtaining the floating-point solution of the corrected first non-optimal subset satellite carrier phase observation ambiguity through the above formula, the LAMBDA method is used to perform partial ambiguity resolution on the floating-point solution of the carrier phase observation ambiguity of this part of the carrier phase observation, and verify whether the integer ambiguity is correct, and obtain the fixed solution of the carrier phase observation ambiguity of the second optimal subset satellite. Finally, the fixed solution of the carrier phase observation ambiguity of the first optimal subset satellite is combined with the fixed solution of the carrier phase observation ambiguity of the first optimal subset satellite. The fixed solution to the ambiguity of the entire set of carrier phase observations is obtained as: Where, represents the ambiguity fixed solution of the carrier phase observations of the second optimal subset obtained by partial ambiguity resolution of the modified first non-optimal subset; Update using the above formula and Will Updated to Get the final and its covariance matrix Expressed as:

7. The INS-assisted positioning system under the GNSS / INS positioning system according to claim 1 or 6, characterized in that: The ambiguity of the floating-point solution of the second-best subset satellite carrier phase observation value is resolved using the LAMBDA method, and rounded based on the sequential rounding method to obtain the fixed solution of the ambiguity of the second-best subset satellite carrier phase observation value. The specific process includes: Perform down-correlation processing on the ambiguity of the second optimal subset satellite carrier phase observation value: Based on the principle of minimum residual sum of squares, the fuzzy objective function is defined as follows: Where N 2P represents the ambiguity vector after correction of the first non-optimal subset satellite; Z 2P A matrix representing the descending correlation transformation of the second best subset of satellites; The Z transform is expressed as: Where z 2P represents the ambiguity after the ambiguity conversion of the second best subset satellite carrier phase observation value; represents the floating-point solution to the ambiguity of the second best subset of satellite carrier phase observations; express The covariance matrix of express The covariance matrix of After the reduction correlation process, the original least squares problem is transformed into the following new least squares problem: Where, represents the ambiguity fixed solution vector of the second best subset satellite after Z transformation; The search space after down-correlation is expressed as: Where, f(z 2P ) represents the search space of the ambiguity vector z after down-correlation of the second optimal subset of satellites; Indicates n 2P Dimension Z 2P Matrix, where n 2P represents the total number of satellites in the second best subset; Perform a discrete search of the ambiguity: The covariance matrix of the floating-point solution to the ambiguities of the second best subset of satellite carrier phase observations Perform Cholesky decomposition, and the ambiguity covariance matrix of the second optimal subset satellite carrier phase observation value after decomposition is for: Where: Where, is the diagonal matrix D after decomposition of the second optimal subset satellites 2P The nth 2P diagonal elements; The lower triangular matrix L represents the second best subset of satellites 2P nth 2P The element of row, column 1; The lower triangular matrix L represents the second best subset of satellites 2P nth 2P The element of row, column 2; The ambiguity covariance matrix of the second optimal subset satellite carrier phase observation value after decomposition is Bringing it into the search space after descending correlation, the corresponding search space is updated as follows: Where, d 2Pi is a diagonal matrix D 2P The 2Pith diagonal element in z 2Pi represents the ambiguity of the 2Pi satellite in the second best subset of satellites after Z transformation, represents the floating point solution of the ambiguity of the 2Pi satellite in the second best subset of satellites after Z transformation; l 2Pji The lower triangular matrix L represents the second best subset of satellites 2P The lower triangular elements with subscript ji; z 2Pj represents the ambiguity of the 2Pjth satellite in the second best subset of satellites after Z transformation, represents the floating-point solution of the ambiguity of the 2Pjth satellite in the second best subset of satellites after Z transformation; set up is the conditional estimate of the second best subset of satellites, indicating is Determine the valuation under the conditions and set Is the conditional variance, then the conditional valuation is: The search space is simplified to: In the fuzzy search, the sequential rounding method is used. First, the fuzzy value of the previous level is determined, and then the search range of the next level of fuzzy is constructed based on this value. In this process, the nth level is first determined. 2P The search range of the satellite ambiguity is determined first, and then the search range of the next level of ambiguity is determined in turn. Finally, the search range of the ambiguity of the first satellite is determined, and so on. The boundaries of each level of ambiguity search are determined as follows: Where, represents the ambiguity conditional variance of the last satellite in the second best subset of satellites; represents the ambiguity conditional variance of the i-th satellite in the second optimal subset of satellites; represents the ambiguity conditional variance of the jth satellite in the second optimal subset of satellites; represents the ambiguity conditional variance of the first satellite in the second optimal subset of satellites; represents the ambiguity of the last satellite in the second best subset of satellites after Z transformation; represents the floating point solution of the ambiguity of the last satellite in the second best subset of satellites after Z transformation; 2P1 represents the ambiguity of the first satellite in the second best subset of satellites after Z transformation; It represents the floating point solution of the ambiguity of the first satellite in the second best subset of satellites after Z transformation; Ratio detection is used to test the reliability of fuzziness: Ratio detection is expressed as: Where, is closest Candidate values ​​for This time close Candidate values ​​for After the fuzziness test, the reverse transformation is performed to restore the original value of the fuzziness. The restoration process is:

8. The INS-assisted positioning system under the GNSS / INS positioning system according to claim 1, characterized in that: Using the INS-assisted modified partial ambiguity resolution method, a tightly coupled GNSS / INS combined positioning solution is performed on the fixed solution of the first optimal subset satellite carrier phase observation ambiguity, the fixed solution of the second optimal subset satellite carrier phase observation ambiguity, and the user's GNSS receiver position. The specific process of obtaining the user position includes: In the GNSS / INS combined system, the nonlinear discrete model of the extended Kalman filter method is: Where, X k represents the parameter vector to be estimated at the kth epoch of the dynamic system, X k-1 represents the parameter vector to be estimated at the k-1th epoch of the dynamic system; F k / k-1 Refers to the discrete-time state transfer matrix of the kth epoch; Z k represents the noise observation vector of the kth epoch; H k It's X k-1 The measurement transfer matrix w k-1 represents the k-1th epoch motion noise sequence with zero mean; ε k represents the observation noise sequence with zero mean at the kth epoch; The standard extended Kalman filter method follows the following processing sequence: initialization: Initial state estimate of the filtering process and its corresponding covariance for: Where X0 represents the initial state value of the filtering process; E[X0] represents the covariance operation of X0; express Covariance operation of ; Status prediction: Where, Represents X k-1 The predicted value of P k-1 Represents X k-1 The system covariance matrix of represents the predicted state vector; express The covariance matrix of k-1 represents the motion noise covariance matrix of the k-1th epoch; Measurement Update: The calculation for making observation predictions in a nonlinear measurement model is as follows: Where, represents observation prediction; represents the noise observation vector Z k The innovation vector of the difference between the measured value and its predicted value in the nonlinear measurement model and its covariance matrix Updated to: Where R k Represents ε k The covariance matrix of Filter gain update: The filter gain is mathematically defined as follows: Where K k represents the filter gain; express The inverse matrix of The user's location estimate is obtained through the following process 9. A GNSS / INS positioning system INS-assisted positioning method, characterized in that: include: The corrected user INS position is used to calculate the distance between the INS position and each satellite, and this is used as the predicted pseudorange between each satellite and the user GNSS receiver. Based on the predicted pseudorange between each satellite and the user's GNSS receiver and the position of each satellite, a floating-point solution for the user's GNSS receiver position is obtained. The carrier phase observation equation of the satellite observation value is solved by the least squares method to obtain a floating-point solution for the ambiguity of the carrier phase observation value of each satellite. All satellites in the GNSS system are divided into the first optimal subset of satellites and the first non-optimal subset of satellites according to the altitude cutoff angle. The ambiguity of the carrier phase observation values ​​of the first optimal subset of satellites is resolved using the LAMBDA method to obtain the fixed solution of the carrier phase observation ambiguity of the first optimal subset of satellites. The floating-point solutions of the carrier phase observation values ​​of the first non-optimal subset satellites are corrected using the fixed solutions of the ambiguities of the carrier phase observation values ​​of the first optimal subset satellites to obtain the corrected floating-point solutions of the carrier phase observation values ​​of the first non-optimal subset satellites, thereby obtaining the corrected first non-optimal subset satellites. The corrected first non-optimal subset satellites are divided into the second optimal subset satellites and the second non-optimal subset satellites according to the size of the altitude cutoff angle, and the floating-point solutions of the carrier phase observation values ​​of the second optimal subset satellites are ambiguity resolved using the LAMBDA method to obtain the fixed solutions of the carrier phase observation values ​​of the second optimal subset satellites. Using the INS-assisted corrected partial ambiguity resolution method, a tightly coupled GNSS / INS combined positioning solution is performed on the fixed solutions of the first optimal subset satellite carrier phase observation ambiguities, the fixed solutions of the second optimal subset satellite carrier phase observation ambiguities, and the user's GNSS receiver position to obtain the user position.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to claim 9 are implemented.

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