Doppler positioning method and device for low-orbit communication satellite based on factor graph optimization

Abstract

The present application relates to a method and device for Doppler positioning of low-orbit communication satellites based on factor graph optimization. The method comprises: after receiving the required observation data and solving the initial value of the ground receiver state, comparing the Doppler positioning observation model, introducing the factor graph framework to set the prior factor, Doppler frequency shift factor, state constraint factor and state variables composed of the three-dimensional position and frequency drift of the receiver, using these factors and variables as nodes to construct the Doppler positioning factor graph model, introducing the sliding window mechanism to update the factor graph in the factor graph optimization solution process, and using the Gauss-Newton algorithm to solve the state variables, and finally obtaining the Doppler positioning result. By modeling the Doppler positioning observation model with a factor graph, the present application takes advantage of the nonlinear modeling, global optimization and full use of historical observations of the factor graph optimization method, and can obtain smaller positioning errors and faster convergence speeds.

Description

Technical Field

[0001] The present application relates to the field of satellite positioning technology, and in particular to a method and device for Doppler positioning of a low-orbit communication satellite based on factor graph optimization. Background Art

[0002] In the joint communication and navigation signals broadcast by low-orbit communication satellites, the navigation signal is a time-slot signal. Its pseudo-range measurement value has low accuracy and cannot guarantee the reception of signals from four or more satellites at the same time. Therefore, it is not suitable for positioning using the pseudo-range positioning method. Low-orbit communication satellites run at a fast speed, have a large Doppler frequency shift and a high diversity of geometric positions of visible stars, and the Doppler positioning method is usually used to achieve positioning.

[0003] For the solution process of the Doppler positioning method, the commonly used algorithms are based on the least squares algorithm and the extended Kalman filter. These two methods use Taylor series expansion in the solution process to retain the linear part and discard the high-order terms. However, due to the strong nonlinearity of the Doppler changes of low-orbit communication satellites, such linearization processing often brings large calculation errors, resulting in reduced Doppler positioning accuracy. Some scholars use the volumetric Kalman filter method to solve the nonlinear problem of the Doppler positioning observation model, but the Kalman filter-based method only considers the value of the previous state in the real-time processing process, and ignores other historical state values. For the complex situation of low-orbit communication satellites with few visible stars and large changes in the received signal strength caused by the fast movement of satellites, it is difficult to achieve the expected convergence speed and accuracy. Summary of the invention

[0004] Based on this, it is necessary to provide a low-orbit communication satellite Doppler positioning method and device based on factor graph optimization to address the problems of low Doppler positioning accuracy and insufficient convergence speed caused by the small number of visible stars and large changes in received signal strength at different epochs when the above-mentioned ground receiver receives the joint communication and navigation signals of low-orbit communication satellites for Doppler positioning.

[0005] A Doppler positioning method for a low-orbit communication satellite based on factor graph optimization, the method comprising:

[0006] The ground receiver receives the time slot navigation signal broadcast by the low-orbit communication satellite to obtain the observation data of the low-orbit communication satellite;

[0007] Searching for the initial state value of the ground receiver according to the received observation data to obtain the initial state value;

[0008] The three-dimensional position coordinates and frequency drift of the ground receiver that need to be solved by the Doppler positioning observation model are taken as state variables, the historical state variable information of the ground receiver is used to construct the prior factor, the Doppler frequency shift factor is constructed using the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal, and the state variable change constraint of the continuous epochs before and after the ground receiver is taken as the state constraint factor, and then the state variable, prior factor, Doppler frequency shift factor and state constraint factor are used as nodes to construct a Doppler positioning factor graph model;

[0009] The objective function of the Doppler positioning factor graph model is constructed according to the cost function of the prior factor, the Doppler frequency shift factor and the state constraint factor. The state variables of the objective function are optimized by introducing a sliding window mechanism until the optimal state variables are iteratively output to obtain the Doppler positioning result of the ground receiver.

[0010] In one embodiment, searching for an initial state value of a ground receiver according to received observation data to obtain an initial state value includes:

[0011] After receiving at least four sets of observation data, the ground receiver uses a grid search algorithm to search for initial state values ​​based on the received observation data to obtain the initial state values ​​of the three-dimensional position coordinates and frequency drift of the ground receiver; the observation data include the position, movement speed and Doppler frequency shift of the low-orbit communication satellite.

[0012] In one embodiment, the grid search algorithm includes: for a low-orbit communication satellite that receives a time-slot navigation signal, dividing the surface area covered by its time-slot navigation signal into equally spaced grids, performing a least squares solution on each grid obtained by the division, and searching for the three-dimensional position coordinates of the ground receiver and the initial value of the frequency drift state.

[0013] In one embodiment, constructing a priori factors using historical state variable information of ground receivers includes:

[0014] The prior factors are used to characterize the historical state variable information of the ground receiver, and the prior factor constraint model of the ground receiver is defined, which is expressed as

[0015] ;

[0016] in, Indicates the ground receiver at epoch i The state variables at represents the prior factor, represents the prior factor error;

[0017] According to the prior factor error Construct the cost function of the prior factor, expressed as

[0018] ;

[0019] in, is the prior factor error The covariance matrix of ; where, at the initial moment, the initial value of the ground receiver's state is taken as the initial value of the prior factor.

[0020] In one embodiment, the Doppler frequency shift factor is constructed using the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal, including:

[0021] When the Doppler frequency shift measurement error is considered, the static instantaneous Doppler positioning observation model of the ground receiver is expressed as

[0022] ;

[0023] in, Epoch i The Doppler shift at is the three-dimensional position coordinates of the ground receiver Sum frequency drift The state variables constituted by T represents transpose; Epoch i Doppler frequency shift measurement error when The frequency of transmitting time-slot navigation signals for low-orbit communication satellites; Epoch i The movement speed of low-orbit communication satellites at the time; , Epoch i The position of low-orbit communication satellites and ground receivers at that time; is the speed of light;

[0024] definition Epoch i The Doppler frequency shift measurement error The variance of the time slot navigation signal received by the ground receiver is calculated based on the carrier-to-noise ratio of the time slot navigation signal received by the ground receiver. Conduct an assessment, obtain The calculation expression is

[0025] ;

[0026] in, For Doppler shift measurements, the parameters related to ground receivers are Represents epoch i The carrier-to-noise ratio of the time slot navigation signal at ;

[0027] according to and Construct the cost function of the Doppler frequency shift factor, expressed as

[0028] .

[0029] In one embodiment, the state variable change constraint of the continuous epochs before and after the ground receiver is used as the state constraint factor, including:

[0030] The constraint model of the state variable change of the continuous epochs before and after the ground receiver is defined as

[0031] ;

[0032] in, and are the ground receiver at epoch i With epoch The state variables at is the state variable error of the ground receiver;

[0033] Considering that the ground receiver is in a stationary state, the change constraint of the state variables of the ground receiver before and after the continuous epoch is defined as 0, and the variance of the state variable error is set to the minimum value. The cost function of the state constraint factor is constructed as follows:

[0034] ;

[0035] in, is the covariance matrix of the ground receiver state variables.

[0036] In one embodiment, the objective function of the Doppler positioning factor graph model is constructed according to the cost function of the prior factor, the Doppler frequency shift factor and the state constraint factor, which is expressed as:

[0037] ;

[0038] in, Indicates the ground receiver from epoch i to the set of state variables of the current epoch, and , Indicates the ground receiver at epoch i The state variables at n From epoch i the number of epochs to the current epoch; , and They represent the cost functions of the prior factor, Doppler frequency shift factor, and state constraint factor, respectively. and denote the covariance matrix of the prior factor error and the ground receiver state variable, Represents the Doppler shift measurement error variance.

[0039] In one embodiment, a sliding window mechanism is introduced to optimize the state variables of the objective function, including:

[0040] Detect and determine whether the number of state variable nodes in the Doppler positioning factor graph model exceeds the sliding window length;

[0041] If the number of state variable nodes does not exceed the sliding window length, the state variable optimization solution will not be performed;

[0042] If the number of state variable nodes reaches the length of the sliding window, the state variable optimization solution is performed on the objective function of the Doppler positioning factor graph model within the sliding window;

[0043] If the number of state variable nodes exceeds the length of the sliding window, the sliding window is slid forward to update the Doppler positioning factor graph model within the sliding window, and then the state variables are optimized and solved based on the objective function of the updated Doppler positioning factor graph model; wherein, the Doppler positioning factor graph model update includes: deleting the earliest state variable node and the corresponding Doppler frequency shift factor node and state constraint factor node in the sliding window, adding new state variable nodes and the corresponding Doppler frequency shift factor node and state constraint factor node, and constructing a new prior factor node based on the state variables and covariance matrix obtained by the optimization solution in the previous sliding window, and adding it to the Doppler positioning factor graph model in the current sliding window.

[0044] In one embodiment, performing state variable optimization on the objective function of the Doppler positioning factor graph model includes:

[0045] The solution of the objective function of the Doppler localization factor graph model is equivalent to the update increment of the state variable The solution is expressed as

[0046] ;

[0047] in, is the increase in the state variable to be updated, For ground receivers k The set of state variables at the iteration, for The initial estimate of The objective function is contains the global Jacobian matrix of all nodes in the sliding window, For The residual term at ;

[0048] Use the Gauss-Newton algorithm to update the increment To solve, specifically, by dimension Perform QR decomposition and get

[0049] ;

[0050] In the above formula, Q for dimensional orthogonal matrix, R is an upper triangular matrix, and Represents the matrix dimension;

[0051] Correspondingly, the residual term It is expressed as:

[0052] ;

[0053] In the above formula, , , superscript T represents transpose;

[0054] but

[0055] ;

[0056] Update Increment The estimation equation is simplified to

[0057] ;

[0058] When updating increments When the given threshold is met, the optimal state variable estimation of the Doppler positioning factor graph model in the current sliding window is output to obtain the Doppler positioning result of the ground receiver; otherwise, Update the state variables for the next iteration until When the given threshold is met, the Doppler positioning result of the ground receiver is output.

[0059] A Doppler positioning device for a low-orbit communication satellite based on factor graph optimization, the device comprising:

[0060] An observation data acquisition module is used to receive the time slot navigation signal broadcast by the low-orbit communication satellite through a ground receiver to obtain the observation data of the low-orbit communication satellite;

[0061] A state initial value search module is used to search for the state initial value of the ground receiver according to the received observation data to obtain the state initial value;

[0062] The factor graph modeling module is used to take the three-dimensional position coordinates and frequency drift of the ground receiver that need to be solved by the Doppler positioning observation model as state variables, use the historical state variable information of the ground receiver to construct a priori factors, use the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal to construct the Doppler frequency shift factor, and take the state variable change constraint of the continuous epochs before and after the ground receiver as the state constraint factor, and then use the state variables, priori factors, Doppler frequency shift factors and state constraint factors as nodes to construct a Doppler positioning factor graph model;

[0063] The sliding window optimization solution module is used to construct the objective function of the Doppler positioning factor graph model according to the cost function of the prior factor, Doppler frequency shift factor and state constraint factor. The state variables of the objective function are optimized and solved by introducing the sliding window mechanism until the optimal state variables are iteratively output to obtain the Doppler positioning result of the ground receiver.

[0064] Compared with the existing Doppler positioning method, the above-mentioned low-orbit communication satellite Doppler positioning method and device based on factor graph optimization have the following beneficial effects:

[0065] 1. According to the Doppler positioning observation model, the factor graph framework is introduced to set the prior factors, Doppler frequency shift factors, state constraint factors and state variables composed of the three-dimensional position and frequency drift of the receiver. These factors and variables are used as nodes to construct the Doppler positioning factor graph model. The advantages of factor graphs, such as nonlinear modeling, global optimization and full use of historical observations, are brought into play, so that smaller Doppler positioning errors and faster convergence speeds can be obtained.

[0066] 2. In the constructed Doppler positioning factor graph model, by retaining the historical observation information in the form of a priori factors, the advantages of historical observations can be fully utilized, the impact of noise and data deviation on Doppler positioning can be reduced, and the accuracy and stability of positioning results can be improved. The accuracy of Doppler frequency shift observations is evaluated by the carrier-to-noise ratio of the time-slot navigation signal, so that the accuracy of the model describing the random characteristics of Doppler frequency shift observations can be improved during the optimization solution process, making the estimation results of state variables better.

[0067] 3. By introducing a sliding window mechanism to update the Doppler positioning factor graph model, the global optimization process of the factor graph only occurs between the latest several state variable nodes, which can effectively reduce the amount of algorithm calculation and improve the algorithm estimation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A schematic diagram of a process of a low-orbit communication satellite Doppler positioning method based on factor graph optimization in one embodiment;

[0069] Figure 2 It is a schematic diagram of the overall architecture of a low-orbit communication satellite Doppler positioning method based on factor graph optimization in one embodiment;

[0070] Figure 3 A schematic diagram of a Doppler positioning factor graph model in one embodiment;

[0071] Figure 4 A schematic diagram of sliding window update in one embodiment. DETAILED DESCRIPTION

[0072] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0073] In one embodiment, Figure 1 and Figure 2 As shown, a low-orbit communication satellite Doppler positioning method based on factor graph optimization is provided, comprising the following steps:

[0074] Step S1, receiving the time slot navigation signal broadcast by the low-orbit communication satellite through a ground receiver to obtain the observation data of the low-orbit communication satellite.

[0075] Among them, the observation data includes information such as the position, movement speed, and Doppler frequency shift of low-orbit communication satellites.

[0076] Step S2, searching for the initial state value of the ground receiver according to the received observation data to obtain the initial state value.

[0077] Specifically, when using low-orbit communication satellite signals for Doppler positioning of ground receivers, since the distance between the low-orbit communication satellite and the ground receiver is much smaller than the distance between the center of the earth and the receiver, if the center of the earth is directly used as the initial value of the receiver position iteration in the GNSS (Global Navigation Satellite System Signal) navigation positioning solution, it may cause the solution process to fail to converge. Therefore, after receiving at least 4 sets of observation data, the ground receiver uses a grid search algorithm to search for the initial state value based on the received observation data. Specifically, for low-orbit communication satellites that receive time-slot navigation signals, the surface area covered by their time-slot navigation signals is divided into equally spaced grids, and the least squares solution is performed on each grid obtained by the division, and the initial state values ​​of the three-dimensional position coordinates and frequency drift of the ground receiver are searched.

[0078] Step S3, taking the three-dimensional position coordinates and frequency drift of the ground receiver that need to be solved by the Doppler positioning observation model as state variables, using the historical state variable information of the ground receiver to construct a priori factors, using the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal to construct the Doppler frequency shift factor, and taking the state variable change constraint of the continuous epochs before and after the ground receiver as the state constraint factor, and then taking the state variables, priori factors, Doppler frequency shift factors and state constraint factors as nodes to construct a Doppler positioning factor graph model.

[0079] The factor graph method is a probabilistic graphical model method that converts the optimization problem into a graph consisting of edges and nodes. The variable nodes represent the unknown random variables in the estimation problem, the factor nodes represent the probability information about these variables, and the edges represent the relationship between the nodes.

[0080] According to Bayes' theorem, the state quantity X and observations Z The joint probability of is equal to the conditional probability multiplied by the marginal probability:

[0081] ;

[0082] In the formula, For the observed quantity Z The corresponding probability; It is the state quantity X The prior probability of . The posterior distribution It is a commonly used method to evaluate the degree of fit between the state set and the observation set. Solving the expected state set can be achieved by maximizing the posterior distribution, that is, finding the maximum a posteriori state estimate:

[0083] ;

[0084] In the factor graph model, the above formula can be further expressed as:

[0085] ;

[0086] According to the above formula, the factor graph can construct the posterior distribution of the inferred positioning state estimation problem based on the Doppler positioning observation model and state constraints. The Doppler positioning factor graph model constructed in this application is as follows: Figure 3 shown.

[0087] Furthermore, the historical state variable information of the ground receiver is used to construct the prior factors, including:

[0088] The prior factors are used to characterize the historical state variable information of the ground receiver, and the prior factor constraint model of the ground receiver is defined, which is expressed as

[0089] ;

[0090] in, Indicates the ground receiver at epoch i The state variables at represents the prior factor, represents the prior factor error;

[0091] According to the prior factor error Construct the cost function of the prior factor, expressed as

[0092] ;

[0093] in, is the prior factor error The covariance matrix of ; wherein, at the initial moment, the initial value of the ground receiver state is used as the initial value of the prior factor, and, due to its poor accuracy, the initial value variance is set to a larger value.

[0094] The subsequent optimization solution process expresses the state nodes and factor nodes as an overall set of equations to solve the state variables, and uses the iterative method to seek the optimal estimate. In this process, the prior factor is equivalent to the initial assignment of the iterative solution process, which has an important impact on the accuracy and stability of the numerical solution. Therefore, when the factor graph is updated, the state value of the prior factor will be updated synchronously. By retaining historical observation information in the form of prior factors, the present application can give full play to the advantages of historical observations, reduce the impact of noise and data deviation on Doppler positioning, and improve the accuracy and stability of positioning results.

[0095] Further, the Doppler frequency shift factor is constructed using the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal, including:

[0096] When the Doppler frequency shift measurement error is considered, the static instantaneous Doppler positioning observation model of the ground receiver is expressed as

[0097] ;

[0098] in, Epoch i The Doppler shift at is the three-dimensional position coordinates of the ground receiver Sum frequency drift The state variables constituted by T represents transpose; Epoch i Doppler frequency shift measurement error when The frequency of transmitting time-slot navigation signals for low-orbit communication satellites; Epochi The movement speed of low-orbit communication satellites at the time; , Epoch i The position of low-orbit communication satellites and ground receivers at that time; is the speed of light;

[0099] definition epoch i The Doppler frequency shift measurement error The variance of the model. In the optimization process, the more accurate the model is in describing the random characteristics of the observed quantity, the better the estimation result of the state variable parameters. For the Doppler frequency shift observed quantity of low-orbit communication satellites, it is more reasonable to use the carrier-to-noise ratio to evaluate its error degree compared with the altitude angle. Therefore, the carrier-to-noise ratio of the time slot navigation signal received by the ground receiver is used in this application. Conduct an assessment, obtain The calculation expression is

[0100] ;

[0101] in, For Doppler shift measurements, the parameters related to ground receivers are Represents epoch i The carrier-to-noise ratio of the time slot navigation signal at ;

[0102] according to and Construct the cost function of the Doppler frequency shift factor, expressed as

[0103] .

[0104] It can be understood that the present application evaluates the accuracy of Doppler shift observation by the carrier-to-noise ratio of the received time slot navigation signal, thereby improving the accuracy of the model describing the random characteristics of Doppler shift observations during the optimization solution process, making the estimation result of the state variable better.

[0105] Furthermore, the state variable change constraints of the continuous epochs before and after the ground receiver are used as state constraint factors, including:

[0106] The constraint model of the state variable change of the continuous epochs before and after the ground receiver is defined as

[0107] ;

[0108] in, and are the ground receiver at epoch i With epoch The state variables at is the state variable error of the ground receiver;

[0109] Considering that the ground receiver is in a stationary state, the change constraint of the state variables of the ground receiver before and after the continuous epoch is defined as 0, and the variance of the state variable error is set to the minimum value. The cost function of the state constraint factor is constructed as follows:

[0110] ;

[0111] in, is the covariance matrix of the ground receiver state variables.

[0112] Step S4, constructing the objective function of the Doppler positioning factor graph model according to the cost function of the prior factor, the Doppler frequency shift factor and the state constraint factor, and optimizing and solving the state variables of the objective function by introducing a sliding window mechanism until the optimal state variables are iteratively outputted to obtain the Doppler positioning result of the ground receiver.

[0113] Specifically, the objective function of the Doppler localization factor graph model is expressed as

[0114] ;

[0115] in, Indicates the ground receiver from epoch i to the set of state variables of the current epoch, and , Indicates the ground receiver at epoch i The state variables when , n From epoch i The number of epochs up to the current epoch is the number of epochs; , and They represent the cost functions of the prior factor, Doppler frequency shift factor, and state constraint factor, respectively. and denote the covariance matrix of the prior factor error and the ground receiver state variable, Represents the Doppler shift measurement error variance.

[0116] In this objective function, the optimization calculation needs to be performed It is a set of state variables, not a single epoch. The essence of Doppler positioning is to find the optimal set of state variables that minimizes the above objective function. This is a nonlinear least squares problem, that is, to obtain the estimated optimal system state after satisfying the threshold of the least squares estimate, usually a linear iterative solution is performed.

[0117] Furthermore, as the epochs gradually increase, the factor nodes generated in the Doppler positioning factor graph model increase synchronously, and the model scale continues to expand. If the state quantity of the entire Doppler positioning factor graph model is estimated, the amount of calculation will continue to increase, and the accuracy of state variable estimation will not be significantly improved after exceeding a certain scale. Therefore, this application introduces a sliding window mechanism so that the global optimization process of the Doppler positioning factor graph model only occurs between the latest several state variable nodes, which can effectively reduce the algorithm calculation amount and improve the algorithm estimation speed. The specific steps include:

[0118] First, check whether the number of state variable nodes in the Doppler positioning factor graph model exceeds the sliding window length, such as Figure 4 As shown, the sliding window length is set to N , is the starting state variable in the sliding window, is the ending state variable in the sliding window.

[0119] If the number of state variable nodes does not exceed the sliding window length, it indicates that it is in the initial stage of positioning and no state variable optimization solution is performed at this time.

[0120] If the number of state variable nodes reaches the length of the sliding window, the state variable optimization solution is performed on the objective function of the Doppler positioning factor graph model within the sliding window.

[0121] If the number of state variable nodes exceeds the length of the sliding window, the sliding window is slid forward to update the Doppler positioning factor graph model within the sliding window, and then the state variable optimization solution is performed based on the objective function of the updated Doppler positioning factor graph model. Among them, the Doppler positioning factor graph model is updated as follows Figure 4 As shown, it includes: deleting the earliest state variable node and the corresponding Doppler frequency shift factor node and state constraint factor node in the sliding window, adding new state variable nodes and the corresponding Doppler frequency shift factor node and state constraint factor node, and constructing a new prior factor node based on the state variable and covariance matrix obtained by the optimization solution in the previous sliding window, and adding it to the Doppler positioning factor graph model in the current sliding window. This can effectively control the scale of the optimization window and effectively retain the historical observation information outside the sliding window.

[0122] Among them, the state variable optimization solution of the objective function of the Doppler positioning factor graph model is performed, including:

[0123] Objective Function The solution of is a nonlinear least squares problem, which is usually solved in an iterative way starting from an initial value, solving the update increment that makes the objective function value decrease, and correcting all states. This application converts the solution of the objective function of the Doppler positioning factor graph model into the update increment of the state variable The solution is expressed as

[0124] ;

[0125] in, is the increase in the state variable to be updated, For ground receivers k The set of state variables at the iteration, for The initial estimate of The objective function is contains the global Jacobian matrix of all nodes in the sliding window, For The residual term at ; Solve Equation, that is, the update increment can be obtained .

[0126] Use the Gauss-Newton algorithm to update the increment To solve, specifically, by dimension Perform QR decomposition and get

[0127] ;

[0128] In the above formula, Q for dimensional orthogonal matrix, R is an upper triangular matrix, and Represents the matrix dimension;

[0129] Correspondingly, the residual term It is expressed as:

[0130] ;

[0131] In the above formula, , , superscript T represents transpose;

[0132] but

[0133] ;

[0134] Update Increment The estimation equation is simplified to

[0135] .

[0136] When updating increments When the given threshold is met, the optimal state variable estimation of the Doppler positioning factor graph model in the current sliding window is output to obtain the Doppler positioning result of the ground receiver; otherwise, Update the state variables for the next iteration until When the given threshold is met, the Doppler positioning result of the ground receiver is output.

[0137] In summary, the present application proposes a method for Doppler positioning of low-orbit communication satellites based on factor graph optimization. After receiving the required observation data and solving the initial value of the ground receiver state, the Doppler positioning observation model is compared, and the factor graph framework is introduced to set the prior factor, Doppler frequency shift factor, state constraint factor and state variables composed of the three-dimensional position and frequency drift of the receiver. These factors and variables are used as nodes to construct the Doppler positioning factor graph model. In the factor graph optimization solution process, a sliding window mechanism is introduced to update the factor graph to control the scale of the graph, and the Gauss-Newton algorithm is used to solve the current factor graph state variables, and finally the Doppler positioning result is obtained. By modeling the Doppler positioning observation model with a factor graph, the present application gives play to the advantages of nonlinear modeling, global optimization, and full use of historical observations of the factor graph optimization method, and can obtain smaller positioning errors and faster convergence speeds.

[0138] In one embodiment, a low-orbit communication satellite Doppler positioning device based on factor graph optimization is provided, comprising:

[0139] An observation data acquisition module is used to receive the time slot navigation signal broadcast by the low-orbit communication satellite through a ground receiver to obtain the observation data of the low-orbit communication satellite;

[0140] A state initial value search module is used to search for the state initial value of the ground receiver according to the received observation data to obtain the state initial value;

[0141] The factor graph modeling module is used to take the three-dimensional position coordinates and frequency drift of the ground receiver that need to be solved by the Doppler positioning observation model as state variables, use the historical state variable information of the ground receiver to construct a priori factors, use the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal to construct the Doppler frequency shift factor, and take the state variable change constraint of the continuous epochs before and after the ground receiver as the state constraint factor, and then use the state variables, priori factors, Doppler frequency shift factors and state constraint factors as nodes to construct a Doppler positioning factor graph model;

[0142] The sliding window optimization solution module is used to construct the objective function of the Doppler positioning factor graph model according to the cost function of the prior factor, Doppler frequency shift factor and state constraint factor. The state variables of the objective function are optimized and solved by introducing the sliding window mechanism until the optimal state variables are iteratively output to obtain the Doppler positioning result of the ground receiver.

[0143] For the specific definition of the low-orbit communication satellite Doppler positioning device based on factor graph optimization, please refer to the definition of the low-orbit communication satellite Doppler positioning method based on factor graph optimization in the above text, which will not be repeated here. Each module in the above-mentioned low-orbit communication satellite Doppler positioning device based on factor graph optimization can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0144] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0145] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A Doppler positioning method for low-orbit communication satellite based on factor graph optimization, characterized in that: The method comprises: The ground receiver receives the time slot navigation signal broadcast by the low-orbit communication satellite to obtain the observation data of the low-orbit communication satellite; Searching for the initial state value of the ground receiver according to the received observation data to obtain the initial state value; The three-dimensional position coordinates and frequency drift of the ground receiver that need to be solved by the Doppler positioning observation model are taken as state variables, the historical state variable information of the ground receiver is used to construct a priori factors, the Doppler frequency shift factor is constructed using the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal, and the state variable change constraint of the continuous epochs before and after the ground receiver is taken as the state constraint factor, and then the state variables, priori factors, Doppler frequency shift factors and state constraint factors are used as nodes to construct a Doppler positioning factor graph model; The objective function of the Doppler positioning factor graph model is constructed according to the cost function of the prior factor, the Doppler frequency shift factor and the state constraint factor. The state variables of the objective function are optimized and solved by introducing a sliding window mechanism until the optimal state variables are iteratively output to obtain the Doppler positioning result of the ground receiver.

2. The method according to claim 1, characterized in that The initial state value of the ground receiver is searched based on the received observation data to obtain the initial state value, including: After receiving at least 4 sets of observation data, the ground receiver uses a grid search algorithm to search for initial state values ​​based on the received observation data to obtain the initial state values ​​of the three-dimensional position coordinates and frequency drift of the ground receiver; wherein the observation data includes the position, movement speed and Doppler frequency shift of the low-orbit communication satellite.

3. The method according to claim 2, characterized in that The grid search algorithm includes: for a low-orbit communication satellite that receives a time-slot navigation signal, the surface area covered by its time-slot navigation signal is divided into equally spaced grids, and each grid obtained by the division is solved by least squares one by one to search for the three-dimensional position coordinates of the ground receiver and the initial value of the frequency drift state.

4. The method according to claim 1, characterized in that The prior factors are constructed using the historical state variable information of the ground receiver, including: The prior factors are used to characterize the historical state variable information of the ground receiver, and the prior factor constraint model of the ground receiver is defined, which is expressed as ； in, Indicates the ground receiver at epoch i The state variables at represents the prior factor, represents the prior factor error; According to the prior factor error Construct the cost function of the prior factor, expressed as ； in, is the prior factor error The covariance matrix of ; where, at the initial moment, the initial value of the ground receiver's state is taken as the initial value of the prior factor.

5. The method according to claim 1, characterized in that The Doppler frequency shift factor is constructed using the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal, including: When the Doppler frequency shift measurement error is considered, the static instantaneous Doppler positioning observation model of the ground receiver is expressed as ； in, Epoch i The Doppler shift at is the three-dimensional position coordinates of the ground receiver Sum frequency drift The state variables composed of T represents transpose; Epoch i Doppler frequency shift measurement error when The frequency of transmitting time-slot navigation signals for low-orbit communication satellites; Epoch i The movement speed of low-orbit communication satellites at the time; , Epoch i The position of low-orbit communication satellites and ground receivers at that time; is the speed of light; definition Epoch i The Doppler frequency shift measurement error The variance of the time slot navigation signal received by the ground receiver is calculated based on the carrier-to-noise ratio of the time slot navigation signal received by the ground receiver. Conduct an assessment, obtain The calculation expression is ； in, For Doppler shift measurements, the parameters related to ground receivers are Represents epoch i The carrier-to-noise ratio of the time slot navigation signal at ; according to and Construct the cost function of the Doppler frequency shift factor, expressed as 。 6. The method according to claim 1, characterized in that The state variable change constraints of the continuous epochs before and after the ground receiver are used as state constraint factors, including: The constraint model of the state variable change of the continuous epochs before and after the ground receiver is defined as ； in, and are the ground receiver at epoch i With epoch The state variables at is the state variable error of the ground receiver; Considering that the ground receiver is in a stationary state, the change constraint of the state variables of the ground receiver before and after the continuous epoch is defined as 0, and the variance of the state variable error is set to the minimum value. The cost function of the state constraint factor is constructed as follows: ； in, is the covariance matrix of the ground receiver state variables.

7. The method according to claim 1, characterized in that The objective function of the Doppler positioning factor graph model is constructed according to the cost function of the prior factor, the Doppler frequency shift factor and the state constraint factor, which is expressed as ； in, Indicates the ground receiver from epoch i to the set of state variables of the current epoch, and , Indicates the ground receiver at epoch i The state variables at n From epoch i the number of epochs to the current epoch; , and They represent the cost functions of the prior factor, Doppler frequency shift factor, and state constraint factor, respectively. and denote the covariance matrix of the prior factor error and the ground receiver state variable, Represents the variance of the Doppler shift measurement error.

8. The method according to claim 7, characterized in that The objective function is optimized and solved by introducing a sliding window mechanism, including: Detect and determine whether the number of state variable nodes in the Doppler positioning factor graph model exceeds the sliding window length; If the number of state variable nodes does not exceed the sliding window length, no state variable optimization solution is performed; If the number of state variable nodes reaches the length of the sliding window, within the sliding window, the state variable optimization solution is performed on the objective function of the Doppler positioning factor graph model; If the number of state variable nodes exceeds the length of the sliding window, the sliding window is slid forward to update the Doppler positioning factor graph model in the sliding window, and then the state variable optimization solution is performed based on the objective function of the updated Doppler positioning factor graph model; wherein the Doppler positioning factor graph model update includes: deleting the earliest state variable node and the corresponding Doppler frequency shift factor node and state constraint factor node in the sliding window, adding new state variable nodes and the corresponding Doppler frequency shift factor node and state constraint factor node, and constructing a new priori factor node based on the state variables and covariance matrix obtained by the optimization solution in the previous sliding window, and adding it to the Doppler positioning factor graph model in the current sliding window.

9. The method according to claim 8, characterized in that The objective function of the Doppler positioning factor graph model is subjected to state variable optimization and solution, including: The solution of the objective function of the Doppler positioning factor graph model is equivalent to converting the update increment of the state variable The solution is expressed as ； in, is the increase in the state variable to be updated, For ground receivers k The set of state variables at the iteration, for The initial estimate of The objective function is contains the global Jacobian matrix of all nodes in the sliding window, For The residual term at ; Use the Gauss-Newton algorithm to update the increment To solve, specifically, by Victoria Perform QR decomposition and get ； In the above formula, Q for dimensional orthogonal matrix, R is an upper triangular matrix, and Represents the matrix dimension; Correspondingly, the residual term It is expressed as: ； In the above formula, , , superscript T represents transpose; but ； Update Increment The estimation equation is simplified to ； When updating increments When the given threshold is met, the optimal state variable estimation of the Doppler positioning factor graph model in the current sliding window is output to obtain the Doppler positioning result of the ground receiver; otherwise, Update the state variables for the next iteration until When the given threshold is met, the Doppler positioning result of the ground receiver is output.

10. A low-orbit communication satellite Doppler positioning device based on factor graph optimization, characterized in that: The device comprises: An observation data acquisition module is used to receive the time slot navigation signal broadcast by the low-orbit communication satellite through a ground receiver to obtain the observation data of the low-orbit communication satellite; A state initial value search module is used to search for the state initial value of the ground receiver according to the received observation data to obtain the state initial value; A factor graph modeling module is used to take the three-dimensional position coordinates and frequency drift of the ground receiver that need to be solved by the Doppler positioning observation model as state variables, use the historical state variable information of the ground receiver to construct a priori factors, use the Doppler frequency shift measurement error variance based on the Doppler positioning observation model and the carrier-to-noise ratio evaluation of the received time slot navigation signal to construct a Doppler frequency shift factor, and take the state variable change constraint of the continuous epochs before and after the ground receiver as a state constraint factor, and then use the state variables, priori factors, Doppler frequency shift factors and state constraint factors as nodes to construct a Doppler positioning factor graph model; The sliding window optimization solution module is used to construct the objective function of the Doppler positioning factor graph model according to the cost function of the prior factor, the Doppler frequency shift factor and the state constraint factor, and optimize the state variables of the objective function by introducing a sliding window mechanism until the optimal state variables are iteratively output to obtain the Doppler positioning result of the ground receiver.

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