A Gravity Adaptability Analysis Method Based on Neural Network Fitting

Abstract

This invention discloses a gravity adaptability analysis method based on neural network fitting. First, it extracts local gravity field samples using an overlapping sliding window, extracting as many samples as possible while ensuring the difference between samples given a limited gravity reference map. Then, it introduces aspect dispersion into the gravity field characteristic parameters of the local region samples to measure the dispersion of the local gravity field aspect distribution. Simultaneously, it constructs a neural network and designs the gravity adaptability direction ratio as the target parameter for neural network fitting, thus measuring the gravity field direction adaptability. Next, it uses supervised training to train the neural network. The trained neural network model directly reflects the relationship between gravity field distribution characteristics and gravity matching performance, enabling quantitative analysis of gravity field direction adaptability, ensuring the comprehensiveness of the selected gravity field adaptability area, and effectively improving the utilization rate of the gravity field background map.

Description

Technical Field

[0001] This invention relates to the fields of navigation, guidance and control technology, and specifically to a gravity adaptability analysis method based on neural network fitting. Background Technology

[0002] Inertial navigation systems (INS) possess advantages such as high stealth, strong anti-interference capability, comprehensive and continuous navigation information, and strong real-time information, making them widely used in underwater navigation. However, INS errors accumulate over time, making it difficult to meet the long-endurance and high-precision requirements of underwater vehicles. Gravity matching navigation is often used as an aid to correct INS errors. The selection of the gravity matching zone is one of the key technologies in gravity-assisted inertial navigation; choosing a suitable matching area helps improve navigation accuracy.

[0003] Traditional adaptability analysis methods mainly involve using feature fusion methods such as the analytic hierarchy process (AHP) to obtain comprehensive feature parameters to measure the adaptability of a local area by fusing various gravity field characteristic parameters such as standard deviation, roughness, correlation coefficient, slope, coefficient of variation, skewness coefficient, kurtosis coefficient, and gravity information entropy.

[0004] In 2019, Wang Bo et al. disclosed a method for evaluating the regional adaptability of gravity-assisted inertial navigation based on virtual heading in their paper "A Method for Evaluating the Regional Adaptability of Gravity-Assisted Inertial Navigation Based on Virtual Heading". This method determines the calculation range of adaptability analysis based on virtual heading, improves the traditional expression of gravity characteristic parameters, and then uses the analytic hierarchy process (AHP) to perform feature fusion to analyze the gravity adaptability of the virtual heading.

[0005] In 2020, Wang Bo et al. disclosed a model-free assisted navigation adaptation region selection method in "A Model-Free Assisted Navigation Adaptation Region Selection Method". This method extracts the gravity field feature parameters of the gravity field background image grid, obtains the comprehensive feature parameters by weighted summation, divides the samples into adaptation regions, general adaptation regions and non-adaptation regions according to the comprehensive feature parameters, and then trains a two-layer binary classifier to classify the adaptation regions.

[0006] Traditional feature fusion adaptation analysis methods and "A Model-Free Navigation Adaptation Region Selection Method" analyze the overall distribution of gravity anomalies in local areas, but cannot measure their directionality. They do not distinguish between directional and omnidirectional adaptation regions, which leads to some regions that are adapted in some directions being evaluated as non-adaptation regions.

[0007] Traditional adaptability analysis methods and the "Gravity-Assisted Inertial Navigation Region Adaptability Evaluation Method Based on Virtual Heading" are unsupervised methods that select adaptability zones based solely on the distribution characteristics of local areas. While the "Model-Free Navigation Adaptability Zone Selection Method" is a supervised method, its training set adaptability labels are added based on the values ​​of comprehensive feature parameters. Neither method establishes a direct link between local area features and gravity matching performance, making it difficult to guarantee the comprehensiveness of the selected adaptability zones. This can lead to situations where some areas have good adaptability but are not marked as adaptability zones. Summary of the Invention

[0008] In view of this, the present invention provides a gravity adaptability analysis method based on neural network fitting, which can realize quantitative analysis of gravity field direction adaptability, ensure the comprehensiveness of the selected gravity field adaptability area, effectively improve the utilization rate of gravity field background map, and make up for the lack of traditional methods in the analysis of gravity field distribution directionality.

[0009] The gravity adaptability analysis method based on neural network fitting of the present invention includes:

[0010] Step 1: Determine the local region template of the gravity field. The size of the template is determined according to the minimum range of the required adaptation area. Use a sliding window to slide through the reference gravity field map to be trained to obtain local region samples of the gravity field.

[0011] Step 2: Extract the gravity field feature parameters of the local gravity field sample and normalize them; the gravity field feature parameters include the aspect dispersion, which is the length of the sum of the aspect unit vectors at each point in the local sample divided by the number of vectors.

[0012] Step 3: Calculate the gravity adaptation direction ratio of the local region sample in the gravity field; the gravity adaptation direction ratio is the ratio of the number of adaptation directions in the local region to the total number of directions.

[0013] Step 4: Construct a neural network. Take the normalized gravity field feature parameters of the local gravity field samples from Step 2 as input and the gravity adaptation direction ratio of the local gravity field samples from Step 3 as output. Train the neural network to obtain a trained neural network.

[0014] Step 5: Use the adaptive analysis neural network trained in Step 4 to perform adaptive analysis on the gravity field background image to be analyzed, and obtain the gravity adaptation direction ratio of each local region of the gravity field background image to be analyzed; based on the obtained gravity adaptation direction ratio and the set threshold, divide the adaptation area.

[0015] Preferably, in step 1, the size of the local region template of the gravity field is an m×n grid, the horizontal sliding length of the sliding window is m / 2, and the vertical sliding length is n / 2.

[0016] Preferably, in step 2, the method for calculating the slope aspect dispersion of the local gravity field sample of size m×n grid is as follows:

[0017] First, calculate the slope aspect A of each grid point (i,j) in the local gravitational field region. ij :

[0018] A ij =arctan(f y / f x )-f x / |f x |×f y / |f y |×90°+f y / |f y |×90°+180° (1)

[0019] f x =[g i-1,j+1 -g i-1,j-1 +2(g i,j+1 -g i,j-1 )+g i+1,j+1 -g i+1,j-1 ] / 8 (2)

[0020] f y =[g i+1,j+1 -g i-1,j+1 +2(g i+1,j -g i-1,j )+g i+1,j-1 -g i-1,j-1 ] / 8 (3)

[0021] Among them, g i,j Let (i,j) be the gravity anomaly value at point (i,j).

[0022] The slope dispersion R of the local region of the gravitational field is

[0023]

[0024] in

[0025]

[0026]

[0027] Preferably, in step 2, the gravity field characteristic parameters further include one or more of the following: standard deviation, information entropy, longitude roughness, latitude roughness, longitude correlation coefficient, latitude correlation coefficient, and directional gradient.

[0028] Preferably, in step 2, the mean-variance normalization method is used to normalize each feature parameter.

[0029] Preferably, in step 3, the gravity matching direction ratio of the local gravity field region is calculated through a gravity matching survey line simulation experiment. Specifically:

[0030] First, n is uniformly distributed within the range of north by east [0°, 180°) at intervals of Δd. d One course;

[0031] For each heading, M survey lines with a length of l sampling points are randomly generated within a local area as the true trajectory. For each survey line, N gravity matching simulations are performed. In each simulation, Gaussian white noise with a mean of 0 and a variance equal to the variance of the gravimeter measurement noise is added to the gravity anomalies of the survey line as the real-time measurement trajectory. A matching algorithm is used for matching, and the matching rate of each simulation is calculated. The matching rate is the proportion of valid matching points in the total sampling points. Then, the average matching rate of the i-th heading survey line within the local area is determined.

[0032] Set a matching rate threshold λ. If the average matching rate of the heading is greater than the matching rate threshold, then the heading is the appropriate heading for the local area. The ratio of all appropriate headings in the local area to all headings is the gravity-adapted heading ratio of the local area.

[0033] A better approach is to use a relevant extreme value matching algorithm for matching.

[0034] Preferably, in step 4, the neural network is a BP neural network; the BP neural network has a three-layer structure, namely an input layer, a hidden layer, and an output layer; wherein, the number of neurons in the input layer is the number of gravity field feature parameters; the hidden layer is a fully connected layer, and the activation function is a linear rectified function; the output layer has 1 neuron, the activation function is a linear function, and the output is the predicted gravity adaptation direction ratio; the loss function of the network is the mean squared error function, and the optimizer is a stochastic gradient descent optimizer.

[0035] Ideally, the thresholds are set to 30% and 70%, meaning that areas with a gravity adaptation direction ratio of less than 30% are non-adaptation areas, areas with a gravity adaptation direction ratio between 30% and 70% are oriented adaptation areas, and areas with a gravity adaptation direction ratio greater than 70% are omnidirectional adaptation areas.

[0036] Beneficial effects:

[0037] This invention first extracts local gravity field samples using an overlapping sliding window, extracting as many samples as possible while ensuring the difference between samples given the limited gravity reference map. Then, it introduces aspect dispersion into the gravity field characteristic parameters of the local samples to measure the dispersion of the local gravity field aspect distribution. Simultaneously, a neural network is constructed, and the gravity fit direction ratio is designed as the target parameter for neural network fitting, achieving a measure of gravity field direction adaptability. Then, supervised training is used to train the neural network, resulting in a fitting model of the mapping relationship between the gravity fit direction ratio and gravity characteristic parameters. This model directly reflects the relationship between gravity field distribution characteristics and gravity matching performance, enabling quantitative analysis of gravity field direction adaptability, ensuring the comprehensiveness of the selected gravity field fit area, and effectively improving the utilization rate of the gravity field background map. The trained neural network performs adaptation analysis on the background gravity field map to be analyzed, obtains the gravity adaptation direction ratio of each local region, and then, combined with the set threshold, divides the adaptation area into three categories: omnidirectional adaptation area, directional adaptation area, and non-adaptation area, thus making up for the lack of traditional methods in analyzing the directionality of gravity field distribution. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the overall process of the method proposed in this invention.

[0039] Figure 2 This is a schematic diagram illustrating the method for dividing a local region of a gravitational field. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0041] This invention provides a gravity adaptability analysis method based on neural network fitting. By constructing and training a neural network with gravity field characteristic parameters such as slope aspect dispersion as input and gravity adaptability direction ratio as output, the relationship between the characteristic parameters and the gravity adaptability direction ratio is fitted to obtain the adaptability analysis neural network. This enables the orientation adaptability analysis of the gravity field background map to be analyzed, and the local region can be divided into three categories: non-adaptable region, directional adaptable region, and omnidirectional adaptable region.

[0042] This embodiment uses a back propagation (BP) neural network as an example, and the method flow is as follows: Figure 1 As shown, the specific steps include the following:

[0043] Step 1: Divide the gravity field baseline map to be trained into several local gravity field regions.

[0044] First, samples are extracted from the reference gravity field map to be trained, and the size of the local gravity field region is determined to be an m×n grid, where the values ​​of m and n are determined based on the minimum range of the required adaptation area. For example... Figure 2 As shown, a sliding window is used to traverse the reference gravity field map to be trained from left to right and from top to bottom to obtain local gravity field samples. The horizontal sliding length is m / 2 and the vertical sliding length is n / 2.

[0045] Step 2: Extract the gravity field feature parameters of the local gravity field samples and normalize them to form sample feature vectors.

[0046] The gravity field characteristic parameters include gravity field distribution characteristic parameters and direction characteristic parameters. In addition to conventional parameters such as standard deviation, information entropy, longitude roughness, latitudinal roughness, longitude correlation coefficient, latitudinal correlation coefficient, and directional gradient, the aspect dispersion characteristic parameter is also introduced to measure the degree of dispersion of the gravity field aspect distribution in a local area. The aspect dispersion is calculated by dividing the length of the sum of the aspect unit vectors at each point within the local area by the number of vectors.

[0047] The method for calculating the aspect dispersion of a local region of a gravity field with an m×n grid size is as follows:

[0048] First, calculate the slope aspect A of each grid point (i,j) in the local gravitational field region. ij :

[0049] A ij =arctan(f y / f x )-f x / |f x |×f y / |f y |×90°+f y / |f y |×90°+180° (1)

[0050] f x =[g i-1,j+1 -g i-1,j-1 +2(g i,j+1 -g i,j-1 )+g i+1,j+1 -g i+1,j-1 ] / 8 (2)

[0051] f y =[g i+1,j+1 -g i-1,j+1 +2(g i+1,j -g i-1,j )+g i+1,j-1 -g i-1,j-1 ] / 8 (3)

[0052] Where g i,j Let be the gravity anomaly value at point (i,j).

[0053] The method for calculating the slope aspect dispersion R of the local region of the gravity field is as follows:

[0054]

[0055] in

[0056]

[0057]

[0058] The larger the slope aspect dispersion R value of a local region of gravity field, the weaker the dispersion of the slope aspect distribution of the gravity field in that local region, and the stronger the directionality of the gravity field distribution in that region.

[0059] To eliminate the influence of dimensions, the mean-variance normalization method is used to normalize each feature parameter. The expression for mean-variance normalization is as follows:

[0060]

[0061] Where, x scale Let be the normalized eigenvalue, x be the original eigenvalue, μ be the mean of the eigenvalue, and s be the standard deviation of the eigenvalue.

[0062] Step 3: Calculate the gravity fit direction ratio of the local region samples in the gravity field; the gravity fit direction ratio is the ratio of the number of fit directions in the local region to the total number of directions. Using the gravity fit direction ratio of the local region samples in the gravity field as the expected output of the samples, the directional fit of the gravity field is measured, and the fit region is further divided into three categories: omnidirectional fit region, directional fit region, and non-fit region, making up for the lack of traditional methods in analyzing the directionality of gravity field distribution.

[0063] This embodiment uses a gravity matching survey line simulation experiment in a local region of the gravity field to calculate the gravity adaptation direction ratio in that region. The specific implementation process is as follows:

[0064] First, n is uniformly distributed within the range of north by east [0°, 180°) at intervals of Δd. d For each heading, M survey lines with a length of l sampling points are randomly generated within a local area as the real trajectory. N gravity matching simulations are performed on each survey line. In each simulation, Gaussian white noise with a mean of 0 and a variance equal to the variance of the gravimeter measurement noise is added to the gravity anomaly values ​​of the survey line as the real-time measurement trajectory. A matching algorithm is used for matching; in this embodiment, the correlation extreme value matching algorithm is used. The matching rate of each simulation is calculated. Assuming that there are l' valid matching points in the nth matching result of the m-th survey line, the matching rate is calculated as follows:

[0065]

[0066] Further calculate the average matching rate (matchrate) of the i-th heading survey line within this local area. i

[0067]

[0068] Set a matching rate threshold λ, matchrate i If the value is greater than λ, it indicates that the local region is a suitable region in the i-th heading. In this embodiment, λ is set to 70%. Finally, the gravity adaptation direction ratio mdr of the local region is calculated.

[0069]

[0070] in

[0071]

[0072] The gravity adaptation direction ratio ranges from [0% to 100%], describing the proportion of the adapted heading in a local area to all headings. The larger the gravity adaptation direction ratio value, the more directions the local area can adapt to, the better the adaptability, and the weaker the directional limitation.

[0073] Step 4: Build a neural network and train it using the training set data formed in Step 3 to obtain the adaptability analysis neural network.

[0074] In this embodiment, the neural network is illustrated using a backpropagation (BP) neural network as an example. The BP neural network consists of three layers: an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is equal to the number of gravitational field feature parameters; the hidden layer is a fully connected layer with a user-defined number of neurons, and the activation function is a rectified linear unit (ReLU); the output layer has one neuron, uses a linear activation function, and outputs the predicted gravity adaptation direction ratio. The network's loss function is the mean squared error (MSE) function, and the optimizer is a stochastic gradient descent (SGD) optimizer.

[0075] The BP neural network is trained using the gravity feature parameters of the training set samples as input and the gravity adaptation direction ratio as the desired output. The optimal network weights are then obtained, and this neural network becomes the fitting model for the mapping relationship between the gravity adaptation direction ratio and the gravity feature parameters. The trained BP neural network is saved as the adaptation analysis neural network.

[0076] This invention employs supervised training to train the adaptability analysis network. A training set is established by providing sample expected outputs through gravity matching lateral line simulation experiments. The trained neural network is a fitting model of the mapping relationship between the gravity adaptability direction ratio and gravity characteristic parameters. This model directly reflects the relationship between the gravity field distribution characteristics and gravity matching performance, enabling quantitative analysis of gravity field direction adaptability, ensuring the comprehensiveness of the selected gravity field adaptability region, and effectively improving the utilization rate of the gravity field background map.

[0077] Step 5: Use the adaptive analysis neural network trained in Step 4 to perform adaptive analysis and adaptive region division on the gravity field background image to be analyzed.

[0078] The method for performing adaptive analysis on the gravity field background image to be analyzed using a trained adaptive analysis neural network is as follows:

[0079] First, based on the m×n grid size of the local gravity field region determined in step 1, the background gravity field image to be analyzed is divided into non-overlapping local regions from left to right and top to bottom. The gravity field characteristic parameters of each local region are calculated and normalized to form a feature vector, as described in step 2. Then, the feature vectors of the local regions are used as input to the adaptive analysis neural network trained in step 4. The network output is the gravity adaptation direction ratio of the corresponding local region. Finally, thresholds can be set to divide the local gravity field region into omnidirectional adaptive regions, directed adaptive regions, and non-adaptive regions. In this example, the thresholds are set to 30% and 70%, meaning that regions with a gravity adaptation direction ratio less than 30% are non-adaptive regions, regions with a ratio between 30% and 70% are directed adaptive regions, and regions with a ratio greater than 70% are omnidirectional adaptive regions.

[0080] 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 gravity adaptability analysis method based on neural network fitting, characterized in that, include: Step 1: Determine the template for a local region of the gravity field. The size of the template is determined based on the minimum range of the required adaptation area. A sliding window is used to traverse the reference gravity field map to be trained, thereby obtaining samples of local gravity field regions. Step 2: Extract the gravitational field feature parameters of the local gravitational field samples and normalize them; The gravity field characteristic parameters include aspect dispersion, which is the sum vector length of the unit aspect vectors at each point in the local region sample divided by the number of vectors. The method for calculating the slope aspect dispersion of a local gravity field sample with an m×n grid size is as follows: First, calculate the value of each grid point in the local region of the gravitational field. slope : (1) (2) (3) in, For point Gravity anomaly at the location; The slope dispersion of the local region of the gravitational field for (4) in (5) (6) Step 3: Calculate the gravity adaptation direction ratio of the local region sample in the gravity field; the gravity adaptation direction ratio is the ratio of the number of adaptation directions in the local region to the total number of directions. Step 4: Construct a neural network. Take the normalized gravity field feature parameters of the local gravity field samples from Step 2 as input and the gravity adaptation direction ratio of the local gravity field samples from Step 3 as output. Train the neural network to obtain a trained neural network. Step 5: Use the adaptive analysis neural network trained in Step 4 to perform adaptive analysis on the gravity field background image to be analyzed, and obtain the gravity adaptation direction ratio of each local region of the gravity field background image to be analyzed; based on the obtained gravity adaptation direction ratio and the set threshold, divide the adaptation area.

2. The method as described in claim 1, characterized in that, In step 1, the size of the local region template of the gravity field is an m×n grid, the horizontal sliding length of the sliding window is m / 2, and the vertical sliding length is n / 2.

3. The method as described in claim 1, characterized in that, In step 2, the gravity field characteristic parameters also include one or more of the following: standard deviation, information entropy, longitude roughness, latitude roughness, longitude correlation coefficient, latitude correlation coefficient, and directional gradient.

4. The method as described in claim 1, characterized in that, In step 2, the mean-variance normalization method is used to normalize each feature parameter.

5. The method as described in claim 1, characterized in that, In step 3, the gravity matching direction ratio of the local gravity field region is calculated through a gravity matching survey line simulation experiment. Specifically: First, in the north-northeast Within the range of For uniformly distributed intervals One course; For each heading, generate randomly within a local area. M The length of the strip is l The survey line at each sampling point is used as the true trajectory; For each measurement line, N gravity matching simulations are performed. In each matching simulation, Gaussian white noise with a mean of 0 and a variance equal to the variance of the gravimeter measurement noise is added to the gravity anomaly value of the measurement line as a real-time measurement trajectory. A matching algorithm is used for matching, and the matching rate of each matching simulation is calculated. The matching rate is the proportion of valid matching points in the total sampling points. Then, the average matching rate of the i-th heading survey line in the local area is calculated. Set a matching rate threshold If the average matching rate of the heading is greater than the matching rate threshold, then the route is the heading that is suitable for the local area; the proportion of all suitable headings in the local area to all headings is the gravity-adapted heading ratio of the local area.

6. The method as described in claim 5, characterized in that, The relevant extreme value matching algorithm is used for matching.

7. The method as described in claim 1, characterized in that, In step 4, a backpropagation (BP) neural network is used. The BP neural network has a three-layer structure: an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is equal to the number of gravity field feature parameters. The hidden layer is a fully connected layer with a linear rectified function as the activation function. The output layer has one neuron, a linear activation function, and outputs the predicted gravity adaptation direction ratio. The network loss function is the mean squared error function, and the optimizer is a stochastic gradient descent optimizer.

8. The method as described in claim 1, characterized in that, The thresholds are set at 30% and 70%. Areas with a gravity adaptation direction ratio of less than 30% are considered non-adaptation areas, areas with a gravity adaptation direction ratio between 30% and 70% are considered oriented adaptation areas, and areas with a gravity adaptation direction ratio greater than 70% are considered omnidirectional adaptation areas.

Images