Single-beacon compass positioning method, device, equipment and storage medium

Abstract

This application provides a single BeiDou dynamic positioning method, device, equipment, and storage medium. It relates to the fields of satellite navigation and train positioning. The method includes: state estimation based on a factor graph, transforming the system state estimation into a joint optimization problem of a global cost function; performing dynamic relative positioning processing, obtaining double-difference measurement results through inter-station and inter-satellite differentials; constructing a factor graph model including pseudorange, carrier phase, Doppler observations, and orbital constraints; iteratively optimizing the objective function, solving the state set, and processing integer ambiguities to obtain the positioning result. This method can fully utilize historical information, improving the accuracy, continuity, and robustness of train relative positioning.

Description

Technical Field

[0001] This application relates to the field of satellite navigation and train positioning technology, and in particular to a single BeiDou dynamic positioning method, device, equipment and storage medium. Background Technology

[0002] In train operation scenarios, dynamic positioning is a key technology for train formation and coordinated control. Currently, pseudorange single-point positioning (SPP) and carrier phase differential positioning (RTK) based on BeiDou are widely used for train positioning. However, in complex environments (such as urban canyons and tunnels), GNSS signals are easily affected by obstruction and multipath effects, leading to a decrease in positioning accuracy and continuity.

[0003] For a long time, filtering methods represented by Kalman filtering (KF) have been the mainstream of information fusion. However, they only use information from the previous epoch to constrain the current state, failing to fully utilize historical information, which limits the positioning accuracy of GNSS in complex environments. To solve this problem, Kschischang proposed the Factor Graph Optimization (FGO) theory in 2001 and derived it based on the sum-product algorithm. Factor graph optimization has been widely used in the field of navigation and positioning. For example, Indelman et al. of Georgia Institute of Technology first used factor graphs for multi-source fusion positioning based on inertial navigation in 2012. ZENGQ et al. proposed a multi-sensor fusion algorithm based on factor graphs for small UAVs, which improved accuracy and optimized computational efficiency.

[0004] Compared to traditional filtering methods, factor graph optimization possesses stronger historical information utilization and global optimization capabilities, enabling multiple iterative optimizations of GNSS measurements to improve positioning accuracy. However, current research on the application of factor graphs in GNSS dynamic positioning is limited. For example, SunderhaufN first introduced factor graphs into GNSS positioning, but only fused pseudorange and Doppler information, failing to fully utilize carrier phase data and limiting its high-precision application. Therefore, researching a single-BeiDou dynamic positioning method based on factor graph optimization to fully utilize single-BeiDou measurement information and combine it with track constraints to improve the accuracy and reliability of train relative positioning is of significant research value. Summary of the Invention

[0005] This application provides a single BeiDou motion positioning method, apparatus, device, and storage medium to address the problems of existing single BeiDou motion positioning methods being limited by factors such as obstruction and multipath interference, and the traditional Kalman filter only utilizing information from the previous epoch, failing to fully exploit the temporal correlation of GNSS observation data, leading to a decrease in positioning accuracy and continuity. Furthermore, orbital constraint information is not fully utilized, affecting relative positioning accuracy.

[0006] Firstly, this application provides a single BeiDou motion positioning method, including:

[0007] A state estimation framework based on factor graphs is established, which links the system state set and measurement set through a factor graph model. The global cost function characterizes the joint constraints of the state transition process and the measurement process. The state transition process depends on historical state parameters, and the measurement process is associated with single BeiDou observation parameters.

[0008] The single BeiDou observation parameters are processed by dynamic relative positioning. Satellite-end errors and strong distance correlation errors are eliminated by inter-station differential to obtain carrier phase single-difference parameters and pseudorange single-difference parameters. Then, the inherent clock error of the vehicle-mounted receiver is removed by inter-satellite differential between the reference satellite and the auxiliary satellite, and the single-difference parameters are converted into double-difference measurement parameters.

[0009] Based on the aforementioned double-difference measurement parameters, a dynamic positioning factor graph model is constructed, with pseudorange double-difference parameters and carrier phase double-difference parameters as measurement factor nodes, and Doppler observation parameters as state transition constraint factor nodes. Combined with orbit constraint parameters, a target function that fuses multi-source parameters is formed.

[0010] The objective function is globally optimized and solved using the state estimation framework to obtain a state set containing the mobile station position parameters and double-difference integer ambiguity parameters. The final positioning result is determined by whether the double-difference integer ambiguity parameters are fixed or not.

[0011] In one possible design, the global cost function is expressed as:

[0012]

[0013] In the formula, X* represents the optimal overall state estimate (trajectory estimation result), x represents the state vector at a certain moment, j represents the index of the j-th observation, k represents the total number of time steps (epochs), and f i Let x represent the state transition function. i -1 represents the state at time i-1, u i z represents the external control variable or prior input. i Let m represent the actual observed value at time i. s h' represents the number of observations at time s, argmin represents the variable that minimizes the value of the function within the parentheses, and h' i (x j ) represents the observation model function, i.e., given state x i Predict the theoretical value of the j-th observation at time i, z' i Let i represent the j-th actual observation at time i. s Let i represent the time epoch, and s be the epoch index symbol.

[0014] In one possible design, by eliminating satellite-end errors and range-strong correlation errors through inter-station differential analysis, the calculation formulas for the carrier phase single-difference parameter and pseudorange single-difference parameter are obtained as follows:

[0015]

[0016] In the formula, These are the carrier phase and pseudorange differences between the vehicle-mounted receiver and the differential base station b and the satellite, respectively. It is a single difference value of carrier phase measured in weeks; It is the geometric distance between a single-difference station and a satellite; δt rb It is the first differential of the receiver clock error; The result is the integer ambiguity single difference between the two antennas; These represent the residual errors of the carrier signal and pseudorange, respectively; λ is the wavelength of the BeiDou signal; and c is the time velocity, referring to 3×10⁻⁶. 8 m / s; The formula for converting the single-difference parameter into a double-difference measurement parameter by removing the inherent clock error of the vehicle-mounted receiver through inter-satellite differential measurement between the reference satellite and the auxiliary satellite is as follows:

[0017]

[0018] In the formula, This represents the true distance between the satellite and the ground, representing the difference between the two. Indicates double-difference ambiguity; These are the two differences between the carrier phase and the pseudorange measurement noise, respectively. λ represents the double-difference carrier phase observation at the nth frequency point (in meters). n This represents the carrier wavelength at the nth frequency point; This represents the carrier phase double-difference observation value (week) at the nth frequency point; The double difference (nth frequency point) represents the ionospheric delay; The double difference represents the tropospheric delay; and This represents the integer ambiguity of the mobile station (or receiver) for satellite i,j at the nth frequency point; This represents the pseudorange double-difference observation value (in meters) at the nth frequency point; This represents the double difference of ionospheric delay at the nth frequency point; This represents the double difference of tropospheric delay at the nth frequency point.

[0019] In one possible design, the measurement model for the pseudorange double-difference parameter is as follows:

[0020]

[0021] In the formula, This represents the pseudorange double-difference observation at epoch t, ​​consisting of satellite s and reference satellite b. p represents the pseudorange double-difference observation model function. u,t p represents the position of the mobile station at time t. b,t This indicates the position of the base station at time t. Indicates the position of reference satellite b in epoch t. This represents the measurement error of the pseudorange double-difference measurement model;

[0022] The cost function of the measurement model for the pseudorange double-difference parameters is determined by the covariance of the pseudorange double-difference measurement error parameters, and its expression is:

[0023]

[0024] In the formula, The residuals representing the pseudo-distance double difference factor, Represents the covariance of the pseudorange double-difference measurement model;

[0025] The observation model corresponding to the carrier phase double difference parameters is:

[0026]

[0027] In the formula, This represents the carrier phase double-difference observation (week). This represents the carrier phase double-difference observation model function;

[0028] The cost function of the observation model corresponding to the carrier phase double-difference parameters is determined by the covariance of the carrier phase double-difference measurement error parameters, and its expression is:

[0029]

[0030] In the formula, The covariance representing the carrier phase difference is... The residual representing the carrier phase double difference factor, This represents the carrier phase double-difference observation at epoch t and satellite pair s. This represents the model function for carrier phase double-difference observations at epoch t and satellite pair s.

[0031] In one possible design, the velocity measurement model corresponding to the Doppler observation parameters is:

[0032] v u,t =f v,t (p u.t+1 ,p u,t )+ω v,t (17)

[0033] In the formula, f v,t (p u.t+1 ,p u,t )=(pu.t+1 -p u,t f / Δt, where Δt is the time interval between the two states, i.e., the reciprocal of the receiver's data reception frequency; v,t p represents the speed measurement observation model function. u,t+1 p represents the position of the mobile station at time t+1. u,t v represents the position of the mobile station at time t. u,t ω represents the velocity observation at epoch t. v,t This represents the measurement error / noise of the speed measurement observation model;

[0034] The velocity measurement model corresponding to the Doppler observation parameters is constructed based on the two-state time interval parameter, and its cost function is determined by the covariance of the Doppler velocity measurement error parameter, expressed as:

[0035]

[0036] In the formula, Σ v,t This represents the covariance of Doppler velocity measurements.

[0037] In one possible design, the objective function for fusing multi-source parameters is expressed as:

[0038]

[0039] In the formula, χ represents the set of state variables; * This represents the objective function value of the weighted sum of squared residuals (MAP / least squares objective).

[0040] In one possible design, the final positioning result is determined by whether or not the double-difference integer ambiguity parameter is fixed, including:

[0041] The optimized double-difference integer ambiguity floating-point parameters are fixed. If the fixing is successful, the positioning result is recalculated based on the parameters; if the fixing fails, the positioning result corresponding to the floating-point parameters is used as the output.

[0042] Secondly, this application provides a single BeiDou dynamic positioning device, the device comprising:

[0043] The state estimation module is configured to establish a factor graph-based state estimation framework, which associates the system state set and measurement set through a factor graph model, and uses a global cost function to characterize the joint constraints of the state transition process and the measurement process. The state transition process depends on historical state parameters, and the measurement process is associated with single BeiDou observation parameters.

[0044] The relative positioning module is configured to perform dynamic relative positioning processing on single BeiDou observation parameters. It eliminates satellite-end errors and strong distance correlation errors through inter-station differential to obtain carrier phase single-difference parameters and pseudorange single-difference parameters. Then, it removes the inherent clock error of the vehicle-mounted receiver through inter-satellite differential between the reference satellite and the auxiliary satellite, and converts the single-difference parameters into double-difference measurement parameters.

[0045] The model building module is configured to build a dynamic positioning factor graph model based on the double-difference measurement parameters, using pseudorange double-difference parameters and carrier phase double-difference parameters as measurement factor nodes, and Doppler observation parameters as state transition constraint factor nodes, and combining them with orbit constraint parameters to form an objective function that fuses multi-source parameters.

[0046] The optimization solution module is configured to perform global optimization solution on the objective function, and use the state estimation framework to solve it to obtain a state set containing the mobile station position parameters and double-difference integer ambiguity parameters. The final positioning result is determined by whether the double-difference integer ambiguity parameters are fixed or not.

[0047] Thirdly, embodiments of this application provide an electronic device, including: at least one processor and a memory; the memory stores computer execution instructions; the at least one processor executes the computer execution instructions stored in the memory, causing the at least one processor to execute the single BeiDou dynamic positioning method as described in the first aspect and various possible designs of the first aspect.

[0048] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the single BeiDou dynamic positioning method described in the first aspect and various possible designs of the first aspect.

[0049] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the single BeiDou dynamic positioning method as described in the first aspect and various possible designs of the first aspect.

[0050] The single BeiDou dynamic positioning method, apparatus, equipment, and storage medium provided in this application have at least the following beneficial effects:

[0051] This application utilizes a factor graph optimization method, treating pseudorange, carrier phase, Doppler observations, and orbital constraint information from a single BeiDou system as factor nodes for global optimization. Compared to the traditional Kalman filtering method, this approach fully leverages the temporal correlation of measurement data, reduces positioning errors caused by multipath effects and occlusion, and improves the relative positioning accuracy of trains.

[0052] Traditional train positioning methods are susceptible to signal interference in heavily obstructed environments (such as tunnels and urban canyons), leading to decreased positioning accuracy. This application integrates historical information through a factor graph optimization method and combines it with track constraints to enhance the positioning system's anti-interference capability in complex environments, thereby improving the continuity and stability of positioning. Attached Figure Description

[0053] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0054] Figure 1 A flowchart of a single BeiDou motion positioning method provided in an embodiment of this application;

[0055] Figure 2 Factor graph for joint optimization of the global cost function provided in the embodiments of this application;

[0056] Figure 3 This is a structural diagram of a single Beidou dynamic positioning device provided in an embodiment of this application.

[0057] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0058] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0059] The collection, storage, use, processing, transmission, provision, and disclosure of financial data or user data involved in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0060] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0061] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0062] Existing single-BeiDou motion positioning methods are limited by factors such as obstruction and multipath interference. Traditional Kalman filtering only utilizes information from the previous epoch and fails to fully exploit the temporal correlation of GNSS observation data, resulting in decreased positioning accuracy and continuity. In addition, orbital constraint information is not fully utilized, affecting relative positioning accuracy.

[0063] Based on this, this application provides a single BeiDou dynamic positioning method. By constructing a dynamic positioning factor graph, pseudorange, carrier phase, Doppler observations, and orbit constraints are used as factor nodes for global optimization. Factor graph optimization can utilize all historical information to improve positioning accuracy and robustness, enhancing the applicability of single BeiDou in train dynamic positioning.

[0064] like Figure 1 The diagram shown is a flowchart of a single BeiDou motion positioning process provided in this embodiment. This embodiment first provides a detailed derivation of the factor graph-based state estimation method, giving the final objective function. Then, based on the pseudorange, carrier phase, and Doppler measurement models in BDS motion positioning, it constructs a model of the BDS motion positioning algorithm optimized by the factor graph. This single BeiDou motion positioning method can be implemented through the following steps S100-S400.

[0065] S100: Establish a state estimation framework based on factor graphs, link the system state set and measurement set through a factor graph model, and use a global cost function to characterize the joint constraints of the state transition process and the measurement process. The state transition process depends on historical state parameters, and the measurement process is associated with single BeiDou observation parameters.

[0066] The purpose of step S100 is to achieve state estimation based on factor graphs. A factor graph is a bipartite graph model that represents the relationship between global and local functions, as well as the relationship between each variable and the local function.

[0067] g(x1,x2,x3,x4,x5)=f A (x1)f B (x2)f C (x1x2x3)f D (x3x4)f E (x3x5) (1)

[0068] The global function g is transformed into a product of local functions f. Each variable x corresponds to a variable node, and each local function f corresponds to a factor node. An edge connects the variable node and the factor node if and only if variable x is the independent variable of the local function f. This "factorization"-like representation greatly simplifies the representation of probabilistic models. The factor graph-based state estimation method understands state estimation as a maximum a posteriori estimation problem of the system's joint probability density function.

[0069] A system can be described by two parts: a state equation and a measurement equation, and the state error and measurement error can be treated as zero-mean white noise.

[0070]

[0071] The true state x can be obtained based on the properties of the normal distribution. k and ideal measurement z k The conditional probability distribution satisfies:

[0072]

[0073] In practical applications, the requirement is to seek the value of the state based on existing measurement results, i.e., to maximize P(X|Z). This can be obtained using Bayes' theorem, which yields the maximum a posteriori estimate.

[0074]

[0075] Among them, X k ={x 0:k} is a set of states, Z k ={z j 0:k} is the set of measurements under all states. If the system follows the Markov assumption, then

[0076]

[0077] Taking the logarithm of equation (3) and substituting it into equation (5) yields the following: the system state estimation can be equivalent to the joint optimization of the global cost function.

[0078]

[0079] In the formula, X* represents the optimal whole-segment state estimate (trajectory estimation result), x represents the state vector at a certain moment, j represents the index of the j-th observation, k represents the total number of time steps (epochs), and f i Let x represent the state transition function. i -1 represents the state at time i-1, u i z represents the external control variable or prior input. iLet m represent the actual observed value at time i. s h' represents the number of observations at time s, argmin represents the variable that minimizes the value of the function within the parentheses, and h' i (x j ) represents the observation model function, i.e., given state x i Predict the theoretical value of the j-th observation at time i, z' i Let i represent the j-th actual observation at time i. s Let i represent the time epoch.

[0080] Equation (6) is the general expression for the estimation based on factor graph optimization. Its left-hand side represents the system state transition process, and its right-hand side represents the measurement process. Σ and Λ are the covariance matrices of the state transition process and the measurement process, respectively. The solution is the state set X, and the resulting factor graph of the joint optimization of the global cost function is shown below. Figure 2 As shown.

[0081] S200: Performs dynamic relative positioning processing on single BeiDou observation parameters, eliminates satellite-end errors and strong distance correlation errors through inter-station differential, and obtains carrier phase single-difference parameters and pseudorange single-difference parameters; then removes the inherent clock error of the vehicle-mounted receiver through inter-satellite differential between the reference satellite and the auxiliary satellite, and converts the single-difference parameters into double-difference measurement parameters.

[0082] In this embodiment, step S200 can be implemented through the following steps:

[0083] First, inter-station differential is performed to eliminate or reduce satellite-end errors and distance-related errors. Then, inter-satellite differential is performed between the reference satellite and the auxiliary satellite to remove the inherent clock bias of the receiver installed on the vehicle.

[0084] When the differential fixed base station is located near the train line, forming a short baseline between them, the inter-station single-difference equations for the carrier phase and pseudorange obtained by performing a single difference between the two receiving antennas are as follows:

[0085]

[0086] in, These are the carrier phase (in meters) and pseudorange difference between the vehicle-mounted receiver and the differential base station b and the satellite, respectively. It is a single difference value of carrier phase measured in weeks; It is the geometric distance between a single-difference station and a satellite; δt rb It is the first differential of the receiver clock error; The result is the integer ambiguity single difference between the two antennas; Let be the residual errors of the carrier signal and pseudorange, respectively; λ be ; and c be .

[0087] Similarly, the observations of satellite i by the two receivers can also be performed using inter-station differential. To eliminate receiver clock errors and other related errors, satellite i is chosen as the reference satellite, and then inter-satellite differential is performed between satellite i and satellite j. The resulting double-difference measurement equation can be written as:

[0088]

[0089] In this context, the superscript represents inter-satellite differential, and the subscript rb represents inter-station differential; and The observations obtained from fixed base stations and train user receivers represent the double-difference carrier phase observations (unit: meters) and double-difference pseudorange observations constructed between reference satellite i and non-reference satellites, respectively. It is the carrier phase observation (cycle) of the station-satellite double difference; This represents the true distance between the satellite and the ground, representing the difference between the two. Indicates double-difference ambiguity; These are the two differences between the carrier phase and the pseudorange measurement noise, respectively.

[0090] Therefore, in a relative positioning scenario, the single BeiDou positioning mode is as follows:

[0091]

[0092] In the formula, f n (n=1, f n =1575.42MHz; n=2, f n =1227.60MHz) frequency, station-satellite double-difference ionospheric delay residual term; This represents the residual term of the double-difference tropospheric error; λ represents the double-difference carrier phase observation at the nth frequency point (in meters). n This represents the carrier wavelength at the nth frequency point; This represents the carrier phase double-difference observation value (week) at the nth frequency point; The double difference (nth frequency point) represents the ionospheric delay; The double difference represents the tropospheric delay; and This represents the integer ambiguity of the mobile station (or receiver) for satellite i,j at the nth frequency point; This represents the pseudorange double-difference observation value (in meters) at the nth frequency point; This represents the double difference of ionospheric delay at the nth frequency point; This represents the double difference of tropospheric delay at the nth frequency point.

[0093] S300: Based on the aforementioned double-difference measurement parameters, a dynamic positioning factor graph model is constructed, with pseudorange double-difference parameters and carrier phase double-difference parameters as measurement factor nodes, and Doppler observation parameters as state transition constraint factor nodes. Combined with orbit constraint parameters, a target function that fuses multiple source parameters is formed.

[0094] In this embodiment, pseudorange, carrier phase, and Doppler are used for fusion, and the selected state variables are... p u,t =[x t ,y t ,z t [This refers to the location of the mobile station.] Let χ be the m-1 double-difference integer-cycle ambiguities between the rover u and the base station r at time t for m co-view satellites, and let the set of state variables be χ = [X1, X2, ..., X]. n The pseudorange double difference and carrier phase double difference were selected as the measured values, and the Doppler velocity measurement results were used as the constraints for the state transition.

[0095] After calculating the inter-station and inter-satellite differences for the base station and the rover, the pseudorange double-difference measurement model can be obtained as follows:

[0096]

[0097] In the formula, This represents the pseudorange double-difference observation at epoch t, ​​consisting of satellite s and reference satellite b. p represents the pseudorange double-difference observation model function. u,t p represents the position of the mobile station at time t. b,t This indicates the position of the base station at time t. This indicates the position of the reference satellite b in epoch t.

[0098] It is important to note that It is the position of the reference satellite among the common-view satellites. In order to make the double-difference measurement model more accurate, the one with the largest elevation angle among the common-view satellites is generally selected as the reference satellite. This refers to the measurement error in the pseudorange double-difference measurement model. Even after double-difference processing, if the atmospheric conditions at the base station and the rover differ significantly, the measurement model still contains errors, with a covariance of [missing information]. Therefore, the cost function of pseudorange double-difference measurement is:

[0099]

[0100] In the formula, This represents the residual of the pseudo-range double difference factor.

[0101] Similarly, the observation model for carrier phase double difference is expressed as:

[0102]

[0103] In the formula, This represents the carrier phase double-difference observation (week).

[0104] It is important to note that:

[0105]

[0106] It is the measurement error of carrier phase double difference, with a covariance of Its cost function is:

[0107]

[0108] In the formula, The residual representing the carrier phase double difference factor, This represents the carrier phase double-difference observation at epoch t and satellite pair s. This represents the model function for carrier phase double-difference observations at epoch t and satellite pair s.

[0109] The observation model for Doppler velocity measurement is as follows:

[0110] v u,t =f v,t (p u.t+1 ,p u,t )+ω v,t (17)

[0111] Among them, f v,t p represents the speed measurement observation model function. u,t+1 p represents the position of the mobile station at time t+1. u,t v represents the position of the mobile station at time t. u,t ω represents the velocity observation at epoch t. v,t f represents the measurement error / noise of the velocity observation model. v,t (p u.t+1 ,p u,t )=(p u.t+1 -p u,t ) / Δt, where Δt is the time interval between the two states, i.e., the reciprocal of the receiver's data reception frequency. It can be predicted that the higher the data reception frequency, the closer the model will be to reality. ω v,t This is the measurement error of Doppler velocities, and its covariance is Σ. v,t This can be adjusted through the receiver's nominal velocity measurement accuracy or through multiple experiments. Therefore, the cost function for Doppler velocity measurement is:

[0112]

[0113] Based on the general model of equation (6), the objective function of the single BeiDou relative positioning solution method based on factor graph optimization, which fuses pseudorange, carrier phase, and Doppler measurements, is:

[0114]

[0115] Where, χ * The objective function value representing the weighted sum of squared residuals (MAP / least squares objective) requires optimization calculation. χ represents the set of states, not individual epochs.

[0116] S400: The objective function is globally optimized and solved using the state estimation framework to obtain a state set containing the mobile station position parameters and double-difference integer ambiguity parameters. The final positioning result is determined by whether the double-difference integer ambiguity parameters are fixed or not.

[0117] In this embodiment, the floating-point solutions for each epoch and the floating-point solutions for double-difference integer ambiguities can be obtained by solving equation (19), and then the integer ambiguities are fixed. If the ambiguities can be fixed, the calculation is performed again to obtain the accurate positioning solution; if the ambiguities cannot be fixed, the floating-point solutions are used as the final solution.

[0118] This application also provides a single BeiDou dynamic positioning device, such as... Figure 3 As shown, the single Beidou dynamic positioning device includes:

[0119] The state estimation module 301 is configured to establish a state estimation framework based on a factor graph, which associates the system state set and the measurement set through a factor graph model, and uses a global cost function to characterize the joint constraints of the state transition process and the measurement process. The state transition process depends on historical state parameters, and the measurement process is associated with single BeiDou observation parameters.

[0120] The relative positioning module 302 is configured to perform dynamic relative positioning processing on single BeiDou observation parameters, eliminate satellite-end errors and strong distance correlation errors through inter-station differential, and obtain carrier phase single-difference parameters and pseudorange single-difference parameters; then remove the inherent clock error of the vehicle-mounted receiver through inter-satellite differential between the reference satellite and the auxiliary satellite, and convert the single-difference parameters into double-difference measurement parameters.

[0121] The model building module 303 is configured to build a dynamic positioning factor graph model based on the double difference measurement parameters, using pseudorange double difference parameters and carrier phase double difference parameters as measurement factor nodes, and Doppler observation parameters as state transition constraint factor nodes, and combining them with orbit constraint parameters to form an objective function that fuses multi-source parameters.

[0122] The optimization solution module 304 is configured to perform global optimization solution on the objective function, and use the state estimation framework to solve it to obtain a state set containing the mobile station position parameters and double-difference integer ambiguity parameters. The final positioning result is determined by whether the double-difference integer ambiguity parameters are fixed or not.

[0123] This application provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0124] The processor executes computer execution instructions stored in memory, causing the processor to perform the schemes in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0125] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0126] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.

[0127] This application also provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed on a computer, the computer performs the technical solution of the single Beidou dynamic positioning method described in the above embodiments.

[0128] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the single Beidou dynamic positioning method in the above embodiments.

[0129] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0130] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0131] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0132] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.

[0133] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules within the processor.

[0134] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0135] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0136] The aforementioned storage medium can be implemented from any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium accessible to general-purpose or special-purpose computers.

[0137] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0138] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A single Beidou dynamic positioning method, characterized in that, The method includes: A state estimation framework based on factor graphs is established, which links the system state set and measurement set through a factor graph model. The global cost function characterizes the joint constraints of the state transition process and the measurement process. The state transition process depends on historical state parameters, and the measurement process is associated with single BeiDou observation parameters. The single BeiDou observation parameters are processed by dynamic relative positioning. Satellite-end errors and strong distance correlation errors are eliminated by inter-station differential to obtain carrier phase single-difference parameters and pseudorange single-difference parameters. Then, the inherent clock error of the vehicle-mounted receiver is removed by inter-satellite differential between the reference satellite and the auxiliary satellite, and the single-difference parameters are converted into double-difference measurement parameters. Based on the aforementioned double-difference measurement parameters, a dynamic positioning factor graph model is constructed, with pseudorange double-difference parameters and carrier phase double-difference parameters as measurement factor nodes, and Doppler observation parameters as state transition constraint factor nodes. Combined with orbit constraint parameters, a target function that fuses multi-source parameters is formed. The objective function is globally optimized and solved using the state estimation framework to obtain a state set containing the mobile station position parameters and double-difference integer ambiguity parameters. The final positioning result is determined by whether the double-difference integer ambiguity parameters are fixed or not. The global cost function is expressed as: (6) In the formula, X * indicates the optimal overall state estimate, i.e., the trajectory estimation result. x This represents the state vector at a certain moment. j This represents the index of the j-th observation. k This represents the total number of time steps. f i Represents the state transition function. x i-1 This represents the state at time i-1. u i This represents external control variables or prior inputs. z i This represents the actual observed value at time i. m s Let represent the number of observations at time s, and argmin represent the variable that minimizes the value of the function within the parentheses. The observation model function represents the state given. x i Predict the theoretical value of the j-th observation at time i. This represents the j-th actual observation at time i. i s Indicates that i represents the time epoch and s is the epoch index symbol; The measurement model for the pseudorange double difference parameter is as follows: (13) In the formula, This represents the pseudorange double-difference observation at epoch t, ​​consisting of satellite s and reference satellite b. This represents the pseudorange double-difference observation model function. This represents the position of the mobile station at time t. This indicates the position of the base station at time t. Indicates the position of reference satellite b in epoch t. This represents the measurement error of the pseudorange double-difference measurement model; The cost function of the measurement model for the pseudorange double-difference parameters is determined by the covariance of the pseudorange double-difference measurement error parameters, and its expression is: (14) In the formula, The residuals representing the pseudo-distance double difference factor, Represents the covariance of the pseudorange double-difference measurement model; The observation model corresponding to the carrier phase double difference parameters is: (15) In the formula, This represents the carrier phase double-difference observation. This represents the carrier phase double-difference observation model function; The cost function of the observation model corresponding to the carrier phase double-difference parameters is determined by the covariance of the carrier phase double-difference measurement error parameters, and its expression is: (16) In the formula, The covariance representing the carrier phase difference is... The residual representing the carrier phase double difference factor, This represents the carrier phase double-difference observation at epoch t and satellite pair s. This represents the model function for carrier phase double-difference observations at epoch t and satellite pair s; The velocity measurement model corresponding to the Doppler observation parameters is: (17) In the formula, , It is the time interval between the two states, which is the reciprocal of the frequency at which the receiver receives data; f v,t This represents the speed measurement observation model function. p u,t+1 This indicates the position of the mobile station at time t+1. This represents the position of the mobile station at time t. v u,t This represents the velocity observation at epoch t. This represents the measurement error / noise of the speed measurement observation model; The velocity measurement model corresponding to the Doppler observation parameters is constructed based on the two-state time interval parameter, and its cost function is determined by the covariance of the Doppler velocity measurement error parameter, expressed as: (18) In the formula, This represents the covariance of Doppler velocity measurements.

2. The single BeiDou dynamic positioning method according to claim 1, characterized in that, By eliminating satellite-end errors and range-strong correlation errors through inter-station differential analysis, the calculation formulas for the carrier phase single-difference parameter and pseudorange single-difference parameter are obtained as follows: (7) (8) In the formula, , These are vehicle-mounted receivers and differential base stations. b The difference between the carrier phase and pseudorange of the satellite; It is a single difference value of carrier phase measured in weeks; It is the geometric distance between a single-difference station and a satellite; It is the first differential of the receiver clock error; The result is the integer ambiguity single difference between the two antennas; , These are the residual errors of the carrier signal and the pseudorange, respectively. The wavelength of the BeiDou signal; c For time speed, refers to ; The formula for converting the single-difference parameter into a double-difference measurement parameter by removing the inherent clock error of the vehicle-mounted receiver through inter-satellite differential measurement between the reference satellite and the auxiliary satellite is as follows: (11) (12) In the formula, This represents the true distance between the satellite and the ground, representing the difference between the two. Indicates double-difference ambiguity; , These are the two differences between the carrier phase and the pseudorange measurement noise, respectively. This represents the carrier phase double-difference observation value at the nth frequency point; This represents the carrier wavelength at the nth frequency point; This represents the carrier phase double-difference observation value at the nth frequency point; The double difference represents the ionospheric delay; The double difference represents the tropospheric delay; and This represents the integer ambiguity of the mobile station or receiver for satellite i,j at the nth frequency point; This represents the pseudorange double-difference observation at the nth frequency point; This represents the double difference of ionospheric delay at the nth frequency point; This represents the double difference of tropospheric delay at the nth frequency point.

3. The single BeiDou dynamic positioning method according to claim 1, characterized in that, The objective function for fusing multi-source parameters is expressed as: (19) In the formula, A set representing state variables; This represents the objective function value of the weighted sum of squared residuals.

4. The single BeiDou dynamic positioning method according to claim 1, characterized in that, The final positioning result is determined by whether or not the double-difference integer ambiguity parameter is fixed, including: The optimized double-difference integer ambiguity floating-point parameters are fixed. If the fixing is successful, the positioning result is recalculated based on the parameters; if the fixing fails, the positioning result corresponding to the floating-point parameters is used as the output.

5. A single BeiDou motion positioning device, used to implement the single BeiDou motion positioning method as described in any one of claims 1-4, characterized in that, The device includes: The state estimation module is configured to establish a factor graph-based state estimation framework, which associates the system state set and measurement set through a factor graph model, and uses a global cost function to characterize the joint constraints of the state transition process and the measurement process. The state transition process depends on historical state parameters, and the measurement process is associated with single BeiDou observation parameters. The relative positioning module is configured to perform dynamic relative positioning processing on single BeiDou observation parameters. It eliminates satellite-end errors and strong distance correlation errors through inter-station differential to obtain carrier phase single-difference parameters and pseudorange single-difference parameters. Then, it removes the inherent clock error of the vehicle-mounted receiver through inter-satellite differential between the reference satellite and the auxiliary satellite, and converts the single-difference parameters into double-difference measurement parameters. The model building module is configured to build a dynamic positioning factor graph model based on the double-difference measurement parameters, using pseudorange double-difference parameters and carrier phase double-difference parameters as measurement factor nodes, and Doppler observation parameters as state transition constraint factor nodes, and combining them with orbit constraint parameters to form an objective function that fuses multi-source parameters. The optimization solution module is configured to perform global optimization solution on the objective function, and use the state estimation framework to solve it to obtain a state set containing the mobile station position parameters and double-difference integer ambiguity parameters. The final positioning result is determined by whether the double-difference integer ambiguity parameters are fixed or not.

6. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes the computer execution instructions stored in the memory to implement the single BeiDou dynamic positioning method as described in any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the single BeiDou motion positioning method as described in any one of claims 1-4.

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