A low earth orbit navigation signal positioning method based on a factor graph method

Abstract

This invention presents a low-Earth orbit (LEO) navigation signal localization method based on factor graphs, belonging to the LEO satellite field of satellite navigation. Various measurement information is obtained through LEO satellites and an inertial navigation system (INS). A factor graph model is then established based on the LEO satellites and INS. Finally, constraints and factor nodes are set, and the cost function is determined. When the cost function reaches its minimum value, the partial derivatives with respect to the state variables are calculated to obtain an estimate of the state variables. This method, by introducing an INS and using a factor graph method to replace the least squares method for LEO navigation signal localization, reduces the complexity of traditional localization methods. This method has significant research and application value in the LEO satellite field.

Description

Technical Field

[0001] This invention relates to a low-Earth orbit navigation signal positioning method based on the factor graph method, belonging to the field of low-Earth orbit satellite navigation. Background Technology

[0002] GNSS navigation currently faces several challenges. GNSS navigation satellites are medium Earth orbit satellites, with orbital altitudes of 20,000-30,000 kilometers. Satellite signals experience significant attenuation as they reach the ground due to spatial losses. Furthermore, the high orbital altitude results in slow satellite geometric changes, making GNSS unable to meet some rapid positioning requirements. Simultaneously, the low transmission rate of existing GNSS navigation messages directly impacts the speed and real-time performance of positioning and navigation services. Low Earth orbit (LEO) satellites, with their lower orbital altitudes (generally several hundred to two thousand kilometers), experience less spatial signal loss and exhibit faster geometric changes, enabling rapid positioning. Moreover, LEO satellites offer higher information transmission rates. These two key advantages of LEO satellites—low orbital altitude and high communication rate—can compensate for the shortcomings of GNSS. Currently, LEO satellite positioning commonly utilizes the Doppler positioning principle and least squares calculations. Least squares calculations suffer from significant redundancy and are computationally cumbersome. Factor graphs, a graphical modeling tool, can reduce computational complexity and are widely used in statistics, artificial intelligence, and other fields. However, research on using factor graphs for LEO satellite positioning is relatively limited.

[0003] Therefore, constructing a low-orbit navigation signal positioning method based on factor graph method has important research significance and application value. Summary of the Invention

[0004] The purpose of this invention is to overcome the complexity of least squares positioning solutions and propose a low-orbit navigation signal positioning method based on factor graph method.

[0005] This invention is achieved through the following technical solution:

[0006] A low-Earth orbit navigation signal positioning method based on factor graph method includes the following steps:

[0007] (101) Obtain various measurement information through low-orbit satellites and inertial navigation systems;

[0008] (102) A factor graph model is established based on low-orbit satellites and inertial navigation systems. The state vector of the navigation system is defined as the variable node of the factor graph, and the various measurement information obtained by low-orbit satellites and inertial navigation systems is defined as the factor node of the factor graph.

[0009] (103) Set constraints and factor nodes, and confirm the cost function. When the cost function reaches its minimum value, calculate the partial derivatives of the state variables to obtain an estimate of the state variables.

[0010] Complete the low-orbit navigation signal positioning based on the factor graph method.

[0011] The bipartite graph model of the factor graph is as follows:

[0012] G = (F, X, E)

[0013] Where, variable node x j ∈X, representing the variable in the global multivariate function, factor node f i ∈F, representing a local function in factorization, marginal function e i，j ∈E, representing if and only if the state variable node x in the factor graph j and the corresponding factor node f i When they are related, there is a connecting edge between them;

[0014] in,

[0015] in, For attitude angle error; δV=[δV e δV n δV u ] T For velocity error; δp=[δL δλ δh] T b is the position error; g =[b gx b gy b gz ] T b is the constant drift of the gyroscope. a =[b ax b ay b az ] T This is the constant bias for the angular velocity meter.

[0016] The present invention has the following advantages over the prior art:

[0017] Compared to the traditional least squares method for low-Earth orbit (LEO) satellite positioning, the factor graph-based LEO satellite positioning solution is calculated only when the measured quantity changes, which can greatly reduce the redundancy and computational complexity of the solution. Attached Figure Description

[0018] Figure 1 This is a flowchart of an embodiment of the present invention. Detailed Implementation

[0019] To better illustrate the purpose and advantages of the present invention, the following description is provided in conjunction with the appendix. Figure 1 The technical solutions of the present invention will be further explained in the examples and embodiments.

[0020] A low-Earth orbit navigation signal positioning method based on factor graph method includes the following steps:

[0021] Step one: Obtain various measurement information through low-orbit satellites and inertial navigation systems.

[0022] Step 2: Establish a factor graph model based on low-Earth orbit satellites and inertial navigation systems.

[0023] The state vector of the navigation system is defined as the variable node of the factor graph, and the measurement information output by inertial navigation and low-Earth orbit satellites is defined as the factor node of the factor graph.

[0024] Let the bipartite graph model of the factor graph be:

[0025] G = (F, X, E)

[0026] Where, variable node x j ∈X, representing a variable in the global multivariate function; factor node f i ∈F, representing a local function in factorization; marginal function e i，j ∈E, representing if and only if the state variable node x in the factor graph j and the corresponding factor node f i When they are related, there is a connecting edge between them.

[0027] In this invention, 15-dimensional state variables of the system are selected:

[0028]

[0029] in, For attitude angle error; δV=[δV e δV n δV u ] T For velocity error; δp=[δL δλ δh] T b is the position error; g =[b gx b gy b gz ] T b is the constant drift of the gyroscope. a =[b ax b ay b az ] T This is the constant bias for the angular velocity meter.

[0030] According to the Doppler positioning principle, the relationship between the measured quantity Z(t) and the system navigation state X(t) can be expressed as:

[0031] Z(t)=HX(t)+ε

[0032] Where H is the transformation matrix from the estimate to the measured data, ε is the error vector, and Z(t) is the actual measured value.

[0033] Step 3: Low-orbit navigation and positioning based on factor graphs.

[0034] The factor graph method is a solution process that finds solutions that satisfy constraint rules. In this invention, the constraints are set as follows:

[0035]

[0036] Where P(X) is the joint distribution function located on X(t). A factor node can be written as f n (X(t))=L(Z(t)-HX(t)) represents the difference between the predicted and actual measurement information obtained by the factor nodes, which is used to construct the corresponding index function to obtain the estimate of the state variable. The factor node fn∈F represents the local function in the factorization, and N represents the set of all factor nodes. For example, if there are three factor nodes, then N is {1, 2, 3}. L(*) is the cost function of the estimated quantity; H is the transformation relationship matrix from the estimated quantity to the measured data. In the navigation framework, H can predict the sensor measurement value based on the given state estimate.

[0037] When the cost function L(*) reaches its minimum value, the partial derivative with respect to the system state variable X(t) is taken, thereby obtaining an estimate of the state variable X(t).

[0038] When the cost function L(*) reaches its minimum:

[0039]

[0040] Where W is the prior weighting matrix, and each state variable in X is weighted by W according to different user needs. Take the partial derivatives of the state variables with respect to the above equation and set them to 0:

[0041]

[0042] Therefore, the estimate of the current state X is:

[0043]

Claims

1. A low-orbit navigation signal positioning method based on factor graph method, characterized in that, Includes the following steps: (101) Obtain various measurement information through low-orbit satellites and inertial navigation systems; (102) A factor graph model is established based on low-Earth orbit satellites and inertial navigation systems. The state vector of the navigation system is defined as the variable node of the factor graph, and the various measurement information obtained by low-Earth orbit satellites and inertial navigation systems is defined as the factor node of the factor graph. (103) Set constraints and factor nodes, and confirm the cost function. When the cost function reaches its minimum value, calculate the partial derivatives with respect to the state variables to obtain an estimate of the state variables; the specific process is as follows: Set the constraints as follows: in, To be positioned in The joint distribution function on the , with one factor node written as This indicates that the factor node obtains the difference between the predicted measurement information and the actual measurement information, and constructs the corresponding index function to obtain the estimate of the state variable; where, These are actual measured values. For system state variables, , Error vector; factor nodes , represents the local function in factorization; N represents the set of all factor nodes; H is the cost function of the estimated quantity; H is the transformation matrix from the estimated quantity to the measured data. In the navigation framework, H predicts the sensor measurements based on the given state estimate. In the cost function When taking the minimum value, the system state variables Find the partial derivatives to obtain the system state variables. The estimate; In the cost function When taking the minimum value: Where W is the prior weighting matrix, which is used to weight users according to their different needs. Each state variable in the equation is weighted; the partial derivatives of the state variables with respect to the above equation are then set to 0: This gives us the current state. The estimate is: ； Complete the low-orbit navigation signal positioning based on the factor graph method.

2. The low-orbit navigation signal positioning method based on the factor graph method according to claim 1, characterized in that, The bipartite graph model of the factor graph is: G = (F, X, E) Among them, variable nodes , representing variables in a global multivariate function, factor nodes , representing a local function in factorization, marginal , representing if and only if the state variable nodes in the factor graph and the corresponding factor nodes When they are related, there is a connecting edge between them; in, ; For attitude angle error, For speed error, For positional error, For gyroscope constant drift, This is the constant bias for the angular velocity meter.

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