A UUV non-cooperative target tracking method based on axial attention

Abstract

The present invention discloses a UUV non-cooperative target tracking method based on axial attention. Aiming at the unreliability of forward-looking sonar observation and the unpredictability of target motion, the present invention constructs a first-order Markov state space model with memory to describe the UUV non-cooperative target tracking mechanism under sonar observation, and proposes a non-cooperative target state multi-step prediction network based on axial attention Transformer, which is used to describe the complex motion process of non-cooperative targets relative to sonar under nonlinear observation. Aiming at the instability of observation and the unknown of posterior distribution, based on the Monte Carlo approximate inference principle, the multi-step prediction network is used to map the sampled particles in the target observation state space to the target prediction state space, and a target tracking method based on axial attention is constructed to improve the adaptability and robustness of UUV non-cooperative target tracking to uncertain inputs.

Description

Technical Field

[0001] The present invention relates to the field of underwater target tracking, and in particular to a UUV non-cooperative target tracking method based on axial attention. Background Art

[0002] Unmanned underwater vehicles (UUVs) have become important equipment in the fields of marine scientific research, marine resource surveys, and marine safety due to their wide range of activities and strong autonomy. UUV target tracking refers to the process of real-time estimation and prediction of the motion state of underwater targets of interest based on observation information with uncertainty interference. It is a key technology to support UUV autonomous navigation and operation. The main problems to be solved by UUV target tracking methods are underwater observation uncertainty and the unpredictability of underwater target motion models. The uncertainty of target states caused by measurement wild values ​​and noise that cannot be avoided and eliminated during the observation process is called observation uncertainty. The unpredictability of the target motion model is also called model uncertainty, which means that the motion law of the target cannot be accurately predicted during the target tracking process. Existing research mainly overcomes the above problems from two aspects: motion modeling and filtering algorithms. Significant progress has been made, but the following challenges still need to be overcome: On the one hand, due to the fluctuation of the hydroacoustic channel, the limitation of sonar observations, and the influence of UUV movement, in addition to the uncertainty of noise distribution, forward-looking sonar observations also have the problem of observation loss, which is highly unreliable, resulting in the inapplicability of the Bayesian theorem relied on by existing methods, resulting in low underwater target tracking accuracy and unstable tracking performance. On the other hand, UUVs often encounter non-cooperative targets during autonomous navigation. The motion of such targets is highly random and difficult to describe using the currently commonly used Markov motion model based on constant state transfer matrix. In addition, the unreliability of underwater observations exacerbates the difficulty of target motion prediction. In view of the above problems, the present invention proposes a UUV non-cooperative target tracking method based on axial attention. Summary of the invention

[0003] Based on the above technical problems, the present invention proposes a UUV non-cooperative target tracking method based on axial attention, constructs a first-order Markov state space model with memory to describe the UUV non-cooperative target tracking mechanism under sonar observation, and then establishes a recursive filtering model. In view of the unreliability of forward-looking sonar observation and the unpredictability of target motion, a non-cooperative target state multi-step prediction network based on axial attention Transformer is proposed to describe the complex motion process of non-cooperative targets relative to sonar under nonlinear observation; in view of the instability of observation and the unknown nature of the posterior distribution, based on the Monte Carlo approximate inference principle, the multi-step prediction network is used to map the sampled particles in the target observation state space to the target prediction state space, and a non-cooperative target tracking algorithm based on the axial attention multi-step prediction network is constructed.

[0004] A UUV non-cooperative target tracking method based on axial attention of the present invention comprises the following steps:

[0005] Step 1: The UUV navigates in the mission space and records the target observation value Z k ;

[0006] Construct a sonar observation model to transform the sonar observation value Z of the target in the time domain k Convert into the target observation state in a fixed coordinate system;

[0007] Step 2: Randomly sample in the observation state space. For the i-th sampled particle, if the observation missing time is κ from time k, then the predicted state of the i-th sampled particle at time k+κ is:

[0008]

[0009] Among them, f pred is a nonlinear prediction function, is the observed feature vector at time [kK, k-1], g is the predicted feature mapping function, f obs is the nonlinear mapping function of the observed characteristics, Sample particles for group P;

[0010] Step 3, using Monte Carlo algorithm to approximate the estimated state of the non-cooperative target;

[0011]

[0012] Furthermore, step 2 also includes constructing a multi-step prediction network of the target state based on axial attention to fit the nonlinear prediction function f pred ;

[0013] The P group of sampling particles In the target observation state set The target observation state set is obtained by random sampling. It is composed of the target observation state at time [kK, k-1] generated by the sonar observation model; P groups of sampling particles Input into the target state multi-step prediction network to obtain the predicted state of the P group of sampled particles

[0014] Furthermore, the target motion equation in step 2, when K = 1, is equivalent to the traditional first-order Markov motion model, and the sonar measurement equation is expressed as:

[0015]

[0016] Among them, fmea is the sonar nonlinear measurement function, is the target state at time k, v k is the observation noise.

[0017] Furthermore, the prediction feature mapping function g in step 2 is a time series prediction function with non-Markov characteristics, which is converted into a first-order Markov function with memory, as follows:

[0018] Describes the impact of the historical prediction state at time [k, k+κ-1] on the prediction state at time [k+κ]. The continuous accumulation of dynamic changes indicates that the predicted state has a regular transfer process; due to the regularity of the state transfer process, the predicted state transfer process at different times is similar, which can be uniformly described by function g1. Then the dynamic prediction feature mapping function can be expanded into the following κ-layer nested function in the time [k, k+κ-1] dimension:

[0019]

[0020] Among them, function g1 selectively retains the information extracted from the historical prediction state at each moment and introduces information about the new prediction state, that is, according to the input Update memory Thus, the multi-step prediction process of non-Markov target states is modeled as a first-order Markov model with memory iteration.

[0021] Furthermore, the target state multi-step prediction network based on axial attention adopts an encoder-decoder structure. The encoder based on the axial self-attention mechanism focuses on the features related to the target motion in the historical observation of the target state, and constructs the observation feature nonlinear mapping function f obs .

[0022] Furthermore, in the target state multi-step prediction network, the encoder obtains target motion related features from the target observation states at the most recent n moments to obtain encoding information, and the decoder, based on the idea of ​​sliding decision, predicts the state of the target at the next moment according to the encoding information and the predicted states at the most recent κ moments output by the target state multi-step prediction network.

[0023] Furthermore, the target state multi-step prediction network based on axial attention adopts an encoder-decoder structure;

[0024] The encoder consists of an input layer, a position encoding layer, and N encoder modules;

[0025] First, the input layer uses a multi-layer perceptron (MLP) to map the target historical observation state into a vector of fixed dimension in preparation for feature extraction.

[0026] Secondly, the position encoding layer uses two-dimensional position encoding to provide time step and sampling information features for the input features, enhancing the model's attention to temporal and spatial expressions;

[0027] Each encoder module consists of two sub-layers: axial multi-head self-attention and MLP. The input data of each sub-layer is batch normalized, and the input and output before normalization are residually connected as the input of the next sub-layer.

[0028] The decoder includes an input layer, a position encoding layer, N decoder modules, and an output layer;

[0029] The input and output layers of the decoder are both MLP networks;

[0030] The position coding layer of the decoder uses two-dimensional position coding;

[0031] The decoder module consists of three sub-layers: axial masked multi-head self-attention, axial multi-head co-attention and MLP. The input data of each sub-layer is batch normalized, and the input and output before normalization are residually connected as the input of the next sub-layer.

[0032] Furthermore, in the process of training the target state multi-step prediction network, an end-to-end supervised training method is adopted, and the batch gradient descent method and Adam optimizer are used to minimize the mean square error loss function for training.

[0033] Furthermore, step 1 also includes constructing a coordinate reference system, taking any position point in the mission space as the origin, establishing a North-East coordinate system NOE as a fixed coordinate system to describe the position and posture of the UUV, using x to represent the northward displacement, y to represent the eastward displacement, and ψ to represent the heading angle; establishing a carrier coordinate system x fixed at the center of gravity of the UUV B o B y B Describe the speed of the UUV, use u to represent the longitudinal velocity, v to represent the transverse velocity, and r to represent the bow angular velocity; establish the sensor coordinate system x with the sonar measurement center as the origin S o S y S , coordinate axis o S x S ,o S y S Respectively with the carrier coordinate system coordinate axis o B x B , o B y B Same direction;

[0034] Then the target observation value in step 1 is is the sonar observation value at time k, It represents the sonar observation at time k, including the distance between the target and the origin of the sensor coordinate system o S The Euclidean distance of Indicates that the target is at x S o S y S Azimuth in coordinate system;

[0035] Construct a sonar observation model and transform the sonar observation value Z of the target in the time domain k Converting into the target observation state in a fixed coordinate system, the fixed coordinate system refers to the North East coordinate system NOE;

[0036] Specifically, firstly, the coordinate system x S o S y S The observation of the non-cooperative target state by the sonar is converted to the carrier coordinate system x B o B y B , and then mapped to the fixed coordinate system NOE, the observation state of the target in the north-east coordinate system NOE is expressed as:

[0037]

[0038] in, is the target observation state at time k, R(ψ) is x B o B y B To the NOE rotation matrix, for o S In x B o B y B The position below is the state of the observed UUV at time k.

[0039] Furthermore, step 1 also includes constructing a depth-determining motion model and a target motion model of the underactuated UUV;

[0040] The following underactuated UUV fixed depth motion model is established:

[0041]

[0042] in, represents the velocity of UUV in NOE coordinate system, [u o ,0,r o ] T Indicates that UUV is at x B o B y B The velocity in the coordinate system;

[0043] In addition, the UUV is subject to the following motion constraints:

[0044]

[0045] The target motion model is as follows:

[0046] Use NOE coordinate system to describe the target pose η t =[x t ,y t ,ψ t ] T , construct a carrier coordinate system fixed to the target to describe the target velocity v t =[u t ,v t ,r t ] T , then the kinematic equation of the target can be expressed as:

[0047]

[0048] In addition, based on the observed UUV motion and sonar observation performance, the kinematics of the non-cooperative target is assumed to satisfy the following constraints:

[0049]

[0050] Compared with the prior art, the advantage of the UUV non-cooperative target tracking method based on axial attention provided by the present invention is that: based on the UUV non-cooperative target tracking mechanism under sonar observation, the present invention establishes a first-order Markov model with memory to describe the non-Markov state space, which provides a new idea for the research of non-cooperative target tracking technology. The method of the present invention samples from the historical observation state of the target, and uses the constructed multi-step prediction network of the target state based on axial attention to predict the future state of the sampled particles, and then fits the distribution of the posterior probability, which can effectively deal with the target tracking problem based on nonlinear non-Gaussian observation. In addition, using the multi-step prediction network of the target state based on axial attention, the motion state of the non-cooperative target can be effectively predicted, and high-precision and stable target tracking can be achieved when the target motion is unpredictable and the observation is lost. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a coordinate reference system diagram for UUV target tracking.

[0052] Figure 2 This is a diagram of the target state multi-step prediction network structure based on axial attention. DETAILED DESCRIPTION

[0053] The following is a description of a UUV non-cooperative target tracking method based on axial attention provided by the present invention in conjunction with the accompanying drawings of the specification:

[0054] A UUV non-cooperative target tracking method based on axial attention of the present invention comprises the following steps:

[0055] Step 1: construct a UUV target tracking model, including: coordinate reference system, sonar observation model, UUV motion model and target motion model;

[0056] 1) Establish the coordinate reference system as follows:

[0057] like Figure 1 As shown in the figure, any position point in the mission space is taken as the origin, and the North-East coordinate system NOE is established as a fixed coordinate system to describe the position and posture of the UUV. x represents the north displacement, y represents the east displacement, and ψ represents the heading angle; the carrier coordinate system x is established fixed at the center of gravity of the UUV B o B y B Describe the speed of the UUV, use u to represent the longitudinal velocity, v to represent the transverse velocity, and r to represent the bow angular velocity; establish the sensor coordinate system x with the sonar measurement center as the origin S o S y S , coordinate axis o S x S ,o S y S Respectively with the carrier coordinate system coordinate axis o B x B , o B y B Same direction;

[0058] 2) The sonar observation model is established as follows:

[0059] To describe the state of a non-cooperative target, firstly transform the coordinate system x S o S y S The observation of the non-cooperative target state by the sonar is converted to the carrier coordinate system x B o B y B , and then mapped to the fixed coordinate system NOE;

[0060] Assume that the sonar observation at time k includes the distance between the target and the origin o of the sensor coordinate system S The Euclidean distance is Target at x S o S y S The azimuth in the coordinate system is Then the observation state of the target under NOE can be expressed as:

[0061]

[0062] in, is the target observation state at time k, is the sonar observation value at time k, R(ψ) is x B o B y B To the NOE rotation matrix, for o S In x B o B y B The position below is the state of the UUV observed at time k;

[0063] 3) The UUV motion model is established as follows:

[0064] The following underactuated UUV fixed depth motion model is established:

[0065]

[0066] in, represents the velocity of UUV in NOE coordinate system, [u o ,0,r o ] T Indicates that UUV is at x B o B y B The velocity in the coordinate system;

[0067] In addition, the UUV is subject to the following motion constraints:

[0068]

[0069] 4) Establish the target motion model as follows:

[0070] Use NOE coordinate system to describe the target pose η t =[x t ,y t ,ψ t ] T , construct a carrier coordinate system fixed to the target to describe the target velocity v t =[u t ,v t ,r t ] T , then the kinematic equation of the target can be expressed as:

[0071]

[0072] In addition, based on the observed UUV motion and sonar observation performance, the present invention assumes that the kinematics of the non-cooperative target satisfies the following constraints:

[0073]

[0074] Step 2: Establish the state equation of the UUV non-cooperative target tracking problem, including the target state transfer equation and sonar measurement equation:

[0075] Traditional target tracking methods usually model this problem as a first-order Markov process, assuming that the current state of the target is only related to the state at the previous moment, ignoring the impact of the historical state on the target motion, resulting in modeling errors. The present invention constructs a non-Markov model to describe the UUV non-cooperative target tracking problem. Assuming that the motion state of the target at time k is related to its state K moments before time k, the target state transfer equation can be expressed as:

[0076]

[0077] Among them, f trans is the target nonlinear state transfer function, is the target state at the moment [kK, k-1], is the target motion process noise; this equation describes a more general target motion process. When K = 1, this equation is equivalent to the traditional first-order Markov motion model;

[0078] The sonar measurement equation can be expressed as:

[0079]

[0080] Among them, f mea is the sonar nonlinear measurement function, is the target state at time k, v k is the observation noise;

[0081] Due to the limitations and unreliability of sonar observation, non-cooperative target tracking based on sonar usually suffers from temporary target loss or temporary observation failure, resulting in temporary observation loss. To address this problem, the present invention establishes a UUV non-cooperative target state estimation equation based on historical observation state and predicted state based on Monte Carlo approximate inference.

[0082] Random sampling is performed in the observation state space. For the i-th sampled particle, if the observation missing time is κ from time k, then the predicted state of the i-th sampled particle at time k+κ is:

[0083]

[0084] Among them, f pred is a nonlinear prediction function, is the observed feature vector at time [kK, k-1], g is the predicted feature mapping function, f obs is the nonlinear mapping function of the observed characteristics, To obey random distribution P group of sampling particles;

[0085] The prediction feature mapping function g is a time series prediction function with non-Markov characteristics, which can be converted into a first-order Markov function with memory, as follows:

[0086] Describes the impact of the historical prediction state at time [k, k+κ-1] on the prediction state at time [k+κ]. The continuous accumulation of dynamic changes indicates that the predicted state has a regular transition process. Since the state transition process has regularity, the predicted state transition process at different times is similar and can be uniformly described by function g1. Then the dynamic prediction feature mapping function can be expanded into the following κ-layer nested function in the time [k, k+κ-1] dimension:

[0087]

[0088] Among them, function g1 selectively retains the information extracted from the historical prediction state at each moment and introduces information about the new prediction state, that is, according to the input Update memory Thus, the multi-step prediction process of non-Markov target states is modeled as a first-order Markov model with memory iteration.

[0089] Based on Monte Carlo approximate inference, the non-cooperative target state estimation equation is:

[0090]

[0091] Step 3: Construct a multi-step prediction network of the target state based on axial attention and fit the nonlinear prediction function f pred ;

[0092] like Figure 2 As shown in the figure, the target state multi-step prediction network based on axial attention adopts an encoder-decoder structure. The encoder based on the axial self-attention mechanism focuses on the features related to the target motion in the historical observation of the target state and constructs the observation feature nonlinear mapping function f obs The decoder combines the axial self-attention and axial co-attention mechanisms to pay attention to the historical observation encoding information and historical predictions output by the encoder, and construct the target state prediction and memory update process. This encoder-decoder structure can realize real-time target state prediction, and when the observation at time k is temporarily invalid, it can predict the target state at time [k+1,k+κ] based on the observation encoding information at time [kK,k-1] and the target state prediction information at time [k,k+κ-1].

[0093] like Figure 2As shown in the figure, the encoder consists of an input layer, a position encoding layer and N encoder modules; first, the input layer uses a multi-layer perceptron (MLP) to map the target historical observation state into a vector of fixed dimension to prepare for feature extraction; secondly, the position encoding layer uses two-dimensional position encoding to provide time step and sampling information features for the input features, enhancing the model's attention to time and space expressions; the encoder module consists of two sub-layers: axial multi-head self-attention and MLP. In order to avoid gradient disappearance and speed up convergence, batch normalization is performed on the input data of each sub-layer, and the input and output before normalization are residually connected as the input of the next sub-layer.

[0094] Input to the encoder forward pass The P group of observed particles sampled from the observed state sequence at time [kK, k-1] constitute the input of the encoder module after MLP encoding and position encoding:

[0095]

[0096] in, pad(·) represents the full zero padding operation, MLP tanh represents a multilayer perceptron with tanh activation function, is a trainable two-dimensional position encoding. When k∈[1,K], the sonar has not collected enough observation data. At this time, this paper uses zero padding operation to construct input data of size 4×P×K. The encoder module first Batch normalization is performed, and then axial multi-head attention, residual connection and multi-layer perceptron are used to focus on and capture the features related to the target motion in the observation state. The forward propagation process can be expressed as:

[0097]

[0098] in, and are the outputs of the normalization layer, the axial multi-head attention layer, and the encoder module respectively; the output of the Nth encoder module is recorded as Represents the encoding information of the target observation state by the encoder at time [kn, k-1]; MultiHead Axis-K and MultiHead Axis-P Respectively represent the following multi-head attention calculations in dimensions d1×n and d1×P:

[0099]

[0100] Among them, Mask(·) is a mask function to prevent the attention layer from focusing on zero-filled data, D k is the dimension of K, and W H represents the trainable parameter matrix and H is the number of attention heads.

[0101] The present invention constructs a target state multi-step prediction network based on an encoder-decoder structure to solve the target tracking problem under observation failure conditions. In the target state multi-step prediction network, the encoder obtains target motion-related features from the target observation state at the most recent n moments to obtain the encoded information The decoder is based on the idea of ​​sliding decision. And the predicted state of the target state multi-step prediction network at the latest output of k times Predict the state of the target at the next moment

[0102] like Figure 2 As shown in the figure, the decoder consists of an input layer, a position encoding layer, N decoder modules and an output layer; the input layer and the output layer are both composed of MLP networks; the position encoding layer adopts two-dimensional position encoding; the decoder module consists of three sub-layers: axial mask multi-head self-attention, axial multi-head co-attention and MLP. The input data of each sub-layer is batch normalized, and the input and output before normalization are residually connected as the input of the next sub-layer.

[0103] The decoder input layer uses zero padding and MLP to Mapped to a matrix of d1×P×K dimensions. Subsequently, the position encoding layer adds position and time sequence labels to the matrix:

[0104]

[0105] in, is the decoder module input, is a trainable two-dimensional position encoding. The decoder module focuses on the key information in the historical predictions and fuses it with the encoded information captured by the encoder:

[0106]

[0107] in, and They are the normalization layer, the axial masked multi-head attention layer, the axial multi-head co-attention layer, and the output of the encoder module; and Represents a multi-head attention calculation using zero-filling mask and attention mask on dimension K. The output layer integrates global information and outputs the target state prediction sequence at time [k, k+κ]

[0108]

[0109] in, is the output feature map of the Nth decoder module; Slice(·) represents the slicing function, which is used to extract the 4×P×(κ+1)-dimensional output matrix from the convolution feature matrix.

[0110] Step 4: Offline training of the target state multi-step prediction network;

[0111] The target state multi-step prediction network is trained through end-to-end supervision, using batch gradient descent and Adam optimizer to minimize the mean square error loss function, so that the network learns the regularity information of sonar observations and target state transitions contained in the observation state sequence and historical prediction sequence from the offline dataset [kK, k-1].

[0112] Step 5: Use the fully trained target state multi-step prediction network to realize UUV non-cooperative target tracking under sonar observation, specifically:

[0113] 1) The UUV navigates in the mission space, and its forward-looking sonar continuously detects the surrounding environment and records the observation value Z of the target. k ;

[0114] 2) Based on the sonar observation model, the sonar observation values ​​of the target in the time domain are converted into the target observation state in a fixed coordinate system to generate the target observation state set

[0115] 3) In the target observation state set Random sampling is performed in to obtain P groups of sampling particles

[0116] 4) Input the P group of sampled particles into the target state multi-step prediction network based on axial attention and convert it into the predicted state of the P group of sampled particles

[0117] 5) Use Monte Carlo algorithm to approximate the target state:

[0118]

Claims

1. A UUV non-cooperative target tracking method based on axial attention, characterized in that: The steps include: Step 1: The UUV navigates in the mission space and records the target observation value Z k ; Construct a sonar observation model to transform the sonar observation value Z of the target in the time domain k Convert into the target observation state in a fixed coordinate system; Step 2: Randomly sample in the observation state space. For the i-th sampled particle, if the observation missing time is κ from time k, then the predicted state of the i-th sampled particle at time k+κ is: Among them, f pred is a nonlinear prediction function, is the observed feature vector at time [kK, k-1], g is the predicted feature mapping function, f obs is the nonlinear mapping function of the observed characteristics, Sample particles for group P; Construct a multi-step prediction network of target state based on axial attention to fit the nonlinear prediction function f pred ; The P group of sampling particles In the target observation state set The target observation state set is obtained by random sampling. It is composed of the target observation state at time [kK, k-1] generated by the sonar observation model; The P group of sampling particles Input into the target state multi-step prediction network to obtain the predicted state of the P group of sampled particles Step 3: Use the Monte Carlo algorithm to approximately infer the estimated state of the non-cooperative target.

2. According to claim 1, a UUV non-cooperative target tracking method based on axial attention is characterized in that: Step 1 also includes constructing a coordinate reference system. Taking any position point in the mission space as the origin, the North-East coordinate system NOE is established as a fixed coordinate system to describe the position and posture of the UUV. x represents the north displacement, y represents the east displacement, and ψ represents the heading angle. The carrier coordinate system x is established fixed at the center of gravity of the UUV. B o B y B Describe the speed of the UUV, with u representing the longitudinal velocity, v representing the transverse velocity, and r representing the bow angular velocity; establish the sensor coordinate system x with the sonar measurement center as the origin S o S y S , coordinate axis o S x S ,o S y S Respectively with the carrier coordinate system coordinate axis o B x B , o B y B Same direction; Then the target observation value in step 1 is is the sonar observation value at time k, It represents the sonar observation at time k, including the distance between the target and the origin of the sensor coordinate system o S The Euclidean distance of Indicates that the target is at x S o S y S Azimuth in coordinate system; Construct a sonar observation model and transform the sonar observation value Z of the target in the time domain k Converting into the target observation state in a fixed coordinate system, the fixed coordinate system refers to the North East coordinate system NOE; Specifically, firstly, the coordinate system x S o S y S The observation of the non-cooperative target state by the sonar is converted to the carrier coordinate system x B o B y B , and then mapped to the fixed coordinate system NOE, the observation state of the target in the north-east coordinate system NOE is expressed as: in, is the target observation state at time k, R(ψ) is x B o B y B To the NOE rotation matrix, for o S In x B o B y B The position below is the state of the observed UUV at time k.

3. According to claim 2, a UUV non-cooperative target tracking method based on axial attention is characterized in that: Step 2 also includes that, assuming that the motion state of the target at time k is related to its state K moments before time k, the target state transfer equation is expressed as: Among them, f trans is the target nonlinear state transfer function, is the target state at the moment [kK, k-1], is the noise of the target motion process; When K = 1, the target state transfer equation is equivalent to the traditional first-order Markov motion model, and the sonar measurement equation is expressed as: Among them, f mea is the sonar nonlinear measurement function, is the target state at time k, v k is the observation noise.

4. According to claim 2, a UUV non-cooperative target tracking method based on axial attention is characterized in that: The prediction feature mapping function g in step 2 is a time series prediction function with non-Markov characteristics, which is converted into a first-order Markov function with memory, as follows: Describes the impact of the historical prediction state at time [k, k+κ-1] on the prediction state at time [k+κ]. The continuous accumulation of dynamic changes indicates that the predicted state has a regular transfer process; due to the regularity of the state transfer process, the predicted state transfer process at different times is similar, which can be uniformly described by function g1. Then the dynamic prediction feature mapping function can be expanded into the following κ-layer nested function in the time [k, k+κ-1] dimension: Among them, function g1 selectively retains the information extracted from the historical prediction state at each moment and introduces information about the new prediction state, that is, according to the input Update memory Thus, the multi-step prediction process of non-Markov target states is modeled as a first-order Markov model with memory iteration.

5. According to claim 2, a UUV non-cooperative target tracking method based on axial attention is characterized in that: The target state multi-step prediction network based on axial attention adopts an encoder-decoder structure. The encoder based on the axial self-attention mechanism focuses on the features related to the target motion in the historical observation of the target state and constructs the observation feature nonlinear mapping function f obs .

6. According to claim 2, a UUV non-cooperative target tracking method based on axial attention is characterized in that: In the target state multi-step prediction network, the encoder obtains target motion related features from the target observation state at the most recent n moments to obtain the encoded information. The decoder, based on the idea of ​​sliding decision, predicts the state of the target at the next moment according to the encoded information and the predicted state at the most recent κ moments output by the target state multi-step prediction network.

7. The UUV non-cooperative target tracking method based on axial attention according to claim 2, characterized in that: The target state multi-step prediction network based on axial attention adopts an encoder-decoder structure; The encoder consists of an input layer, a position encoding layer, and N encoder modules; First, the input layer uses a multi-layer perceptron (MLP) to map the target historical observation state into a vector of fixed dimension in preparation for feature extraction. Secondly, the position encoding layer uses two-dimensional position encoding to provide time step and sampling information features for the input features, enhancing the model's attention to temporal and spatial expressions; Each encoder module consists of two sub-layers: axial multi-head self-attention and MLP. The input data of each sub-layer is batch normalized, and the input and output before normalization are residually connected as the input of the next sub-layer. The decoder includes an input layer, a position encoding layer, N decoder modules, and an output layer; The input and output layers of the decoder are both MLP networks; The position coding layer of the decoder uses two-dimensional position coding; The decoder module consists of three sub-layers: axial masked multi-head self-attention, axial multi-head co-attention and MLP. The input data of each sub-layer is batch normalized, and the input and output before normalization are residually connected as the input of the next sub-layer.

8. The UUV non-cooperative target tracking method based on axial attention according to claim 2, characterized in that: In the process of training the target state multi-step prediction network, an end-to-end supervised training method is adopted, and the batch gradient descent method and Adam optimizer are used to minimize the mean square error loss function for training.

9. The UUV non-cooperative target tracking method based on axial attention according to claim 2, characterized in that: Step 1 also includes constructing a depth-determining motion model and a target motion model for the underactuated UUV; The following underactuated UUV fixed depth motion model is established: in, represents the velocity of UUV in NOE coordinate system, [u o ,0,r o ] T Indicates that UUV is at x B o B y B The velocity in the coordinate system; In addition, the UUV is subject to the following motion constraints: The target motion model is as follows: Use NOE coordinate system to describe the target pose η t =[x t ,y t ,ψ t ] T , construct a carrier coordinate system fixed to the target to describe the target velocity v t =[u t ,v t ,r t ] T , then the kinematic equation of the target can be expressed as: In addition, based on the observed UUV motion and sonar observation performance, the kinematics of the non-cooperative target is assumed to satisfy the following constraints:

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