A three-star positioning method based on an attention mechanism enhanced time convolution network

Abstract

This invention discloses a three-satellite positioning method based on an attention-enhanced temporal convolutional network, belonging to the field of satellite navigation and positioning technology. The method utilizes an attention-enhanced temporal convolutional network receiver clock bias predictor. First, when there are sufficient visible satellites, the predictor models the clock bias based on historically calculated receiver clock biases. This predictor is used to predict the receiver clock bias at future times based on historically calculated receiver clock biases. The predictor is trained using the training samples to obtain a trained predictor. Then, when there are three visible satellites, the predictor uses the predicted receiver clock bias to assist a navigation filter for positioning.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, and specifically to a three-star positioning method based on attention mechanism-enhanced temporal convolutional networks. Background Technology

[0002] While Global Navigation Satellite Systems (GNSS) can provide high-precision navigation and positioning services, several challenges exist. First, due to the high orbital altitude of GNSS satellites, the signal strength is relatively weak by the time it reaches the ground receiver. Second, in complex environments such as underground, underwater, and densely populated urban areas and forested regions, satellite signals are susceptible to obstruction and multipath effects, leading to severe signal attenuation and impacting navigation and positioning accuracy. In complex environments, the received GNSS satellite signals may be weak, or even insufficient satellites may be available for navigation calculations, severely affecting the reliability and continuity of navigation and positioning services. Therefore, in-depth research into navigation and positioning technologies under conditions of insufficient GNSS visible satellites is of great significance.

[0003] In navigation and positioning, receiver clock bias and three-dimensional position are treated as four unknowns, which are solved epoch-by-epoch in the navigation filter. Solving these four unknowns requires observations from at least four satellites. However, in complex environments, GNSS satellite signals are inherently vulnerable due to their weak signal strength, poor penetration, and susceptibility to interference, resulting in fewer than four satellites being used by the receiver. When the number of visible satellites is insufficient, navigation and positioning technologies mainly fall into two categories. On the one hand, predicting and constraining the receiver clock bias or altitude at the software level can reduce the number of satellites involved in the navigation calculation, ensuring the independence of the GNSS receiver. On the other hand, adding additional components can obtain more navigation information for multi-source information fusion, thus improving the redundancy of navigation information. The first type of method, predicting the receiver clock bias, can reduce the number of satellites used for navigation, is low-cost, and can be further combined with the second type of method to improve the accuracy and continuity of GNSS navigation and positioning in complex environments. However, when adding receiver clock bias parameters for navigation calculations, the common errors in the measurement errors and model errors of various observations are absorbed by the parameter estimation results of the receiver clock bias. Therefore, the receiver clock bias is not only related to the frequency characteristics of the time reference, but also to the common errors of the correction model and parameter estimation in GNSS navigation calculations. Low-cost receivers often use quartz crystal oscillators as the time reference. The receiver clock bias obtained through navigation calculations, in addition to reflecting the changes in the quartz crystal oscillator, also absorbs the common errors from different correction models and navigation calculation errors. Therefore, the receiver clock bias model varies greatly and is complex for different clock sources and navigation calculation methods.

[0004] Receiver clock bias prediction involves modeling the receiver clock bias into different models and predicting the receiver clock bias based on the model parameters. Conventional receiver clock bias models include polynomial models, time series models, spectral analysis models, grey models, artificial neural network models, and combined models. However, conventional models have limited expressive power. 1) Low-cost receivers often use quartz crystal oscillators as the time reference. The frequency of the crystal oscillator is affected by environmental conditions such as temperature, atmospheric pressure, power supply fluctuations, and operating time, thus the time-frequency characteristics of the time reference exhibit nonlinearity over long periods. 2) Conventional models typically only model the time reference and cannot represent the model errors and solution errors absorbed in the receiver clock bias. Therefore, conventional methods have limited expressive power and require high-precision calibration models and solution methods to ensure the accuracy of receiver clock bias prediction.

[0005] Compared to conventional methods, time-series neural network-based models can better represent the trends, periodicity, and randomness of data in satellite clock bias modeling. Attention-enhanced temporal convolutional networks (TCNNs) offer superior time-series modeling capabilities. 1) TCNNs combine the characteristics of convolutional networks and recurrent neural networks, possessing parallel processing capabilities and a longer memory effect, achieving better results than recurrent neural networks and long short-term memory networks in various time-series modeling tasks. 2) Attention mechanisms can learn the correlations between data points and characterize the periodicity of the data. Therefore, combining TCNN models with attention mechanisms enables better modeling of receiver clock bias.

[0006] Therefore, when the number of visible GNSS satellites is insufficient for an extended period, improving positioning continuity and accuracy by accurately predicting receiver clock bias remains an unsolved problem. Summary of the Invention

[0007] In view of this, the present invention provides a three-satellite positioning method based on an attention-enhanced temporal convolutional network, which utilizes an attention-enhanced temporal convolutional network receiver clock bias predictor. First, when there are sufficient visible satellites, the predictor models the clock bias based on historically calculated receiver clock biases. Then, when there are three visible satellites, the predictor performs positioning by outputting the predicted receiver clock bias to assist the navigation filter.

[0008] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0009] When there are sufficient visible stars, the EKF navigation filter calculates the receiver position and clock bias / drift, and the calculation results are used as training samples.

[0010] A predictor based on an attention mechanism-enhanced temporal convolutional network is constructed. This predictor is used to predict the receiver clock error at future times based on the receiver clock error calculated in the past. The predictor is trained using the training samples to obtain a trained predictor.

[0011] With three visible satellites, the receiver position is calculated using the predicted receiver clock error output by the trained predictor and the auxiliary navigation filter.

[0012] Furthermore, when there are sufficient visible satellites, the EKF navigation filter calculates the receiver position and clock bias / drift, specifically as follows:

[0013] With sufficient visible satellites, navigation calculations are performed using an EKF navigation filter to obtain the receiver's three-dimensional position and clock bias; the state estimation vector in the EKF is x = [r u T ,δt u ,δf u ] T , where r u T ,δt u ,δf u These are the receiver's three-dimensional position, receiver clock error, and clock drift, respectively.

[0014] Therefore, under sufficient star conditions, the time update and measurement update in EKF parameter estimation are as follows:

[0015] (1) The EKF time update step calculates the prior state estimate and the mean square error matrix of the prior estimated state.

[0016]

[0017] P(k+1|k)=P(k|k)+Q (3)

[0018] in, The state at time k+1 is estimated based on the state at time k, which is the state prior estimate; A and Q are the mean square error matrices of the state transition matrix and the process noise w(k), respectively; P(k+1|k) and P(k|k) are the mean square error matrices of the state at time k+1 and time k, respectively, which are the state prior estimates estimated at time k.

[0019] (2) The state posterior estimate and the mean square error matrix of the posterior estimate obtained by the measurement update step of EKF are:

[0020]

[0021] P(k+1|k+1)=[IK(k+1)H(k+1)]P(k+1|k) (7)

[0022] in, ν(k+1) is the posterior estimate of the state at time k+1; K(k+1) is the Kalman gain at time k+1; ν(k+1) is the residual vector at time k+1; H(k+1) is the Jacobian matrix of the measurement; P(k+1|k+1) is the mean square error matrix of the posterior estimate at time k+1.

[0023] Based on the time update and measurement update in the above EKF parameter estimation, the state estimation vector in EKF is solved to obtain the EKF navigation filter for receiver position, clock error, and clock drift.

[0024] Furthermore, a predictor based on an attention mechanism to enhance the temporal convolutional network is constructed, specifically as follows:

[0025] The predictor's structure includes an input layer, a multi-group layer, a self-attention mechanism layer, a temporal convolutional network, a soft attention mechanism layer, an output layer, and a temporal convolutional network.

[0026] The input layer takes the clock difference sequence b(k) at time k as input. After data downsampling and normalization of the clock difference sequence b(k), b'(k) is obtained. b'(k) is sent to the multi-group layer on one hand and to the soft attention mechanism layer on the other.

[0027] The multi-layer division divides b'(k) into multiple sequences b of length D. i '(k) is fed into the self-attention mechanism layer.

[0028] The output A of the self-attention mechanism layer s It is fed into the temporal convolutional network.

[0029] The temporal convolutional network consists of three temporal modules, including a dilated causal convolutional layer, a weight normalization layer, a rectified linear unit (ReLU), a randomized dropout layer, and a residual connection structure. The input to the temporal convolutional network is the output A of the self-attention mechanism. s The output is X TCN .

[0030] The output layer takes the output data X from the temporal convolutional network. TCN After dimensionality reduction using a linear layer, the output A of the same soft attention mechanism is... soft , merge and splice into Then X merge Dimensionality reduction via linear layers Will After inverse normalization and upsampling operations, the predicted receiver clock bias sequence is obtained.

[0031] Furthermore, given three visible satellites, the receiver position is calculated using the predicted receiver clock error output by the trained predictor and the auxiliary navigation filter, specifically as follows:

[0032] With three visible satellites, the navigation filter for three-satellite positioning no longer calculates the receiver clock bias. Instead, it predicts the receiver clock bias using a temporal convolutional network enhanced by an attention mechanism, thereby correcting the pseudorange observation z(k+1). When there are insufficient visible satellites, the state estimation vector is... Then, in EKF parameter estimation, time updates and measurement updates are...

[0033] (1) The EKF time update step calculates the prior state estimate and the mean square error matrix of the state as follows:

[0034]

[0035] P1(k+1|k)=P1(k|k)+Q1 (17)

[0036] in, The state at time k+1 is estimated based on the state at time k, which is the state prior estimate; the state transition matrix A1 is the identity matrix, and Q1 is the mean square error matrix of the process noise, denoted as γI. 3×3 P1(k+1|k) and P1(k|k) are the mean square error matrices of the prior estimated states at time k+1 and time k, respectively, estimated at time k.

[0037] (2) The state posterior estimate and the mean square error matrix of the posterior estimate obtained by the measurement update step of EKF are:

[0038]

[0039] P1(k+1|k+1)=[IK(k+1)H(k+1)]P1(k+1|k) (19)

[0040] in, ν1(k+1) is the state posterior estimate based on time k+1; K1(k+1) is the Kalman gain at time k+1; ν1(k+1) is the residual vector corrected by the predicted receiver clock error sequence of the temporal convolutional network output through the attention mechanism; and H(k+1) is the Jacobian matrix of the measurement value.

[0041] Beneficial effects:

[0042] This invention addresses the problem of receivers being unable to complete normal navigation and positioning when there are insufficient visible GNSS satellites. It proposes a receiver clock bias predictor based on an attention-enhanced temporal convolutional network, which assists the navigation filter in achieving long-term three-satellite positioning. The predictor models the time-series signal using a temporal convolutional network and extracts correlations between data based on self-attention and soft-attention mechanisms. When there are sufficient visible satellites, the predictor models the receiver clock bias based on historically calculated receiver clock biases. When only three visible satellites are available, the predictor outputs the receiver clock bias to assist the EKF navigation filter in calculating the receiver position. The proposed method ensures the continuity of long-term three-satellite positioning. Attached Figure Description

[0043] Figure 1 This is a block diagram of a receiver based on clock bias prediction.

[0044] Figure 2 Block diagram of a receiver clock bias predictor for an attention-enhancing temporal convolutional network;

[0045] Figure 3 This is a block diagram of the timing module structure;

[0046] Figure 4 This is a block diagram of self-attention and soft attention mechanisms. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0048] This invention provides a receiver block diagram based on clock bias prediction, as shown below. Figure 1 As shown, the receiver's time reference is a quartz crystal oscillator, and the navigation filter is an extended Kalman filter (EKF). Taking pseudorange observations as an example, the receiver's positioning processing flow is summarized as follows: First, the receiver receives radio signals transmitted by GNSS satellites through its antenna. Then, after processing the signals, the receiver obtains the corrected pseudorange observation value ρ. c The data is then output to the navigation filter. Next, the navigation filter calculates the receiver's position r based on multiple observations. u and clock difference δt u Finally, when there are sufficient visible satellites, the predictor is trained based on the input receiver clock bias sequence; when the number of satellites is insufficient, the predictor outputs the predicted receiver clock bias. Auxiliary navigation filters are used for navigation calculations.

[0049] At time k, the pseudorange measurement model received by the receiver from the satellite is:

[0050] ρ i (k)=||r u(k)-r si (k)||2+c[δt u (k)-δt si (k)]+c[I i (k)+T i (k)]+v i (k) (1)

[0051] Where, ρ i (k) is the pseudorange observation measured by the receiver at time k from the i-th satellite, r u (k)=[x u ,y u ,z u ] T It is the three-dimensional coordinate vector of the receiver at time k. Let be the three-dimensional coordinate vector of the satellite at time k, where c is the speed of light, and δt is the velocity of light. u (k) is the receiver clock error at time k. It is the satellite clock difference at time k, I i (k) is the ionospheric delay at time k, T i (k) is the tropospheric delay at time k; v i (k) represents the observation noise of the pseudorange at time k, modeled as having a mean of 0 and a variance of σ. i 2 Gaussian random variables.

[0052] The pseudorange observations at the same time can be expressed as a vector z(k)=[ρ1(k),...,ρ L (k)] T , where L is the number of satellites visible at time k.

[0053] The specific steps of this invention are as follows:

[0054] Step 1: When there are sufficient visible satellites, the EKF navigation filter calculates the receiver position and clock bias / drift. In this embodiment of the invention, when there are sufficient visible satellites, navigation calculation is performed using EKF to obtain the receiver's three-dimensional position and receiver clock bias. The state estimation vector in EKF is x = [r u T ,δt u ,δf u ] T This includes receiver three-dimensional position, receiver clock bias, and clock drift, where r u T ,δt u ,δf u These are the receiver's three-dimensional position, receiver clock bias, and clock drift, respectively. The time update and measurement update in EKF parameter estimation under conditions of sufficient visible satellites are summarized below.

[0055] (1) The EKF time update step calculates the prior state estimate and the mean square error matrix of the state as follows:

[0056]

[0057] P(k+1|k)=P(k|k)+Q (3)

[0058] in, The state at time k+1 is estimated based on the state at time k, which is the state prior estimate; A and Q are the mean square error matrices of the state transition matrix and the process noise w(k), respectively; P(k+1|k) and P(k|k) are the mean square error matrices of the prior estimates of the state at time k+1 and time k, respectively.

[0059] A and Q are the state transition matrix and the mean square error matrix of the process noise w(k), respectively.

[0060]

[0061]

[0062] Where γ is a very small positive number, I 3×3 T is a three-dimensional identity matrix. s This is the update time of EKF. and is the diffusion coefficient.

[0063] (2) The state posterior estimate and the mean square error matrix of the posterior estimate obtained by the measurement update step of EKF are:

[0064]

[0065] P(k+1|k+1)=[IK(k+1)H(k+1)]P(k+1|k) (7)

[0066] in, ν(k+1) is the posterior estimate of the state at time k+1; K(k+1) is the Kalman gain at time k+1; ν(k+1) is the residual vector at time k+1; H(k+1) is the Jacobian matrix of the measurement; P(k+1|k+1) is the mean square error matrix of the posterior estimate at time k+1.

[0067] K = P(k+1|k)H T (k)(H(k)P(k+1|k)H T (k)+R) -1 It is the standard Kalman gain and the residual vector. for

[0068]

[0069] Where r u (k+1|k) is the estimated three-dimensional coordinate vector of the receiver at time k+1. It is the three-dimensional coordinate vector of the satellite at time k+1; δt u (k+1|k) represents the receiver clock bias estimated at time k+1 from time k. The Jacobian matrix H(k+1) of the measurement is...

[0070] H(k+1)=[h1(k+1),...,h L (k+1)] T (9)

[0071]

[0072] Where h1(k+1),...,h L (k+1) represent the 1st to Lth component vectors in the Jacobian matrix, r u (k|k+1) is the posterior estimate of the three-dimensional coordinate vector of the receiver at time k+1 based on the data at time k. It is the three-dimensional coordinate vector of the satellite at time k+1.

[0073] Step 2: The predictor models the clock bias based on the receiver clock bias calculated in the past.

[0074] This invention first constructs a predictor based on an attention mechanism-enhanced temporal convolutional network. This predictor is used to predict the receiver clock error at future times based on the receiver clock error calculated in the past. The predictor is trained using the training samples to obtain a trained predictor.

[0075] Predictor architectures based on attention mechanisms to enhance temporal convolutional networks include: Figure 2 As shown, its main structure consists of a self-attention mechanism, a soft attention mechanism, and a temporal convolutional network.

[0076] At time k, the input sequence of the predictor is b(k) = [δt] u (k-N+1),...,δt u (k)] T Its length is N, δt u (k-N+1),...,δt u (k) represents N receiver clock bias values. The predicted clock bias sequence output by the predictor is: Its length is M. These are the predicted clock difference values ​​from the 1st to the Mth.

[0077] The processing flow of the predictor for the attention-based enhancement of the temporal convolutional network is summarized as follows.

[0078] (1) The clock difference sequence b(k) obtained from the navigation solution is obtained by data downsampling and normalization to obtain b'(k).

[0079] (2) Divide b'(k) into multiple sequences b of length D. i The signal is '(k), and after passing through a self-attention mechanism, it is input into a temporal convolutional network. The slice grouping signal input to the self-attention mechanism is... Where i = 1, ..., MD.

[0080] The input-output relationship of the self-attention mechanism can be represented as:

[0081]

[0082] Where Q, K, and V are the query matrix, key matrix, and value matrix in the self-attention mechanism, respectively, and Q = XW Q K = XW K V = XW V X = [b'1,...,b' M-D ] T W Q W K W V These are the weight matrices corresponding to QKV, d k This is a scaling factor, which can be set to the length of the input sequence.

[0083] A temporal convolutional network consists of three temporal modules. The temporal modules are as follows: Figure 3 As shown, it includes dilated causal convolutional layers, weight normalization layers, rectified linear units (ReLU), dropout layers, and residual connection structures. The input to the temporal convolutional network is the output A of the self-attention mechanism. s The output is X TCN .

[0084] For a one-dimensional input sequence and filter The dilated convolution operation F is defined as follows:

[0085]

[0086] Where d is the dilation coefficient, k is the filter size, and x s-di Let x be the (s-di)th element of the input sequence, where s-di means that the operation direction is to step into the past data.

[0087] The residual connection structure is divided into a direct mapping part and a residual part. The output of the residual connection can be expressed as:

[0088] o=Act(x+F R (x)) (13)

[0089] Wherein, the transformation function F R (·)represent Figure 2 The left half of the operation is performed, with Act(·) as the activation function. The residual connection uses a modified linear unit as the activation function, defined as Act(x) = max(0,x). The residual connection structure uses the activation function to connect the input x and the transformation function output F. R The superposition result of (x) is mapped to the output of the residual connection.

[0090] (3) Input b'(k) into the soft attention mechanism. The input-output relationship of the soft attention mechanism is expressed as follows:

[0091] A soft (X)=sigmoid(XW)⊙X (14)

[0092] Where ⊙ represents the Kronecker product operation, W is the weight matrix of the soft attention mechanism, and X is the input signal b'(k) of the soft attention mechanism.

[0093] (3) The output data X of the temporal convolutional network TCN After dimensionality reduction using a linear layer, the output A of the same soft attention mechanism is... soft , merge and splice into Then X merge Dimensionality reduction via linear layers

[0094] (4) After inverse normalization and upsampling operations, the predicted receiver clock bias sequence is obtained. If this is a prediction step, then one prediction of the receiver clock bias has been completed at this point. If this is a training process, then further calculation of the loss function based on the minimum mean square error criterion is required.

[0095]

[0096] Step 3: With three visible satellites, the attention mechanism-enhanced temporal convolutional network calculates the receiver position using the predicted receiver clock error and the auxiliary navigation filter.

[0097] After training, the attention-enhanced temporal convolutional network predicts the receiver clock bias, which then assists the navigation filter in three-star positioning. During three-star positioning, the navigation filter no longer calculates the receiver clock bias itself; instead, it outputs the predicted receiver clock bias through the attention-enhanced temporal convolutional network, thereby correcting the pseudorange observation z1(k+1). It is evident that under insufficient satellite coverage, the state estimation vector is... The time update and measurement update in EKF parameter estimation are summarized as follows.

[0098] (1) The EKF time update step calculates the prior state estimate and the mean square error matrix of the state as follows:

[0099]

[0100] P1(k+1|k)=P1(k|k)+Q1 (17)

[0101] in, The state at time k+1 is estimated based on the state at time k, which is the state prior estimate; the state transition matrix A1 is the identity matrix, and Q1 is the mean square error matrix of the process noise, denoted as γI. 3×3 P1(k+1|k) and P1(k|k) are the mean square error matrices of the prior estimated states at time k+1 and time k, respectively, estimated at time k.

[0102] (2) The state posterior estimate and the mean square error matrix of the posterior estimate obtained by the measurement update step of EKF are:

[0103]

[0104] P1(k+1|k+1)=[I-K1(k+1)H1(k+1)]P1(k+1|k) (19)

[0105] in, ν1(k+1) is the posterior estimate of the state at time k+1 based on the state at time k+1; K1(k+1) is the Kalman gain at time k+1; ν1(k+1) is the residual vector corrected by the predicted receiver clock error sequence from the output of the temporal convolutional network through the attention mechanism, defined as... H1(k+1) is the Jacobian matrix of the measured values.

[0106] The observed vector predicted from the prior state for:

[0107]

[0108]

[0109] in These are the 1st to Lth quantities in the observation vector predicted based on the prior state, r u (k+1|k) is the estimated three-dimensional coordinate vector of the receiver at time k+1. It is the three-dimensional coordinate vector of the satellite at time k+1.

[0110] The Jacobian matrix H1(k+1) of the measured values ​​is

[0111] H1(k+1)=[h 11 (k+1),...,h 1L(k+1)] T (twenty two)

[0112]

[0113] Where h 11 (k+1),…,h 1L (k+1) are the first to Lth component vectors in the Jacobian matrix H1(k+1).

[0114] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A three-star positioning method based on an attention mechanism enhanced time convolutional network, characterized in that, Includes the following steps: When there are sufficient visible stars, the EKF navigation filter calculates the receiver position and clock bias / drift, and the calculation results are used as training samples, specifically: With sufficient visible satellites, navigation calculations are performed using the EKF navigation filter to obtain the receiver's three-dimensional position and clock bias; the state estimation vector in the EKF is... ,in These are the receiver's three-dimensional position, receiver clock error, and clock drift, respectively. Therefore, under sufficient star conditions, the time update and measurement update in EKF parameter estimation are as follows: (1) The EKF time update step calculates the prior state estimate and the mean square error matrix of the prior estimated state as follows: （2） （3） in, The state at time k+1 is estimated based on the state at time k, which is the state prior estimate; and These are the state transition matrix and the process noise, respectively. The mean square error matrix; and These are the mean square error matrices of the prior estimated states at time k+1 and time k, respectively; (2) The state posterior estimate and the mean square error matrix of the posterior estimate obtained by the measurement update step of EKF are: （6） （7） in, This is the posterior estimate of the state at time k+1; The Kalman gain at time k+1 Let be the residual vector at time k+1; The Jacobian matrix of the measured values; Let be the mean square error matrix of the posterior estimate at time k+1; Based on the time update and measurement update in the above EKF parameter estimation, the state estimation vector in EKF is solved to obtain the receiver position, clock error and clock drift; A predictor based on an attention-based enhanced temporal convolutional network is constructed. This predictor is used to predict the receiver clock offset at future times based on the receiver clock offset calculated in the past. The predictor is trained using the training samples to obtain a trained predictor. The specific steps for constructing the predictor are as follows: The predictor's structure includes an input layer, a multi-group partitioned layer, a self-attention mechanism layer, a temporal convolutional network, a soft attention mechanism layer, an output layer, and a temporal convolutional network. The input layer is k Clock difference sequence of time As input, the clock difference sequence After data downsampling and normalization, we obtain , On the one hand, it sends data to a multi-layered structure, and on the other hand, it sends data to a soft attention mechanism layer. The division into multiple layers will Divide into multiple groups of length D sequences It is fed into the self-attention mechanism layer; The output of the self-attention mechanism layer The data is fed into the temporal convolutional network. The temporal convolutional network consists of three temporal modules, including a dilated causal convolutional layer, a weight normalization layer, a rectified linear unit (ReLU), a randomized dropout layer, and a residual connection structure. The input of the temporal convolutional network is the output of the self-attention mechanism. The output is ; The output layer processes the output data of the temporal convolutional network. After dimensionality reduction using a linear layer, the output is the same as that of the soft attention mechanism. , merge and splice into Then Dimensionality reduction via linear layers ;Will After inverse normalization and upsampling operations, the predicted receiver clock bias sequence is obtained. ; With three visible satellites, the receiver position is calculated using the predicted receiver clock error output by the trained predictor and the auxiliary navigation filter.

2. The three-star localization method based on attention mechanism-enhanced temporal convolutional networks as described in claim 1, characterized in that, When three satellites are visible, the receiver position is calculated using the predicted receiver clock error output by the trained predictor and the auxiliary navigation filter. Specifically: With three visible satellites, the navigation filter for three-satellite positioning no longer calculates the receiver clock bias. Instead, it predicts the receiver clock bias by outputting an attention-enhanced temporal convolutional network, thereby correcting the pseudorange observations. It can be seen that, under insufficient star conditions, the state estimation vector is... Then, in EKF parameter estimation, time updates and measurement updates are... (1) The EKF time update step calculates the state prior estimate and the state mean square error matrix as follows: （16） （17） in, The state at time k+1 is estimated based on the state at time k, which is the state prior estimate; the state transition matrix. As a unit array, Let be the mean square error matrix of the process noise, denoted as... , It is a very small positive number. It is a three-dimensional identity matrix; and These are the mean square error matrices of the prior estimated states at time k+1 and time k, respectively; (2) The state posterior estimate and the mean square error matrix of the posterior estimate obtained by the measurement update step of EKF are: （18） （19） in, This is the posterior estimate of the state at time k+1; The Kalman gain at time k+1 It enhances the residual vector of the predicted receiver clock error sequence output by the temporal convolutional network through an attention mechanism. Let be the Jacobian matrix of the measured values.

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