Dynamic fuzzy neural network integrated navigation positioning method based on multi-head self-attention

Abstract

This invention discloses a dynamic fuzzy neural network-based integrated navigation and positioning method based on multi-head self-attention, belonging to the field of integrated navigation and positioning technology. Addressing the problem of rapid accumulation of inertial navigation errors during GNSS lock-up periods in shipborne inertial / satellite integrated navigation systems, this invention integrates a multi-head self-attention mechanism with a dynamic fuzzy neural network (GDFNN). First, a basic GDFNN model is trained through a non-attention phase. Then, multi-head attention guidance vectors for different tasks are derived from the model weights. After attention reweighting, a second training is completed to obtain the fused model. When GNSS lock-up occurs, time-decayed multi-head self-attention is used to reweight navigation features, and inertial navigation error compensation is achieved through the fused model. This invention decomposes self-attention according to the physical navigation task, making feature weighting more targeted. Simultaneously, by combining residual fusion and attention decay mechanisms, it effectively improves the positioning accuracy and robustness of integrated navigation in shipborne GNSS lock-up scenarios.

Description

Technical Field

[0001] This invention belongs to the field of integrated navigation and intelligent information processing technology, specifically relating to a dynamic fuzzy neural network navigation error compensation method based on multi-head self-attention guidance, used for inertial navigation error prediction and compensation in SINS / GNSS integrated navigation systems during GNSS signal loss. Background Technology

[0002] Strapdown inertial navigation systems (SINS) offer advantages such as high autonomy and continuity, but their navigation errors accumulate and diverge over time. Global Navigation Satellite Systems (GNSS) boast high long-term positioning accuracy, but are prone to short-term or intermittent loss of lock in scenarios involving obstruction, interference, complex water environments, or areas such as bridges and ports. Integrated navigation systems typically use Kalman filtering to correct inertial navigation errors when the GNSS is operating normally, but during GNSS lock-up phases, they can only rely on autonomous calculations by the inertial navigation system, leading to a rapid accumulation of velocity and position errors, especially noticeable in shipboard scenarios where level errors dominate. Existing methods for loss-of-lock compensation using neural networks or fuzzy neural networks typically involve directly inputting the navigation state into the network for error regression. While this can improve loss-of-lock compensation capabilities to some extent, it still suffers from the following problems: First, different output tasks (such as velocity compensation, latitude compensation, and longitude compensation) have varying sensitivities to input features. Using a single input representation uniformly can easily lead to feature averaging, making it difficult to consider different error paths. Second, the dependence on compensation information differs between the initial and later stages of GNSS loss of lock. Reweighting the input with a fixed intensity can easily lead to overcompensation in the later stages. Third, in application scenarios with relatively small elevation changes, such as shipboard navigation, horizontal errors often dominate. An improved method is needed that can both preserve the original integrated navigation framework and enhance the targeting and stability of horizontal error compensation accuracy. Summary of the Invention

[0003] Purpose of the invention: To address the issues of insufficient targeting of horizontal error compensation and overcompensation in the later stages of GNSS lock-up in existing SINS / GNSS integrated navigation systems, this invention provides a SINS / GNSS integrated navigation lock-up compensation method based on multi-head feature attention and time-varying decay control. This method improves the stability and targeting of velocity and position compensation during the GNSS lock-up stage without altering the original integrated navigation framework.

[0004] Technical solution: To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A dynamic fuzzy neural network-based navigation and localization method based on multi-head self-attention includes the following steps:

[0006] S1: During periods when GNSS signals are normal, collect training data and construct input and output samples. The input samples are 15-dimensional navigation and filtering feedback combined state variables, and the output samples are 6-dimensional velocity and position errors.

[0007] S2: Normalize the input and output samples, and use the normalized samples to train a dynamic growing fuzzy neural network base model.

[0008] S3: Based on the TSK consequent parameters of the base model, extract the feature importance vectors corresponding to the dynamic head, latitude head and longitude head respectively, and construct a multi-head feature attention guidance matrix;

[0009] S4: Use the multi-head feature attention guidance matrix to reweight the normalized input samples to complete the second stage training of the dynamic growing fuzzy neural network and obtain the final fuzzy neural network parameters.

[0010] S5: During the GNSS lockout phase, the current 15-dimensional input is normalized and reweighted based on the multi-head feature attention guidance matrix to obtain the attention-enhanced input; the attention-enhanced input is then input into the final fuzzy neural network to output the velocity error compensation amount and the position error compensation amount.

[0011] S6: The attention mixing factor is time-varyingly decayed according to the duration of the lockout, and the strapdown inertial navigation solution is compensated and corrected in real time based on the decayed attention mixing factor.

[0012] Furthermore, step S1 specifically includes the following sub-steps:

[0013] S1-1: Define the 15-dimensional navigation and filter feedback combined state variable as the input vector. : in The attitude error angle is... For speed error, For positional error, For gyroscope zero bias error, For accelerometer zero bias error, superscript Indicates transpose;

[0014] S1-2: Define the 6-dimensional output sample as the output vector. : in , , These represent the speed errors in the east, north, and sky directions, respectively. For latitude error, For longitude error, This is for height error;

[0015] S1-3: Continuous acquisition of GNSS signals during normal periods Input / output data pairs at each time point, This constitutes the training dataset, where Indicates the first Input samples at each time point, Represents the training dataset. Indicates the first Output samples at each time point This indicates the dimension of the input sample. This represents the total number of training samples.

[0016] Furthermore, step S2 specifically includes the following sub-steps:

[0017] S2-1: Normalize the input and output samples, mapping the data to... The normalization formula for the interval is: in This represents the original input sample. This represents the normalized input sample. , These represent the minimum and maximum values ​​of the input sample, respectively. This represents the original output sample. This represents the normalized output sample. , These represent the minimum and maximum values ​​of the output samples, respectively.

[0018] S2-2: Using normalized training samples Training a dynamically growing fuzzy neural network base model, wherein the base model adopts the TS fuzzy model, and the fuzzy layer neurons are Gaussian radial basis functions, and their 6th... The output of the fuzzy rule for in, For input variable index, The first input vector One portion, and The first The fuzzy rule of the first The Gaussian membership function centers and widths of the input variables are given, and the network output layer is: in This represents the normalized output obtained from the prediction of the fuzzy neural network. This represents the normalized rule activation strength. Indicates the first The consequent output of a fuzzy rule For the first The consequent parameter vector of a fuzzy rule For the number of fuzzy rules;

[0019] S2-3: Apply square root capacitive Kalman filtering to the parameters of the base model. , , Training is performed to obtain the set of base model parameters. .

[0020] Furthermore, step S3 specifically includes the following sub-steps:

[0021] S3-1: The resulting parameter matrix of the base model obtained from training. Rearranged into a three-dimensional tensor, where the first dimension corresponds to the input features and bias terms, and the second dimension corresponds to the number of fuzzy rules. The third dimension corresponds to the 6-dimensional output;

[0022] S3-2: Based on the physical meaning of navigation error, the 6-dimensional output is divided into three semantic heads: the dynamic head corresponds to the output dimension. Latitude head corresponds to output dimension Right now Longitude header output ;

[0023] S3-3: For the dynamic head, extract the corresponding consequent parameter sub-tensor. Calculate the importance of each input feature : in Indicates the input feature index. This represents a fuzzy rule index. This indicates the internal output dimension index of the dynamic head. The first parameter in the dynamic head afterbody parameter subtensor represents the first parameter in the dynamic head afterbody parameter subtensor. The input feature, the first The fuzzy rule and the first The importance of the parameters corresponding to each output component to the input features Perform mean normalization and limit the amplitude. The dynamic head guidance vector is obtained. ;

[0024] S3-4: Similarly, extract the latitude head-and-after parameter subtensors respectively. and longitude head after parameter subtensor Calculate the latitude head guiding vector and longitude head guiding vector Finally, the three guiding vectors are concatenated column-wise to form a multi-head feature attention guiding matrix. : .

[0025] Furthermore, step S4 specifically includes the following sub-steps:

[0026] S4-1: For each input sample First, centralized processing is performed: in, This represents the mean of each dimension of the input sample. Centering can reduce the impact of the input common bias on the calculation of the attention score.

[0027] S4-2: For the first Size Take the guiding vector The vector is then nonnegated, mean normalized, and amplitude-limited before a query vector is constructed. and key vector : in This represents element-wise multiplication, further calculating the... Attention score matrix for each individual: Where d represents the dimension, we obtain the th... Attention weight matrix of size And perform Softmax normalization on each row. in For the first The attention weight matrix is ​​obtained by normalizing the semantic heads.

[0028] S4-3: Calculate the... Attention output by size: in The fusion vector is obtained by weighted fusion of multi-head attention outputs, with a preset head weight vector. The outputs of each head are weighted and merged: .

[0029] Further introduction of attention mixing factor The attention-enhanced input is obtained through residual connections: in, The original input vector after normalization. The attention output vector is obtained by weighted fusion of the normalized input vector through multi-head self-attention. The attention-enhanced input vector is obtained through residual connections. This is the attention blending factor, used to control the fusion ratio between the normalized original input vector and the attention output vector.

[0030] S4-4: Obtain a new training set with enhanced attention by processing all input samples in the training set through steps S4-1 to S4-3. The dynamic growing fuzzy neural network was then retrained using square root capillary Kalman filtering on this new training set to obtain the final network parameters. Then, using the consequent parameters in the final network parameters, the guiding matrix is ​​recalculated according to step S3. This is used in the subsequent reasoning stage.

[0031] Furthermore, step S5 specifically includes the following steps:

[0032] S5-1: During the GNSS lock-out phase, obtain the 15-dimensional navigation and filter feedback combined state variables at the current moment. First, normalize it using the normalization parameters saved in step S2-1: in, The input vector is the normalized value at the current time step. and The minimum and maximum values ​​of the input samples are saved during the training phase;

[0033] S5-2: Normalize the input vector at the current time step. The multi-head self-attention module described in steps S4-1 to S4-4 is used, wherein the guiding matrix is ​​updated using the one described in step S4-4. The attention blending factor uses the attention blending factor at the current moment. The attention-enhanced input is calculated in step S6. ;

[0034] S5-3: Enhance Input Attention Input the final fuzzy neural network and calculate the network output: in This represents the consequent parameters of the final network. Indicates the activation strength of the rule. This represents the prediction error vector output by the fuzzy neural network at the current moment.

[0035] S5-4: Perform inverse normalization on the network output to obtain the actual velocity error and position error compensation amounts: in This represents the predicted output in the normalized domain. and These represent the minimum and maximum values ​​of the output samples during the training phase, respectively, and an amplitude limit is applied to feed the compensation amount back to the strapdown inertial navigation system to correct the velocity and position.

[0036] Furthermore, step S6 specifically includes the following steps:

[0037] S6-1: Let the duration of GNSS lockout be... Unit: seconds, Calculates the attention mixing factor at the current moment. : in As the initial mixing factor, The attenuation rate is set, and a lower limit is defined. To prevent excessive attenuation;

[0038] S6-2: The calculated result Substitute this into step S5-2 for attention reweighting at the current moment;

[0039] S6-3: For different semantic headers, if differentiated attenuation is required, the attenuation rate can be set separately. , , And independently calculate the attention mixing factor for each head. The following steps are applied in the head-weighted fusion process of step S4-3: in Indicates the first Each component uses its corresponding mixing factor to perform residual connection and outputs the result. Finally, when the GPS signal is restored, it switches back to the conventional SINS / GPS Kalman filter combined navigation mode.

[0040] Beneficial Effects: Compared with existing technologies, this invention innovatively proposes a dynamic fuzzy neural network navigation error compensation method based on multi-head self-attention guidance. This method achieves task-oriented dynamic enhancement of input features through mechanisms such as multi-task semantic head partitioning, feature importance inverse calculation, multi-head self-attention reweighting, two-stage training, and attention decay during the lock-out phase. It solves the problem of insufficient specificity caused by traditional models sharing feature representations across all outputs, thus enhancing the model's ability to model complex motion states. This invention significantly improves the prediction accuracy of navigation errors during GNSS lock-out, effectively suppresses the divergence of pure inertial calculations, and shows significant improvements in both velocity and position errors compared to existing methods, providing strong support for continuous high-precision positioning of integrated navigation systems in complex environments. Attached Figure Description

[0041] Figure 1 This is an overall block diagram of the present invention;

[0042] Figure 2 This is a comparison of the dimensional error between traditional neural network methods and the method of this invention; Figure 3 This is a comparison chart of longitude errors between traditional neural network methods and the method of this invention. Detailed Implementation

[0043] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0044] This invention provides a dynamic fuzzy neural network-based navigation and localization method based on multi-head self-attention. Figure 1 As shown, it specifically includes:

[0045] This invention provides a shipborne integrated navigation and positioning method based on task-segmented multi-head self-attention. This method addresses the inertial navigation error compensation problem during GPS lock-up periods in shipborne SINS / GPS integrated navigation systems. It uses TSK fuzzy neural network consequent parameters to infer feature importance, constructs a multi-head self-attention mechanism adapted to shipborne navigation characteristics, and combines a two-layer strategy of global time decay and latitude head-specific decay to achieve targeted weighting and dynamic error compensation of navigation features. The method includes the following steps:

[0046] S1: During periods when GNSS signals are normal, collect training data and construct input and output samples. The input samples are 15-dimensional navigation and filtering feedback combined state variables, and the output samples are 6-dimensional velocity and position errors.

[0047] S2: Normalize the input and output samples, and use the normalized samples to train a dynamic growing fuzzy neural network base model.

[0048] S3: Based on the TSK consequent parameters of the base model, extract the feature importance vectors corresponding to the dynamic head, latitude head and longitude head respectively, and construct a multi-head feature attention guidance matrix;

[0049] S4: Use the multi-head feature attention guidance matrix to reweight the normalized input samples to complete the second stage training of the dynamic growing fuzzy neural network and obtain the final fuzzy neural network parameters.

[0050] S5: During the GNSS lockout phase, the current 15-dimensional input is normalized and reweighted based on the multi-head feature attention guidance matrix to obtain the attention-enhanced input; the attention-enhanced input is then input into the final fuzzy neural network to output the velocity error compensation amount and the position error compensation amount.

[0051] S6: The attention mixing factor is time-varyingly decayed according to the duration of the lockout, and the strapdown inertial navigation solution is compensated and corrected in real time based on the decayed attention mixing factor.

[0052] In this embodiment, the collection and construction of training data in step S1 specifically includes the following sub-steps:

[0053] S1-1: Define the 15-dimensional navigation and filter feedback combined state variable as the input vector. : in The attitude error angle is... For speed error, For positional error, For gyroscope zero bias error, For accelerometer zero bias error, superscript Indicates transpose;

[0054] S1-2: Define the 6-dimensional output sample as the output vector. : in , , These represent the speed errors in the east, north, and sky directions, respectively. For latitude error, For longitude error, This is for height error;

[0055] S1-3: Continuous acquisition of GNSS signals during normal periods Input / output data pairs at each time point, This constitutes the training dataset, where Indicates the first Input samples at each time point, Represents the training dataset. Indicates the first Output samples at each time point This indicates the dimension of the input sample. This represents the total number of training samples.

[0056] In this embodiment, the training of the dynamically grown fuzzy neural network base model in step S2 specifically includes the following sub-steps:

[0057] S2-1: Normalize the input and output samples, mapping the data to... The normalization formula for the interval is: in This represents the original input sample. This represents the normalized input sample. , These represent the minimum and maximum values ​​of the input sample, respectively. This represents the original output sample. This represents the normalized output sample. , These represent the minimum and maximum values ​​of the output samples, respectively.

[0058] S2-2: Using normalized training samples Training a dynamically growing fuzzy neural network base model, wherein the base model adopts the TS fuzzy model, and the fuzzy layer neurons are Gaussian radial basis functions, and their 6th... The output of the fuzzy rule for in, For input variable index, The first input vector One portion, and The first The fuzzy rule of the first The Gaussian membership function centers and widths of the input variables are given, and the network output layer is: in This represents the normalized output obtained from the prediction of the fuzzy neural network. This represents the normalized rule activation strength. Indicates the first The consequent output of a fuzzy rule For the first The consequent parameter vector of a fuzzy rule For the number of fuzzy rules;

[0059] S2-3: Apply square root capacitive Kalman filtering to the parameters of the base model. , , Training is performed to obtain the set of base model parameters. .

[0060] Preferably, the specific method for constructing the multi-head feature attention guidance matrix in step S3 is as follows:

[0061] S3-1: The resulting parameter matrix of the base model obtained from training. Rearranged into a three-dimensional tensor, where the first dimension corresponds to the input features and bias terms, and the second dimension corresponds to the number of fuzzy rules. The third dimension corresponds to the 6-dimensional output;

[0062] S3-2: Based on the physical meaning of navigation error, the 6-dimensional output is divided into three semantic heads: the dynamic head corresponds to the output dimension. Latitude head corresponds to output dimension Right now Longitude header output ;

[0063] S3-3: For the dynamic head, extract the corresponding consequent parameter sub-tensor. Calculate the importance of each input feature : in Indicates the input feature index. This represents a fuzzy rule index. This indicates the internal output dimension index of the dynamic head. The first parameter in the dynamic head afterbody parameter subtensor represents the first parameter in the dynamic head afterbody parameter subtensor. The input feature, the first The fuzzy rule and the first The importance of the parameters corresponding to each output component to the input features Perform mean normalization and limit the amplitude. The dynamic head guidance vector is obtained. ;

[0064] S3-4: Similarly, extract the latitude head-and-after parameter subtensors respectively. and longitude head after parameter subtensor Calculate the latitude head guiding vector and longitude head guiding vector Finally, the three guiding vectors are concatenated column-wise to form a multi-head feature attention guiding matrix. :

[0065] As a preferred embodiment, the specific method for feature reweighting and second-stage training based on multi-head self-attention in step S4 is as follows:

[0066] S4-1: For each input sample First, centralized processing is performed: in, This represents the mean of each dimension of the input sample. Centering can reduce the impact of the input common bias on the calculation of the attention score.

[0067] S4-2: For the first Size Take the guiding vector The vector is then nonnegated, mean normalized, and amplitude-limited before a query vector is constructed. and key vector : in This represents element-wise multiplication, further calculating the... Attention score matrix for each individual: Where d represents the dimension, we obtain the th... Attention weight matrix of size And perform Softmax normalization on each row. in For the first The attention weight matrix is ​​obtained by normalizing the semantic heads.

[0068] S4-3: Calculate the... Attention output by size: in The fusion vector is obtained by weighted fusion of multi-head attention outputs, with a preset head weight vector. The outputs of each head are weighted and merged: Further introduction of attention mixing factor The attention-enhanced input is obtained through residual connections: in, The original input vector after normalization. The attention output vector is obtained by weighted fusion of the normalized input vector through multi-head self-attention. The attention-enhanced input vector is obtained through residual connections. This is the attention blending factor, used to control the fusion ratio between the normalized original input vector and the attention output vector.

[0069] S4-4: Obtain a new training set with enhanced attention by processing all input samples in the training set through steps S4-1 to S4-3. The dynamic growing fuzzy neural network was then retrained using square root capillary Kalman filtering on this new training set to obtain the final network parameters. Then, using the consequent parameters in the final network parameters, the guiding matrix is ​​recalculated according to step S3. This is used in the subsequent reasoning stage.

[0070] Preferably, the specific method for error compensation during the GNSS lockout phase in step S5 is as follows:

[0071] S5-1: During the GNSS lock-out phase, obtain the 15-dimensional navigation and filter feedback combined state variables at the current moment. First, normalize it using the normalization parameters saved in step S2-1: in, The input vector is the normalized value at the current time step. and The minimum and maximum values ​​of the input samples are saved during the training phase;

[0072] S5-2: Normalize the input vector at the current time step. The multi-head self-attention module described in steps S4-1 to S4-4 is used, wherein the guiding matrix is ​​updated using the one described in step S4-4. The attention blending factor uses the attention blending factor at the current moment. The attention-enhanced input is calculated in step S6. ;

[0073] S5-3: Enhance Input Attention Input the final fuzzy neural network and calculate the network output: in This represents the consequent parameters of the final network. Rule activation strength, This represents the prediction error vector output by the fuzzy neural network at the current moment.

[0074] S5-4: Perform inverse normalization on the network output to obtain the actual velocity error and position error compensation amounts: in This represents the predicted output in the normalized domain. and These represent the minimum and maximum values ​​of the output samples during the training phase, respectively, and an amplitude limit is applied to feed the compensation amount back to the strapdown inertial navigation system to correct the velocity and position.

[0075] Preferably, the time-varying decay of attention intensity in step S6 adopts an exponential decay strategy, the specific method of which is as follows:

[0076] S6-1: Let the duration of GNSS lockout be... Unit: seconds, Calculates the attention mixing factor at the current moment. : in As the initial mixing factor, The attenuation rate is set, and a lower limit is defined. To prevent excessive attenuation;

[0077] S6-2: The calculated result Substitute this into step S5-2 for attention reweighting at the current moment;

[0078] S6-3: For different semantic headers, if differentiated attenuation is required, the attenuation rate can be set separately. , , And independently calculate the attention mixing factor for each head. The following steps are applied in the head-weighted fusion process of step S4-3: in Indicates the first Each component uses its corresponding mixing factor to perform residual connection and outputs the result. Finally, when the GPS signal is restored, it switches back to the conventional SINS / GPS Kalman filter combined navigation mode.

[0079] To verify the effectiveness of the proposed multi-head attention mechanism-based SINS / GNSS integrated navigation lock-out compensation method, a simulation experiment was conducted using a SINS / GNSS integrated navigation system. The total experiment duration was 2200 s, with the GNSS lock-out interval from 1001 s to 1020 s. The method of this invention was compared with the traditional KF-GDFNN method, and the results are as follows: Figure 2 and Figure 3As shown in the figure. The results show that the present invention has better horizontal position compensation performance during the GNSS lock-out phase. Regarding position errors, the root mean square value and maximum value of the latitude error of the present invention are 0.868 m and 2.187 m, respectively, which are reduced by approximately 70.2% and 60.3% compared to 2.909 m and 5.515 m of the traditional KF-GDFNN method; the root mean square value and maximum value of the longitude error are 0.479 m and 1.075 m, respectively, which are reduced by approximately 39.7% and 33.9% compared to 0.794 m and 1.627 m of the traditional KF-GDFNN method. In terms of the overall horizontal position error, the overall root mean square error of the present invention is reduced from 3.015 m to 0.991 m, a reduction of approximately 67.1%. This indicates that the present invention can more effectively suppress the accumulation and spread of horizontal position errors during GNSS lock-out, thereby improving the horizontal positioning accuracy and overall robustness of the integrated navigation system under short-term lock-out conditions.

Claims

1. A dynamic fuzzy neural network-based navigation and positioning method based on multi-head self-attention, characterized in that, This method integrates a multi-head self-attention mechanism with a dynamic fuzzy neural network and applies it to a SINS / GNSS integrated navigation system to achieve inertial navigation error compensation during GNSS lock-up periods. The method includes the following steps: S1: During periods when GNSS signals are normal, collect training data and construct input and output samples. The input samples are 15-dimensional navigation and filtering feedback combined state variables, and the output samples are 6-dimensional velocity and position errors. S2: Normalize the input and output samples, and use the normalized samples to train a dynamic growing fuzzy neural network base model. S3: Based on the fuzzy model consequent parameters of the base model, extract the feature importance vectors corresponding to the dynamic head, latitude head and longitude head respectively, and construct a multi-head feature attention guidance matrix; S4: Use the multi-head feature attention guidance matrix to reweight the normalized input samples to complete the second stage training of the dynamic growing fuzzy neural network and obtain the final fuzzy neural network parameters. S5: During the GNSS lockout phase, the current 15-dimensional input is normalized and reweighted based on the multi-head feature attention guidance matrix to obtain the attention-enhanced input; the attention-enhanced input is then input into the final fuzzy neural network to output the velocity error compensation amount and the position error compensation amount. S6: The attention mixing factor is time-varyingly decayed according to the duration of the lockout, and the strapdown inertial navigation solution is compensated and corrected in real time based on the decayed attention mixing factor.

2. The dynamic fuzzy neural network-based navigation and positioning method based on multi-head self-attention as described in claim 1, characterized in that, The specific steps of step S1 include: S1-1: Define the 15-dimensional navigation and filter feedback combined state variable as the input vector. : in The attitude error angle is... For speed error, For positional error, For gyroscope zero bias error, For accelerometer zero bias error, superscript Indicates transpose; S1-2: Define the 6-dimensional output sample as the output vector. : in , , These represent the speed errors in the east, north, and sky directions, respectively. For latitude error, For longitude error, This is for height error; S1-3: Continuous acquisition of GNSS signals during normal periods Input / output data pairs at each time point, This constitutes the training dataset, where Indicates the first Input samples at each time point, Represents the training dataset. Indicates the first Output samples at each time point This indicates the dimension of the input sample. This represents the total number of training samples.

3. The dynamic fuzzy neural network-based navigation and positioning method based on multi-head self-attention as described in claim 2, characterized in that, The specific steps of step S2 include: S2-1: Normalize the input and output samples, mapping the data to... The normalization formula for the interval is: in This represents the original input sample. This represents the normalized input sample. , These represent the minimum and maximum values ​​of the input sample, respectively. This represents the original output sample. This represents the normalized output sample. , These represent the minimum and maximum values ​​of the output samples, respectively. S2-2: Using normalized training samples A dynamically growing fuzzy neural network base model is trained, wherein the base model adopts the TS fuzzy model, and the fuzzy layer neurons are Gaussian radial basis functions, and their 6th... The output of the fuzzy rule for: in, For input variable index, The first input vector One portion, and The first The fuzzy rule of the first The Gaussian membership function centers and widths of the input variables are given, and the network output layer is: in This represents the normalized output obtained from the prediction of the fuzzy neural network. This represents the normalized rule activation strength. Indicates the first The consequent output of a fuzzy rule For the first The consequent parameter vector of a fuzzy rule For the number of fuzzy rules; S2-3: Apply square root capacitive Kalman filtering to the parameters of the base model. , , Training is performed to obtain the set of base model parameters. .

4. The method for compensating navigation errors based on a dynamic fuzzy neural network guided by multi-head self-attention as described in claim 3, characterized in that, The specific steps of step S3 include: S3-1: The resulting parameter matrix of the base model obtained from training. Rearranged into a three-dimensional tensor, where the first dimension corresponds to the input features and bias terms, and the second dimension corresponds to the number of fuzzy rules. The third dimension corresponds to the 6-dimensional output; S3-2: Based on the physical meaning of navigation error, the 6-dimensional output is divided into three semantic heads: the dynamic head corresponds to the output dimension. Right now Latitude head corresponds to output dimension ,Right now Longitude header output ,Right now ; S3-3: For the dynamic head, extract the corresponding consequent parameter sub-tensor. Calculate the importance of each input feature : in Indicates the input feature index. Indicates a fuzzy rule index. This indicates the internal output dimension index of the dynamic head. The first parameter in the dynamic head afterbody parameter subtensor represents the first parameter in the dynamic head afterbody parameter subtensor. The input feature, the first The first fuzzy rule and the first The importance of the parameters corresponding to each output component to the input features Perform mean normalization and limit the amplitude. The dynamic head guidance vector is obtained. ; S3-4: Similarly, extract the latitude head-and-after parameter subtensors respectively. and longitude head after parameter subtensor Calculate the latitude head guiding vector and longitude head guiding vector Finally, the three guiding vectors are concatenated column-wise to form a multi-head feature attention guiding matrix. :

5. The method for compensating navigation errors based on a dynamic fuzzy neural network guided by multi-head self-attention as described in claim 4, characterized in that, The specific steps of step S4 include: S4-1: For each normalized input sample, perform centering to reduce the impact of the input common bias on the attention score calculation; S4-2: For each semantic head, extract the guidance vector corresponding to the semantic head from the multi-head feature attention guidance matrix constructed in step S3, and perform nonnegation, mean normalization and amplitude limiting on it. Then, use the processed guidance vector to perform feature reweighting on the input sample after the centering process in step S4 to obtain the attention weight corresponding to the semantic head. S4-3: Obtain the attention output of each semantic head based on its corresponding attention weight, and perform weighted fusion according to the preset head weights. Further introduce an attention mixing factor, and obtain the attention-enhanced input through residual connections. in, The original input vector after normalization. The attention output vector is obtained by weighted fusion of the normalized input vector through multi-head self-attention. The attention-enhanced input vector is obtained through residual connections. This is the attention fusion factor, used to control the fusion ratio between the normalized original input vector and the attention output vector; S4-4: Obtain a new training set with enhanced attention by processing all input samples in the training set through steps S4-1 to S4-3. The dynamic growing fuzzy neural network was then retrained using square root capillary Kalman filtering on this new training set to obtain the final network parameters. Then, using the consequent parameters in the final network parameters, the guiding matrix is ​​recalculated according to step S3. This is used in the subsequent reasoning stage.

6. The method for compensating navigation errors based on a dynamic fuzzy neural network guided by multi-head self-attention as described in claim 5, characterized in that, The specific steps of step S5 include: S5-1: During the GNSS lock-out phase, obtain the 15-dimensional navigation and filter feedback combined state variables at the current moment. First, normalize it using the normalization parameters saved in step S2-1: in, The input vector is the normalized value at the current time step. and The minimum and maximum values ​​of the input samples are saved during the training phase; S5-2: Normalize the input vector at the current time step. The multi-head self-attention module described in steps S4-1 to S4-4 is used, wherein the guidance matrix is ​​updated using the version from step S4-4. The attention blending factor uses the attention blending factor at the current moment. The attention-enhanced input is calculated in step S6. ; S5-3: Incorporate the attention-enhanced input The input is then fed into the final fuzzy neural network to calculate the predicted outputs of velocity error and position error; S5-4: Perform inverse normalization on the predicted output to obtain the actual velocity error compensation amount and position error compensation amount, and apply amplitude limiting before feeding it back to the strapdown inertial navigation system to correct the velocity and position.

7. The method for compensating navigation errors based on a dynamic fuzzy neural network guided by multi-head self-attention as described in claim 6, characterized in that, The specific steps of step S6 include: S6-1: Let the duration of GNSS lockout be... Unit: seconds, Calculates the attention mixing factor at the current moment. : in As the initial mixing factor, The attenuation rate is set, and a lower limit is defined. To prevent excessive attenuation; S6-2: The calculated result Substitute this into step S5-2 for attention reweighting at the current moment; S6-3: For different semantic heads, different decay rates are set as needed to differentiate the time-varying adjustment of the attention intensity of different semantic heads, and are applied in the weighted fusion and residual connection processes of S4-3 respectively.

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