AUV State Estimation Method Based on Flexray Protocol

Abstract

A method for AUV state estimation based on the FlexRay protocol includes the following steps: S1, constructing a 6-DOF model of the underwater vehicle system; S2, designing the FlexRay protocol for the underwater vehicle system; S3, designing an augmentation system based on the FlexRay protocol mechanism; and S4, establishing a cladding filter for a fully symmetric polytope, and using a cladding estimator of the fully symmetric polytope shell to provide high-precision state set estimation. The purpose of this invention is to propose an AUV state estimation method based on the FlexRay protocol, achieving high-precision positioning of AUVs in complex, unknown, but bounded noise environments.

Description

Technical Field

[0001] This invention relates to underwater vehicle technology, and in particular to an AUV state estimation method based on the Flexray protocol. Background Technology

[0002] When AUVs (underwater vehicles) perform missions in underwater environments, they need to accurately estimate their own trajectories to ensure they can complete their missions and return to their designated locations. However, due to the unique challenges of the underwater environment, AUV trajectory estimation faces a series of technical difficulties, mainly including the following aspects:

[0003] Factors such as water flow, turbulence, and temperature variations in the underwater environment all affect the navigation of AUVs. These factors make the trajectory of AUVs extremely difficult to predict; severe attenuation of optical signals underwater limits the use of visual navigation and imaging systems, further increasing the difficulty of trajectory estimation. In unknown or dynamically changing underwater environments, AUVs must be able to estimate their own trajectory in real time and perform path planning and dynamic obstacle avoidance based on environmental changes. However, due to the complexity and dynamism of the underwater environment, accurate real-time trajectory estimation is a significant challenge.

[0004] Set membership estimation has become a suitable and effective state estimation method for dealing with noise, considering unknown but bounded noise. However, classical set membership filtering considers set membership algorithms with ellipsoids as boundaries. In ellipsoidal set operations, the Minkowski sum step often requires a more conservative circumscribed ellipsoid for envelopment, which leads to a decrease in estimation accuracy to some extent. Another ellipsoidal algorithm using linear matrix inequalities (LMIs) is typically computationally complex in high-dimensional systems and suffers from slow real-time response. Therefore, designing a set membership estimation algorithm with a more compact estimation set and faster response speed has become a research topic.

[0005] As the demand for AUVs to perform complex underwater tasks increases, the application of network technology plays a crucial role in improving system communication capabilities and data transmission efficiency. However, the unique environment and limited resources of underwater communication present challenges to communication networks. When navigating underwater, AUVs typically need to perform high-precision sensor data sharing, real-time status updates, path planning, and collaborative control. These operations require substantial data transmission, but due to limited underwater resources, the communication bandwidth and computing resources between AUVs cannot meet the demands, potentially leading to system performance degradation or mission failure. To effectively resolve data conflicts, a reasonable communication scheduling protocol must be designed to ensure orderly data exchange between multiple AUVs, thereby avoiding frequent signal interference and conflicts.

[0006] In the fields of network communication and multitasking scheduling, the Round-Robin Protocol (RRP) and the Try-on-Drop Protocol (TODP) are often used to handle scheduling problems related to resource sharing and data transmission. However, RRP, as a fixed scheduling method, lacks flexibility, especially when some devices have no data to transmit for a long time, the Round-Robin Protocol still wastes time checking these devices; while TODP improves scheduling flexibility, it cannot guarantee the stability of the system under certain contention rules.

[0007] Therefore, it is urgent to study a membership estimation algorithm for AUVs under new communication scheduling protocols to achieve accurate trajectory estimation of AUVs in complex underwater environments. Summary of the Invention

[0008] To address the aforementioned shortcomings, the present invention aims to propose an AUV state estimation method based on the Flexray protocol. By effectively improving the utilization efficiency of underwater network resources and achieving flexible and stable data transmission, it enables high-precision positioning of AUVs in complex, unknown, but bounded noise environments.

[0009] To achieve this objective, the present invention adopts the following technical solution:

[0010] A method for AUV state estimation based on the Flexray protocol includes the following steps:

[0011] S1. Construct a 6-DOF model of the underwater vehicle system. Model the system based on the position information and the dynamic equations of Euler angles of the underwater vehicle. Based on the dynamic equations of the continuous-time system, transform the continuous-time system into a discrete-time system using the zero-order hold method.

[0012] S2. Based on the FlexRay protocol, and referring to the core part of its transmission protocol, the transmission protocol is roughly divided into two categories: one is based on time multiple access connection mode, and the other is based on flexible time multiple access connection mode. Based on this, the FlexRay protocol for underwater vehicle system is designed, and the protocol is divided into a polling protocol in the static segment and an attempt-on-discard protocol in the dynamic segment.

[0013] S3. Due to the use of the FlexRay protocol, there is a one-unit estimator working interval in the arrival time of data packets. This phenomenon is regarded as a partial delay problem. To address the partial delay problem of the mechanism based on the FlexRay protocol, the system state is augmented to become a higher-dimensional discrete system, which solves the problems of synchronization difficulties, error accumulation, and decreased algorithm stability of general state estimation algorithms under mixed delay.

[0014] S4. Since the augmented system has a large dimension, it involves a problem of high computational complexity; establish a set-membership filter for a fully symmetric polytope and use the shell of the fully symmetric polytope to provide a more accurate state set estimation.

[0015] Preferably, in step S1, the dynamic model of the AUV is described as a 6-DOF model based on a body-fixed coordinate system and a Earth-fixed coordinate system.

[0016] Since roll has a negligible effect on translational motion, roll velocity is not considered. Below are the kinematic and dynamic models of the AUV in the discrete case:

[0017]

[0018] In Equation 1, s = [x, y, z] T and θ=[φ,ψ] T These represent the 3D position and Euler angles of the AUV, respectively. and Represents the velocity at the corresponding component; defines the system state as follows;

[0019]

[0020] In Equation 2, x k This represents the system's state parameters at time k;

[0021] Therefore, the dynamic equations of the initial AUV system can be obtained.

[0022] x k+1 =Ax k +w k Equation (3)

[0023] The raw measurements are obtained from the sensor measurements.

[0024]

[0025] Among them, the unknown but bounded noise w k and v k Limited by the subsequent set of multiple cells; C is the measurement matrix. Sensors typically cannot directly obtain data about state x, therefore C represents the physical parameters of the sensor:

[0026]

[0027] in,<c,P> Let w represent a set of polycells centered at vector c and generating matrix P; therefore w k and v k They are located in sets of multicellular bodies with the origin at the center and generating matrices W and V, respectively.

[0028] Preferably, in step 2, the uniform quantizer is set to a scalar b such that the interval [-b, b] can be divided into 2^n bits according to the allocated bits rbps.r -1 quantization intervals are used to determine which small interval the received information falls into and output the corresponding interval code.

[0029] We define the quantified measurement as:

[0030] y k =Cx k +v k +d k Equation (6)

[0031] In Equation 6, This represents the quantization error, and the quantization error is related to the number of bits in the data packet; the quantization error is defined as a polytope:

[0032] d k ∈<0,D k >; Equation (7)

[0033] In Equation 7, <0, D k The origin is the center, and the generating matrix is ​​D. k A collection of multiple cells;

[0034] In automotive network communication, dynamic segments are widely used for diagnostic flashing; therefore, the timing parameters for dynamic segments are inconsistent with those for static loops. Here, the rate of change of the Euler angle of the AUV is defined as the number of packets that the protocol attempts to discard in the dynamic segment, i.e., the rate of change of the Euler angle in the dynamic segment. We will perform the write operation; considering that only one data packet can access the channel resource during the transmission cycle, we will divide the measurement into N data packets and divide them into two sets. and Nodes belonging to set l1 are scheduled using the round-robin protocol, while nodes belonging to set l2 are scheduled using the try-and-drop protocol, with the following scheduling rules:

[0035] A. Polling Protocol:

[0036] λ(j)=mod(j-1,h)+1(8)

[0037] In Equation 8, λ(j)∈l1 represents the node that acquires the transmission right at time j, and mod() is the modulo function;

[0038] B. Try the discard protocol once:

[0039]

[0040] In Equation 9, y′ j，k α represents the information of node j that was last transmitted before time k. k ∈l2 represents the node that most needs to transmit at time k under the "maximum error priority" rule; It is a given positive definite weight matrix;

[0041] Therefore, based on the Flexray protocol in high-speed networks, measurements can be divided into static and dynamic segments of data packets to be scheduled:

[0042]

[0043] Similarly, define the measurement matrix:

[0044]

[0045] The measurement received by the receiver is defined as:

[0046] Based on the assumption of high-speed networks, we can divide the communication cycle of a Flexray protocol into... The transmission cycle is reduced by a significant increase in transmission speed due to advancements in hardware technology; however, the state update cycle remains unchanged despite the change in transmission speed, allowing at most [number missing] data to be received in each state update cycle. Each data packet; furthermore, the received measurement is defined as:

[0047]

[0048] in, and These represent the quantization error and measurement noise of the received data packet, respectively.

[0049] Furthermore, in step 3, under the communication scheduling of the Flexray protocol, the static segment data packets and dynamic segment data packets will naturally have different times. That is, the receiving end faces a mixture of instantaneous measurements and measurements with a unit delay. This makes it necessary to preprocess before estimation to convert it into a standard delay-free system.

[0050] We set the augmented state as follows: We have the following augmentation system:

[0051]

[0052] in,

[0053]

[0054] Furthermore, in step 4, using a fully symmetric multicellular structure as the shell of the set, we define the initial state as being located within the multicellular structure based on prior knowledge. Compared to existing ellipsoid algorithms, the Minkowski algorithm for polytopes satisfies the closure property of set operations, meaning that the result is still a polytope, i.e.:

[0055]

[0056] This reduces the conservatism of the estimates in various steps, makes the size of the set of estimates smaller, and makes the final estimation result less erroneous;

[0057] For the state at time k, first perform a one-step prediction on the augmented system to obtain the one-step predicted multicell. in:

[0058]

[0059] In Equation 14, and These represent the center and generator matrix of the predicted state in one step, respectively;

[0060] The next step is to estimate the multicellularity. in:

[0061]

[0062] In Equation 15, and Let represent the center and the generator matrix of the final estimated state set, respectively.

[0063] Furthermore, in step 4, the specific steps are as follows:

[0064] S41. Initialization: Input the initial state using prior knowledge. Generating matrix

[0065] S42. Calculate the one-step predicted multicell set, and find the set center of the one-step predicted set according to the following formula. and generating matrix

[0066]

[0067] Therefore, we get:

[0068]

[0069] S43. Calculate the estimated set of multiple cells, and determine the set center of the one-step prediction set using the following formula. and generating matrix

[0070]

[0071] Therefore, we get:

[0072]

[0073] S44. Minimizing the F-radius based on a matrix to design the gain G k+1 To facilitate minimizing the matrix radius F We define the generating matrix The covariance matrix is:

[0074] P = cov(<c,R> ) = RR T Equation (20)

[0075] Therefore, a similar covariance matrix can be represented as:

[0076]

[0077] According to the optimality theorem, we can obtain...

[0078]

[0079] S45, Iteration: Finally, based on the AUV's dynamic model and measurements obtained using the Flexray protocol, we obtain the AUV's trajectory in three-dimensional space for each step.

[0080] One of the above technical solutions includes the following beneficial effects:

[0081] This patented 3D trajectory estimation algorithm based on the FlexRay protocol in high-speed networks addresses the resource-limited problem in underwater networks. By transmitting only one packet at a time in a shared network channel, it effectively avoids data collisions. Furthermore, the use of a hybrid protocol retains the stability advantages of RRP while offering the flexibility of TODP. Compared to existing methods, it effectively improves the utilization efficiency of underwater network resources and achieves flexible and stable data transmission. Attached Figure Description

[0082] Figure 1 This is a schematic diagram of the overall steps of one embodiment of the present invention;

[0083] Figure 2 This is an AUV model under 6-DOF according to an embodiment of the present invention;

[0084] Figure 3 This is a schematic diagram of the components within a single communication cycle of the Flexray protocol;

[0085] Figure 4 It is a dynamic segment scheduling table under the Flexray protocol;

[0086] Figure 5 This is a flight path diagram of an AUV according to an embodiment of the present invention;

[0087] Figure 6 This is a set-membership estimation envelope diagram of the relevant state of an AUV according to an embodiment of the present invention. Detailed Implementation

[0088] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0089] like Figure 1 As shown, an AUV state estimation method based on the Flexray protocol includes the following steps:

[0090] S1. Construct a 6-DOF model of the underwater vehicle system. Model the system based on the position information and the dynamic equations of Euler angles of the underwater vehicle. Based on the dynamic equations of the continuous-time system, transform the continuous-time system into a discrete-time system using the zero-order hold method.

[0091] S2. Based on the FlexRay protocol, and referring to the core part of its transmission protocol, the transmission protocol is roughly divided into two categories: one is based on time multiple access connection mode, and the other is based on flexible time multiple access connection mode. Based on this, the FlexRay protocol for underwater vehicle system is designed, and the protocol is divided into a polling protocol in the static segment and an attempt-on-discard protocol in the dynamic segment.

[0092] S3. Due to the use of the FlexRay protocol, there is a one-unit estimator working interval in the arrival time of data packets. This phenomenon is regarded as a partial delay problem. To address the partial delay problem of the mechanism based on the FlexRay protocol, the system state is augmented to become a higher-dimensional discrete system, which solves the problems of synchronization difficulties, error accumulation, and decreased algorithm stability of general state estimation algorithms under mixed delay.

[0093] S4. Since the augmented system has a large dimension, it involves a problem of high computational complexity; establish a set-membership filter for a fully symmetric polytope and use the shell of the fully symmetric polytope to provide a more accurate state set estimation.

[0094] S1: This patent is for a 6-DOF underwater vehicle. Through dynamic analysis of continuous-time systems and the zero-order hold method, a general discrete model of the 6-DOF underwater vehicle in the corresponding sampling time is obtained.

[0095] S2: Inspired by the FlexRay protocol in automotive networks, a transmission mechanism for underwater networks is designed. By transmitting only one packet at a time in a shared network channel, data collisions are effectively avoided, addressing the resource-limited problem in underwater networks. Furthermore, the use of a hybrid protocol retains the stability advantages of polling protocols while providing flexibility through a try-and-drop approach. Compared to existing methods, this effectively improves the utilization efficiency of underwater network resources and achieves flexible and stable data transmission. S3: Addressing the hybrid delay measurement problem encountered when applying the FlexRay protocol, which leads to synchronization difficulties, error accumulation, decreased algorithm stability, and increased computational burden on general state estimation algorithms, a method for augmenting system states is proposed. This method unifies hybrid delay measurements into a delay-free measurement system, transforming it into standard AUV trajectory estimation and avoiding error accumulation and convergence impact caused by time inconsistencies. S4: Design a set membership estimation algorithm based on Zonotope. By utilizing Zonotope as the outer shell of the set, the set operation of Minkowski sum is closed, ensuring that the resulting set remains a polytope. Furthermore, the estimation process employs a simpler Zonotope Kalman Filter (ZKF) algorithm, involving only simple linear affine and matrix operations, significantly reducing computational complexity and improving real-time response speed. Compared to existing ellipsoidal set membership filters, it provides a more compact set in certain directions, resulting in smaller estimation errors and explicit optimization regarding the set norm. TDMA (Time Multiple Access) is a time-multiplexed access method, Flexible TDMA (Flexible Time Multiple Access) is a flexible time-multiplexed access method, Zonotope is a fully symmetric polytope, RRP (Round-Robin Protocol) is a polling protocol, and TODP (Try-on-Drop Protocol) is an attempt-on-one-drop protocol.

[0096] like Figure 2 As shown, in step S1, the dynamic model of the AUV is described as a 6-DOF model based on the body fixed coordinate system and the earth fixed coordinate system.

[0097] Since roll has a negligible effect on translational motion, roll velocity is not considered. Below are the kinematic and dynamic models of the AUV in the discrete case:

[0098]

[0099] In Equation 1, s = [x, y, z] T and θ=[φ,ψ] T These represent the 3D position and Euler angles of the AUV, respectively. and Represents the velocity at the corresponding component; defines the system state as follows;

[0100]

[0101] In Equation 2, x k This represents the system's state parameters at time k;

[0102] Therefore, the dynamic equations of the initial AUV system can be obtained.

[0103] x k+1 =Ax k +w k Equation (3)

[0104] The raw measurements are obtained from the sensor measurements.

[0105]

[0106] Among them, the unknown but bounded noise w k and v k Limited by the subsequent set of multiple cells; C is the measurement matrix. Sensors typically cannot directly obtain data about state x, therefore C represents the physical parameters of the sensor:

[0107]

[0108] in,<c,P> Let w represent a set of polycells centered at vector c and generating matrix P; therefore w k and v k They are located in sets of multicellular bodies with the origin at the center and generating matrices W and V, respectively.

[0109] Defining the perturbation as an unknown but bounded set variable, compared to traditional Kalman filtering, requires no prior knowledge of the statistical distribution, thus better aligning with engineering practices. Secondly, in set-membership filtering, fully symmetric polytopes, compared to ellipsoidal sets, better address the overpacking problem in computation. This reduces the feedback time and improves the real-time response rate.

[0110] Specifically, in step 2, the uniform quantizer is set with a scalar b such that the interval [-b, b] can be divided into 2^n bits according to the allocated bits r bps. r -1 quantization intervals are used to determine which small interval the received information falls into and output the corresponding interval code.

[0111] We define the quantified measurement as:

[0112] y k =Cx k +v k +d k Equation (6)

[0113] In Equation 6, This represents the quantization error, and the quantization error is related to the number of bits in the data packet; the quantization error is defined as a polytope:

[0114] d k ∈<0,D k >; Equation (7)

[0115] In Equation 7, <0,D k The origin is the center, and the generating matrix is ​​D. k A collection of multiple cells;

[0116] In automotive network communication, dynamic segments are widely used for diagnostic flashing; therefore, the timing parameters for dynamic segments are inconsistent with those for static loops. Here, the rate of change of the Euler angle of the AUV is defined as the number of packets that the protocol attempts to discard in the dynamic segment, i.e., the rate of change of the Euler angle in the dynamic segment. We will perform the write operation; considering that only one data packet can access the channel resource during the transmission cycle, we will divide the measurement into N data packets and divide them into two sets. and Nodes belonging to set l1 are scheduled using the round-robin protocol, while nodes belonging to set l2 are scheduled using the try-and-drop protocol, with the following scheduling rules:

[0117] A. Polling Protocol:

[0118]

[0119] In Equation 8, λ(j)∈l1 represents the node that acquires the transmission right at time j, and mod() is the modulo function;

[0120] B. Try the discard protocol once:

[0121]

[0122] In Equation 9, y′ j，k α represents the information of node j that was last transmitted before time k. k ∈l2 represents the node that most needs to transmit at time k under the "maximum error priority" rule; It is a given positive definite weight matrix;

[0123] Therefore, based on the Flexray protocol in high-speed networks, measurements can be divided into static and dynamic segments of data packets to be scheduled:

[0124]

[0125] Similarly, define the measurement matrix:

[0126]

[0127] The measurement received by the receiver is defined as:

[0128] Based on the assumption of high-speed networks, we can divide the communication cycle of a Flexray protocol into... The transmission cycle is reduced by a significant increase in transmission speed due to advancements in hardware technology; however, the state update cycle remains unchanged despite the change in transmission speed, allowing at most [number missing] data to be received in each state update cycle. Each data packet; furthermore, the received measurement is defined as:

[0129]

[0130] in, and These represent the quantization error and measurement noise of the received data packet, respectively.

[0131] The Flexray protocol is a type of periodic transmission protocol, in which each communication cycle consists of a static segment, a dynamic segment, a symbol window, and a network idle time (NIT), such as... Figure 3 As shown, a static segment implemented by RRP consists of time slots of equal length. On the other hand, a dynamic segment implemented by TODP consists of several smaller slots, much shorter than the static slots. The length of the dynamic slot depends on the information that nodes need to transmit for different frame lengths. Furthermore, the symbol window and NIT play crucial roles in ensuring the stability and synchronization of communication cycles within the FRP, respectively. Ignoring the duration of the symbol window and NIT does not affect the effectiveness of the protocol itself. Compared to existing methods, the Flexray protocol is primarily used in automotive networks; this patent is the first to apply it to AUVs in underwater environments. Figure 4 This is a dynamic segment scheduling table, which shows the protocol details.

[0132] Furthermore, in step 3, the communication scheduling using the Flexray protocol naturally results in the problem that the static segment data packets and dynamic segment data packets are at different times. That is, the receiving end faces a mixture of instantaneous measurements and measurements with a unit delay. This requires preprocessing before estimation to convert it into a standard delay-free system.

[0133] We set the augmented state as follows: We have the following augmentation system:

[0134]

[0135] in,

[0136]

[0137] Furthermore, in step 4, using a fully symmetric multicellular structure as the shell of the set, we define the initial state as being located within the multicellular structure based on prior knowledge. Compared to existing ellipsoid algorithms, the Minkowski algorithm for polytopes satisfies the closure property of set operations, meaning that the result is still a polytope, i.e.:

[0138]

[0139] This reduces the conservatism of the estimates in various steps, makes the size of the set of estimates smaller, and makes the final estimation result less erroneous;

[0140] For the state at time k, first perform a one-step prediction on the augmented system to obtain the one-step predicted multicell. in:

[0141]

[0142] In Equation 14, and These represent the center and generator matrix of the predicted state in one step, respectively;

[0143] The next step is to estimate the multicellularity. in:

[0144]

[0145] In Equation 15, and Let represent the center and the generator matrix of the final estimated state set, respectively.

[0146] Compared with existing ellipsoidal set-membership filters, this method provides an estimation result with a smaller set size and lower error, and features explicit optimization with respect to the set norm, reducing computational complexity and improving real-time response speed. It enables high-precision trajectory positioning of AUVs in complex underwater environments.

[0147] Furthermore, in step 4, the specific steps are as follows:

[0148] S41. Initialization: Input the initial state using prior knowledge. Generating matrix

[0149] S42. Calculate the one-step predicted multicell set, and find the set center of the one-step predicted set according to the following formula. and generating matrix

[0150]

[0151] Therefore, we get:

[0152]

[0153] S43. Calculate the estimated set of multiple cells, and determine the set center of the one-step prediction set using the following formula. and generating matrix

[0154]

[0155] Therefore, we get:

[0156]

[0157] S44. Minimizing the F-radius based on a matrix to design the gain G k+1 To facilitate minimizing the matrix radius F We define the generating matrix The covariance matrix is:

[0158] P = cov(<c,R> ) = RR T Equation (20)

[0159] Therefore, a similar covariance matrix can be represented as:

[0160]

[0161] According to the optimality theorem, we can obtain...

[0162]

[0163] S45, Iteration: Finally, based on the AUV's dynamic model and measurements obtained using the Flexray protocol, we obtain the AUV's trajectory in three-dimensional space for each step.

[0164] Beneficial Effects: Based on the evaluation function that minimizes segment size, we obtained an explicit optimized solution. Therefore, we avoided using optimization algorithms in the program, significantly reducing computational complexity. This improves the real-time response speed and ensures the stability of the estimation system. Finally, simulations yielded good results, demonstrating the effectiveness of the proposed algorithm. Figure 4 , Figure 5 As shown.

[0165] The technical principles of the present invention have been described above with reference to specific embodiments. These descriptions are merely for explaining the principles of the invention and should not be construed as limiting the scope of protection of the invention in any way. Based on this explanation, those skilled in the art can readily conceive of other specific embodiments of the invention without inventive effort, and these embodiments will all fall within the scope of protection of the present invention.

Claims

1. A method for AUV state estimation based on the Flexray protocol, characterized in that, Includes the following steps: S1. Construct a 6-DOF model of the underwater vehicle system. Model the system based on the position information and the dynamic equations of Euler angles of the underwater vehicle. Based on the dynamic equations of the continuous-time system, transform the continuous-time system into a discrete-time system using the zero-order hold method. S2. Based on the FlexRay protocol, and referring to the core part of its transmission protocol, the transmission protocol is roughly divided into two categories: one is based on time multiple access connection mode, and the other is based on flexible time multiple access connection mode. Based on this, the FlexRay protocol for underwater vehicle system is designed, and the protocol is divided into a polling protocol in the static segment and an attempt-on-discard protocol in the dynamic segment. S3. Due to the use of the FlexRay protocol, there is a one-unit estimator working interval deviation in the data packet arrival time; by augmenting the system state, the current time and the state of the system at the previous moment are estimated simultaneously to solve the mixed delay problem caused by the mechanism based on the FlexRay protocol. S4. Establish a set-membership filter for a fully symmetric multicell and use the shell of the fully symmetric multicell to provide a higher accuracy state set estimation. In step S1, the dynamic model of the AUV is described as a 6-DOF model based on a body-fixed coordinate system and a Earth-fixed coordinate system. The following are the kinematic and dynamic models of an AUV in discrete cases: Equation (1) In Equation 1, and These represent the 3D position and Euler angles of the AUV, respectively. and Represents the velocity at the corresponding component; defines the system state as follows; Equation (2) In Equation 2, It means that in k The state parameters of the system at any given time; Therefore, the dynamic equations of the initial AUV system can be obtained. Equation (3) The raw measurements are obtained from the sensor measurements. , Equation (4) Among them, the unknown but bounded noise and Limited by the subsequent set of multiple cells; C is the measurement matrix. Sensors typically cannot directly obtain data about state x, therefore C is determined by the physical parameters of the sensor: Equation (5) in, Let P represent a set of polycells centered at vector c and generating matrix P; therefore and They are located in sets of multiple cells with the origin at the center and generating matrices W and V, respectively.

2. The AUV state estimation method based on the Flexray protocol according to claim 1, characterized in that, In step 2, the uniform quantizer is set to a scalar. This makes in The interval is based on the allocated bits bps divided into Each quantization interval is used to determine which smaller interval the received information falls into, and the corresponding interval code is output. We define the quantified measurement as: Equation (6) In Equation 6, This represents the quantization error, and the quantization error is related to the number of bits in the data packet; the quantization error is defined as a polytope: Equation (7) In Equation 7, The origin is the center, and the generating matrix is... A collection of multiple cells; Here, the rate of change of the Euler angle of the AUV is defined as the number of packets transmitted in the dynamic segment of the attempt to discard the protocol, i.e., the number of packets transmitted in the dynamic segment. We perform the write operation; only one data packet can access the channel resource during the transmission cycle. We divide the measurement into N data packets and divide them into two sets. and , where belongs to set The nodes are scheduled by a round-robin protocol and belong to The nodes are scheduled using the one-attempt drop protocol, with the following scheduling rules: A. Polling Protocol: Equation (8) In Equation 8, This represents the node that acquires the transmission right at time j, and mod() is the modulo function; B. Try the discard protocol once: Equation (9) In Equation 9, This represents the information of node j that was last transmitted before time k. This indicates the node that most needs to transmit data at time k under the "maximum error priority" rule; It is a given positive definite weight matrix; Therefore, based on the Flexray protocol in high-speed networks, measurements can be divided into static and dynamic segments of data packets to be scheduled: Equation (10) Similarly, define the measurement matrix: Equation (11) The measurement received by the receiver is defined as: ; Based on the assumption of high-speed networks, we can divide the communication cycle of a Flexray protocol into... Each transmission cycle receives at most [number] data points in each state update cycle. Each data packet; furthermore, the received measurement is defined as: Equation (12) in, and These represent the quantization error and measurement noise of the received data packet, respectively.

3. The AUV state estimation method based on the Flexray protocol according to claim 2, characterized in that, In step 3, preprocessing is performed before estimation to transform it into a standard time-delay-free system; We set the augmented state as follows: We now have the following augmentation system: ； in, , .

4. The AUV state estimation method based on the Flexray protocol according to claim 3, characterized in that, In step 4, a fully symmetric multicellular structure is used as the outer shell of the set, and the initial state is defined based on prior knowledge as being located within the multicellular structure. The Minkowski sum of a polytope satisfies the closure property of set operations, meaning that the result of the operation is still a polytope, i.e.: Equation (13) For the state at time k, first perform a one-step prediction on the augmented system to obtain the one-step predicted multicell. ,in: , Equation (14) In Equation 14, and These represent the center and generator matrix of the predicted state in one step, respectively; The next step is to estimate the multicellularity. ,in: ， Equation (15) In Equation 15, and Let represent the center and the generator matrix of the final estimated state set, respectively.

5. The AUV state estimation method based on the Flexray protocol according to claim 4, characterized in that, In step 4, the specific steps are as follows: S41. Initialization: Input the initial state using prior knowledge. Generate matrix ; S42. Calculate the one-step predicted multicell set, and find the set center of the one-step predicted set according to the following formula. and generating matrix : Equation (16) Therefore, we get: ， Equation (17) S43. Calculate the estimated set of multiple cells, and determine the set center of the one-step prediction set using the following formula. and generating matrix : Equation (18) Therefore, we get: ， ； Equation (19) S44. Minimizing the design gain based on the matrix-based F-radius. To facilitate minimizing the matrix radius F We define the generating matrix The covariance matrix is: Equation (20) Therefore, a similar covariance matrix can be represented as: Equation (21) According to the optimality theorem, we can obtain... Equation (22) S45, Iteration: Finally, based on the AUV's dynamic model and measurements obtained using the Flexray protocol, we obtain the AUV's trajectory in three-dimensional space for each step.

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