A Multi-AUV Distributed Cooperative Flow Field Estimation Method Based on a Tree-Type Network

Abstract

The present invention proposes a multi-AUV distributed cooperative flow field estimation method based on a tree-shaped network, including: considering the incompressibility of the real ocean flow field and the negligible vertical component of the flow field, establishing a three-dimensional flow field parameterization model; establishing a dynamic model of AUVs in three-dimensional space; for the situation where underwater GPS signals cannot reach and the ocean flow field cannot be directly measured, during the underwater navigation of AUVs, the relative positions with adjacent AUVs are measured through distance sensors, and the absolute water emergence positions are obtained after surfacing; when all AUVs surface, a tree-shaped network is obtained according to the relative position measurement relationship and communication distance among AUVs; in the generated tree-shaped network, each AUV runs the same algorithm to cooperatively estimate the flow field parameters. The method of the present invention can achieve high-precision large-scale ocean flow field estimation without relying on local flow velocity measurement and a centralized computing center.

Description

Technical Field

[0001] The present invention belongs to the field of multi - underwater - robot collaborative environmental monitoring, and mainly relates to a multi - AUV distributed collaborative flow - field estimation method based on a tree - type network. Background Art

[0002] Human understanding of the status of the ocean, ocean resource development, and the value of ocean scientific research has been continuously deepening. Ocean monitoring is the basis for studying, developing, and utilizing the ocean. Among them, the ocean flow field is a representative ocean environmental quantity in ocean monitoring. The ocean flow field is a large - scale seawater movement with relatively stable flow velocity and direction, which affects the evolution of ocean climate, the distribution of marine organisms, and the trajectories of underwater and surface vehicles. Due to the important significance of ocean flow - field information, how to achieve high - precision sea - current estimation and reconstruct the flow field within a sea area has important research significance.

[0003] Autonomous Underwater Vehicles (AUVs) are widely used in the estimation task of the ocean flow field due to their high reliability, low cost, and strong flexibility. Most existing studies consider single - AUV for ocean flow - field estimation, and all require carrying corresponding sensors to measure the local flow velocity around the AUV. However, in some scenarios, accurate local flow - velocity measurement cannot be obtained. For example, the most commonly used flow - velocity measuring instrument, the Acoustic Doppler Current Profiler (ADCP), cannot accurately measure the flow velocity in scenarios with too deep water depth, too turbid or clear water quality, and sandy bottom. In addition, the single - AUV - based flow - field estimation method is difficult to handle large - scale ocean flow - field estimation tasks. And the existing multi - AUV flow - field estimation methods do not consider the collaborative operation between AUVs, so the efficiency and accuracy of large - scale ocean flow - field estimation need to be improved. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi - AUV distributed collaborative flow - field estimation method based on a tree - type network, aiming at the deficiencies of the existing technology, to solve the problem of collaborative estimation of large - scale ocean flow fields with high efficiency and high precision by multi - AUVs when local flow - velocity measurement cannot be obtained and centralized calculation cannot be realized.

[0005] To solve the above problems, the present invention provides the following technical solutions:

[0006] The present invention first provides a multi - AUV distributed collaborative flow - field estimation method based on a tree - type network, which includes the following steps:

[0007] Step 1: Consider the three - dimensional flow field f(r) within the target ocean area as N zA set formed by stacking horizontal two-dimensional flow fields along the vertical direction; for the l-th layer flow field Establish the following parametric model:

[0008]

[0009]

[0010] where represents the position in three-dimensional space; ι = 1, 2, …, N z represents the number of layers of the horizontal two-dimensional flow field; [x; y] represents the horizontal position; and respectively represent the weight, center, and width of the p-th Gaussian radial basis function of the stream function φ l (r, α) of the l-th layer flow field; and its x-component and y-component are respectively denoted as and P l is the number of Gaussian radial basis functions that make up φ l (r, α); the flow field parameter α to be estimated is defined as follows:

[0011]

[0012]

[0013]

[0014] Step 2: Establish the dynamic model of the AUV in three-dimensional space:

[0015]

[0016] where, r i (t) = [x i (t); y i (t); z i (t)] represents the position of the vehicle v i in three-dimensional space at time t; i = 1, 2, …, N, and N is the number of AUVs; represents the velocity of the vehicle v i relative to the ground at time t; f(r i (t)) is the three-dimensional true flow field to be estimated; is the velocity of the vehicle v i relative to the water at time t;

[0017] Step 3: Let the AUV start to dive from the water surface in the target ocean area navigate underwater for a period of time and finally surface; during the underwater navigation of the AUV, measure the relative position with adjacent AUVs through the distance sensors carried by itself; after the AUV surfaces, obtain its absolute surfacing position through GPS;

[0018] Step 4: After all AUVs surface, obtain a tree network in a distributed manner according to the relative position measurement relationship and communication distance among AUVs Tree network In the tree network, each node is each AUV;

[0019] Step 5: In the tree network generated in Step 4 each AUV runs the same estimation algorithm to collaboratively estimate the flow field parameters. After sufficient rounds of iteration, the true flow field parameters are finally estimated.

[0020] As a preferred solution of the present invention, the specific steps of Step 3 include the following sub-steps:

[0021] Step 3.1: During underwater navigation, the vehicle v i measures the relative position with its adjacent AUVs through its own distance sensors at time, which can be expressed as

[0022]

[0023] where represents the set of AUVs for which the vehicle v i needs to measure the relative position and can be empty; s = 1, 2,..., S i , is the set of times when the vehicle v i measures the relative position; S i is the number of times when the vehicle v i measures the relative position;

[0024] Step 3.2: After the vehicle v i surfaces, obtain its absolute position through GPS signals; since GPS signals cannot reach underwater, for the entire navigation time interval the true position of the vehicle v i is only measurable at t = 0 and time, that is, only r i (0) and are known.

[0025] As a preferred solution of the present invention, the specific steps of Step 4 include the following sub-steps: After all AUVs surface, the vehicle v iExecute the following steps:

[0026] Step 4.1: Search for AUVs within the communication range and establish a two-way communication connection with them;

[0027] Step 4.2: Obtain the distance d(i,j) between itself and communication neighbor v j through GPS, and use this distance as the initial weight of the corresponding communication connection, i.e., w C (i,j);

[0028] Step 4.3: If the relative position between itself and communication neighbor v j is measured, divide the weight of the corresponding communication connection by a large number A; let w C (i,j) = w C (i,j) / A;

[0029] Step 4.4: Run any distributed minimum spanning tree algorithm on the multi-AUV communication network obtained through the above steps to obtain its minimum spanning tree, i.e., the tree-shaped network where, the undirected edge (i,j) ∈ ε T means that v i and v j can communicate bidirectionally; denote the neighbor set of vehicle v in the tree-shaped network as i For the tree-shaped network in Step 4.4

[0030] Denote the root node as v r , and denote the leaf nodes as where ζ represents the number of leaf nodes; in the tree-shaped network , if node v i is on the path from v r to v k , then v i is called the predecessor node of v k , denoted as v i < v j , and correspondingly, v j is called the successor node of v i , denoted as v j > v i ; if v j > v i and (j,i) ∈ ε T , then v φ is called the direct successor node of v i , and correspondingly, v i is called the direct predecessor node of v j ​The direct predecessor node; denote in which v i The set of direct successor nodes of

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] (1) The present invention only requires the absolute position information at the moments when the AUV enters and exits the water and the relative position information underwater as the input of the flow field estimation algorithm, does not require the AUV to carry equipment to measure the local flow velocity, nor does it require the absolute position information of the AUV underwater, and is applicable to scenarios where the local flow velocity cannot be measured and the flow field measurement scenarios in deep water areas.

[0033] (2) The present invention proposes a multi-AUV distributed cooperative flow field estimation algorithm based on a tree-shaped network. This method only requires that the communication network between AUVs is connected, and the final algorithm runs on a tree-shaped network, with low communication cost, and is applicable to scenarios where communication resources are limited and there is no centralized computing center, and can solve the problem of efficient estimation of large-scale ocean flow fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a schematic diagram of the principle in the method of the present invention.

[0035] Figure 2 is a schematic diagram of the relationship between the relative position measurement network, communication network and the tree-shaped network for algorithm deployment among AUVs in the method of the present invention.

[0036] Figure 3 is a schematic diagram of the simulated real continuous flow field in the embodiment of the method of the present invention.

[0037] Figure 4 is a schematic diagram of the initial guessed trajectories of each AUV in the embodiment of the method of the present invention.

[0038] Figure 5 is a schematic diagram of the estimated flow field and estimated trajectories finally obtained in the embodiment of the method of the present invention.

[0039] Figure 6 is a schematic diagram of the error of the estimated flow field finally obtained in the embodiment of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following will describe in detail the implementation manners of the method of the present invention with reference to the drawings.

[0041] Based on the understanding of the prior art, the present invention establishes a method for multi-AUV distributed collaborative flow field estimation based on a tree-shaped network. This method takes into account the actual situation that AUVs cannot obtain GPS position information during underwater navigation and does not require AUVs to directly measure the local ocean flow field. This method uses the relative position information between AUVs measured during underwater navigation and the GPS position information after AUVs surface to estimate a three-dimensional continuous flow field with a hierarchical structure. Considering scenarios where the multi-AUV system encounters large application scales or involves data privacy, centralized computing cannot be achieved. Therefore, this method is a distributed method, that is, the behavior of each AUV only depends on local observations and communication with adjacent AUVs.

[0042] For the method for multi-AUV distributed collaborative flow field estimation based on a tree-shaped network proposed by the present invention, first, a three-dimensional continuous flow field parameter model of the target sea area is established; then, a kinematic model of AUVs in three-dimensional space is established, where the movement of AUVs is affected by the flow field to be estimated. During underwater navigation, AUVs measure the relative position with adjacent AUVs through distance sensors carried by themselves and obtain their absolute water surface positions through GPS after surfacing. Next, after all AUVs surface, according to the communication distance between AUVs and the relative position measurement relationship, a tree-shaped network is obtained through any distributed minimum spanning tree algorithm. Finally, based on the obtained tree-shaped network, each AUV runs the same flow field estimation algorithm to achieve parameter estimation of the continuous flow field in a distributed framework.

[0043] A method for multi-AUV distributed collaborative flow field estimation based on a tree-shaped network proposed by the present invention has the principle as Figure 1 shown, and the specific steps include:

[0044] Step 1: Consider the three-dimensional flow field f(r) within the target ocean area as a set formed by stacking N z horizontal two-dimensional flow fields along the vertical direction; for the ι-th layer flow field the following parametric model is established:

[0045]

[0046]

[0047] where, represents the position in three-dimensional space; ι = 1, 2,..., N z represents the number of layers of the horizontal two-dimensional flow field; [x; y] represents the horizontal position; and respectively represent the stream function φ corresponding to the l-th layer flow field l(r, α) Weight, center, and width of the p-th Gaussian radial basis function; And its x and y components are denoted as and P ι is the number of Gaussian radial basis functions that make up φ t (r, α); The flow field parameter α to be estimated is defined as follows:

[0048]

[0049]

[0050]

[0051] Step 2: Establish the dynamic model of the AUV in three-dimensional space:

[0052]

[0053] where, represents the position of the vehicle v i in three-dimensional space at time t; i = 1, 2, …, N, and N is the number of AUVs; represents the velocity of the vehicle v i relative to the ground at time t; f(r i (t)) is the three-dimensional true flow field to be estimated; is the velocity of the vehicle v i relative to the water at time t, specifically:

[0054]

[0055] where, θ i (t) and are the pitch angle and yaw angle of the vehicle v i respectively; v i (t) is the velocity of the vehicle v i relative to the water. Among them, θ i (t) and can be measured by the attitude sensors carried by the AUV; v i (t) can be measured by correlating the rotational speed of the AUV propeller. Therefore, v i (t) is measurable.

[0056] Step 3: Let the AUV start to dive from the water surface and in the target ocean area It sails underwater for a period of time and finally surfaces. During the underwater navigation of the AUV, the relative position between the AUV and adjacent AUVs is measured by the distance sensors carried by itself; after the AUV surfaces, its absolute surfacing position is obtained through GPS. This method has no requirements for the speed, direction, time, and depth of the AUV during underwater navigation, and it can be determined according to the performance of the actual AUV equipment. The measurements carried out by the AUV during the entire navigation process include the following two parts:

[0057] Step 3.1: During the underwater navigation process, the vehicle v i measures the relative position with its adjacent AUVs through its own distance sensors at time, which can be expressed as

[0058]

[0059] where represents the set of AUVs for which the vehicle v i needs to measure the relative position and can be empty; s = 1, 2, …, S i , is the time when the vehicle v i measures the relative position; S i is the number of times when the vehicle v i measures the relative position.

[0060] Step 3.2: When the vehicle v i surfaces, its absolute position is obtained through the GPS signal; since the GPS signal cannot reach underwater, for the entire navigation time interval the true position of the vehicle v i is only measurable at t = 0 and time, that is, only r i (0) and are known.

[0061] Step 4: When all AUVs surface, the vehicle v i performs the following steps:

[0062] Step 4.1: Search for AUVs within the communication range and establish a two-way communication connection with them;

[0063] Step 4.2: Obtain the distance d(i, j) between itself and the communication neighbor v j through GPS and use this distance as the preliminary weight of the corresponding communication connection, that is, w C (i, j);

[0064] Step 4.3: If it has measured the distance from itself to the communication neighbor v jFor the relative position, divide the weight of the corresponding communication connection by a large number 100; let w C (i,j) = w C (i,j) / 100;

[0065] Step 4.4: Run any distributed minimum spanning tree algorithm on the multi-AUV communication network obtained through the above steps to obtain the minimum spanning tree, i.e., the tree-shaped network wherein, the undirected edge (i,j) ∈ ε indicates that v T and v i can perform two-way communication; denote the neighbor set of the vehicle v j in the tree-shaped network as i For the tree-shaped network in Step 4.4

[0066] Denote the root node as v and denote the leaf nodes as r where ζ represents the number of leaf nodes; in the tree-shaped network if the node v is on the path from v i to v r to v j then v i is called the predecessor node of v j and is denoted as v i < v j , correspondingly, v j is called the successor node of v i and is denoted as v j > v i ; if v j > v i and (j,i) ∈ ε T then v j is called the direct successor node of v i and correspondingly, v i is called the direct predecessor node of v j ; denote the set of direct successor nodes of v in i as For define the weight wherein, is the cardinality of

[0067] Step 5: In the tree-shaped network formed in Step 4.4 each node v iAll run the following estimation algorithm to collaboratively estimate the flow field parameters; before the algorithm starts, the initial parameter guess value of the root node is given as Set the number of iteration rounds to k = 0:

[0068] Step 5.1: Let n = 0; if v i = v r , let Otherwise, set to the latest estimated value sent from the direct predecessor node;

[0069] Step 5.2: Perform the iteration of the parameter according to the following formula:

[0070] 1. Let

[0071] 2. Let n = n + 1;

[0072] 3. Let

[0073] 4. Let n = n + 1;

[0074] Step 5.3: For all and s = 1, 2,..., S i , perform the iteration of the parameter in sequence according to the following steps:

[0075] 1. Send and to v j , and wait for v j to send back and

[0076] 2. Let

[0077] 3. Let n = n + 1;

[0078] 4. Send and to v j , and wait for v j to send back and

[0079] 5. Let

[0080] 6. Let n = n + 1;

[0081] Step 5.4: Let Then pass to all nodes in ;

[0082] Step 5.5: If Let Otherwise, let

[0083] Step 5.6: Transmit to the direct predecessor node; let Let k = k + 1;

[0084] Step 5.7: Go back to Step 5.1;

[0085] Among them, the coefficients in Step 5.2 and Step 5.3 and each value can be different each time;

[0086] Among them, the set in Step 5.3

[0087] Among them, in Step 5.2 and are respectively 's x and y components, where are in the following specific form:

[0088]

[0089] Among them, is the expected position, calculated according to ; is the current estimated position, calculated according to ;

[0090] Among them, in Step 5.3 and are respectively 's x and y components, where are in the following specific form:

[0091]

[0092] Through the distributed algorithm in Step 5, after sufficient iterations, each node will calculate the true flow field parameter α ★ , that is to achieve distributed parameter estimation of the continuous flow field.

[0093] The underwater AUV and sensors adopted by the method of the present invention are all conventional model devices; those skilled in the art can implement the method of the present invention through programming.

[0094] The following combines a specific implementation to verify the effectiveness of the present invention.

[0095] Consider a three-dimensional ocean current field of 10 km × 10 km × 2 km, and the simulated true flow field parameters are: Nz = 4, P ι = 5, and the parameters of the stream function are in the order of ι = 1 to N z and p = 1 to P l After sorting, they are η 1 = [36, 48, 30, 36, 42], η 2 = [30, 36, 30, 54, 42], η 3 = [54, 48, 60, 36, 36], η 4 = [60, 42, 72, 30, 48] (m / s); σ 1 = [2.25, 2.7, 2.36, 2.1, 2.4]; σ 2 = [2.25, 2.25, 2.48, 2.4, 2.55]; σ 3 = [2.4, 2.7, 2.36, 2.25, 2.4]; σ 4 = [2.7, 2.7, 2.18, 2.1, 2.1] (km). The simulated real continuous flow field is as Figure 3 shown. Deploy N = 7 AUVs to navigate in this flow field area. The pitch angles of all AUVs are set as:

[0096]

[0097] The remaining parameters are shown in the following table:

[0098]

[0099] The actual motion trajectories of the AUVs in the real flow field and the initial guess trajectories in the initial guess flow field (randomly generated flow field parameters) are as Figure 4 shown. Since the guessed flow field is not consistent with the real flow field, the guessed trajectory and the real trajectory do not coincide. Since the specific topological structure of the tree network does not affect the performance of the algorithm, a tree network is directly specified in this experiment where v1 is the root node, as shown in the above table. Set the termination condition of the iteration as k max = 70, and the relaxation parameter After the distributed flow field estimation algorithm ends, the finally obtained estimated flow field and the estimated trajectories of the AUVs are as Figure 5 shown. From Figure 5 it can be seen that the finally estimated flow field and Figure 3The real flow field shown is very similar. And under the influence of the estimated flow field, the estimated trajectory and the real trajectory of the vehicle basically coincide, which further proves that the accuracy of the estimated flow field is very high and can be applied to the navigation of underwater vehicles. At each layer in the target sea area, 10×10 equally spaced points are taken, and the flow field errors at these positions are calculated and plotted. The results are as Figure 6 shown. Figure 6 The greater the flow field error at the brighter positions in the figure, and the smaller the flow field error at the darker positions. It can be seen that compared with the flow velocity magnitude of the real flow field, the estimated error of the finally obtained flow field is relatively small. The root mean square error of the entire flow field is calculated to be In summary, the proposed distributed flow field estimation method can accurately estimate the flow field of the target area.

[0100] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the purpose of the present invention and the scope protected by the claims. These all fall within the protection scope of the present invention.

Claims

1. A multi-AUV distributed cooperative flow field estimation method based on a tree-shaped network, characterized in that It includes the following steps: Step 1: Consider the three-dimensional flow field f(r) within the target ocean area as a set formed by stacking N z horizontal two-dimensional flow fields along the vertical direction; for the ι-th layer flow field establish the following parametric model: Among them, represents a position in three-dimensional space; ι = 1, 2, …, N z represents the number of layers of the horizontal two-dimensional flow field; [x; y] represents the horizontal position; and respectively represent the weight, center, and width of the p-th Gaussian radial basis function of the stream function φ l (r, α) of the ι-th layer of the flow field; and its x-component and y-component are respectively denoted as and P ι is the number of Gaussian radial basis functions that make up φ ι (r, α); the flow field parameter α to be estimated is defined as follows: Step 2: Establish the dynamic model of the AUV in three-dimensional space: where r i (t) = [x i (t); y i (t); z i (t)] represents the position of the vehicle v i in three-dimensional space at time t; i = 1, 2, …, N, where N is the number of AUVs; represents the velocity of the vehicle v i relative to the ground at time t; f(r i (t)) is the three-dimensional true flow field to be estimated; is the velocity of the vehicle v i relative to the water at time t; Step 3: Let the AUV start diving from the water surface and navigate in the target ocean area for a period of time and finally surface; during the underwater navigation of the AUV, measure the relative position with adjacent AUVs through the distance sensors carried by itself; after the AUV surfaces, obtain its absolute surfacing position through GPS; Step 4: After all the AUVs surface, a tree network is obtained in a distributed manner based on the relative position measurement relationship and communication distance among the AUVs. Tree network In the tree network, each node is each AUV. Step 5: In the tree-shaped network generated in Step 4 each AUV runs the same estimation algorithm to collaboratively estimate the flow field parameters. After sufficient rounds of iteration, the true flow field parameters are finally estimated.

2. The multi-AUV distributed collaborative flow field estimation method based on a tree-shaped network according to claim 1, wherein In step 3, there are no requirements for the speed, direction, time, and depth of the AUV during underwater navigation, which can be determined according to the performance of the actual AUV equipment.

3. A multi-AUV distributed collaborative flow field estimation method based on a tree-shaped network according to claim 1, characterized in that The specific steps of step 3 include the following sub-steps: Step 3.1: During underwater navigation, vehicle v i measures the relative position with its adjacent AUV at a moment through its own distance sensor, which can be expressed as ​ Among them, represents the set of AUVs v i for which relative position measurement is to be performed and can be empty; is the set of times when relative position measurement is performed for the vehicle v i ; S i is the number of times when relative position measurement is performed for the vehicle v i ; Step 3.2: When the vehicle v i surfaces, its absolute position is obtained through GPS signals; since GPS signals cannot reach underwater, for the entire navigation time interval the vehicle v i the true position is only measurable at t = 0 and moments, that is, only r i (0) and are known.

4. A multi-AUV distributed collaborative flow field estimation method based on a tree-shaped network according to claim 1, characterized in that, The specific steps of step 4 are as follows: After all AUVs surface, the vehicle v i performs the following steps: Step 4.1: Search for AUVs within the communication range and establish a two-way communication connection with them; Step 4.2: Obtain the distance d(i, j) between itself and communication neighbor v j through GPS, and use this distance as the preliminary weight of the corresponding communication connection, i.e., w C (i, j); Step 4.3: If the relative position with the communication neighbor v has been measured by itself j , then divide the weight of the corresponding communication connection by a large number A; let w C (i,j) = w C (i,j) / A; Step 4.4: On the multi-AUV communication network obtained through the above steps run any one of the distributed minimum spanning tree algorithms to obtain the minimum spanning tree, i.e., the tree-shaped network where the undirected edge (i, j) ∈ ε T indicates that v i and v j can communicate bidirectionally; denote the neighbor set of the vehicle v in the tree-shaped network as i and For the tree network in step 4.4 Denote the root node as v r , and denote the leaf nodes as where ζ represents the number of leaf nodes; in the tree network , if node v i is on the path from v r to v j , then v i is called the predecessor node of v j , denoted as v i <v j . Correspondingly, v j is called the successor node of v i , denoted as v j >v i ; if v j >v i and (j, i) ∈ ε T , then υ j is called the direct successor node of υ i . Correspondingly, υ i is called the direct predecessor node of υ j ; denote the set of direct successor nodes of v i in as 5. A method for multi-AUV distributed collaborative flow field estimation based on a tree-shaped network according to claim 1, characterized in that The specific steps of step 5 include the following sub-steps: In the tree-shaped network obtained in step 4 each node v i runs the following estimation algorithm to collaboratively estimate the flow field parameters; before the algorithm starts, the initial parameter guess value of the root node is given as Set the value of the iteration round k to 0: Step 5.1: Set the value of index n to 0; if v i is the root node, let represent the nth iteration value in the kth large loop; otherwise, set to the latest estimated value sent from the direct predecessor node; Step 5.2: Perform iteration of the parameters using the constraints related to the integral error of the absolute motion, and only consider the x and y components of the constraint equations. Specifically, the iteration steps for the parameters are as follows: The iteration steps for the parameters are as follows:

1. Let 2. Add 1 to the value of index n; 3. Let 4. Add 1 to the value of index n; Among them, Denote the node v i is the relaxation parameter during the n-th iteration in the k-th major loop, and The symbol is the differential operator; ‖·‖ is the norm symbol; the expression and are respectively the x and y components of is the constraint corresponding to the absolute motion integral error of the node v i Specifically: Here, d i is the difference between the actual water emergence position and the expected water emergence position of the vehicle v i ; the expected position of the vehicle is the position calculated without considering the influence of the flow field; represents the flow velocity value of the flow field calculated according to the current estimated parameters at the position; while is the position of the vehicle v calculated considering the influence of the flow field i at time t; Step 5.3: Perform iteration of the parameters using the constraints related to the relative motion integration error, and only consider the x and y components of the constraint equations; specifically, traverse each node v in the set and each moment in the set in turn, and perform iteration on the parameters j in sequence. The iteration steps are as follows: for each moment in the set and perform iteration on the parameters 1. Send and to v j , and wait for v j to send back and 2. Let 3. Add 1 to the value of index n; 4. Send and to v j , and wait for v j to send back and 5. Let 6. Add 1 to the value of index n; Among them, Set is a tree - type network the set of neighbors of vehicle v i and the set of AUVs for which vehicle v i is to perform relative position measurement; is the set of times at which vehicle v i performs relative position measurement; and are respectively the x - and y - components of, is the constraint corresponding to the integral error of relative motion with respect to node v i Specifically: Here, Subsection reserved for relative motion integration error constraint at node v i of Subsection reserved for relative motion integration error constraint at node v j of, specifically: Here, and are the positions of the vehicle v i and v j calculated without considering the influence of the flow field at moment; is the relative position between the measured position of the vehicle v at i and v j ; and are respectively the x and y components of and are respectively the x and y components of Step 5.4: Let Then is passed to all the nodes in Step 5.5: If Let Otherwise, let Here is the cardinality of the set ; is the set of direct successor nodes of the node v in the tree-shaped network i ; Step 5.6: Transfer to the direct predecessor node; Let increment the value of the iteration round k by 1; Step 5.7: Return to step 5.1.

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