Lunar base equipment inter-device measurement optimization cooperative navigation method

CN117146817BActive Publication Date: 2026-11-03BEIJING INST OF TECH
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Patent Information

Application Number
CN202310902016.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-07-21
Publication Date
2026-11-03
Estimated Expiration
2043-07-21

AI Technical Summary

Technical Problem

Cooperative navigation methods among lunar-based equipment struggle to meet high-precision requirements in the complex lunar environment. In particular, traditional ranging and inertial navigation fusion methods cannot effectively address the challenges posed by factors such as object obstruction and dust, thus failing to improve navigation accuracy and robustness.

Method used

By constructing a performance function, utilizing the information entropy and state covariance among lunar-based equipment, the ranging quality and positioning accuracy are optimized. Multiple UWB ranging nodes are combined for ranging, and the relative pose is determined by minimizing the ranging residual. Finally, the information is fused and filtered with autonomous navigation information to achieve cooperative navigation.

Benefits of technology

It improves the collaborative navigation accuracy and robustness of lunar-based equipment, enhances navigation performance in complex environments, and meets the requirements for long-term high-precision navigation.

✦ Generated by Eureka AI based on patent content.

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Abstract

The moon-based equipment inter-device measurement optimization cooperative navigation method disclosed by the application belongs to the field of autonomous navigation. The implementation method of the application is as follows: a moon-based equipment system navigation model is established, the installation positions of UWB nodes are determined, and the position vector P of the nodes relative to the center point is stored to the moon-based equipment navigation system; a performance function is constructed according to the information entropy and state covariance between moon-based equipments, the ranging quality and positioning accuracy of the moon-based equipment to be cooperated are evaluated, and a group of moon-based equipments are selected for cooperative measurement and pose estimation; the ranging of the optimized group of moon-based equipments is carried out by using the multiple UWB nodes carried on the moon-based equipments, the measurement information between the moon-based equipments is obtained, the best estimation of the relative pose between the moon-based equipments is found by minimizing the ranging residual error; the optimized cooperative measurement information is fused and filtered with the autonomous navigation data of the moon-based equipment, namely, the moon-based equipment pose is updated, and the cooperative navigation of the moon-based equipment on the moon surface is realized.
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Description

Technical Field

[0001] This invention relates to a measurement optimization cooperative navigation method among lunar-based equipment, and more particularly to a multi-lunar-based equipment cooperative navigation method suitable for pose estimation using relative information among lunar-based equipment, belonging to the field of autonomous navigation. Background Technology

[0002] Accurate estimation of the relative pose of lunar-based equipment is a crucial prerequisite for conducting collaborative lunar surface exploration. Due to the complex terrain, vast area to be explored, and unknown environment of the lunar surface, the collaborative navigation methods among lunar-based equipment must possess strong robustness. Furthermore, environmental factors such as rocks and dust can affect signal propagation, leading to difficulties in information exchange between lunar-based equipment and reduced quality of collaborative measurement information. Traditional collaborative navigation methods that combine ranging and inertial navigation are no longer sufficient to meet the high-precision requirements of exploration missions. Therefore, lunar-based equipment must possess strong collaborative navigation capabilities.

[0003] Utilizing relative information among lunar-based equipment for pose estimation can enhance the cooperative navigation capabilities of lunar-based equipment, thereby improving its survivability. When exploring the complex lunar environment, the quality of prior information obtained from the environment is often low, causing lunar-based equipment's autonomous navigation to fail to meet the requirements of long-term, high-precision navigation. Using the relative pose of lunar-based equipment as cooperative navigation information can improve its navigation performance and robustness. Methods for cooperative navigation using relative pose information have become a research hotspot. Optimizing relative pose information under the influence of object occlusion, dust interference, and non-line-of-sight signal propagation is a key technology for cooperative navigation using relative pose information, directly affecting the accuracy of cooperative navigation and determining the success or failure of the exploration mission. Therefore, the optimal selection method for cooperative measurement information is one of the key issues currently being addressed by researchers. Summary of the Invention

[0004] The purpose of this invention is to provide a measurement optimization cooperative navigation method for lunar-based equipment. A performance function is constructed based on the information entropy and state covariance among the lunar-based equipment to evaluate the ranging quality and positioning accuracy of the lunar-based equipment to be coordinated. A set of lunar-based equipment is then optimally selected for cooperative navigation. Multiple UWB ranging nodes are provided for each lunar-based equipment, and ranging is performed on the selected set of lunar-based equipment to obtain measurement information between the equipment. The optimal estimate of the relative pose between the lunar-based equipment is found by minimizing the ranging residual. All measurements are then combined to obtain the pose information of the lunar-based equipment to be estimated. Finally, the optimized cooperative measurement pose information is fused and filtered with the autonomous navigation information of the lunar-based equipment to achieve cooperative navigation of lunar-based equipment on the lunar surface.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] This invention discloses a method for optimized cooperative navigation of lunar-based equipment, comprising the following steps:

[0007] Step 1: Establish a navigation model for the lunar base equipment system, determine the installation location of the UWB nodes, and store the position vector P of the nodes relative to the center point in the lunar base equipment navigation system for subsequent pose estimation between lunar base equipment.

[0008] Define the pose state of the lunar-based equipment at time t as:

[0009] X (t) =[x (t) y (t) θ (t) ] T (1)

[0010] Where, x (t) and y (t) Let θ be the position coordinates of the lunar base equipment in the two-dimensional plane at time t. (t) Let represent the heading angle of the lunar base equipment at time t. The discretized two-dimensional kinematic model of the lunar base equipment i is as follows:

[0011]

[0012] Where T is the sampling period of the internal sensors of the lunar-based equipment, v (t) and ω (t) The forward and yaw speeds of the lunar-based equipment are indicated by the outputs of the equipment's sensors.

[0013] After adding noise, equation (2) can be rewritten as:

[0014] X (t+1) =X (t) +Φ (t) ·u (t) (3)

[0015] Where, Φ (t) Represents the input matrix, u (t) The input vector is represented as follows:

[0016]

[0017] in, Indicates sensor input, Represents the measurement noise vector. and Gaussian white noise is used to measure velocity and angular velocity, respectively.

[0018] Formula (3) can be expressed in the form of a nonlinear system state equation:

[0019]

[0020] The measurement equation between lunar base equipment i and lunar base equipment j is expressed as follows:

[0021]

[0022] in, Let be the two-dimensional coordinates of lunar base equipment i and lunar base equipment j at time t, respectively. Let be the distance between lunar base equipment i and lunar base equipment j at time t. Gaussian white noise for distance measurement Let h be the Jacobian matrix.

[0023] The measurement equation is linearized and expressed as:

[0024]

[0025] Where H is Z relative to X all Jacobian matrix, Let N be the column vector formed by the position vectors of the N lunar base equipment. To measure Gaussian white noise, H can be represented as:

[0026]

[0027] Considering that measurement Z depends only on the relative positions between lunar base equipment i and lunar base equipment j, H is rewritten as follows:

[0028]

[0029] By combining equations (5), (7), and (9), we can obtain the navigation model of lunar base equipment i based on the measurement of lunar base equipment j.

[0030] The position of UWB node k relative to the center of lunar base equipment i is P. i k (k = 1, 2, ..., K), where K represents the total number of UWB nodes installed on lunar-based equipment i. Similarly, the position of UWB node l relative to the center of lunar-based equipment j is... Where L represents the total number of UWB nodes installed on lunar base equipment i.

[0031] Let be the distance measured between UWB node k on lunar base equipment i and UWB node l on lunar base equipment j at time t. At this time, lunar base equipment i obtains K×L measurement data through measurements of lunar base equipment j, which can be represented in matrix form as follows:

[0032]

[0033] Due to terrain and distance limitations, lunar-based equipment i cannot receive information from all other lunar-based equipment. This represents the set of lunar base equipment i that can receive data from at time t. Therefore, the set of all data that the UWB node of lunar base equipment i can measure at time t is:

[0034]

[0035] Before the exploration mission begins, the installation position of the UWB node on each lunar-based equipment is determined, and the position vector P of the node relative to the center point is stored in the lunar-based equipment navigation system for subsequent pose estimation between lunar-based equipment.

[0036] Step 2: Construct a performance function based on the information entropy and state covariance among lunar base equipment, evaluate the ranging quality and positioning accuracy of the lunar base equipment to be coordinated, and optimize the selection of a group of lunar base equipment for coordinated measurement and pose estimation.

[0037] The information entropy algorithm is represented as:

[0038]

[0039] Wherein, E[ΔS z / x ] represents the expected value of the entropy change of the system itself.

[0040] The probability distribution of lunar-based equipment state X follows a Gaussian distribution; therefore, the optimization criterion based on information entropy is:

[0041]

[0042] In the formula, Λ represents the covariance matrix of the state variables of the entire lunar base equipment formation, and Σ ii Let Σ represent the covariance matrix of the state variables of lunar base equipment i. ij Let Λ represent the correlation matrix between the state variables of lunar base equipment i and the state variables of lunar base equipment j.

[0043]

[0044] By integrating information entropy and estimated covariance, a performance function for optimizing measurement information is established. Considering the inconsistency in units for each factor, standardization is required. When there are N lunar base stations, the information entropy of lunar base station i observing lunar base station j is I. j The estimated covariance matrix of lunar base equipment j is P. j Where j = 1 to N, j ≠ i, therefore, the performance function of lunar base equipment i with respect to lunar base equipment j is:

[0045]

[0046] in:

[0047]

[0048] According to equation (15), a sequence of lunar base equipment is selected at time t for cooperative pose estimation of lunar base equipment i. express.

[0049] Step 3: Using multiple UWB nodes mounted on the lunar base equipment, distance measurement is performed on a group of lunar base equipment selected in Step 2 to obtain measurement information between the lunar base equipment. The optimal estimate of the relative pose between the lunar base equipment is found by minimizing the distance measurement residual.

[0050] The actual distance between UWB node k on lunar base equipment i and UWB node l on lunar base equipment j at time t is obtained by mutual distance measurement between the nodes. The theoretical distance is determined by the given positioning attitude information based on geometric relationships. The theoretical distance between UWB node k on lunar base equipment i and UWB node l on lunar base equipment j is calculated to be:

[0051]

[0052] The objective function for minimizing the ranging residual is:

[0053]

[0054] in, Equation (18) is a nonlinear optimization problem. By solving it through graph optimization, the optimal estimate of the relative pose between lunar base equipment i and lunar base equipment j at time t can be obtained.

[0055] Step 4: The optimized collaborative measurement information is fused and filtered with the autonomous navigation data of the lunar-based equipment, that is, the pose of the lunar-based equipment is updated to realize the collaborative navigation of the lunar-based equipment.

[0056] Beneficial effects:

[0057] 1. The present invention discloses a measurement optimization cooperative navigation method among lunar-based equipment, which evaluates the ranging quality and positioning accuracy of the lunar-based equipment to be cooperated with based on information entropy, avoids the impact of low-quality cooperative measurement information on the navigation system, and thus improves the overall accuracy and robustness of the lunar-based equipment formation cooperative navigation system.

[0058] 2. The present invention discloses a measurement optimization cooperative navigation method between lunar base equipment, which equips each lunar base equipment with multiple UWB ranging nodes, performs ranging on a selected group of lunar base equipment, obtains measurement information between lunar base equipment, and determines the relative pose between lunar base equipment by minimizing the ranging residuals of all UWB nodes, thereby improving the pose estimation accuracy and enhancing the quality of measurement information.

[0059] 3. The present invention discloses a measurement optimization cooperative navigation method for lunar-based equipment. Based on the beneficial effects 1 and 2, it integrates all measurements to obtain the pose information of the lunar-based equipment to be estimated; and fuses and filters the optimized cooperative measurement pose information with the autonomous navigation information of the lunar-based equipment to achieve cooperative navigation of lunar-based equipment on the lunar surface. Attached Figure Description

[0060] Figure 1 This is a flowchart of the measurement optimization cooperative navigation method between lunar-based equipment disclosed in this invention;

[0061] Figure 2 This is a schematic diagram of the lunar base equipment formation operation route in a specific embodiment of the present invention;

[0062] Figure 3 This is a diagram showing the installation location of the UWB node in a specific embodiment of the present invention;

[0063] Figure 4 This is a diagram showing the operational path of lunar base equipment 1 using different navigation methods in a specific embodiment of the present invention;

[0064] Figure 5 shows the simulation results of position error of lunar base equipment 1 using different navigation methods in a specific embodiment of the present invention. Figure 5(a) is a comparison of x-axis position error, 5(b) is a comparison of y-axis position error, and 5(c) is a comparison of heading angle θ error. Detailed Implementation

[0065] To better illustrate the purpose and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0066] To verify the feasibility of the present invention, this embodiment takes a five-vehicle lunar-based equipment formation for lunar surface exploration as an example.

[0067] like Figure 1 As shown in the figure, the specific implementation steps of the lunar-based equipment measurement optimization cooperative navigation method disclosed in this embodiment are as follows:

[0068] Step 1: Establish a navigation model for the lunar base equipment system and determine the installation location of the UWB node.

[0069] Define the pose state of the lunar-based equipment at time t as:

[0070] X (t) =[x (t) y (t) θ (t) ] T (19)

[0071] Where, x (t) and y (t)Let θ be the position coordinates of the lunar base equipment in the two-dimensional plane at time t. (t) Let represent the heading angle of the lunar base equipment at time t. The discretized two-dimensional kinematic model of the lunar base equipment i is:

[0072]

[0073] Where T is the sampling period of the internal sensors of the lunar-based equipment, and v (t) and ω (t) The forward and yaw speeds of the lunar-based equipment are obtained from the outputs of the equipment's sensors.

[0074] After adding noise, equation (20) can be rewritten as:

[0075] X (t+1) =X (t) +Φ (t) ·u (t) (twenty one)

[0076] Where, Φ (t) Represents the input matrix, u (t) The input vector is represented as follows:

[0077]

[0078] in, Indicates sensor input, Represents the measurement noise vector. and Gaussian white noise is used to measure velocity and angular velocity, respectively.

[0079] Formula (3) can be expressed in the form of a nonlinear system state equation:

[0080]

[0081] The initial position of Lunar Base Equipment 1 is the origin of the navigation coordinate system, the initial velocity is 0, and the initial pose is... The initial velocities and initial poses of the other lunar-based equipment are the same as those of lunar-based equipment 1. The initial poses and noise variances are shown in Table 1.

[0082] Table 1. Simulation Parameter Settings for Lunar Base Equipment

[0083]

[0084] Lunar-based equipment formation operation route as follows: Figure 2 As shown.

[0085] The measurement equation between lunar base equipment i and lunar base equipment j is expressed as follows:

[0086]

[0087] in, Let be the two-dimensional coordinates of lunar base equipment i and lunar base equipment j at time t, respectively. Let be the distance between lunar base equipment i and lunar base equipment j at time t. is the Gaussian white noise used for distance measurement, and h is the Jacobian matrix.

[0088] The measurement equation is linearized and expressed as:

[0089]

[0090] Where H is Z relative to X all Jacobian matrix, Let N be the column vector formed by the position vectors of the N lunar base equipment. To measure Gaussian white noise, H can be represented as:

[0091]

[0092] Considering that measurement Z depends only on the relative positions between lunar base equipment i and lunar base equipment j, H can be rewritten as follows:

[0093]

[0094] By combining equations (23), (25), and (27), we can obtain the navigation model of lunar base equipment i based on the measurement of lunar base equipment j.

[0095] The position of UWB node k relative to the center of lunar base equipment i is denoted as P. i k (k = 1, 2, ..., K), where K represents the total number of UWB nodes installed on lunar-based equipment i. Similarly, the position of UWB node l relative to the center of lunar-based equipment j is represented as... Where L represents the total number of UWB nodes installed on lunar-based equipment i. The installation locations of the UWB nodes are as follows: Figure 3 As shown, the greater the relative distance between UWB nodes on the lunar base equipment, the higher the pose estimation accuracy between lunar base equipment. Therefore, we chose to install the UWB nodes on the four corners of the solar panel.

[0096] Let t represent the measurement between UWB node k on lunar base equipment i and UWB node l on lunar base equipment j at time t. At this time, lunar base equipment i obtains K×L measurement data through the measurement of lunar base equipment j, which can be represented in matrix form as follows:

[0097]

[0098] Due to terrain and distance limitations, lunar-based equipment i cannot receive information from all other lunar-based equipment. This represents the set of lunar base equipment i that can receive data from at time t. Therefore, the set of all data that the UWB node of lunar base equipment i can measure at time t is:

[0099]

[0100] Before the exploration mission begins, the installation position of the UWB node on each lunar-based equipment is determined, and the position vector P of the node relative to the center point is stored in the lunar-based equipment navigation system for subsequent pose estimation between lunar-based equipment.

[0101] Step 2: Construct a performance function based on the information entropy and state covariance among lunar base equipment, evaluate the ranging quality and positioning accuracy of the lunar base equipment to be coordinated, and optimize the selection of a group of lunar base equipment for coordinated measurement and pose estimation.

[0102] The information entropy algorithm is represented as:

[0103]

[0104] Wherein, E[ΔS z / x ] represents the expected value of the entropy change of the system itself.

[0105] The probability distribution of lunar-based equipment state X follows a Gaussian distribution; therefore, the optimization criterion based on information entropy is:

[0106]

[0107] In the formula, Λ represents the covariance matrix of the state variables of the entire lunar base equipment formation, and Σ ii Let Σ represent the covariance matrix of the state variables of lunar base equipment i. ij Let Λ represent the correlation matrix between the state variables of lunar base equipment i and the state variables of lunar base equipment j.

[0108]

[0109] By integrating information entropy and estimated covariance, a performance function for optimizing measurement information is established. Considering the inconsistency in units for each factor, standardization is required. Assuming there are N lunar base stations, the information entropy of lunar base station i observing lunar base station j is I. j The estimated covariance matrix of lunar base equipment j is P. j Where j = 1 to N, j ≠ i, therefore, the performance function of lunar base equipment i with respect to lunar base equipment j is:

[0110]

[0111] in:

[0112]

[0113] According to equation (33), a set of lunar base equipment sequences for cooperative pose estimation of lunar base equipment i is selected at time t. express.

[0114] Step 3: Using multiple UWB nodes mounted on the lunar base equipment, distance measurement is performed on a group of lunar base equipment selected in Step 2 to obtain measurement information between the lunar base equipment. The optimal estimate of the relative pose between the lunar base equipment is found by minimizing the distance measurement residual.

[0115] The actual distance between UWB node k on lunar base equipment i and UWB node l on lunar base equipment j at time t is obtained by mutual distance measurement between the nodes. The theoretical distance is determined by the given positioning attitude information based on geometric relationships. The theoretical distance between UWB nodes k and l on lunar base equipment i and lunar base equipment j, calculated from the data, can be expressed as:

[0116]

[0117] like Figure 3 As shown, the theoretical distance between UWB node k on lunar base equipment i and UWB node l on lunar base equipment j can be calculated as follows:

[0118]

[0119] The objective function for minimizing the ranging residual is:

[0120]

[0121] in, The above equation is a nonlinear optimization problem, which can be solved by general graph optimization to obtain the optimal estimate of the relative pose between lunar base equipment i and lunar base equipment j at time t.

[0122] Step 4: The optimized collaborative measurement information is fused and filtered with the autonomous navigation data of the lunar-based equipment, that is, the pose of the lunar-based equipment is updated to realize the collaborative navigation of the lunar-based equipment.

[0123] To verify the superiority of our proposed method for lunar base equipment pose estimation, we used randomly selected cooperative measurement information between two lunar base equipment units to update the pose of lunar base equipment 1, thus comparing it with our proposed method. The operational path diagrams for lunar base equipment 1 using different navigation methods are shown below. Figure 4 As shown in Figure 5, the simulation results of position errors of lunar base equipment 1 using different navigation methods are presented. Figure 5(a) is a comparison of x-axis position errors, 5(b) is a comparison of y-axis position errors, and 5(c) is a comparison of heading angle θ errors. The pose estimation results are shown in the table below.

[0124] Table 2. Pose estimation results of the method in this paper and the randomly selected method.

[0125]

[0126] Simulation results demonstrate that the method described in this invention exhibits higher pose estimation accuracy and stability, both in terms of mean and standard deviation, thus validating the effectiveness of the selected results. This indicates that the quality of cooperative measurement information significantly impacts pose determination accuracy. Based on mutual measurements among multiple UWB nodes, this method introduces information entropy to evaluate cooperative measurement information, ensuring that the selected cooperative measurement information not only possesses good self-positioning accuracy but also high ranging quality, thereby improving the cooperative pose estimation accuracy of lunar-based equipment.

[0127] Thus, the optimized collaborative navigation method for lunar equipment measurement was completed.

[0128] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimized collaborative navigation between lunar-based equipment and spacecraft, characterized in that: Includes the following steps, Step 1: Establish a navigation model for the lunar-based equipment system, determine the installation locations of UWB nodes, and assign position vectors of the nodes relative to the center point. Stored in the lunar-based equipment navigation system for subsequent pose estimation between lunar-based equipment; Step 2: Construct a performance function based on the information entropy and state covariance among lunar base equipment, evaluate the ranging quality and positioning accuracy of the lunar base equipment to be coordinated, and optimize the selection of a set of lunar base equipment for coordinated measurement and pose estimation. The second step is implemented as follows: The information entropy algorithm is represented as: in, This represents the expected value of the system's entropy change. Indicates the status of lunar base equipment; Lunar base equipment status The probability distribution of follows a Gaussian distribution; therefore, the optimization criterion based on information entropy is: In the formula, It is a Jacobian matrix. This represents the covariance matrix of the state variables of the entire lunar base equipment formation. Indicates lunar-based equipment The covariance matrix of the state variables, Indicates lunar-based equipment State variables and lunar base equipment The correlation matrix between the state variables, then Represented as: Integrate information entropy and estimated covariance to establish a performance function for the measured information; considering the inconsistency of units for each factor, standardization is required; when there are multiple factors... If it's a monthly base equipment, then it's a monthly base equipment. Observed lunar-based equipment Information entropy is Lunar equipment The estimated covariance matrix is ,in Therefore, lunar-based equipment Lunar-based equipment The performance function is: in: According to the formula Select A set of time for lunar-based equipment Lunar equipment sequence for collaborative pose estimation, using express; Step 3: Using multiple UWB nodes mounted on the lunar base equipment, distance is measured on a group of lunar base equipment from Step 2 to obtain measurement information between the lunar base equipment. The optimal estimate of the relative pose between the lunar base equipment is found by minimizing the distance measurement residual. The method for implementing step three is as follows: Lunar equipment UWB nodes on With lunar-based equipment UWB nodes on The actual distance between nodes is obtained by measuring the distance between them, while the theoretical distance is determined by the given positioning pose information based on geometric relationships. , Lunar-based equipment UWB nodes on and lunar-based equipment UWB nodes on The calculated theoretical distance is: , , , They are respectively Lunar equipment and lunar-based equipment The position coordinates, and the objective function to minimize the ranging residual are: in, , for Lunar equipment UWB nodes on With lunar-based equipment UWB nodes on The distance between them; Equation (18) is a nonlinear optimization problem, which can be solved by graph optimization, that is, the distance between them. Lunar equipment With lunar-based equipment The optimal estimate of the relative pose between them; Step 4: The optimized collaborative measurement information is fused and filtered with the autonomous navigation data of the lunar-based equipment, that is, the pose of the lunar-based equipment is updated to realize the collaborative navigation of the lunar-based equipment.

2. The lunar-based equipment inter-vessel measurement optimization cooperative navigation method as described in claim 1, characterized in that: The implementation method for step one is as follows: Define lunar-based equipment The pose state at time t is: in, and They are respectively The position coordinates of the lunar base equipment in a two-dimensional plane at any given time. express The heading angle of the lunar base equipment at any given time; the discretized lunar base equipment The two-dimensional kinematic model is as follows: in, The sampling period for the internal sensors of the lunar-based equipment. and The forward and yaw speeds of the lunar-based equipment are obtained from the outputs of the lunar-based equipment's sensors. After adding noise Rewritten as: in, Represents the input matrix, The input vector is represented as follows: in, Indicates sensor input, Represents the measurement noise vector. and Gaussian white noise was used to measure velocity and angular velocity, respectively. The formula is expressed in the form of the state equation of a nonlinear system. : Lunar-based equipment and lunar-based equipment The measurement equation between them is expressed as: in, , They are respectively Lunar equipment and lunar-based equipment Two-dimensional coordinates, for Lunar equipment and lunar-based equipment The distance between them Gaussian white noise for distance measurement The Jacobian matrix, abbreviated as ; The measurement equation is linearized and expressed as: in, for Compared to Jacobian matrix, for The column vector formed by the position vectors of the lunar base equipment. To measure Gaussian white noise; Represented as: Consider measurement Relying solely on lunar-based equipment and lunar-based equipment The relative positions between them, Rewritten as Comprehensive ,Mode Japanese style That is, obtain lunar-based equipment Based on lunar-based equipment Measurement navigation model; UWB node Compared to lunar-based equipment The center position is , ,in Indicates installation on lunar base equipment The total number of UWB nodes; similarly, the number of UWB nodes. Compared to lunar-based equipment The center position is Location is , ,in Indicates installation on lunar base equipment The total number of UWB nodes on the platform; for Lunar equipment UWB nodes on With lunar-based equipment UWB nodes on The distance between them, at this time the lunar base equipment Through lunar base equipment The measurement yielded The measurement data are represented in matrix form as follows: Limited by terrain and distance, lunar-based equipment It cannot receive information about all other lunar-based equipment. Indicates lunar-based equipment exist A collection of lunar-based equipment that can be received at any time, therefore Lunar equipment The set of all data that a UWB node can measure is: Before the exploration mission begins, the installation location of the UWB node on each lunar-based vehicle is determined, and the position vector of the node relative to the center point is calculated. The data is stored in the lunar-based equipment navigation system for subsequent pose estimation among lunar-based equipment.

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