A method for proactive compensation of AUV communication delay based on parameter vector adaptive state prediction

Abstract

This invention provides an active compensation method for AUV communication delay based on parameter vector adaptive state prediction, comprising: defining the state variables and communication delay parameters of a multi-AUV formation system; constructing an autoregressive model of AUV motion state with unknown parameter vectors and determining the undetermined order of the autoregressive model; defining the output estimation error of the AUV motion state autoregressive model and designing an ideal online update law; introducing a first-order low-pass filter to filter the current motion state vector, regression vector, and comprehensive error respectively, to obtain a filtered autoregressive AR model; defining the output estimation error of the filtered autoregressive AR model and designing an achievable parameter adaptive law; designing a parameter vector adaptive state predictor for the i-th AUV to predict the motion state of the i-th AUV with delay, obtaining a predicted value of the motion state with delay, and applying the predicted value to the formation control law design to achieve active compensation for communication delay among multiple AUVs.

Description

Technical Field

[0001] This invention relates to the field of communication delay technology for underwater robots, and more particularly to an active compensation method for communication delay of AUVs (Autonomous Underwater Vehicles) based on parameter vector adaptive state prediction. Background Technology

[0002] Autonomous underwater vehicles (AUVs) possess irreplaceable application value in civilian and military fields such as marine resource exploration, seabed topography mapping, marine environmental monitoring, and underwater defense operations, thanks to their advantages of maneuverability, stealth, and wide operating range. For large-scale, long-term, and highly complex marine operations, a single AUV is limited by hardware constraints such as payload capacity, endurance, and operational efficiency, making it difficult to meet mission requirements. However, multi-AUV collaborative formation operations, through functional complementarity and task division, can achieve a significant increase in operational efficiency, and have become a research hotspot in the field of underwater robotics.

[0003] The core premise of multi-AUV coordinated formation is the exchange of state information between individuals. However, in the underwater environment, AUVs can only transmit data through underwater acoustic communication. The speed of sound in seawater is only about 1500 m / s, far lower than the speed of electromagnetic waves in air, resulting in significant communication delays in information transmission between AUVs. If communication delays are not effectively addressed in formation control, it will directly lead to a decrease in the accuracy of coordinated formation control, formation instability, and even collisions between individuals, seriously threatening the safety and reliability of multi-AUV formation operations.

[0004] The paper "Distributed Formation Control of Autonomous Underwater Vehicles with Communication Constraints," published in the *Journal of Huazhong University of Science and Technology* in 2009, Vol. 2, discloses a distributed formation control method for autonomous underwater vehicles (AUVs) applicable to communication delay conditions. This method first transforms the nonlinear kinematic model of the AUV into a linear system model using feedback linearization techniques. Based on this, consensus theory is introduced into the controller design, constructing a distributed formation control law capable of compensating for the effects of communication delay. To ensure system stability, Lyapunov-Krasovskii functional theory and linear matrix inequality theory are further utilized to derive and quantify the sufficient conditions and design parameter boundaries for the closed-loop system to maintain asymptotic stability under this control law. Chinese patent CN108490961A proposes a novel strategy for controlling multi-AUV circular formation. It divides the pose relationship between the navigator and followers into distance and angle relationships relative to the origin of the coordinate axis, constructs attitude angle, heading angle, and velocity error models, and uses a PID controller to control each AUV in the formation to achieve circular formation motion. Followers receive only the pose information of the navigator in real time, reducing delays and data loss that occur when AUVs communicate with multiple systems, thus enhancing the stability and reliability of formation control. The paper "Formation Control of Under-Driven Autonomous Underwater Vehicles under Communication Delay," published in the 6th issue of *Firepower Command and Control* in 2011, discloses a multi-AUV formation control method under communication delay conditions. This method decouples the multi-AUV formation problem into a path-tracking problem for each AUV and applies a consensus algorithm to design a distributed synchronization control law based on path parameters, which considers the impact of communication delay. Based on this, the method derives and limits the feasible range of design parameters in the synchronization control law according to the stability theory of distributed consensus systems, so as to realize multi-AUV formation control under communication delay. The above methods are all passive adaptations to communication delay, only providing sufficient conditions for system stability under delay conditions through theoretical analysis, without fundamentally compensating for the lag in state information caused by delay; at the same time, the control law design is highly dependent on the consensus algorithm framework, with a fixed structure, making it difficult to combine with advanced control theory to achieve further optimization of control performance. Chinese invention patent CN108594845A discloses a multi-AUV formation method based on predictive control under communication constraints, which designs the AUV cooperative path tracking control law through inverse reasoning and introduces a cooperative tracking error prediction module to suppress the impact of communication delay. However, the design and implementation of this method strictly depends on the accurate mathematical model of AUV motion. When the model parameters are perturbed or underwater environmental disturbances cause model mismatch, its delay compensation effect will decrease significantly, making it unsuitable for complex marine operation scenarios with unknown model parameters.

[0005] To address the model dependency problem, data-driven state estimation and time series forecasting methods have been gradually introduced into the field of underwater robot delay compensation. Among existing time series forecasting technologies for marine moving bodies, some patented technologies achieve high-precision forecasting of ship motion sequences through intelligent algorithms such as graph neural networks and echo state networks. However, these technologies suffer from complex network structures and high computational overhead, failing to meet the online real-time computing requirements of AUV embedded systems. Summary of the Invention

[0006] To address the aforementioned technical problems, this paper proposes an AUV communication delay proactive compensation method based on parameter vector adaptive state prediction. By constructing an AUV motion state AR model with unknown parameter vectors and combining filtering techniques to design an adaptive update law for the parameter vectors, high-precision online prediction of the AUV motion state is achieved. This fundamentally solves the problem of proactive communication delay compensation when AUV model parameters are unknown, while significantly reducing online computation and improving the method's engineering practicality.

[0007] The technical means employed in this invention are as follows:

[0008] An active delay compensation method for AUV communication based on parameter vector adaptive state prediction includes: S1. Define the state variables and communication delay parameters of the multi-AUV formation system; S2. Based on the defined state variables and communication delay parameters, construct an autoregressive model of AUV motion state with unknown parameter vectors; S3. Determine the undetermined order value of the autoregressive model of AUV motion state; S4. Define the output estimation error of the AUV motion state autoregressive model, and design an ideal online update law for the parameter vector based on the output estimation error; S5. Introduce a first-order low-pass filter to filter the motion state vector, regression vector and comprehensive error at the current moment, respectively, to obtain the autoregressive AR model of AUV motion after filtering. S6. Define the output estimation error of the autoregressive AR model of the filtered AUV motion, design an achievable parameter adaptive law, perform online estimation of the unknown parameter vector, and obtain the estimated value of the parameter vector. S7. Based on the estimated values ​​of the parameter vector, design the first... The parameter vector adaptive state predictor for the i-th AUV, for the i-th The motion state of each AUV with a delay is estimated to obtain the estimated value of the motion state with delay. The estimated value is applied to the formation control law design to realize active compensation for communication delay between multiple AUVs.

[0009] Further, step S1 includes: S11, Assuming a multi-AUV formation system includes Taiwan's autonomous underwater robot, defining the first Taiwanese AUVs The actual motion state at time t is ; S12. Assume the inherent delay of communication between multiple AUVs is... Define the time. Next The AUV received the neighbor node's number The motion state of the AUV is a historical state with time delay. , , .

[0010] Further, step S2 includes: Using the first The AUV exhibits a delayed motion state. and A historical motion state vector with a time delay ,Establish The autoregressive model of the motion state of the AUV is as follows:

[0011] in, express Time of the first The motion state output vector of the AUV. ; This represents the parameter matrix of the autoregressive model. , A vector of unknown parameters; express dimensional regression vector, , Indicates the first AUV A historical motion state vector with a time delay. ; This represents the combined error, including unmodeled dynamics and measurement noise. .

[0012] Further, step S3 includes: S31. Define the Akaike information content criterion function of the AUV motion state autoregressive model as follows:

[0013] in, Indicated by model order The Akaike information criterion function value is used to measure the overall goodness of fit and complexity penalty of the model at different orders. This indicates the undetermined order of the autoregressive model; This indicates the length of the data sample used in the calculation of the criterion function; Represents the natural logarithm; This represents the variance of the modeling error. , It is a positive integer. Indicates from the first Each sampling time point begins to participate in the statistical calculation of the modeling error variance. express Time of the first The motion state output vector of the AUV. Represents the first in the regression vector Each historical motion state component corresponds to a specific time. Next The movement status of the AUV in Taiwan This indicates that when the model order is taken as At that time, the first unknown parameter vector of order The estimated value; S32. Assume the maximum order of the autoregressive model of AUV motion state is... , Calculate in sequence The order of the autoregressive model for AUV motion state is determined as follows: .

[0014] Further, step S4 includes: S41. Define the output estimation error of the AUV motion state autoregressive model as follows:

[0015] in, Represents the vector of unknown parameters Online estimates; S42. Taking the time derivative of the defined output estimation error, we get:

[0016] S43, Order The ideal adaptive law for parameters is obtained as follows:

[0017] in, Design constant; Represents the regression vector Regarding time The derivative of the historical motion state vector is the rate of change of the vector. Represents the motion state output vector Regarding time The derivative of is the rate of change of the actual received historical state with delay.

[0018] Further, step S5 includes: S51. Introduce a first-order low-pass filter to filter the motion state vector at the current moment, as shown in the following formula:

[0019] in, This represents the time constant of a first-order low-pass filter. It is used to adjust the cutoff frequency of the filter and control the degree of suppression of high-frequency measurement noise; Represents the filtered motion state vector Regarding time The derivative of the filtered signal is the rate of change of the filtered signal. This represents the filtered motion state vector, i.e., the vector obtained after smoothing by a first-order low-pass filter. The motion state output vector of the AUV; S52. Introduce a first-order low-pass filter to filter the regression vector, as shown in the following formula:

[0020] in, Represents the filtered regression vector Regarding time The derivative of the filtered regression vector is the rate of change of the regression vector. This represents the filtered regression vector, i.e., the first-order low-pass vector obtained after smoothing by the first-order low-pass filter. Taiwan AUV dimensional historical motion state regression vector; S53. Introduce a first-order low-pass filter to filter the synthesis error, as shown in the following formula:

[0021] in, Indicates the overall error after filtering. Regarding time The derivative of the filtered composite error signal is the rate of change of the composite error signal. This represents the overall error after filtering, which is the filtered error term obtained after smoothing by a first-order low-pass filter and includes unmodeled dynamics and measurement noise. S54, Based on the filtered motion state vector Regression vector and combined error The filtered autoregressive AR model of AUV motion is obtained as follows: .

[0022] Further, step S6 includes: S61. Define the output estimation error of the autoregressive AR model for the filtered AUV motion as follows:

[0023] in, This represents the estimation error of the autoregressive AR model output after filtering the AUV motion; S62. Calculate the time derivative of the output estimation error of the autoregressive AR model of the filtered AUV motion to obtain:

[0024] in, This indicates the estimation error of the filtered model output. Regarding time The derivative of the error signal, i.e., the rate of change of the filtered error signal over time; Represents the parameter estimation matrix Regarding time The derivative of the parameter estimate, i.e., the online update rate of the parameter estimate; S63. Design an achievable adaptive law for parameters, as follows:

[0025] in, The square of the L2 norm of the filtered regression vector; Design constant; Use small positive numbers to prevent the denominator from being zero and to ensure numerical stability.

[0026] Further, step S7 includes: S71. Based on the updated parameter vector estimates, for the... AUV We calculate the weighted sum of the time-delayed motion state vectors to determine the _th ... AUV at time The estimated value of the motion state is given by the following formula:

[0027] S72, Based on the calculated motion state prediction and the first The historical motion state vector of the nth AUV is iteratively calculated. AUV at time The estimated value of the motion state is given by the following formula:

[0028] in, Indicates the first In the parameter vector adaptive state predictor of the nth AUV, the one currently being computed is the nth... An estimated value of a motion state with a time delay. ; S73, when At that time, the first The AUV obtains its neighbor's number. The existence of a delayed motion state of an AUV The estimated value This enables proactive compensation for communication delays.

[0029] Compared with the prior art, the present invention has the following advantages: 1. This invention designs an adaptive update law for parameter vectors with low-pass filtering to ensure the exponential convergence of the AUV motion state estimation error, thereby achieving active compensation for underwater acoustic communication delay between multiple AUVs, rather than passive adaptation to the delay, and significantly improving the accuracy and stability of multi-AUV formation control under delay conditions.

[0030] 2. The parameter adaptive update law designed in this invention does not require the calculation of the covariance matrix composed of historical data. It can complete the online update of parameters through simple algebraic operations. Compared with the traditional recursive least squares method, it significantly reduces the online calculation burden and adapts to the real-time computing requirements of AUV embedded systems. At the same time, by introducing a first-order low-pass filter, it avoids the direct use of the differential operation of state variables in the adaptive law, effectively suppressing high-frequency measurement noise. It has the advantages of simple structure and easy engineering implementation.

[0031] 3. The active compensation method for communication delay between multiple AUVs proposed in this invention is parameter vector adaptive. By introducing a first-order low-pass filter, it avoids directly using the differential of AUV motion in the parameter adaptation law, offering advantages such as ease of engineering implementation and elimination of high-frequency measurement noise; model output estimation error... It exhibits exponential convergence, thereby improving the accuracy of the parameter vector adaptive state predictor.

[0032] In summary, the technical solution of this invention solves the problems of existing technologies, such as passively adapting to communication delays without actively compensating, strong model dependence, heavy online computing burden, and difficulty in adapting to embedded real-time computing requirements. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the 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 based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart of the active compensation method for communication delay of multiple AUVs based on parameter vector adaptive state predictor according to the present invention. Detailed Implementation

[0035] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0036] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product or device.

[0037] like Figure 1 As shown, this invention provides an AUV communication delay active compensation method based on parameter vector adaptive state prediction, comprising: S1. Define the state variables and communication delay parameters of the multi-AUV formation system; S2. Based on the defined state variables and communication delay parameters, construct an autoregressive model of AUV motion state with unknown parameter vectors; S3. Determine the undetermined order value of the autoregressive model of AUV motion state; S4. Define the output estimation error of the AUV motion state autoregressive model, and design an ideal online update law for the parameter vector based on the output estimation error; S5. Introduce a first-order low-pass filter to filter the motion state vector, regression vector and comprehensive error at the current moment, respectively, to obtain the autoregressive AR model of AUV motion after filtering. S6. Define the output estimation error of the autoregressive AR model of the filtered AUV motion, design an achievable parameter adaptive law, perform online estimation of the unknown parameter vector, and obtain the estimated value of the parameter vector. S7. Based on the estimated values ​​of the parameter vector, design the first... The parameter vector adaptive state predictor for the i-th AUV, for the i-th The motion state of each AUV with a delay is estimated to obtain the estimated value of the motion state with delay. The estimated value is applied to the formation control law design to realize active compensation for communication delay between multiple AUVs.

[0038] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes: S11, Assuming a multi-AUV formation system includes Taiwan's autonomous underwater robot, defining the first Taiwanese AUVs The actual motion state at time t is ; S12. Assume the inherent delay of communication between multiple AUVs is... Define the time. Next The AUV received the neighbor node's number The motion state of the AUV is a historical state with time delay. , , .

[0039] In a specific implementation, as a preferred embodiment of the present invention, step S2 includes: Using the first The AUV exhibits a delayed motion state. and A historical motion state vector with a time delay ,Establish The autoregressive model of the motion state of the AUV is as follows:

[0040] in, express Time of the first The motion state output vector of the AUV. ; This represents the parameter matrix of the autoregressive model. , A vector of unknown parameters; express dimensional regression vector, , Indicates the first AUV A historical motion state vector with a time delay. ; This represents the combined error, including unmodeled dynamics and measurement noise. .

[0041] In a specific implementation, as a preferred embodiment of the present invention, step S3 includes: S31. Define the Akaike information content criterion function of the AUV motion state autoregressive model as follows:

[0042] in, Indicated by model order The Akaike information criterion function value is used to measure the overall goodness of fit and complexity penalty of the model at different orders. This indicates the undetermined order of the autoregressive model; This indicates the length of the data sample used in the calculation of the criterion function; Represents the natural logarithm; This represents the variance of the modeling error. , It is a positive integer. Indicates from the first Each sampling time point begins to participate in the statistical calculation of the modeling error variance. express Time of the first The motion state output vector of the AUV. Represents the first in the regression vector Each historical motion state component corresponds to a specific time. Next The movement status of the AUV in Taiwan This indicates that when the model order is taken as At that time, the first unknown parameter vector of order The estimated value; S32. Assume the maximum order of the autoregressive model of AUV motion state is... , Calculate in sequence The order of the autoregressive model for AUV motion state is determined as follows: .

[0043] In a specific implementation, as a preferred embodiment of the present invention, step S4 includes: S41. Define the output estimation error of the AUV motion state autoregressive model as follows:

[0044] in, Represents the vector of unknown parameters Online estimates; S42. Taking the time derivative of the defined output estimation error, we get:

[0045] S43, Order The ideal adaptive law for parameters is obtained as follows:

[0046] in, Design constant; Represents the regression vector Regarding time The derivative of the historical motion state vector is the rate of change of the vector. Represents the motion state output vector Regarding time The derivative of is the rate of change of the actual received historical state with delay.

[0047] In a specific implementation, as a preferred embodiment of the present invention, step S5 includes: S51. Introduce a first-order low-pass filter to filter the motion state vector at the current moment, as shown in the following formula:

[0048] in, This represents the time constant of a first-order low-pass filter. It is used to adjust the cutoff frequency of the filter and control the degree of suppression of high-frequency measurement noise; Represents the filtered motion state vector Regarding time The derivative of the filtered signal is the rate of change of the filtered signal. This represents the filtered motion state vector, i.e., the vector obtained after smoothing by a first-order low-pass filter. The motion state output vector of the AUV; S52. Introduce a first-order low-pass filter to filter the regression vector, as shown in the following formula:

[0049] in, Represents the filtered regression vector Regarding time The derivative of the filtered regression vector is the rate of change of the regression vector. This represents the filtered regression vector, i.e., the first-order low-pass vector obtained after smoothing by the first-order low-pass filter. Taiwan AUV dimensional historical motion state regression vector; S53. Introduce a first-order low-pass filter to filter the synthesis error, as shown in the following formula:

[0050] in, Indicates the overall error after filtering. Regarding time The derivative of the filtered composite error signal is the rate of change of the composite error signal. This represents the overall error after filtering, which is the filtered error term obtained after smoothing by a first-order low-pass filter and includes unmodeled dynamics and measurement noise. S54, Based on the filtered motion state vector Regression vector and combined error The filtered autoregressive AR model of AUV motion is obtained as follows: .

[0051] In a specific implementation, as a preferred embodiment of the present invention, step S6 includes: S61. Define the output estimation error of the autoregressive AR model for the filtered AUV motion as follows:

[0052] in, This represents the estimation error of the autoregressive AR model output after filtering the AUV motion; S62. Calculate the time derivative of the output estimation error of the autoregressive AR model of the filtered AUV motion to obtain:

[0053] in, This indicates the estimation error of the filtered model output. Regarding time The derivative of the error signal, i.e., the rate of change of the filtered error signal over time; Represents the parameter estimation matrix Regarding time The derivative of the parameter estimate, i.e., the online update rate of the parameter estimate; S63. Design an achievable adaptive law for parameters, as follows:

[0054] in, The square of the L2 norm of the filtered regression vector; Design constant; Use small positive numbers to prevent the denominator from being zero and to ensure numerical stability.

[0055] In a specific implementation, as a preferred embodiment of the present invention, step S7 includes: S71. Based on the updated parameter vector estimates, for the... AUV We calculate the weighted sum of the time-delayed motion state vectors to determine the _th ... AUV at time The estimated value of the motion state is given by the following formula:

[0056] S72, Based on the calculated motion state prediction and the first The historical motion state vector of the nth AUV is iteratively calculated. AUV at time The estimated value of the motion state is given by the following formula:

[0057] in, Indicates the first In the parameter vector adaptive state predictor of the nth AUV, the one currently being computed is the nth... An estimated value of a motion state with a time delay. ; S73, when At that time, the first The AUV obtains its neighbor's number. The existence of a delayed motion state of an AUV The estimated value This enables proactive compensation for communication delays.

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for proactive compensation of AUV communication delay based on parameter vector adaptive state prediction, characterized in that, include: S1. Define the state variables and communication delay parameters of the multi-AUV formation system; S2. Based on the defined state variables and communication delay parameters, construct an autoregressive model of AUV motion state with unknown parameter vectors; S3. Determine the undetermined order value of the autoregressive model of AUV motion state; S4. Define the output estimation error of the AUV motion state autoregressive model, and design an ideal online update law for the parameter vector based on the output estimation error; S5. Introduce a first-order low-pass filter to filter the motion state vector, regression vector and comprehensive error at the current moment, respectively, to obtain the autoregressive AR model of AUV motion after filtering. S6. Define the output estimation error of the autoregressive AR model of the filtered AUV motion, design an achievable parameter adaptive law, perform online estimation of the unknown parameter vector, and obtain the estimated value of the parameter vector. S7. Based on the estimated values ​​of the parameter vector, design the first... The parameter vector adaptive state predictor for the i-th AUV, for the i-th The motion state of each AUV with a delay is estimated to obtain the estimated value of the motion state with delay. The estimated value is applied to the formation control law design to realize active compensation for communication delay between multiple AUVs.

2. The AUV communication delay active compensation method based on parameter vector adaptive state prediction according to claim 1, characterized in that, Step S1 includes: S11, Assuming a multi-AUV formation system includes Taiwan's autonomous underwater robot, defining the first Taiwanese AUVs The actual motion state at time t is ; S12. Assume the inherent delay of communication between multiple AUVs is... Define the time. Next The AUV received the neighbor node's number The motion state of the AUV is a historical state with time delay. , , .

3. The AUV communication delay active compensation method based on parameter vector adaptive state prediction according to claim 1, characterized in that, Step S2 includes: Using the first The AUV exhibits a delayed motion state. and A historical motion state vector with a time delay ,Establish The autoregressive model of the motion state of the AUV is as follows: in, express Time of the first The motion state output vector of the AUV. ; This represents the parameter matrix of the autoregressive model. , A vector of unknown parameters; express dimensional regression vector, , Indicates the first AUV A historical motion state vector with a time delay. ; This represents the combined error, including unmodeled dynamics and measurement noise. .

4. The AUV communication delay active compensation method based on parameter vector adaptive state prediction according to claim 1, characterized in that, Step S3 includes: S31. Define the Akaike information content criterion function of the AUV motion state autoregressive model as follows: in, Indicated by model order The Akaike information criterion function value is used to measure the overall goodness of fit and complexity penalty of the model at different orders. This indicates the undetermined order of the autoregressive model; This indicates the length of the data sample used in the calculation of the criterion function; Represents the natural logarithm; This represents the variance of the modeling error. , It is a positive integer. Indicates from the first Each sampling time point begins to participate in the statistical calculation of the modeling error variance. express Time of the first The motion state output vector of the AUV. Represents the first in the regression vector Each historical motion state component corresponds to a specific time. Next The movement status of the AUV in Taiwan This indicates that when the model order is taken as At that time, the first unknown parameter vector of order The estimated value; S32. Assume the maximum order of the autoregressive model of AUV motion state is... , Calculate in sequence The order of the autoregressive model for AUV motion state is determined as follows: 。 5. The AUV communication delay active compensation method based on parameter vector adaptive state prediction according to claim 1, characterized in that, Step S4 includes: S41. Define the output estimation error of the AUV motion state autoregressive model as follows: in, Represents the vector of unknown parameters Online estimates; S42. Taking the time derivative of the defined output estimation error, we get: S43, Order The ideal adaptive law for parameters is obtained as follows: in, Design constant; Represents the regression vector Regarding time The derivative of the historical motion state vector is the rate of change of the vector. Represents the motion state output vector Regarding time The derivative of is the rate of change of the actual received historical state with delay.

6. The AUV communication delay active compensation method based on parameter vector adaptive state prediction according to claim 1, characterized in that, Step S5 includes: S51. Introduce a first-order low-pass filter to filter the motion state vector at the current moment, as shown in the following formula: in, This represents the time constant of a first-order low-pass filter. It is used to adjust the cutoff frequency of the filter and control the degree of suppression of high-frequency measurement noise; Represents the filtered motion state vector Regarding time The derivative of the filtered signal is the rate of change of the signal. This represents the filtered motion state vector, i.e., the vector obtained after smoothing by a first-order low-pass filter. The motion state output vector of the AUV; S52. Introduce a first-order low-pass filter to filter the regression vector, as shown in the following formula: in, Represents the filtered regression vector Regarding time The derivative of the filtered regression vector is the rate of change of the regression vector. This represents the filtered regression vector, i.e., the first-order low-pass vector obtained after smoothing by the first-order low-pass filter. Taiwan AUV dimensional historical motion state regression vector; S53. Introduce a first-order low-pass filter to filter the synthesis error, as shown in the following formula: in, Indicates the overall error after filtering. Regarding time The derivative of the filtered composite error signal is the rate of change of the composite error signal. This represents the overall error after filtering, which is the filtered error term obtained after smoothing by a first-order low-pass filter and includes unmodeled dynamics and measurement noise. S54, Based on the filtered motion state vector Regression vector and combined error The filtered autoregressive AR model of AUV motion is obtained as follows: 。 7. The AUV communication delay active compensation method based on parameter vector adaptive state prediction according to claim 1, characterized in that, Step S6 includes: S61. Define the output estimation error of the autoregressive AR model for the filtered AUV motion as follows: in, This represents the estimation error of the autoregressive AR model output after filtering the AUV motion; S62. Calculate the time derivative of the output estimation error of the autoregressive AR model of the filtered AUV motion to obtain: in, This indicates the estimation error of the filtered model output. Regarding time The derivative of the error signal, i.e., the rate of change of the filtered error signal over time; Represents the parameter estimation matrix Regarding time The derivative of the parameter estimate, i.e., the online update rate of the parameter estimate; S63. Design an achievable adaptive law for parameters, as follows: in, The square of the L2 norm of the filtered regression vector; Design constant; Use small positive numbers to prevent the denominator from being zero and to ensure numerical stability.

8. The AUV communication delay active compensation method based on parameter vector adaptive state prediction according to claim 1, characterized in that, Step S7 includes: S71. Based on the updated parameter vector estimates, for the... AUV We calculate the weighted sum of the time-delayed motion state vectors to determine the _th ... AUV at time The estimated value of the motion state is given by the following formula: S72, Based on the calculated motion state prediction and the first The historical motion state vector of the nth AUV is iteratively calculated. AUV at time The estimated value of the motion state is given by the following formula: in, Indicates the first In the parameter vector adaptive state predictor of the nth AUV, the one currently being computed is the nth... An estimated value of a motion state with a time delay. ; S73, when At that time, the first The AUV obtains its neighbor's number. The existence of a delayed motion state of an AUV The estimated value This enables proactive compensation for communication delays.

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