Positioning method based on FM signal knowledge distillation

Abstract

The invention provides a positioning method based on FM signal knowledge distillation, and aims to improve the accuracy and stability of positioning in a real-time resource limited application scene. The method comprises the following steps: firstly, collecting FM signals in a positioning area, and constructing a training set and a verification set of the FM signals through random interception and power normalization processing; thirdly, constructing a teacher and student convolutional neural network, enhancing the spatial expression ability of the model by using a spatial attention mechanism, and transmitting deep features and classified knowledge of the teacher model to the student model through a knowledge distillation method; the student model optimizes own parameters by learning the feature extraction capability of the teacher model so as to approach the positioning precision of the teacher model. And finally, through Bayesian position estimation, in combination with the confidence coefficient output by the network, predicting the target position. According to the method, through wavelet packet transformation and knowledge distillation, the accuracy and stability of positioning are improved, the calculation cost and parameter quantity of the model are reduced, and the method is suitable for equipment and scenes with limited resources.

Description

Technical Field

[0001] The present invention relates to the field of positioning and navigation technology, and in particular to a positioning method based on FM knowledge distillation. Background Art

[0002] With the rapid development of the Internet of Things, the demand for accurate, reliable and real-time positioning technology has increased dramatically in various fields, including autonomous driving, logistics tracking and health monitoring. Global navigation satellite systems, such as the Global Positioning System, perform well in outdoor environments with strong signals and provide high-precision positioning services. However, global navigation satellite systems also have obvious limitations. First, satellite positioning systems rely on precise signal synchronization to determine the position by measuring the signal propagation time. Time synchronization errors at the microsecond level can cause significant positioning deviations, so highly accurate time synchronization is required. Second, the accuracy of these systems is greatly affected in complex environments (such as indoors or densely populated cities). In urban environments, signals are easily affected by electromagnetic interference, blocked and blocked by buildings, resulting in signal attenuation, reducing the accuracy and stability of positioning, and often failing to meet users' needs for accurate and real-time positioning services. Frequency Modulation (FM) signals, as an opportunistic navigation source, have demonstrated excellent positioning accuracy in the presence of non-navigation RF signals in the environment for positioning the target signal. However, traditional methods mainly rely on the received signal strength indication as a fingerprint feature. Focusing only on energy characteristics, they limit the ability to fully capture the rich information in the original signal. In addition, since these methods mainly use traditional machine learning techniques, they may lack the ability to learn complex and deep features, and existing deep learning-based methods bring a lot of computational burden. Therefore, how to reduce computational intensity and improve overall efficiency while ensuring positioning accuracy is still a problem that needs to be solved urgently in the current field. Summary of the invention

[0003] The present invention aims to provide a positioning method based on FM signal knowledge distillation, which improves the accuracy of fingerprint positioning by analyzing the time-frequency domain information of FM signals, while avoiding the complex manual feature extraction and excessive calculation complexity of traditional fingerprint positioning algorithms. The present invention discloses a positioning method based on FM signal knowledge distillation, comprising the following steps:

[0004] Step 1: Divide the grid and collect FM signals;

[0005] The positioning area is divided into K grids, each grid represents an independent location unit, and FM signal samples are collected in each grid, each sampling is performed for a period of time and multiple times;

[0006] Step 2: preprocessing the collected FM signal samples;

[0007] The collected FM signal samples are processed, including random interception of signal segments and power normalization. First, a signal segment with a fixed length of N (N is less than the original signal length) is randomly intercepted from the original FM signal sample. Then, the signal segment is power normalized. The process is repeated so that each grid point obtains a sequence of l FM signal segments.

[0008] Step 3: Calculate the FM signal wavelet packet transform matrix

[0009] Perform wavelet packet transform on each FM signal segment sequence, and construct a wavelet packet transform matrix based on the transformed high and low frequency detail components;

[0010] Step 4: Construct FM signal training set and validation set

[0011] The wavelet packet transform matrices of all FM signal segments are randomly divided into training sets and validation sets according to a certain ratio. The sample data in the training set and validation set include the wavelet packet transform matrix and sample labels. The sample labels correspond to the grid positions where the FM signal segments are collected.

[0012] Step 5: Construct FM positioning teacher model and student model

[0013] A teacher model and a student model for FM positioning are constructed. The teacher model adds a spatial attention mechanism to the head to enhance the spatial expression ability of the model, so that it focuses on the features of different positions and improves the recognition accuracy. The student model has fewer parameters than the teacher model. The input of the teacher model and the student model is the wavelet packet transform matrix of the FM signal, and the output layer is the classification layer, whose number of hidden nodes is consistent with the number of grid points.

[0014] Step 6: Train the FM positioning teacher model

[0015] Use the FM signal training set and validation set to train and validate the teacher model, optimize its network parameters, and obtain the trained and validated teacher model;

[0016] Step 7: Train FM positioning student model

[0017] During the training process, the teacher model and the student model receive the same input (FM signal training set and validation set), and the total loss of the student model is the weighted sum of the student loss and the distillation loss. Through iterative optimization, the parameters of the student model are updated according to the gradient of the loss function, where the distillation error only affects the update of the student network parameters, but not the teacher network parameters. In addition, balancing the student loss and distillation loss ensures that the student model can learn both the true label information of the data and useful patterns from the teacher model. The student model can learn the knowledge of the teacher model through the iteration of the loss function, thereby improving its positioning accuracy and approaching the performance of the teacher model.

[0018] Step 8: Collect FM signals of the points to be located

[0019] Collect the FM signal of the point to be located, and the signal sampling points shall not be less than N;

[0020] Step 9: Intercept the FM signal segment of the point to be located

[0021] The FM signal of the point to be located is randomly intercepted and the power is normalized. The interception length is fixed to N each time, and the power is normalized to 1. This is repeated many times to obtain the FM signal segments of M points to be located.

[0022] Step 10: Calculate the wavelet packet transform matrix of the FM signal at the point to be located

[0023] For the FM signal segment sequences of the M points to be located, the wavelet packet transform domain sequence of each signal segment sequence is calculated respectively, and a wavelet packet transform matrix is ​​constructed based on the transformed approximate components and detail components.

[0024] Step 11: Estimate the position of the point to be located

[0025] The M wavelet packet transform matrices of the points to be located are input into the trained student model, the position corresponding to the sample is calculated based on the confidence and grid coordinates output by the student model, and the positions of the M samples are averaged to obtain the final position.

[0026] Compared with the prior art, the present invention can at least achieve the following beneficial effects:

[0027] 1. The present invention uses wavelet packet transform to perform multi-scale decomposition of signals, which is particularly suitable for capturing local features of non-stationary signals. Compared with traditional wavelet analysis, wavelet packet analysis can achieve more refined frequency band division, thereby improving the accuracy and efficiency of time-frequency analysis and revealing the multi-level features of signals.

[0028] 2. The present invention transfers complex teacher model knowledge to a simple student model through knowledge distillation, which not only significantly reduces the computational cost and parameter amount of the model, but also makes the model lighter while maintaining positioning accuracy, making it more suitable for devices and scenarios with limited resources.

[0029] 3. The present invention randomly divides the FM signal samples of the position to be located, and inputs them into the trained student convolutional neural network model, and further optimizes the decision by combining confidence fusion. The Bayesian estimation based on grid coordinate points and confidence effectively reduces the position estimation error and improves the accuracy of positioning.

[0030] Other features and advantages of the present invention will be described in the following description, and some advantages may become apparent from the description, or may be understood by practicing the present invention. The purpose and other advantages of the present invention may be realized and obtained through the contents particularly pointed out in the description and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0032] Figure 1 This is a flow chart of the fingerprint positioning method based on FM signal knowledge distillation of the present invention.

[0033] Figure 2 Locate the teacher model for the constructed FM.

[0034] Figure 3 Position the student model for the constructed FM.

[0035] Table 1 shows the experimental results of the fingerprint positioning method based on FM signal knowledge distillation. DETAILED DESCRIPTION

[0036] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the implementation examples of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0037] like Figure 1 As shown, the present invention provides a positioning method based on FM signal knowledge distillation, comprising the following steps:

[0038] Step S1: Divide the grid and collect FM signals

[0039] The positioning area is divided into K grids, each grid represents an independent location unit, and FM signal samples are collected in each grid. Each sampling is for a period of time, and the sampling is repeated multiple times. All of them are discretized digital signal sequences with equal lengths. The sampled FM signal sequence s(n) = s(t)δ T (t), where s(t) is the analog domain FM signal, δ T (t) is the impulse function, T = 1 / F s is the sampling period, F s is the sampling frequency.

[0040] Step S2: Preprocessing FM signal samples

[0041] The collected FM signal samples are processed, including random interception of signal segments and power normalization; first, a signal segment with a fixed length of N (N is less than the original signal length N) is randomly intercepted from the original FM signal sample.s ), then, the signal segment is power normalized, and the process is repeated so that each grid point obtains a sequence of l FM signal segments;

[0042] The specific process of each step is as follows.

[0043] Step S2-1: Randomly intercept signal segments

[0044] A signal segment is randomly intercepted from the original FM signal sample. The length of the intercepted signal segment is fixed to N and is smaller than the original signal length. The intercepted FM signal segment can be expressed as s t (n) = s(n+b), where n = 0, 1, ..., N-1, and the length of the original signal sequence s(n) is N s A positive integer, b is a randomly generated integer less than N s -N is a non-negative integer.

[0045] Step S2-2 Power Normalization

[0046] The intercepted signal segment is subjected to power normalization and normalized to 1. The normalized signal segment is expressed as

[0047] Step S3: Calculate the FM signal wavelet packet transform matrix

[0048] For the l FM signal segment sequences, the wavelet packet transform matrix of each signal segment sequence is calculated respectively. The FM wavelet packet transform sequence calculation process is: for the power normalized FM signal segment sequence s w (n) Perform P-order wavelet transform, the wavelet basis uses the "haar" wavelet, P is greater than 1 and less than floor(log2(N)), where floor(log2(N)) represents the largest integer not exceeding log2(N), and the high and low frequency detail components of the root node after wavelet packet transform are concatenated into a matrix according to the root node coefficients from small to large to obtain the wavelet packet transform matrix of the FM signal. Get the FM wavelet packet transform vector matrix x w (n);

[0049] Step S4: Constructing FM signal training set and verification set

[0050] The wavelet packet transform matrices of all FM signal segments are randomly divided into training sets and validation sets according to a certain ratio. The sample data in the training set and validation set include the wavelet packet transform matrix and sample labels. The sample labels correspond to the grid positions where the FM signal segments are collected.

[0051] Step S5: Construct FM positioning teacher model and student model

[0052] The teacher model and student model for FM positioning are constructed as follows: Figure 2 and Figure 3 As shown in the figure. The teacher model adds a spatial attention mechanism to the head to enhance the spatial expression ability of the model, so that it pays attention to the features of different positions and improves the recognition accuracy. The student model has fewer parameters than the teacher model. The input of the teacher model and the student model is the FM signal wavelet packet transform matrix, and the output layer is the classification layer, whose number of hidden nodes is consistent with the number of grid points.

[0053] The convolutional neural network used in the teacher model is as follows Figure 2 As shown in the figure. “ResnextBlock(64)” indicates that the convolutional layer is a residual network block, a residual block of 64 filters (Bottleneck). The convolutional neural network used in the student model is as follows Figure 3 As shown in the figure. "Conv,32,3×3" indicates that the convolution layer is a traditional convolution layer, the number of convolution kernels is 32, and the convolution kernel size is 3×3. The "Conv" layer in the figure corresponds to the sequence convolution layer + batch normalization layer + activation layer, where the activation function is Relu. "Max_Pool" is the maximum pooling layer with stride (1, 2), "Global_Avgpool" is the global average pooling, and "FC" is a linear layer with an output of K (the number of grids).

[0054] Step S6: Training FM positioning teacher model

[0055] The teacher model was trained and verified using the FM signal training set and validation set, and its network parameters were optimized to obtain a trained and verified teacher model. The convolutional neural network was trained using the training set, and the network performance was evaluated using the validation set periodically during the training process. The AdamW optimizer was used for training, and the loss function was the cross entropy function. To improve the training effect, the learning rate was decayed to half of the original value after every two rounds of training, and the initial learning rate was set to 10 -3 During the entire training process, the model parameters with the highest accuracy on the validation set are saved as the optimal parameters of the convolutional neural network.

[0056] Step S7: Training FM positioning student model

[0057] During the training process, the knowledge distillation technique is used. The teacher model and the student model receive the same input (FM signal training set and validation set), and the total loss of the student model is the weighted sum of the student loss and the distillation loss. Through iterative optimization, the parameters of the student model are updated according to the gradient of the loss function, where the distillation loss only affects the update of the student network parameters, but not the teacher network parameters. In addition, balancing the student loss and the distillation loss ensures that the student model can learn both the true label information of the data and the useful patterns from the teacher model. The student model can learn the knowledge of the teacher model through the iteration of the loss function, thereby improving its positioning accuracy and approaching the performance of the teacher model.

[0058] In the knowledge distillation process, the teacher model first performs inference on the training set to generate soft labels, that is, labels containing the predicted probability distribution of the input features. Among them, q i Indicates the probability of each category output by the model, z i Represents the value of the output Logits of the i-th category, and T is the temperature coefficient. The student model uses these soft labels as the training target loss function to learn the knowledge of the teacher model while maintaining simplicity and low computational cost; the loss function consists of the KL divergence loss function (for soft labels) and the cross entropy (CE) loss function (for hard labels). total =α·L KL +(1-α)·L CE , where L KL =KL(q i teacher |q i student ), q i teacher represents the softened probability of the teacher model outputting the i-th category, q i student represents the softened probability of the i-th category output by the student model, h i is the one-hot encoding of the true label, q 1 i It indicates that when T = 1, the student model outputs the probability of the i-th category. α is a hyperparameter between 0 and 1, which is used to balance the importance of KL divergence loss and cross entropy loss in the total loss. The distillation temperature T used in training is 5 and α is 0.5.

[0059] Step S8: Collect FM signal of the point to be located

[0060] Collect the FM signal to be detected and obtain y(n), n=0,1,...,N y -1, its length is N y >N.

[0061] Step S9: intercept the FM signal segment of the point to be located

[0062] The FM signal of the location point is randomly intercepted and the power is normalized. The interception length is fixed to N each time, and the power is normalized to 1. This is repeated many times to obtain M FM signal segments of the location to be estimated. The specific interception and normalization operations are as follows.

[0063] Step S9-1: Randomly intercept signal segments

[0064] A signal segment is randomly intercepted from the FM signal sample y(n) of the point to be located. The length of the intercepted signal segment is fixed to N. The intercepted FM signal segment can be expressed as y t (n) = y(n+c), where n = 0, 1, ..., N-1, and c is a randomly generated number less than N. y -N is a non-negative integer.

[0065] Step S9-2 Power Normalization

[0066] The power of the intercepted signal is normalized to 1. The normalized FM signal segment of the position to be estimated is

[0067] Step S10: Calculate the wavelet packet transform matrix of the FM signal at the point to be located

[0068] For the FM signal segment sequences of the M positions to be estimated, the wavelet packet transform domain sequence of each signal segment sequence is calculated respectively, and the high and low frequency detail components of the transformed root node are spliced ​​into a matrix from small to large according to the root node coefficients. The specific calculation process is consistent with that in step S3.

[0069] Step S11: Estimate the position of the point to be located

[0070] The M wavelet packet transform matrices of the points to be located are input into the trained student model in turn, and the position corresponding to the sample is calculated based on the confidence and grid coordinates output by the model, and the positions of the M samples are averaged to obtain the final position. The steps include: calculating the confidence of each grid point based on each sample, and using Bayesian estimation to obtain the predicted position based on the coordinate value of each grid, Where (x i ,y i ) is the collected grid coordinate value, For the predicted position of each sample, p(i) is the confidence of the i-th grid point output by the model, that is, q 1 i The final position is obtained by averaging the positions of M samples. Experimental data

[0071] This method was compared with the FM-Pnet model, and four performance indicators were used: the mean distance error (MDE) reflects the average Euclidean distance between the estimated position and the true position. The smaller the value, the higher the positioning accuracy; the standard deviation (STD) measures the discreteness of the positioning error. The smaller the STD, the better the stability of the positioning result; the number of floating-point operations (#FLOPs) is an indicator of the computational complexity of the model. The smaller the value of #FLOPs, the less computing resources the model requires when processing data; the number of parameters (#Params) is an indicator of the size of the model. It indicates the total number of trainable parameters in the model. The fewer the number of parameters, the lighter the model.

[0072] The MDE of our method is lower than that of FM-Pnet in both indoor and outdoor environments, which indicates that our positioning accuracy is higher. STD is lower than that of FM-Pnet in both indoor and outdoor environments, which means that our positioning results are more stable. The floating-point operation amount of the FM-Pnet model is 2848M, while the floating-point operation amount of our model is 117M, achieving a reduction of about 95.9%. Similarly, the parameter amount of the FM-Pnet model is 14M, compared with 0.10M for our model, achieving a reduction of about 99.3%.

[0073] Table 1

[0074]

[0075] Those skilled in the art will appreciate that all or part of the above-mentioned implementation methods can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0076] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A positioning method based on FM signal knowledge distillation, characterized in that: The steps include: Step 1: Divide the grid and collect FM signals; The positioning area is divided into K grids, each grid represents an independent location unit, and FM signal samples are collected in each grid, each sampling is performed for a period of time and multiple times; Step 2: preprocessing the collected FM signal samples; The collected FM signal samples are processed, including random interception of signal segments and power normalization; first, a signal segment of a fixed length of N is randomly intercepted from the original FM signal sample, where N is less than the original signal length; then the signal segment is power normalized, and the process is repeated so that each grid point obtains a sequence of l FM signal segments; Step 3: Calculate the FM signal wavelet packet transform matrix Perform wavelet packet transform on each FM signal segment sequence, and construct a wavelet packet transform matrix based on the transformed high and low frequency detail components; Step 4: Construct FM signal training set and validation set The wavelet packet transform matrices of all FM signal segments are randomly divided into training sets and validation sets according to a certain ratio. The sample data in the training set and validation set include the wavelet packet transform matrix and sample labels. The sample labels correspond to the grid positions where the FM signal segments are collected. Step 5: Construct FM positioning teacher model and student model A teacher model and a student model for FM positioning are constructed. The teacher model adds a spatial attention mechanism to the head to enhance the spatial expression ability of the model, so that it focuses on the features of different positions and improves the recognition accuracy. The student model has fewer parameters than the teacher model. The input of the teacher model and the student model is the wavelet packet transform matrix of the FM signal, and the output layer is the classification layer, whose number of hidden nodes is consistent with the number of grid points. Step 6: Train the FM positioning teacher model Use the FM signal training set and validation set to train and validate the teacher model respectively, optimize the network parameters of the teacher model, and obtain the trained and validated teacher model; Step 7: Train FM positioning student model During the student model training process, the teacher model and the student model receive the same input, namely the FM signal training set and validation set; the total loss of the student model is the weighted sum of the student loss and the distillation loss; through iterative optimization, the network parameters of the student model are updated according to the gradient of the loss function, balancing the student loss and the distillation loss to ensure that the student model can learn both the real label information of the data and the useful patterns from the teacher model; the student model can learn the knowledge of the teacher model through the iteration of the loss function, thereby improving its positioning accuracy and approaching the performance of the teacher model; Step 8: Collect FM signals of the points to be located Collect the FM signal of the point to be located, and the signal sampling points shall not be less than N; Step 9: Intercept the FM signal segment of the point to be located The FM signal of the point to be located is randomly intercepted and the power is normalized. The interception length is fixed to N each time, and the power is normalized to 1. This is repeated many times to obtain the FM signal segments of M points to be located. Step 10: Calculate the wavelet packet transform matrix of the FM signal at the point to be located For the FM signal segment sequences of the M points to be located, respectively calculating the wavelet packet transform domain sequence of each signal segment sequence, and constructing a wavelet packet transform matrix based on the transformed approximate component and detail component; Step 11: Estimate the position of the point to be located The M wavelet packet transform matrices of the points to be located are input into the trained student model, the position corresponding to the sample is calculated based on the confidence and grid coordinates output by the student model, and the positions of the M samples are averaged to obtain the final position.

2. The positioning method based on FM signal knowledge distillation according to claim 1 is characterized in that: The calculation steps of the FM signal wavelet packet transform matrix are: perform P-order wavelet packet transform on the FM signal segment sequence, P is greater than 1 and less than floor(log2(N)), where floor(log2(N)) represents the maximum integer not exceeding log2(N), and the high and low frequency detail components of the root node after wavelet packet transform are spliced ​​into a matrix from small to large according to the root node coefficients to obtain the wavelet packet transform matrix of the FM signal.

3. The positioning method based on FM signal knowledge distillation according to claim 2 is characterized in that: The calculation formula of the spatial attention mechanism in the teacher model is: H s (F s )=σ(f 7×7 ([AvgPool(G s );MaxPool(G s )])) Among them, G s ∈R C*H*W As the input of spatial attention, AvgPool(·) and MaxPool(·) represent global average pooling and global maximum pooling, σ represents the sigmoid function, and H s For input G s The spatial attention representation of f 7×7 represents a convolution operation with a filter size of 7×7.

4. The positioning method based on FM signal knowledge distillation according to claim 2 is characterized in that: The structure of the teacher model is as follows: first, SpatialAttention is used to focus on spatially important areas; then, the model performs feature extraction and channel relationship modeling through a series of ResNeXt blocks, which contain 64, 128, 256 and 512 channels respectively, and the number of block repetitions for each channel number is [3, 4, 5, 3], so as to gradually increase the expressive power of the model; after being processed by the ResNeXt block, the feature map is globally averaged pooled by Global_Avg_Pool to compress the spatial dimension and retain the key feature information to obtain a one-dimensional feature vector; then, the one-dimensional feature vector is mapped by a fully connected layer FC; finally, the Softmax layer converts the output of the fully connected layer into a probability distribution for multi-classification tasks, and the output represents the probability that the input belongs to each category; through the combination of these layers, the entire model can extract key features from the original FM signal and finally be used for positioning tasks.

5. The positioning method based on FM signal knowledge distillation according to claim 4 is characterized in that: The structure of the student model: The structure of the student model starts with the input original FM signal, first extracts local features through a 3x3 convolution layer; then downsamples the feature map through a maximum pooling layer to reduce its spatial size; Subsequently, the model extracts features again through the convolution layer, and finally downsamples through the maximum pooling layer. The process is repeated once, and the convolution layer and the maximum pooling layer are used to extract deeper features and reduce the size of the feature map. After multiple convolution and pooling operations, the feature map is converted into a one-dimensional feature vector through the global average pooling layer. This vector contains the global information of the entire feature map. Then, this feature vector is mapped through the fully connected layer. Finally, the Softmax layer converts the output of the fully connected layer into a probability distribution for multi-classification tasks. The output represents the probability that the input belongs to each category.

6. The positioning method based on FM signal knowledge distillation according to claim 1, characterized in that: In the knowledge distillation process of training the student model, the teacher model first performs inference on the training set to generate soft labels, i.e., labels containing the predicted probability distribution of the input features. Among them, q i Indicates the probability of each category output by the model, z i represents the value of the output Logits of the i-th category, and T is the temperature coefficient; the student model uses the soft label as the training target loss function to learn the knowledge of the teacher model while maintaining simplicity and low computational cost; the loss function consists of the KL divergence loss function for the soft label and the cross entropy loss function for the hard label: L total =α·L KL +(1-α)·L CE , where L KL =KL(q i teacher |q i student ), q i teacher represents the softened probability of the teacher model outputting the i-th category, q i student Represents the softened probability of the student model outputting the i-th category, y i is the one-hot encoding of the true label, q 1 i It indicates that when T=1, the student model outputs the probability of the i-th category, and α is a hyperparameter between 0 and 1.

7. The positioning method based on FM signal knowledge distillation according to claim 1, characterized in that: The final position prediction result is obtained by performing Bayesian estimation based on the grid coordinate points and the confidence level; the steps include: calculating the confidence level of each grid point based on each sample, and obtaining the predicted position based on the coordinate value of each grid using Bayesian estimation, Where (x i ,y i ) is the collected grid coordinate value, is the predicted position of each sample, and p(i) is the confidence of each grid point output by the model; The final position is obtained by averaging the positions of M samples.

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