Underwater gravity navigation integrity assessment method based on deep learning and time sequence modeling

Abstract

The invention discloses an underwater gravity navigation integrity evaluation method based on deep learning and time sequence modeling, and the method comprises the steps: firstly, achieving the matching positioning of an inertial navigation position and actually measured gravity data through the combination of a TERCOM algorithm and MSD correlation, and eliminating gross error points through confidence evaluation; for a data breakpoint area, B spline interpolation is adopted to carry out preliminary compensation. Furthermore, a DNN-LSTM cascade model is constructed, inertial navigation position increment and gravity data increment are input into a deep neural network, modeling is performed in combination with time sequence characteristics of a long and short-term memory network, and fine dynamic compensation of a gravity matching position is realized. According to the method, the continuity and precision of navigation position output and the system robustness are effectively improved, and the method is suitable for high-reliability autonomous navigation in a complex underwater environment.

Description

Technical Field

[0001] The present invention relates to the field of surveying and mapping science and technology, and in particular to an underwater gravity navigation integrity assessment method based on deep learning and time series modeling. Background Art

[0002] With the increasing number of tasks such as ocean exploration, deep-sea resource development, and seabed operations, the demand for autonomous navigation and positioning accuracy and system continuity for underwater vehicles (AUVs / ROVs) has increased significantly. However, traditional satellite navigation systems (such as GPS and BeiDou) cannot effectively transmit signals in underwater environments, resulting in a high reliance on inertial navigation systems (INS) for long-range underwater positioning. INS is widely used for its high update rate and excellent positioning performance in a short period of time. However, due to the accumulation of small sensor drift and integral errors, its navigation error can quickly diverge over time, affecting the positioning accuracy of the vehicle during long-term or large-scale operations.

[0003] To address the problem of INS error accumulation, geophysical aided navigation (GAN) has become a mainstream solution, with gravity matching navigation (GMN) technology being one of its most representative implementations. GMN uses the spatial alignment of measured ambient gravity anomalies with a high-resolution prior gravity field map to provide a periodic error correction reference for the INS. Its core advantage lies in the uniqueness and repeatability of the Earth's gravity field over a wide range. Gravity sensors can collect data unimpeded by physical obstructions such as seawater and terrain, enabling full-time, full-ocean passive navigation correction. The development of underwater GMN has spanned decades, evolving from initial correlation matching methods such as the Terrain Contour Matching (TERCOM) algorithm and the Iterative Contour Nearest Neighbor Point (ICCP) algorithm to advanced algorithms such as the particle filter (PF) that fuses filters and multi-source observations, and the extended / unscented Kalman filter (EKF / UKF). Furthermore, in recent years, new heuristic intelligent methods such as neural networks and swarm intelligence optimization have been explored. The underwater GMN technology ecosystem continues to expand and improve.

[0004] Chinese Patent Publication No. CN118376243A discloses an underwater gravity matching navigation method based on gravity field adaptation region preprocessing. This method extracts and optimizes adaptation region features from a priori gravity fields before navigation, screening out regions with rich gravity variations and optimal matching results, thereby improving the matching efficiency and initial positioning accuracy of the TERCOM algorithm. Chinese Patent Publication No. CN119322979A discloses a gravity matching navigation method based on dynamic segmentation of the adaptation region. This method dynamically adjusts the pre-divided adaptation region of the gravity field by combining the initial position of the INS with real-time changes in gravity data to adapt to the uneven distribution of the gravity field in the ocean during navigation, thereby improving the matching success rate. Chinese Patent Publication No. CN119223275A discloses an underwater gravity matching search method based on salp swarm algorithm optimization. This method uses a salp swarm intelligent optimization strategy to adaptively adjust the matching blocks and search step size during TERCOM or ICCP searches, achieving faster and more global correlation matching searches. Chinese Patent Publication No. CN119737947A discloses a gravity matching navigation method optimized by an adaptive variable-scale particle swarm algorithm. This method improves the convergence speed of the matching search and the ability to find the global optimal solution by dynamically adjusting the particle distribution and velocity update strategy within a multi-scale search domain using a particle swarm algorithm. Chinese Patent Publication No. CN115855061A discloses an integrated navigation method that integrates gravity field features with an improved particle filter. This method enhances the robustness and anti-divergence capability of the integrated navigation system in complex ocean environments by integrating high-resolution gravity field features and adaptive weight adjustment within a traditional particle filter framework. Chinese Patent Publication No. CN118548879A discloses a vector-corrected iterative contour matching (ICCP) method. This method optimizes the matching path by geometrically correcting the vector direction and step size of the nearest contour point in the ICCP algorithm, thereby improving positioning accuracy under conditions of small initial error. Chinese patent publication number CN116182898A discloses an underwater gravity matching method based on a cross-line adaptive domain. By incorporating a geometric adjustment strategy for the cross-line adaptive matching domain into the ICCP or TERCOM algorithm, this method achieves real-time optimization of the matching search area, reducing the search computational complexity and improving matching efficiency.

[0005] The above patents reflect the multiple rounds of innovation and iteration of current underwater gravity matching navigation technology, but still have the following key defects: insufficient model adaptability and feature modeling capabilities, traditional correlation matching algorithms or filtering algorithms are difficult to fully model complex ocean environments and highly nonlinear gravity distributions, matching results are sensitive to initial conditions, and are prone to gross errors and outliers in the face of sea area changes, instrument noise, abnormal sampling, etc.

[0006] It is difficult to guarantee the output data breakpoints and navigation continuity. No matter which matching algorithm is used, it is inevitable that during the navigation process, factors such as abnormally smooth gravity, local lack of sampling or interference noise will cause the confidence of some matching results to drop significantly or even data to be interrupted, affecting navigation continuity and engineering application safety.

[0007] There is a lack of real-time dynamic compensation and intelligent integrity assessment methods. Current methods mostly focus on improving matching efficiency and single positioning accuracy. There are few closed-loop integrity algorithms that continuously monitor the navigation process, intelligently identify matching result anomalies, and dynamically compensate and correct them. As a result, it is impossible to achieve "uninterrupted" and high-reliability guarantees for position output in practical applications.

[0008] The advantages of deep learning have not been fully utilized. Although some studies have attempted to introduce neural networks or intelligent optimization algorithms, in the field of gravity matching navigation, it still mainly remains at the level of offline training or single-point feature mapping. There is a lack of end-to-end deep model design and real-time dynamic prediction compensation strategies for spatial nonlinear relationships, long-term drift of inertial navigation, and multi-source data fusion. Summary of the Invention

[0009] In response to the defects of the TERCOM algorithm in the existing technology that it is prone to gross errors and breakpoints and difficult to achieve navigation continuity and high-precision compensation, the present invention proposes an underwater gravity navigation integrity assessment method based on deep learning and time series modeling. By performing confidence assessment on the TERCOM matching position and eliminating low-confidence gross error points, using B-spline interpolation to perform preliminary compensation on the breakpoint area, and constructing a DNN-LSTM network to extract and predict the spatiotemporal features of the inertial navigation position increment and the measured gravity increment, real-time monitoring and dynamic correction of the navigation output position are achieved, thereby obtaining uninterrupted high-precision underwater gravity matching positioning results. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling described in the present invention specifically includes the following steps:

[0010] S1: Preliminary calculation of gravity matching position: Using the position data output by the inertial navigation system (INS) and the measured gravity data as input, a real-time gravity map is constructed and gridded. The gravity matching area is delineated based on the position data output by the INS and the position error range. The best matching position is determined using the mean square deviation (MSD) algorithm in the terrain matching TERCOM algorithm, and preliminary gravity matching position data is output.

[0011] S2: Gravity matching position confidence assessment and gross error elimination: Taking the preliminary gravity matching position data as input, a confidence assessment method is used to identify and eliminate gross error position points with low confidence, and output gravity matching position data containing data breakpoints;

[0012] S3: Preliminary compensation processing of data breakpoints: using the gravity matching position data containing data breakpoints outputted in step S2 as input, preliminary compensation is performed on the data breakpoints by using the B-spline interpolation method, and the gravity matching position data after preliminary compensation is outputted;

[0013] S4: Build a DNN-LSTM deep learning integrity model: Based on the gravity matching position data after preliminary compensation, build a DNN-LSTM-based deep learning model to perform fine compensation prediction. The specific steps include:

[0014] S4-1: Model input and output parameter design: Using the inertial navigation system output position data, measured gravity data, and gravity matching position data after preliminary compensation as the original data, the increments between adjacent points are calculated to obtain the inertial navigation position increment, measured gravity data increment, and gravity matching position increment;

[0015] S4-2: DNN network spatial feature extraction: Using the inertial navigation position increment and the measured gravity data increment as the input features of the DNN network, the gravity data is nonlinearly mapped and spatial features are extracted through a multi-layer neural network, and the spatial feature vector is output. The calculation formula for the DNN extracted features is as follows:

[0016]

[0017] Among them, x represents the input data, w i is the weight coefficient, which is an important parameter connecting input data and neurons. i Constitute the weight vector w; b is the bias function, which can adjust the activation threshold of the neuron; z is the net input of the neuron, which is the result of weighted summation of the input data and adding the bias; n represents the number of input features, and the specific feature L is calculated as follows:

[0018]

[0019] Among them, y represents the output data, y i is the model prediction value of the i-th sample, is the true value of the i-th sample, and L is calculated by averaging the sum of the squares of their differences. m is the number of training samples.

[0020] S4-3: LSTM network temporal feature modeling: The spatial feature vector is used as the input of the LSTM network. Through the gating mechanism of input gate, forget gate and output gate, the temporal feature modeling of the inertial navigation data is performed, and the output is the implicit state vector containing the spatial-temporal fusion features.

[0021] S4-4: DNN-LSTM integrity model training: Using high-confidence gravity matching position increments as supervisory output data, the implicit state vector and supervisory output data are used for model training to obtain the trained DNN-LSTM deep learning integrity monitoring model;

[0022] S5: Gravity matching position fine compensation prediction: Using the inertial navigation position increment and measured gravity data increment at the data breakpoint corresponding to the preliminary compensated gravity matching position data output in step S3 as input, the DNN-LSTM deep learning integrity monitoring model trained in step S4 is used to perform fine prediction compensation, and output high-precision gravity matching position data after fine compensation;

[0023] S6: Navigation position data output: Use the high-precision gravity matching position data after fine compensation as the final navigation output position to complete the integrity monitoring and accurate output of the underwater gravity matching navigation position.

[0024] As a preferred technical solution of the present invention, in step S1, the mean square deviation (MSD) algorithm is used to calculate the correlation between the real-time gravity data map and the reference gravity data sequence. The specific calculation formula is:

[0025]

[0026] Where H represents the height of the measured sequence, W represents the width of the measured sequence, P is the gravity gradient measured sequence, B is the gravity gradient reference sequence, (x, y) represents the starting position of P sliding in B, i and j are index variables for double summation, and i is used to adjust the height direction of the measured sequence.

[0027] As a technical preferred solution of the present invention, the confidence assessment method in step S2 uses a preset threshold to determine the MSD value corresponding to each point in the matching position data. When the MSD value exceeds the threshold, it is determined to be a gross error position point and is eliminated to generate a data breakpoint area.

[0028] As a technical preferred solution of the present invention, the B-spline interpolation preliminary compensation method in step S3 is specifically to perform B-spline interpolation in the data breakpoint area using adjacent high-confidence matching position data points, and the compensated data is used as the initial input data for subsequent fine compensation.

[0029] As a technical preferred solution of the present invention, the forget gate described in step S4-3 is used to selectively filter redundant information in the inertial navigation historical data; the input gate is used to control the real-time input inertial navigation position increment and the measured gravity data increment information; the output gate is used to fuse the processing results of the forget gate and the input gate to generate an implicit state vector that simultaneously contains the navigation data temporal characteristics and spatial gravity matching information.

[0030] As a preferred technical solution of the present invention, the calculation method of the LSTM information flow process described in step S4-3 is:

[0031] i t =σ(W i [h t-1 ,x t ]+b i ) (4)

[0032] f t =σ(W f [h t-1 ,x t ]+b f ) (5)

[0033] o t =σ(W o [h t-1 ,x t ]+b o ) (6)

[0034]

[0035] h t =o t tanh(C t ) (9)

[0036] Where t represents the time step index; t is the input vector at the current moment; h t-1 and h t are the hidden state vectors of the previous moment and the current moment respectively; C t-1 and C t are the cell state vectors at the previous moment and the current moment respectively; i t ,f t ,o t They are the values ​​of the input gate, forget gate, and output gate, which control the flow of information; is the candidate cell state; W i 、W f 、W o 、W C is the weight matrix corresponding to the gate and candidate state; b i 、b f 、b o 、b C is the corresponding bias vector; σ is the Sigmoid activation function; tanh is the hyperbolic tangent activation function; ⊙ represents element-by-element multiplication; [h t-1 ,x t ] indicates vector concatenation.

[0037] As a preferred technical solution of the present invention, the preset network structure of the DNN-LSTM integrity model described in step S4-4 includes, from its input end to its output end, an input layer, a DNN feature extraction layer, a multi-layer LSTM network layer, a fully connected layer, and an output layer. It includes the following structural features:

[0038] The DNN feature extraction layer includes multiple fully connected neural network sublayers connected in series, each sublayer is composed of a linear mapping module and a nonlinear activation module;

[0039] The multi-layer LSTM network layer is composed of three layers of long short-term memory units connected in series. Each layer of LSTM is a gated recurrent unit structure, including an input gate, a forget gate, an output gate and a unit state update module; wherein the three layers of long short-term memory units specifically include the following three layers: LSTM1, LSTM2, and LSTM3;

[0040] The fully connected layer is used to map the high-order temporal representation of the multi-layer LSTM output to the output space;

[0041] The output layer is used to generate the final output result. The DNN-LSTM integrity model further includes the following structural features:

[0042] The output dimension of each fully connected neural network sublayer in the DNN feature extraction layer can be the same or reduced layer by layer, and a ReLU function or a tanh function is used as an activation function to enhance the nonlinear expression ability of the feature;

[0043] In the multi-layer LSTM network layer, the hidden state dimensions of each LSTM layer are the same, supporting state transfer across time steps, and the multi-layer structure can abstract and refine time series information layer by layer;

[0044] The fully connected layer is a linear transformation layer that uses Softmax or linear activation to output classification probabilities or regression values.

[0045] Compared with the related prior art, the beneficial effects of the present invention are:

[0046] By performing confidence assessment on TERCOM matching results, low-confidence gross errors and outliers can be identified and eliminated online, avoiding the problem of positioning breakpoints or large errors that are prone to occur in traditional correlation matching algorithms.

[0047] After removing anomalies, B-spline interpolation is first used to preliminarily fill the breakpoints. Then, the trained DNN-LSTM model is used to perform fine prediction and compensation of inertial navigation and gravity data, achieving uninterrupted and continuous output of the compensated navigation position.

[0048] The DNN automatically mines the multi-scale spatial features of the gravity reference map, while the LSTM captures the temporal dynamics of long-sequence drift of the inertial navigation system. The cascaded joint modeling of the two significantly enhances the ability to express complex nonlinear relationships and effectively improves the accuracy of gravity matching positioning.

[0049] The inner layer dynamically removes outliers through confidence gating, and the outer layer uses the residual chi-square statistical test to evaluate the matching accuracy and trigger the compensation process, forming a closed-loop integrity monitoring mechanism, which greatly improves the navigation system's tolerance to environmental noise and data anomalies. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A flow chart of the underwater gravity navigation integrity assessment method based on deep learning and time series modeling provided by the present invention;

[0051] Figure 2 Provides a DNN-LSTM flow chart of an embodiment of the present invention;

[0052] Figure 3 This is a simulation experiment track diagram of an embodiment provided by the present invention;

[0053] Figure 4 is a line graph of the error value of the TRECOM algorithm according to an embodiment of the present invention;

[0054] Figure 5 This is a comparison chart of the compensation effects of the integrity monitoring algorithm according to the embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention is further described below with reference to the accompanying drawings and examples. However, the present invention can be implemented in many different ways and should not be construed as limited to the illustrated embodiments; rather, these embodiments provide those skilled in the art with implementation methods that meet applicable legal requirements.

[0056] Example 1: Figure 1 As shown, the present invention provides a method for underwater gravity navigation integrity assessment based on deep learning and time series modeling. This embodiment is based on the long-range navigation mission of an underwater vehicle in an actual ocean environment. The specific implementation steps are as follows:

[0057] S1: Preliminary calculation of gravity matching position. First, during the normal navigation of the vehicle, the inertial navigation system INS outputs position data in real time, and simultaneously collects measured gravity data along the track line, using the above two sets of data as input. Through the gridding method, a real-time gravity map centered on the INS output position data is constructed, and the gravity matching area is delineated according to the position error range estimated by the INS position data. The terrain contour matching algorithm TERCOM is used for position matching, and the mean square error (MSD) algorithm is used for correlation calculation. The specific calculation formula is:

[0058]

[0059] Where H represents the height of the measured sequence, W represents the width of the measured sequence, P is the measured gravity gradient sequence, B is the reference gravity gradient sequence, x and y represent the starting position coordinates of P sliding in B; i and j are index variables for double summation, i is used to traverse the height direction of the measured sequence (ranging from 0 to (H-1), and j is used to traverse the width direction of the measured sequence (ranging from 0 to (W-1). Then, the preliminary gravity matching position data is found and output, that is, the best matching position point with the smallest MSD value is found;

[0060] S2: Gravity matching position confidence assessment and gross error elimination: Using the preliminary gravity matching position data output in step S1 as input, analyze the MSD value corresponding to each matching position based on a pre-set confidence threshold. When the MSD of a position point exceeds the threshold, it indicates that the matching quality of the point is low, and it is defined as a gross error position point and eliminated. After the gross error elimination process, the output data contains several data breakpoint areas, that is, discontinuous position areas;

[0061] S3: Preliminary Data Breakpoint Compensation Processing: Using the gravity matching position data containing the data breakpoint output from step S2 as input, the B-spline interpolation method is used, with the adjacent high-confidence matching points on both sides of the data breakpoint as control points for interpolation, thereby performing preliminary compensation for the data breakpoint position. After interpolation is completed, the preliminarily compensated gravity matching position data is output for use in the next stage of deep learning fine prediction compensation.

[0062] S4: Construct a DNN-LSTM deep learning integrity model: Based on the gravity matching position data after the initial compensation in step S3, a DNN-LSTM-based deep learning model is constructed. The specific implementation method is as follows:

[0063] S4-1: Model input and output parameter design: The position data output by the inertial navigation, the measured gravity data, and the gravity matching position data after preliminary compensation are used as raw data. The increments between adjacent data points are calculated to form the inertial navigation position increment, the measured gravity data increment, and the gravity matching position increment, which are used as the input and output parameters of the DNN-LSTM model.

[0064] S4-2: DNN network spatial feature extraction: Using the inertial navigation position increment and measured gravity data increment obtained in step S4-1 as input, a multi-layer deep neural network (DNN) is constructed to implement nonlinear mapping of the input data and multi-scale spatial feature extraction, outputting a spatial feature vector. The network calculation method is shown in formulas (1) and (2);

[0065]

[0066] Where x is the input data; w i is the weight coefficient, all w i The weight vector w is formed; b is the bias function, which can adjust the activation threshold of the neuron; z is the net input of the neuron, which is the result of weighted summation of the input data and adding the bias; n represents the number of input features. The specific feature L is calculated as follows:

[0067]

[0068] Among them, y represents the output data, y i is the model prediction value of the i-th sample, is the true value of the i-th sample, and L is calculated by averaging the sum of the squares of their differences; m is the number of training samples.

[0069] S4-3: LSTM network temporal feature modeling: The spatial feature vector output from step S4-2 is used as the input to the LSTM network. The long-term temporal feature modeling of the inertial navigation data is implemented through a multi-layer LSTM structure (a total of 3 layers: LSTM1, LSTM2, and LSTM3). The input gate, forget gate, and output gate are set in the LSTM unit to selectively filter and fuse the current data and historical data respectively. The specific gate control formulas are shown in the following formulas (4) to (9). The final output is the implicit state vector containing the spatial-temporal fusion features.

[0070] i t =σ(W i [h t-1 ,x t ]+b i ) (4)

[0071] f t =σ(W f [ht-1 ,x t ]+b f ) (5)

[0072] o t =σ(W o [h t-1 ,x t ]+b o ) (6)

[0073]

[0074]

[0075] h t =o t tanh(C t ) (9)

[0076] Where t represents the time step index; t is the input vector at the current moment; h t-1 and h t are the hidden state vectors of the previous moment and the current moment respectively; C t-1 and C t are the cell state vectors at the previous moment and the current moment respectively; i t ,f t ,o t They are the values ​​of the input gate, forget gate, and output gate, which control the flow of information; is the candidate cell state; W i 、W f 、W o 、W C is the weight matrix corresponding to the gate and candidate state; b i 、b f 、b o 、b C is the corresponding bias vector; σ is the Sigmoid activation function; tanh is the hyperbolic tangent activation function; ⊙ represents element-by-element multiplication; [h t-1 ,x t ] indicates vector concatenation.

[0077] S4-4: DNN-LSTM integrity model training: Using the spatial-temporal fusion feature implicit state vector output from step S4-3 as the feature input and the high-confidence gravity matching position increment as the supervision output, the model is trained using the backpropagation algorithm and the mean square error function (MSE) to obtain the trained DNN-LSTM deep learning integrity monitoring model.

[0078] like Figure 2As shown in the DNN-LSTM flow chart of the embodiment provided by the present invention, the specific network topology is: input layer → DNN feature extraction layer (including multiple layers of fully connected neural network sublayers, each layer using ReLU activation function) → multiple layers of LSTM layers (LSTM1, LSTM2, LSTM3, with hidden layer dimensions uniformly set to 128) → fully connected mapping layer → output layer;

[0079] The trained model can achieve spatiotemporal dynamic coupling mapping of inertial navigation and gravity data, providing real-time prediction capabilities for fine compensation of gravity matching navigation;

[0080] S5: Prediction of fine compensation of gravity matching position. Using the inertial navigation position increment and measured gravity data increment at the corresponding data breakpoint in the preliminary compensated gravity matching position data output in step S3 as input, the DNN-LSTM integrity monitoring model trained in step S4 is imported for real-time prediction calculation, thereby achieving fine prediction compensation of the data breakpoint position and outputting high-precision gravity matching position data after fine compensation.

[0081] S6: Navigation position data output. Finally, the high-precision gravity matching position data after fine compensation in step S5 is used as the final navigation output position of the underwater vehicle, realizing real-time dynamic correction of INS drift error during long-range underwater navigation, integrity monitoring of navigation positioning results and continuous, high-precision output.

[0082] This embodiment achieves a significant improvement in the continuity of underwater navigation data output through a complete confidence elimination, multi-level interpolation and deep learning prediction compensation process. Compared with the traditional TERCOM matching algorithm, the navigation accuracy is improved by about 30%, and the positioning continuity reaches more than 99%, effectively improving the safety and reliability of long-range navigation of underwater vehicles.

[0083] Example 2: This example is based on Figure 3 Based on the simulation experiment track data shown, the complete implementation process and actual effect of the underwater gravity navigation integrity assessment method based on deep learning and time series modeling of the present invention are specifically demonstrated.

[0084] Figure 3 The gravity reference data for the experimental area shown is derived from the S&SV30.1 ocean gravity model, which is currently one of the most accurate in the world. Its spatial resolution is 1×1, and the data coverage range is -5°S45°N latitude and 95°E145°E longitude. The gravity anomaly in the area where the experimental track is located ranges from -352.5mGal to 565.5mGal, and the data accuracy is approximately 2-3mGal. The total length of the track is 300 matching points, which overall represents a relatively typical complex sea navigation scenario. The implementation process specifically includes the following steps:

[0085] First, using the inertial navigation position data and measured gravity data as input, the mean square error (MSD) correlation algorithm is used to search and match in the gravity reference map to calculate the matching position of each track point. The position with the minimum MSD function value is output as the TERCOM best matching position. The matching position obtained by the TERCOM algorithm is compared with the real GPS position to calculate the error, and the result is Figure 4 The error value line graph of the TRECOM algorithm is shown in Figure 2. Figure 4 As shown in the figure, the TERCOM algorithm keeps the error small (0.12 mGal) in most positions, but there is a significant anomaly in the position segment 100200, with the maximum error reaching 5.3956 mGal.

[0086] For the obvious error areas mentioned above, we used the Hampel filter to perform confidence assessment analysis and determined that the errors between points 100 and 200 significantly exceeded the normal confidence interval, indicating that there were gross errors in this section. Based on this result, the abnormal matching points in this section were removed to form a data breakpoint area.

[0087] For the data breakpoint area formed by eliminating gross error points, the adaptive B-spline interpolation function is used to perform preliminary interpolation compensation for the missing position to maintain the initial continuity of the navigation position data and provide initial data support for subsequent fine compensation prediction.

[0088] The DNN-LSTM integrity monitoring model is constructed and trained: First, the sequential increments between adjacent points of the inertial navigation position, measured gravity data, and initially compensated gravity matching position are calculated, forming the inertial navigation position increment sequence, gravity data increment sequence, and matching position increment sequence as input and output parameters, respectively. Then, data from areas of the track with high confidence (i.e., low error) are used as training samples. The inertial navigation position increment sequence and gravity data increment sequence are used as model input features, and the matching position increment sequence is used as the model output label. These are fed into the DNN-LSTM network for training. During training, the DNN network automatically extracts the spatial features of the gravity data through multi-layer convolution and fully connected neuron structure, while the LSTM network is responsible for temporal modeling of the long-term drift characteristics of the inertial navigation increment sequence. The spatial features extracted by the DNN are then integrated to achieve joint modeling of spatial and temporal features, resulting in a nonlinear mapping relationship between gravity data, inertial navigation error, and matching position.

[0089] The trained DNN-LSTM model is applied to the data breakpoint area that has undergone preliminary interpolation compensation in step S3. The inertial navigation position increment sequence and gravity data increment sequence in this area are used as model inputs. The compensated gravity matching position increment sequence is precisely predicted, and the corrected gravity matching position is further calculated.

[0090] The fine compensation results obtained by the DNN-LSTM integrity monitoring model proposed in this embodiment are as follows: Figure 5 As shown in the figure, compared with the original output results of the TERCOM algorithm, it can be clearly seen that the error in the position segment 100 to 200 is greatly reduced, the error peak is significantly reduced, and the continuity of the position output is significantly improved.

[0091] Table 1: Performance comparison of TERCOM algorithm and integrity assessment model

[0092] Maximum error Minimum error variance average value TERCOM 5.3956 0.1161 1.6052 1.8096 DNN-LSTM 2.4203 0.1161 0.5388 1.1570

[0093] like Figure 5 As shown in Table 1, the DNN-LSTM model demonstrates significant advantages over the traditional TERCOM algorithm in navigation position integrity monitoring and compensation accuracy, reducing the maximum error by approximately 55.1%, the error variance by approximately 66.5%, and the average error by approximately 36.0%. This result demonstrates that the dual compensation strategy of confidence assessment and deep learning proposed in this paper can significantly improve the reliability and accuracy of gravity matching navigation results, making it suitable for long-range underwater navigation and positioning applications in complex ocean environments.

[0094] The specific demonstration of the above implementation process fully reflects the technical concept and implementation method of the present invention, proving that the method of the present invention has high practical value and significant technological progress in the field of gravity matching navigation.

[0095] The above embodiments merely illustrate the implementation methods of the present invention. Although the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that a person skilled in the art may make various modifications and improvements without departing from the scope of the present invention, and such modifications and improvements are all within the scope of protection of the present invention.

Claims

1. An underwater gravity navigation integrity assessment method based on deep learning and time series modeling, characterized by: The specific steps include: S1: Preliminary calculation of gravity matching position: Using the position data output by the inertial navigation system (INS) and the measured gravity data as input, a real-time gravity map is constructed and gridded. The gravity matching area is delineated based on the position data output by the INS and the position error range. The best matching position is determined using the mean square deviation (MSD) algorithm in the terrain matching TERCOM algorithm, and preliminary gravity matching position data is output. S2: Gravity matching position confidence assessment and gross error elimination: Using the preliminary gravity matching position data output in step S1 as input, the confidence assessment method is used to identify and eliminate low-confidence gross error position points, and the gravity matching position data containing data breakpoints is output; S3: Preliminary compensation processing of data breakpoints: using the gravity matching position data containing data breakpoints outputted in step S2 as input, preliminary compensation is performed on the data breakpoints by using the B-spline interpolation method, and the gravity matching position data after preliminary compensation is outputted; S4: Build a DNN-LSTM deep learning integrity model: Based on the gravity matching position data after preliminary compensation, build a DNN-LSTM-based deep learning model to perform fine compensation prediction. The specific steps include: S4-1: Model input and output parameter design: Using the inertial navigation system output position data, measured gravity data, and gravity matching position data after preliminary compensation as the original data, the increments between adjacent points are calculated to obtain the inertial navigation position increment, measured gravity data increment, and gravity matching position increment; S4-2: DNN network spatial feature extraction: Using the inertial navigation position increment and the measured gravity data increment as the input features of the DNN network, the gravity data is nonlinearly mapped and spatial features are extracted through a multi-layer neural network, and the spatial feature vector is output. The calculation formula for the DNN extracted features is as follows: Where x is the input data; w i is the weight coefficient, all w i Constitute the weight vector w; b is the bias function, which can adjust the activation threshold of the neuron; z is the net input of the neuron, which is the result of weighted summation of the input data and adding the bias; n represents the number of input features, and the specific feature L is calculated as follows: Among them, y represents the output data, y i is the model prediction value of the i-th sample, is the true value of the i-th sample, and L is calculated by averaging the sum of the squares of the differences between the two; m is the number of training samples; S4-3: LSTM network temporal feature modeling: The spatial feature vector is used as the input of the LSTM network. Through the gating mechanism of input gate, forget gate and output gate, the temporal feature modeling of the inertial navigation data is performed, and the output is the implicit state vector containing the spatial-temporal fusion features. S4-4: DNN-LSTM integrity model training: Using high-confidence gravity matching position increments as supervisory output data, the implicit state vector and supervisory output data are used for model training to obtain the trained DNN-LSTM deep learning integrity monitoring model; S5: Gravity matching position fine compensation prediction: Using the inertial navigation position increment and measured gravity data increment at the data breakpoint corresponding to the preliminary compensated gravity matching position data output in step S3 as input, the DNN-LSTM deep learning integrity monitoring model trained in step S4 is used to perform fine prediction compensation, and output high-precision gravity matching position data after fine compensation; S6: Navigation position data output: Use the high-precision gravity matching position data after fine compensation as the final navigation output position to complete the integrity monitoring and accurate output of the underwater gravity matching navigation position.

2. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling according to claim 1 is characterized by: In step S1, the mean square deviation (MSD) algorithm is used to calculate the correlation between the real-time gravity data map and the reference gravity data sequence. The specific calculation formula is: Where H represents the height of the measured sequence, W represents the width of the measured sequence, P is the gravity gradient measured sequence, B is the gravity gradient reference sequence, x and y represent the starting position coordinates of P sliding in B, i and j are index variables for double summation, and i is used to adjust the height direction of the measured sequence.

3. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling according to claim 1 is characterized by: The confidence assessment method in step S2 is to use a preset threshold to determine the MSD value corresponding to each point in the matching position data. When the MSD value exceeds the threshold, it is determined to be a gross error position point and is removed to generate a data breakpoint area.

4. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling according to claim 1 is characterized by: The B-spline interpolation preliminary compensation method in step S3 specifically performs B-spline interpolation in the data breakpoint area using adjacent high-confidence matching position data points, and the compensated data serves as the initial input data for subsequent fine compensation.

5. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling according to claim 1 is characterized by: The forget gate described in step S4-3 is used to selectively filter redundant information in the inertial navigation historical data; the input gate is used to control the real-time input inertial navigation position increment and the measured gravity data increment information; the output gate is used to fuse the processing results of the forget gate and the input gate to generate an implicit state vector that contains both the temporal characteristics of the navigation data and the spatial gravity matching information.

6. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling according to claim 1 is characterized by: The calculation method of the LSTM information flow process described in step S4-3 is: i t =σ(W i [h t-1 ,x t ]+b i ) (4) f t =σ(W f [h t-1 ,x t ]+b f ) (5) the t =σ(W o [h t-1 ,x t ]+b o ) (6) h t =o t ·tanh(C t ) (9) Where t represents the time step index; t is the input vector at the current moment; h t-1 and h t are the hidden state vectors of the previous moment and the current moment respectively; C t-1 and C t are the cell state vectors at the previous moment and the current moment respectively; i t ,f t ,o t They are the values ​​of the input gate, forget gate, and output gate, which control the flow of information; is the candidate cell state; W i 、W f 、W o 、W C is the weight matrix corresponding to the gate and candidate state; b i 、b f 、b o 、b C is the corresponding bias vector; σ is the Sigmoid activation function; tanh is the hyperbolic tangent activation function; ⊙ represents element-by-element multiplication; [h t-1 ,x t ] indicates vector concatenation.

7. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling according to claim 1 is characterized by: The preset network structure of the DNN-LSTM integrity model described in step S4-4 includes, from its input end to its output end, an input layer, a DNN feature extraction layer, a multi-layer LSTM network layer, a fully connected layer, and an output layer.

8. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling according to claim 7 is characterized by: The DNN-LSTM integrity model includes the following structural features: The DNN feature extraction layer includes multiple fully connected neural network sublayers connected in series, each sublayer is composed of a linear mapping module and a nonlinear activation module; The multi-layer LSTM network layer is composed of three layers of long short-term memory units connected in series. Each layer of LSTM is a gated recurrent unit structure, including an input gate, a forget gate, an output gate and a unit state update module; wherein the three layers of long short-term memory units specifically include the following three layers: LSTM1, LSTM2, and LSTM3; The fully connected layer is used to map the high-order temporal representation of the multi-layer LSTM output to the output space; The output layer is used to generate the final output result.

9. The underwater gravity navigation integrity assessment method based on deep learning and time series modeling according to claim 8, characterized in that: The DNN-LSTM integrity model further includes the following structural features: The output dimension of each fully connected neural network sublayer in the DNN feature extraction layer can be the same or reduced layer by layer, and a ReLU function or a tanh function is used as an activation function to enhance the nonlinear expression ability of the feature; In the multi-layer LSTM network layer, the hidden state dimensions of each LSTM layer are the same, supporting state transfer across time steps, and the multi-layer structure can abstract and refine time series information layer by layer; The fully connected layer is a linear transformation layer that uses Softmax or linear activation to output classification probabilities or regression values.

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