An extensible consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection

Abstract

The application is a scalable consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection. The application relates to the field of underwater AUV cooperative positioning technology. The application stores and updates historical original measurement information, stores the cumulative displacement measurement value broadcast by the target AUV, the ranging measurement value of the target AUV and the corresponding covariance matrix; analytically calculates the relative position solution set, simultaneously solves the current ranging equation and the historical supplementary constraint equation, and obtains the relative position solution set; determines the feasible region, eliminates ambiguous points and error points, and identifies the inner point set around the true relative position; and fuses the remaining relative position solutions, fuses the inner points by using the covariance intersection algorithm, and obtains the final relative position estimation. The application has natural robustness advantage when facing underwater communication delay and data packet loss.

Description

Technical Field

[0001] This invention relates to the field of underwater AUV cooperative positioning technology, and is a scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection. Background Technology

[0002] Significant progress has been made in the field of underwater robotics over the past few decades. Autonomous Underwater Vehicles (AUVs), as a prime example, have been widely used in various underwater missions, including underwater search and rescue, shipwreck salvage, and submarine cable inspection. AUV swarms are typically teams of multiple AUVs that collaborate through acoustic communication, making them far more efficient as mission execution units compared to a single AUV. To achieve formation control and obstacle avoidance, each unit in an underwater unmanned vehicle swarm needs to obtain real-time relative position information of other units, a requirement that has spurred the development of relative positioning technology.

[0003] In practical engineering applications, while ultra-short baseline systems can directly measure relative position, their high cost and complex installation procedures limit their widespread application. Current mainstream research methods focus on relative positioning schemes based on multi-sensor information fusion. Against this backdrop, the requirements for estimation consistency and robustness in specific underwater environments are becoming increasingly prominent. Most current cutting-edge research prioritizes solving the absolute self-localization problem through integrated navigation systems, and then obtains the relative position through differential operations. Only a very few studies focus on the direct relative positioning problem, the core idea of ​​which is to directly calculate the relative position based on interactive measurement data such as inter-cell ranging and azimuth. Direct relative positioning methods can be divided into two paradigms: those based on holistic modeling and those based on relative modeling.

[0004] The advantage of indirect relative positioning lies in its elimination of the need to model the kinematics of other autonomous underwater vehicles (AUVs), which are often difficult to obtain due to communication limitations. However, a major drawback of indirect relative positioning methods is the significant challenge of ensuring consistency during measurement updates, especially in underwater environments. Estimated consistency is crucial for navigation tasks as it provides a range of uncertainties for redundant collision avoidance. In contrast, direct relative positioning methods implicitly account for the correlations between AUVs by simulating relative states, making the measurement update process remarkably simple and consistent. Despite its inherent advantage in estimation consistency, the difficulty in acquiring kinematic information from other AUVs hinders the execution of time-update procedures for filters, thus limiting the development of direct relative positioning methods.

[0005] Furthermore, underwater acoustic ranging exhibits strong nonlinear characteristics. Existing methods based on Gaussian approximation filters (such as extended Kalman filtering, unscented Kalman filtering, and capacitive Kalman filtering) approximate the posterior probability density function as a Gaussian distribution. In strongly nonlinear scenarios, this fails to accurately describe posterior uncertainty, easily leading to severe estimation inconsistencies. While particle filters can handle nonlinear and non-Gaussian problems, they fail to consider the correlation between AUVs, resulting in significant estimation inconsistencies, and their computational complexity is significantly higher than other filters. Factor graph methods formulate the relative position estimation problem as a sparse nonlinear least-squares optimization, but typically consume more computational resources than filter-based methods. Summary of the Invention

[0006] This invention addresses the aforementioned problems by deriving a novel direct relative positioning framework based on the intersection of multiple ranging circles, without requiring knowledge of the actual kinematics of other autonomous underwater vehicles (AUVs). The proposed framework requires each AUV to operate an independent filter and only needs to exchange accumulated displacements between two broadcasts. It also discloses a scalable, consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection.

[0007] This invention provides the following technical solutions: A scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection, the method comprising the following steps: Step 1: Update the storage of historical raw measurement information, storing the cumulative displacement measurement value broadcast by the target AUV, the distance measurement value between itself and the target AUV, and the corresponding covariance matrix; Step 2: Perform analytical calculation of the relative position solution set, solve the current distance measurement equation and the historical supplementary constraint equation simultaneously to obtain the relative position solution set; Step 3: Determine the feasible region, eliminate ambiguous and erroneous points, and identify the set of interior points surrounding the true relative position; Step 4: Consistent fusion of the remaining relative position solutions. The covariance intersection algorithm is used to fuse interior points to obtain the final relative position estimate.

[0008] Preferably, AUV is set Let a triplet Sub-filter exist Constant time about the target AUV The stored content, namely:

[0009] in, Store recent A UV that passes through the target Displacement measurements obtained from broadcasting Store the most recent data between two AUVs For each subsequent distance measurement, the stored content will be updated to include the latest original odometer and distance measurements, while the oldest data will be discarded. exist The measurement and storage of time is written as: .

[0010] Preferably, when receiving from the target AUV During broadcasting, AUV Target AUV Cumulative displacement estimation included in the broadcast and the corresponding covariance matrix Store displacement measurement set For future use, the self-displacement estimate and distance measurement values ​​and their corresponding covariance matrices are stored in the same way.

[0011] Preferably, step 2: acoustic ranging, the horizontal ranging measurement value is obtained based on the time difference of arrival and the depth difference:

[0012] in, Denotes the Euclidean norm. Indicates the speed of sound. These represent the reception time and broadcast time of the acoustic packet, respectively. Autonomous Underwater Vehicle (AUV) With Autonomous Underwater Vehicle (AUV) The depth difference between them Indicates that the autonomous underwater vehicle (AUV) was broadcasting. With the receiving autonomous underwater vehicle (AUV) The relative positions between them; Using the first Based on historical ranging measurements and the cumulative displacement during that period, an error-free supplementary relative position constraint is derived, expressed as:

[0013] in, Defined as AUV and Between moments arrive Relative displacement at any given moment; Using this constraint and the obtained original measurements, a set of equations is derived regarding the estimated relative position, with subscripts... This indicates that the estimate is based on the current distance measurement value and the most recent [number] [unit]. Generated from historical ranging measurements and corresponding cumulative displacement estimates:

[0014] in, It is an estimate of the actual cumulative displacement.

[0015] Preferably, by utilizing more supplementary constraints, other paired solutions can be obtained, up to a maximum of [number missing]. Each relative position estimate constitutes a relative position solution set; When two measuring circles intersect, two intersection points appear, and the one furthest from the true relative position is defined as the fuzzy point.

[0016] Preferably, the following description is given to define the predefined almost tangent case: Statistical external tangency: Two circular rings, tangent from their inner circles to their outer circles; Statistical inscribed circle: Two circular rings, from the intersection of the outer diameter of the larger circle and the inner diameter of the smaller circle, to the intersection of the inner diameter of the larger circle and the outer diameter of the smaller circle.

[0017] Preferably, the statistical external and statistical internal cases are described as follows:

[0018] in, Indicates the distance between the centers of the two circles. and These represent the larger and smaller radii of the two intersecting circles, respectively. It is the sum of the widths of the two rings. and These represent the current standard deviation of the distance measurement and the standard deviation of the distance measurement after historical translation, respectively.

[0019] Preferably, after obtaining the covariance matrix of the internal relative position set and its estimated values, the covariance intersection algorithm is used to provide a better and more consistent relative position estimate for the internal relative position set. and the corresponding covariance set The final relative position estimate The expression is as follows: .

[0020] A computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a scalable, consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection.

[0021] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement a scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection.

[0022] The present invention has the following beneficial effects: This invention creatively proposes an engineering-feasible relative positioning framework that is scalable and adaptable to variations in the number of crew members in autonomous underwater vehicles (AUVs). The proposed framework exhibits inherent robustness against underwater communication delays and packet loss. Furthermore, under the same computational load and storage conditions, this framework demonstrates significant advantages in estimation accuracy and consistency.

[0023] This invention provides a scalable and consistent AUV swarm relative positioning method based on asynchronous ranging circular intersection. In practical applications, for specific underwater problems such as extremely limited communication capabilities and strong acoustic ranging nonlinearities, the proposed framework implements a set of individual sub-filters, the number of which is equal to the number of agents in the underwater vehicle swarm. In each sub-filter, feasible relative position solutions are first generated by solving the nonlinear ranging intersection equation, and then unreasonable or even erroneous solutions are eliminated using a statistical classification method. Finally, the accurate relative position result is obtained by fusing the remaining solutions. Numerical and physical simulation experiments demonstrate that the proposed framework outperforms existing state-of-the-art methods in terms of scalability, estimation accuracy, and consistency. Attached Figure Description

[0024] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0025] Figure 1 This is shown as the uncertainty region for the two cases (intersecting and tangent) of the present invention; Figure 2 Displayed as a simulated trajectory ("SP" indicates the starting point); Figure 3 The data is displayed as the root mean square error (RMSE) of four AUVs. Figure 4 The normalized estimate of squared errors (NEES) for four AUVs is shown. Figure 5 The display shows the operating trajectories of four AUVs (physical simulation experiment); Figure 6 Shown as the average relative position error of all algorithms and 3- curve. Detailed Implementation

[0026] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] The present invention will be described in detail below with reference to specific embodiments. Specific Implementation Example 1: according to Figures 1 to 6 As shown, the specific optimized technical solution adopted by the present invention to solve the above-mentioned technical problems is: The present invention relates to a scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection.

[0029] This invention provides a scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection, the method comprising the following steps: The method includes the following steps: Step 1: Historical raw measurement information storage and update, storing the cumulative displacement measurement value broadcast by the target AUV, the distance measurement value between itself and the target AUV, and the corresponding covariance matrix; Step 2: Analytical calculation of the relative position solution set. Solve the current distance measurement equation and the historical supplementary constraint equation simultaneously to obtain the relative position solution set; Step 3: Determine the feasible region, eliminate ambiguous and erroneous points, and identify the set of interior points surrounding the true relative position; Step 4: Consistent fusion of the remaining relative position solutions. The covariance intersection algorithm is used to fuse the interior points to obtain the final relative position estimate.

[0030] Setting AUV Let a triplet Sub-filter exist Constant time about the target AUV The stored content, namely:

[0031] in, Store recent A UV that passes through the target Displacement measurements obtained from broadcasting Store the most recent data between two AUVs For each subsequent distance measurement, the stored content will be updated to include the latest original odometer and distance measurements, while the oldest data will be discarded. exist The measurement and storage of time is written as: .

[0032] When receiving from the target AUV During broadcasting, AUV Target AUV Cumulative displacement estimation included in the broadcast and the corresponding covariance matrix Store displacement measurement set For future use, the self-displacement estimate and distance measurement values ​​and their corresponding covariance matrices are stored in the same way.

[0033] Step 2: Acoustic ranging, horizontal ranging measurements are obtained based on the time difference of arrival and depth difference:

[0034] in, Denotes the Euclidean norm. Indicates the speed of sound. These represent the reception time and broadcast time of the acoustic packet, respectively. Autonomous Underwater Vehicle (AUV) With Autonomous Underwater Vehicle (AUV) The depth difference between them Indicates that the autonomous underwater vehicle (AUV) was broadcasting. With the receiving autonomous underwater vehicle (AUV) The relative positions between them; Using the first Based on historical ranging measurements and the cumulative displacement during that period, an error-free supplementary relative position constraint is derived, expressed as:

[0035] in, Defined as AUV and Between moments arrive Relative displacement at any given moment; Using this constraint and the obtained original measurements, a set of equations is derived regarding the estimated relative position, with subscripts... This indicates that the estimate is based on the current distance measurement value and the most recent [number] [unit]. Generated from historical ranging measurements and corresponding cumulative displacement estimates:

[0036] in, It is an estimate of the actual cumulative displacement.

[0037] By utilizing more supplementary constraints, other paired solutions can be obtained, at most [number missing]. Each relative position estimate constitutes a relative position solution set; When two measuring circles intersect, two intersection points appear, and the one furthest from the true relative position is defined as the fuzzy point.

[0038] The following description is given to define the predefined near-tangent case: Statistical external tangency: Two circular rings, tangent from their inner circles to their outer circles; Statistical inscribed circle: Two circular rings, from the intersection of the outer diameter of the larger circle and the inner diameter of the smaller circle, to the intersection of the inner diameter of the larger circle and the outer diameter of the smaller circle.

[0039] The statistical external and internal cases are described as follows:

[0040] in, Indicates the distance between the centers of the two circles. and These represent the larger and smaller radii of the two intersecting circles, respectively. It is the sum of the widths of the two rings. and These represent the current standard deviation of the distance measurement and the standard deviation of the distance measurement after historical translation, respectively.

[0041] After obtaining the covariance matrix of the internal relative position set and its estimates, the covariance intersection algorithm is used to provide a better and more consistent relative position estimate for the internal relative position set. and the corresponding covariance set The final relative position estimate The expression is as follows: .

[0042] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection.

[0043] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement a scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection. Specific Implementation Example 2: The only difference between Embodiment 2 and Embodiment 1 of this application is that: This invention provides a scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection, comprising: Step 1: Storing and updating historical raw measurement information Step 2: Analytical calculation of the solution set of relative positions Step 3: Determining the Feasible Area Step 4: Consistency fusion of remaining relative position solutions Furthermore, in step 1, AUV is used. For example, let's consider a triplet. Sub-filter exist Constant time about the target AUV The stored content, namely:

[0045] in, Store recent A UV that passes through the target Displacement measurements obtained from broadcasting. Store the most recent data between two AUVs The stored data will be updated to include the latest original odometer and distance measurements, while the oldest data will be discarded. The measurement and storage of time can be written as:

[0046] When receiving from the target AUV During broadcasting, AUV Target AUV Cumulative displacement estimation included in the broadcast and the corresponding covariance matrix Store displacement measurement set For future use. The self-displacement estimate and distance measurement values ​​and their corresponding covariance matrices are also stored in the same way.

[0047] Step 2 aims to obtain a set of relative position solutions by solving multiple ranging measurement functions constructed with respect to relative positions. According to the principles of acoustic ranging, horizontal ranging measurements can be obtained based on the time difference of arrival and the depth difference.

[0048]

[0049] in Denotes the Euclidean norm. This indicates the speed of sound (1500 meters per second). These represent the reception time of the acoustic packet (relative to the autonomous underwater vehicle AUV). ) and broadcast time (relative to autonomous underwater vehicle AUV) ), indicating an autonomous underwater vehicle (AUV). With Autonomous Underwater Vehicle (AUV) The depth difference between them Indicates that the autonomous underwater vehicle (AUV) was broadcasting. With the receiving autonomous underwater vehicle (AUV) The relative positions between them.

[0050] Two-dimensional relative position cannot be calculated using only one-dimensional distance measurement values. This invention utilizes the first... Based on historical ranging measurements and the cumulative displacement during that period, an error-free supplementary relative position constraint can be derived, expressed as:

[0051] in, Defined as AUV and Between moments arrive The relative displacement at time t. Using this constraint and the obtained original measurements, a set of equations can be derived regarding the estimated relative position, with subscripts... This indicates that the estimate is based on the current distance measurement value and the most recent [number] [unit]. This is generated from historical ranging measurements and corresponding cumulative displacement estimates.

[0052]

[0053] in, This is an estimate of the actual cumulative displacement. It should be noted that at most two solutions representing possible relative positions can be obtained from this system of equations.

[0054] Based on the above system of equations, the form of the estimated value and the corresponding covariance matrix can be easily obtained. Solving this system of equations yields at most two solutions (when they intersect) and at least zero solutions (when they do not intersect). Similarly, other paired solutions can be obtained using additional constraints. Therefore, at most... There are several relative position estimates, which constitute the relative position solution set. As mentioned earlier, when two ranging circles intersect, there may be two possible intersection points, the one farther away from the true relative position is defined as the fuzzy point.

[0055] In step 3, to ensure the efficiency and correctness of the fusion, a feasible region determination method incorporating two classification approaches is proposed to eliminate ambiguous and erroneous points and identify the set of interior points surrounding the true relative position. This step ensures that a unique most feasible region is found, rather than multiple regions. Specifically: Step 3.1: Considering that the relative position solutions in the original relative position solution set may form several scattered uncertainty regions, this part proposes a fuzzy point elimination method to provide the statistically most likely region, and then identify the relative position solutions in the region for further use. Figure 1 A schematic diagram is shown illustrating the uncertainty region under two scenarios, differing only in the center position to represent tangency and intersection. Clearly, due to... Figure 3In the case of intersection on the right, the two uncertain regions overlap, while in the case of tangency, the size of the uncertain region is at least twice that of any single region in the case of intersection.

[0056] Furthermore, the uncertainty region in the tangent case varies considerably in different directions. It is subsequently found that, by utilizing more supplementary constraints, one of the two regions in the intersection case can be removed. Therefore, points generated by two nearly tangent ranging circles are statistically ambiguous. Conversely, points generated by the intersection of good circles can usually be easily distinguished as good or bad points using certain classification techniques. To achieve this, the following description is first given to define the predefined nearly tangent case.

[0057] Statistical external tangency: Two rings, tangent from their inner circles to their outer circles.

[0058] Statistical inscribed circle: Two circular rings, from the intersection of the outer diameter of the larger circle and the inner diameter of the smaller circle, to the intersection of the inner diameter of the larger circle and the outer diameter of the smaller circle.

[0059] In mathematical terms, these two statistical tangency cases can be expressed as follows:

[0060] in, Indicates the distance between the centers of the two circles. and These represent the larger and smaller radii of the two intersecting circles, respectively. It is the sum of the widths of the two rings. and These represent the current standard deviation of the distance measurement and the standard deviation of the distance measurement after historical translation, respectively. The latter can be approximated by a conservative bound that considers both distance measurement error and displacement error.

[0061] Step 3.2: After eliminating ambiguous points that may mislead the classification process, a classification algorithm is designed to identify the correct relative position solution around the true relative position.

[0062] After obtaining the covariance matrix of the internal relative position set and its estimates in step 4, considering the strong correlation between these internal relative position solutions due to sharing mutual displacement estimation information and current ranging measurement information, the covariance intersection algorithm is used to provide a better and more consistent relative position estimate. It should be noted that accurately estimating the correlation between these internal points is also feasible, but not necessary for simplifying calculations. For the internal relative position set... and the corresponding covariance set The final relative position estimate This can be expressed as:

[0063] Compared with existing methods, this method has the following three advantages: (1) The framework is scalable and can adapt well to changes in the number of crew members of autonomous underwater vehicles. (2) The proposed framework has a natural robustness advantage in the face of underwater communication delays and packet loss. (3) Under the same computational load and storage space conditions, the framework has significant advantages in estimation accuracy and consistency.

[0064] To verify the performance advantages of the scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection proposed in this invention, numerical simulation experiments and physical simulation experiments were conducted.

[0065] Numerical simulation experiments were conducted to compare the proposed method with state-of-the-art relative positioning methods using simulation data, including the Extended Kalman Filter (EKF), Covariance Intersection (CI), Interleaved Update (IU), Belief Propagation (BP), and Centralized EKF (CEKF). CEKF was used as a reference algorithm for estimation accuracy. Among these algorithms, some are commonly used in engineering, while others excel in relative positioning accuracy and consistency. This simulation considers a typical four-AUV underwater cooperative relative positioning scenario, with trajectories as follows... Figure 2 As shown in the diagram, each AUV is equipped with a DVL (Depth-of-Vehicle) and compass for dead reckoning, as well as an acoustic communication module for broadcast communication and ranging. Each AUV broadcasts in a predefined sequence at whole-second intervals. Notably, to obtain continuous relative position estimates, each AUV uses the velocity and heading from the broadcast packets to perform a first-order extrapolation of the positions of other AUVs. This explains the frequent fluctuations in the error curve. To simulate the complexity of the real underwater environment, underwater acoustic communication delays and packet loss are considered in the simulation.

[0066] The total simulation time is 1440 seconds. Fifty Monte Carlo simulations will be performed on all algorithms to eliminate randomness, and the root mean square error and normalized squared estimation error will be used as performance metrics to evaluate estimation accuracy and consistency, respectively. Since AUVs compute other AUVs... The relative position is calculated, and the average of the root mean square error (RMSE) and normalized estimation error square (NEES) of the relative positioning estimates is taken as the AUV. RMSE or NEES.

[0067] The proposed algorithm achieves state-of-the-art performance in estimation accuracy (except for CEKF), both in terms of estimation error after stabilization and convergence stability. Furthermore, the proposed algorithm outperforms other comparable algorithms in estimation consistency, thanks to its superior filter structure, which better handles nonlinearity and correlation. In handling nonlinearity, the proposed algorithm directly solves multiple ranging equations about relative positions, rather than recursively weighting prior and sparse individual ranging measurements, which can lead to poor updates. In handling correlation, the proposed algorithm employs multiple parallel sub-filters to achieve absolute isolation of relevant information.

[0068] In the physical simulation experiments, to further verify the effectiveness and superiority of the proposed algorithm, the open-source ROS underwater robot platform—the UUV simulator—was used to implement realistic underwater robot dynamics simulations. Utilizing the existing ROS acoustic communication framework, broadcast ranging and communication functions based on time-division multiple access were added. Based on the established Gazebo physical simulation experimental system, it can effectively simulate real underwater characteristics, including AUV dynamics, acoustic communication delay, and packet loss.

[0069] The physical simulation results are largely similar to those of the numerical simulation. It should be noted that the BP algorithm was not compared in the experiment because its particle filtering operation consumes excessive computational resources, resulting in poor real-time performance in the designed physical simulation experiment. Furthermore, from the perspective of estimation error, the proposed algorithm outperforms other compared algorithms, which is consistent with the numerical simulation results.

[0070] In summary, this invention presents a scalable and consistent underwater relative positioning framework. This framework fully considers specific underwater problems, achieving estimation consistency and scalability with extremely low communication and storage requirements. Simulation tests demonstrate that the proposed algorithm outperforms existing competing methods in terms of estimation accuracy and consistency.

[0071] The above description is merely a preferred embodiment of a scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection. The scope of protection for this method is not limited to the above embodiments; all technical solutions falling within this framework are within the protection scope of this invention. It should be noted that for those skilled in the art, any improvements and variations made without departing from the principles of this invention should also be considered within the protection scope of this invention.

Claims

1. A scalable and consistent AUV cluster relative positioning method based on asynchronous ranging circle intersection, characterized by: The method includes the following steps: Step 1: Update the storage of historical raw measurement information, storing the cumulative displacement measurement value broadcast by the target AUV, the distance measurement value between itself and the target AUV, and the corresponding covariance matrix; Step 2: Perform analytical calculation of the relative position solution set, solve the current distance measurement equation and the historical supplementary constraint equation simultaneously to obtain the relative position solution set; Step 3: Determine the feasible region, eliminate ambiguous and erroneous points, and identify the set of interior points surrounding the true relative position; Step 4: Consistent fusion of the remaining relative position solutions. The covariance intersection algorithm is used to fuse interior points to obtain the final relative position estimate.

2. The method according to claim 1, characterized in that: Setting AUV Let a triplet Sub-filter exist Constant time about the target AUV The stored content, namely: in, Store recent A UV that passes through the target Displacement measurements obtained from broadcasting Store the most recent data between two AUVs For each subsequent distance measurement, the stored content will be updated to include the latest original odometer and distance measurements, while the oldest data will be discarded. exist The measurement and storage of time is written as: 。 3. The method according to claim 2, characterized in that: When receiving from the target AUV During broadcasting, AUV Target AUV Cumulative displacement estimation included in the broadcast and the corresponding covariance matrix Store displacement measurement set For future use, the self-displacement estimate and distance measurement values ​​and their corresponding covariance matrices are stored in the same way.

4. The method according to claim 3, characterized in that: Step 2: Acoustic ranging, horizontal ranging measurements are obtained based on the time difference of arrival and depth difference: in, Describes the Euclidean norm. Indicates the speed of sound. These represent the reception time and broadcast time of the acoustic packet, respectively. Autonomous Underwater Vehicle (AUV) With Autonomous Underwater Vehicle (AUV) The depth difference between them Indicates that the autonomous underwater vehicle (AUV) was broadcasting. With the receiving autonomous underwater vehicle (AUV) The relative positions between them; Using the first Based on historical ranging measurements and the cumulative displacement during that period, an error-free supplementary relative position constraint is derived, expressed as: in, Defined as AUV and Between moments arrive Relative displacement at any given moment; Using this constraint and the obtained original measurements, a set of equations is derived regarding the estimated relative position, with subscripts... This indicates that the estimate is based on the current distance measurement value and the most recent [number] [unit]. Generated from historical ranging measurements and corresponding cumulative displacement estimates: in, It is an estimate of the actual cumulative displacement.

5. The method according to claim 4, characterized in that: By utilizing more supplementary constraints, other paired solutions can be obtained, at most [number missing]. Each relative position estimate constitutes a relative position solution set; When two measuring circles intersect, two intersection points appear, and the one furthest from the true relative position is defined as the fuzzy point.

6. The method according to claim 5, characterized in that: The following description is given to define the predefined near-tangent case: Statistical external tangency: Two circular rings, tangent from their inner circles to their outer circles; Statistical inscribed circle: Two circular rings, from the intersection of the outer diameter of the larger circle and the inner diameter of the smaller circle, to the intersection of the inner diameter of the larger circle and the outer diameter of the smaller circle.

7. The method according to claim 6, characterized in that: The statistical external and internal cases are described as follows: in, Indicates the distance between the centers of the two circles. and These represent the larger and smaller radii of the two intersecting circles, respectively. It is the sum of the widths of the two rings. and These represent the current standard deviation of the distance measurement and the standard deviation of the distance measurement after historical translation, respectively.

8. The method according to claim 7, characterized in that: After obtaining the covariance matrix of the internal relative position set and its estimates, the covariance intersection algorithm is used to provide a better and more consistent relative position estimate for the internal relative position set. and the corresponding covariance set The final relative position estimate The expression is as follows: 。 9. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the method as claimed in any one of claims 1-8.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the method of any one of claims 1-8.

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