Quasi-real-time high-precision positioning method based on multi-source data fusion of manned submersible

Abstract

The present invention discloses a multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible, which belongs to the field of underwater positioning technology and is used for underwater positioning of a manned submersible, including obtaining different sensor accuracies and observation noises, performing data fusion processing on heterogeneous sound velocity profiles in the sound velocity profiles of equal depth points, and obtaining an accurate sound velocity profile after fusion processing; processing the accurate sound velocity profile after fusion processing to obtain a full-sea-depth sound velocity profile; performing sound velocity profile replacement, using a quasi-real-time sound velocity profile for hydroacoustic positioning, and feeding back the real-time position of the manned submersible through hydroacoustic communication equipment; performing fusion processing based on the sound velocity profile of the day in the diving sea area and the historical multi-source sound velocity profile, obtaining a quasi-real-time sound velocity profile of the day, and used for the manned submersible diving positioning the next day. The present invention fully considers the temporal and spatial parameter errors, reduces the influence of the temporal and spatial errors of the sound velocity profile on positioning, and improves the underwater positioning accuracy of the manned submersible.

Description

Technical Field

[0001] The invention discloses a multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible, belonging to the technical field of underwater positioning. Background Art

[0002] When a submersible conducts long-term and long-distance operations in the deep sea, the accuracy of its navigation and positioning becomes a key factor that directly affects whether it can successfully complete the scheduled mission. The complex and changeable marine environment is a key issue that restricts the accuracy of underwater navigation and positioning, especially underwater acoustic navigation and positioning, which requires careful consideration of the impact of marine environmental errors. Although the sound field inversion technology can obtain sound velocity parameters, the high-precision sound field construction technology is still immature. In addition, manned submersible operations have significant regional characteristics, and generally work is carried out in mining areas that have been applied for by the country or hydrothermal areas that have been discovered. Therefore, regional sound field construction technology is a means to solve the high-precision sound field model. Based on known sea areas, there are already rich historical sound velocity profile data that can be fully utilized, and before the operation, temperature, salinity and depth data are usually observed, which is also a traditional sound velocity profile acquisition method for the positioning of submersibles. However, due to the dynamic nature of the marine environment, the sound velocity has significant temporal and spatial characteristics, so it is necessary to reduce the impact of this error. Summary of the invention

[0003] The purpose of the present invention is to provide a quasi-real-time high-precision positioning method based on multi-source data fusion of a manned submersible, so as to solve the problem of insufficient accuracy of the sound velocity profile used for positioning of a manned submersible in the prior art.

[0004] The multi-source data fusion quasi-real-time high-precision positioning method based on manned submersibles includes:

[0005] S1. Preprocess the historical multi-source sound velocity profiles, the sound velocity profiles calculated using the temperature-salinity-depth instrument data, and the multi-source sound velocity profiles observed on-site by manned submersibles to obtain the sound velocity profile data of equal depth points. The preprocessing includes data interpolation, outlier removal, motion smoothing, and consistency check.

[0006] S2. Obtain the sensor observation noise index, use the improved minimum variance estimation method, perform data fusion processing on the heterogeneous sound velocity profiles in the sound velocity profiles of equal depth points, and obtain the accurate sound velocity profile after fusion processing;

[0007] S3. Processing the accurate sound velocity profile after fusion processing to obtain the full sea depth sound velocity profile;

[0008] S4. Replace the sound velocity profile, use the full-sea-depth sound velocity profile as a quasi-real-time sound velocity profile, deploy a hydroacoustic array, use the quasi-real-time sound velocity profile for hydroacoustic positioning, feedback the real-time position of the manned submersible through hydroacoustic communication equipment, and perform accuracy assessment through a depth gauge;

[0009] S5. After recovering the manned submersible, the sound speed profile of the diving area on that day is obtained through the diving observation information of the manned submersible on that day. The sound speed profile of the diving area on that day and the historical multi-source sound speed profile are fused to obtain the quasi-real-time sound speed profile of the day, which is used for the diving positioning of the manned submersible the next day.

[0010] Data interpolation includes using cubic spline interpolation method if there is data missing in the sound velocity profile, and making the interpolation curve smoother through piecewise cubic polynomial approximation. Sound velocity profile data points , construct a cubic polynomial :

[0011] ;

[0012] In the formula, , , , is the parameter to be requested, It is The sound velocity value of the sound velocity profile, It is The depth of the sound velocity profile.

[0013] Removing outliers involves calculating the absolute deviation for each speed point :

[0014] ;

[0015] In the formula, is the median value of the speed of sound;

[0016] The median is , set the threshold Identify and remove outliers:

[0017] ;

[0018] In the formula, is the boundary value for removing outliers.

[0019] Moving smoothing includes moving smoothing of all sound velocity profiles:

[0020] ;

[0021] In the formula, It is The smoothed value of the sound velocity profile data point, is the counting parameter, It is The sound velocity value of a sound velocity profile.

[0022] Perform consistency checks on all sound velocity profiles to ensure that the rate of change of adjacent depth points is consistent. In the preset range:

[0023] ;

[0024] The sound velocity profile calculated using the temperature-salinity-depth instrument data includes: the mother ship carrying the manned submersible arrives at the working sea area, the mother ship performs fixed-point operations to obtain the temperature-salinity-depth instrument data and calculates the sound velocity profile as follows:

[0025] ;

[0026] In the formula, represents the speed of sound, Indicates temperature, Indicates salinity, Indicates depth.

[0027] Obtaining the sensor observation noise index includes querying the observation noise index of different sensors. The sensor observation noise index of the historical multi-source sound velocity profile is The sensor observation noise index of the sound velocity profile calculated using the temperature-salinity-depth instrument data is The sensor observation noise index of the multi-source sound velocity profile observed in the manned submersible is , the accuracy of the sound velocity profile is determined based on the sensor observation noise index;

[0028] Calculate the noise variance based on the sensor observation noise index, represents the noise variance of the historical multi-source sound velocity profile, represents the noise variance of the sound velocity profile calculated using the temperature-salinity-depth instrument data, Represents the noise variance of the multi-source sound velocity profile observed in situ by a manned submersible.

[0029] Using the improved minimum variance estimation method, data fusion processing of heterogeneous sound velocity profiles in the sound velocity profiles of equal depth points includes:

[0030] ;

[0031] In the formula, is the fused heterogeneous sound velocity profile, They are the weight coefficients of the historical multi-source sound velocity profile, the sound velocity profile calculated using the temperature-salinity-depth instrument data, and the multi-source sound velocity profile observed on-site by a manned submersible;

[0032] ;

[0033] In the formula, They are The corresponding weights, is the reliability coefficient of the sound velocity profiles obtained by different sensors, represents the credibility coefficient of the sound velocity profile of the submersible, , Represents the credibility coefficient of the sound velocity profile of the submersible's ascent, Represents the credibility coefficient of the sound velocity profile of the submersible diving, Determined based on time error and sea area overlap, According to the area difference of the two sound velocity profiles, the credibility of the sound velocity profile of the submersible's ascent and descent is the most reliable, and the credibility of the sound velocity profile obtained by the temperature-salinity-depth instrument sensor is the second most reliable.

[0034] The accurate sound velocity profile after fusion processing is processed to obtain the full-sea depth sound velocity profile, including extrapolating the sound velocity profile according to the method of calculating the sound velocity profile using the temperature-salinity-depth instrument data, and setting the fitting function after extrapolation. for:

[0035] ;

[0036] In the formula, is the initial temperature value, is the temperature variation coefficient, is a natural constant, is the initial depth value, To fit the power exponent, a feedback-assisted grid search is used to find and The optimal value of is obtained by using the least squares solution of 70% of the known accurate sound velocity profile after fusion processing. and , is the full-sea-depth sound velocity profile of the extrapolated part.

[0037] When the fusion processing is performed based on the sound velocity profile of the diving area on the day and the historical multi-source sound velocity profile, the The same sound velocity profile fusion method.

[0038] Compared with the prior art, the present invention has the following beneficial effects: the present invention fully considers the time and space parameter errors, reduces the influence of the time and space errors of the sound speed profile on positioning, and improves the underwater positioning accuracy of manned submersibles. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The historical sound speed profiles of the sea area in different seasons;

[0040] Figure 2 It is the sound velocity profile converted from the temperature-salinity-depth instrument CTD;

[0041] Figure 3The sound velocity profiles were measured twice for the manned submersible during its descent and ascent;

[0042] Figure 4 The quasi-real-time sound velocity profile is obtained after preprocessing and fusing the sound velocity profile data;

[0043] Figure 5 The sound speed error diagram is a comparison between the quasi-real-time sound speed profile obtained after fusion and the original sound speed profile;

[0044] Figure 6 This is the result diagram of extrapolation of sound velocity profile;

[0045] Figure 7 This is the result diagram after the sound velocity profile is simplified;

[0046] Figure 8 To simplify the propagation time error diagram caused;

[0047] Fig. 9 It is a technical flow chart of the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] The multi-source data fusion quasi-real-time high-precision positioning method based on manned submersibles includes:

[0050] S1. Preprocess the historical multi-source sound velocity profiles, the sound velocity profiles calculated using the temperature-salinity-depth instrument data, and the multi-source sound velocity profiles observed on-site by manned submersibles to obtain the sound velocity profile data of equal depth points. The preprocessing includes data interpolation, outlier removal, motion smoothing, and consistency check.

[0051] S2. Obtain the sensor observation noise index, use the improved minimum variance estimation method, perform data fusion processing on the heterogeneous sound velocity profiles in the sound velocity profiles of equal depth points, and obtain the accurate sound velocity profile after fusion processing;

[0052] S3. Processing the accurate sound velocity profile after fusion processing to obtain the full sea depth sound velocity profile;

[0053] S4. Replace the sound velocity profile, use the full-sea-depth sound velocity profile as a quasi-real-time sound velocity profile, deploy a hydroacoustic array, use the quasi-real-time sound velocity profile for hydroacoustic positioning, feedback the real-time position of the manned submersible through hydroacoustic communication equipment, and perform accuracy assessment through a depth gauge;

[0054] S5. After recovering the manned submersible, the sound speed profile of the diving area on that day is obtained through the diving observation information of the manned submersible on that day. The sound speed profile of the diving area on that day and the historical multi-source sound speed profile are fused to obtain the quasi-real-time sound speed profile of the day, which is used for the diving positioning of the manned submersible the next day.

[0055] Data interpolation includes using cubic spline interpolation method if there is data missing in the sound velocity profile, and making the interpolation curve smoother through piecewise cubic polynomial approximation. Sound velocity profile data points , construct a cubic polynomial :

[0056] ;

[0057] In the formula, , , , is the parameter to be requested, It is The sound velocity value of the sound velocity profile, It is The depth of the sound velocity profile.

[0058] Removing outliers involves calculating the absolute deviation for each speed point :

[0059] ;

[0060] In the formula, is the median value of the speed of sound;

[0061] The median is , set the threshold Identify and remove outliers:

[0062] ;

[0063] In the formula, is the boundary value for removing outliers.

[0064] Moving smoothing includes moving smoothing of all sound velocity profiles:

[0065] ;

[0066] In the formula, It is The smoothed value of the sound velocity profile data point, is the counting parameter, It is The sound velocity value of a sound velocity profile.

[0067] Perform consistency checks on all sound velocity profiles to ensure that the rate of change of adjacent depth points is consistent. In the preset range:

[0068] .

[0069] The sound velocity profile calculated using the temperature-salinity-depth instrument data includes: the mother ship carrying the manned submersible arrives at the working sea area, the mother ship performs fixed-point operations to obtain the temperature-salinity-depth instrument data and calculates the sound velocity profile as follows:

[0070] ;

[0071] In the formula, represents the speed of sound, Indicates temperature, Indicates salinity, Indicates depth.

[0072] Obtaining the sensor observation noise index includes querying the observation noise index of different sensors. The sensor observation noise index of the historical multi-source sound velocity profile is The sensor observation noise index of the sound velocity profile calculated using the temperature-salinity-depth instrument data is The sensor observation noise index of the multi-source sound velocity profile observed in the manned submersible is , the accuracy of the sound velocity profile is determined based on the sensor observation noise index;

[0073] Calculate the noise variance based on the sensor observation noise index, represents the noise variance of the historical multi-source sound velocity profile, represents the noise variance of the sound velocity profile calculated using the temperature-salinity-depth instrument data, Represents the noise variance of the multi-source sound velocity profile observed in situ by a manned submersible.

[0074] Using the improved minimum variance estimation method, data fusion processing of heterogeneous sound velocity profiles in the sound velocity profiles of equal depth points includes:

[0075] ;

[0076] In the formula, is the fused heterogeneous sound velocity profile, They are the weight coefficients of the historical multi-source sound velocity profile, the sound velocity profile calculated using the temperature-salinity-depth instrument data, and the multi-source sound velocity profile observed on-site by a manned submersible;

[0077] ;

[0078] In the formula, They are The corresponding weights, is the reliability coefficient of the sound velocity profiles obtained by different sensors, represents the credibility coefficient of the sound velocity profile of the submersible, , Represents the credibility coefficient of the sound velocity profile of the submersible's ascent, Represents the credibility coefficient of the sound velocity profile of the submersible diving, Determined based on time error and sea area overlap, According to the area difference of the two sound velocity profiles, the credibility of the sound velocity profile of the submersible's ascent and descent is the most reliable, and the credibility of the sound velocity profile obtained by the temperature-salinity-depth instrument sensor is the second most reliable.

[0079] The accurate sound velocity profile after fusion processing is processed to obtain the full-sea depth sound velocity profile, including extrapolating the sound velocity profile according to the method of calculating the sound velocity profile using the temperature-salinity-depth instrument data, and setting the fitting function after extrapolation. for:

[0080] ;

[0081] In the formula, is the initial temperature value, is the temperature variation coefficient, is a natural constant, is the initial depth value, To fit the power exponent, a feedback-assisted grid search is used to find and The optimal value of is obtained by using the least squares solution of 70% of the known accurate sound velocity profile after fusion processing. and , is the full-sea-depth sound velocity profile of the extrapolated part.

[0082] When the fusion processing is performed based on the sound velocity profile of the diving area on the day and the historical multi-source sound velocity profile, the The same sound velocity profile fusion method.

[0083] The present invention adopts nonlinear fitting in the extrapolation part and uses distance for weighting:

[0084] ;

[0085] In the formula, It is Depth points, It is The weight of the depth point, is the total number of depth points.

[0086] After extrapolating the full-sea-depth sound velocity profile, the simplified sound ray loss minimum criterion is used to simplify the sound velocity profile.

[0087] The vertical depth based on the hydroacoustic positioning coordinates and the depth of the high-precision depth gauge Perform comparison and precision assessment to ensure reliability and accuracy and calculate root mean square error :

[0088] ;

[0089] In the formula, is the data sample size. The present invention selects experimental data, where the historical sound velocity profiles of the sea area in different seasons are as follows: Figure 1 As shown in the figure, the sound velocity profile converted from the temperature-salinity-depth instrument CTD is as follows: Figure 2 As shown in the figure, the sound velocity profiles measured by the manned submersible during the dive and ascent are as follows: Figure 3 As shown in the figure, the submersible SVP1 is used for diving, and the submersible SVP2 is used for surfacing. The quasi-real-time sound velocity profile obtained after preprocessing and fusing the sound velocity profile data is shown in the figure below. Figure 4 As shown in the figure, the sound speed error of the quasi-real-time sound speed profile obtained after fusion compared with the original sound speed profile is as follows: Figure 5 As shown in the figure, the sound speed error 2 is the original sound speed profile, the sound speed error 1 is the quasi-real-time sound speed profile obtained after fusion, and the sound speed profile extrapolation result is shown in the figure Figure 6 As shown, the simplified sound velocity profile is as follows Figure 7 As shown in the figure, there is a comparison between before and after simplification. After simplification, 55 points are retained. The propagation time error caused by simplification is shown in Figure 8 shown.

[0090] The technical process of the present invention is as follows Fig. 9As shown in FIG, firstly, multi-source sound velocity profile data are obtained, including historical sound velocity profile, on-site CTD observation information, and submersible sound velocity profile, wherein the submersible sound velocity profile includes the diving sound velocity profile and the surfacing sound velocity profile, and then the sound velocity profile preprocessing is performed, the historical sound velocity profile, the on-site CTD observation information, and the submersible sound velocity profile are subjected to cubic spline difference, and then the absolute deviation is performed to eliminate outliers, and moving smoothing and consistency check are performed, and then a one-step processing, i.e., multi-source data fusion, is performed, the result of the consistency check is subjected to the improved minimum variance estimation sound velocity profile, and the weight coefficient is increased, and at the same time, the historical sound velocity profile is , on-site CTD observation information, and the sound speed profile of the submersible are used to calculate the equipment observation noise level, and then the noise variance is calculated and the data fusion weight is performed. The result is used to improve the minimum variance estimation of the sound speed profile, and then a two-step processing is performed, namely, the extrapolation and simplification of the sound speed profile. The results of the improved minimum variance estimation of the sound speed profile are used in sequence to perform quasi-real-time and accurate sound speed profile calculation, sound speed profile fitting extrapolation, sound speed profile sound line loss minimum criterion simplification, and full-sea depth streamlined quasi-real-time sound speed profile calculation. Finally, the manned bathymetric device is positioned and the latest sound speed profile observation data is obtained as the sound speed profile of the submersible in the next day's calculation.

[0091] The test results show the errors in three directions of the Northeast Sky ENU as shown in Table 1.

[0092] Table 1 Errors of test results in three directions of ENU

[0093] ;

[0094] It can be seen from the analysis of the test results that, considering the accuracy of the sound velocity profile sensor and the spatial-temporal error of observation, the temperature-salinity-depth instrument CTD is the observation data within 1-2 days before the submersible dives, which causes the largest positioning error; the observation time of the submersible measured profile is very close to the diving operation time, and its spatial-temporal error is small, and the positioning result is better than the CTD measured profile; the multi-data fusion quasi-real-time sound velocity profile based on the present invention combines the historical sound velocity profile, the CTD measured profile and the structural characteristics of multiple submersible measured profiles, and considers the weight coefficient of spatial-temporal error during fusion, so it is closer to the actual sound velocity distribution, and the positioning error of the submersible is the smallest. The test results show that the multi-source data fusion quasi-real-time high-precision positioning method based on manned submersibles proposed by the present invention reduces the influence of spatial-temporal error of the sound velocity profile on positioning, and improves the underwater positioning accuracy of manned submersibles.

[0095] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features may be replaced by equivalents, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A quasi-real-time high-precision positioning method based on multi-source data fusion of manned submersibles, characterized in that: include: S1. Preprocess the historical multi-source sound velocity profiles, the sound velocity profiles calculated using the temperature-salinity-depth instrument data, and the multi-source sound velocity profiles observed on-site by manned submersibles to obtain the sound velocity profile data of equal depth points. The preprocessing includes data interpolation, outlier removal, motion smoothing, and consistency check. S2. Obtain the sensor observation noise index, use the improved minimum variance estimation method, perform data fusion processing on the heterogeneous sound velocity profiles in the sound velocity profiles of equal depth points, and obtain the accurate sound velocity profile after fusion processing; S3. Processing the accurate sound velocity profile after fusion processing to obtain the full sea depth sound velocity profile; S4. Replace the sound velocity profile, use the full-sea-depth sound velocity profile as a quasi-real-time sound velocity profile, deploy a hydroacoustic array, use the quasi-real-time sound velocity profile for hydroacoustic positioning, feedback the real-time position of the manned submersible through hydroacoustic communication equipment, and perform accuracy assessment through a depth gauge; S5. After the manned submersible is recovered, the sound velocity profile of the diving area on that day is obtained through the observation information of the manned submersible on that day, and the sound velocity profile of the diving area on that day and the historical multi-source sound velocity profile are fused to obtain the quasi-real-time sound velocity profile of that day, which is used for the manned submersible's diving positioning the next day; Using the improved minimum variance estimation method, data fusion processing of heterogeneous sound velocity profiles in the sound velocity profiles of equal depth points includes: ； In the formula, is the fused heterogeneous sound velocity profile, is the historical multi-source sound velocity profile, is the sound velocity profile calculated using the temperature-salinity-depth instrument data. It is a multi-source sound velocity profile observed in situ by a manned submersible. They are the weight coefficients of the historical multi-source sound velocity profile, the sound velocity profile calculated using the temperature-salinity-depth instrument data, and the multi-source sound velocity profile observed on-site by a manned submersible; ； In the formula, represents the noise variance of the historical multi-source sound velocity profile, represents the noise variance of the sound velocity profile calculated using the temperature-salinity-depth instrument data, represents the noise variance of the multi-source sound velocity profile observed in situ by a manned submersible, They are The corresponding weights, is the reliability coefficient of the sound velocity profiles obtained by different sensors, represents the credibility coefficient of the sound velocity profile of the submersible, , Represents the credibility coefficient of the sound velocity profile of the submersible's ascent, Represents the credibility coefficient of the sound velocity profile of the submersible diving, Determined based on time error and sea area overlap, According to the area difference of the two sound velocity profiles, the credibility of the sound velocity profile of the submersible's ascent and descent is the most reliable, and the credibility of the sound velocity profile obtained by the temperature-salinity-depth instrument sensor is the second most reliable.

2. The multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible according to claim 1 is characterized in that: Data interpolation includes using cubic spline interpolation method if there is data missing in the sound velocity profile, and making the interpolation curve smoother through piecewise cubic polynomial approximation. For n+1 sound velocity profile data points , construct a cubic polynomial : ； In the formula, , , , is the parameter to be requested. It is The sound velocity value of the sound velocity profile, It is The depth of the sound velocity profile.

3. The multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible according to claim 2 is characterized in that: Removing outliers involves calculating the absolute deviation for each sound velocity point : ； In the formula, is the median value of the speed of sound; The median is , set the threshold Identify and remove outliers: ； In the formula, is the boundary value for removing outliers.

4. The multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible according to claim 3 is characterized in that: Moving smoothing includes moving smoothing of all sound velocity profiles: ； In the formula, It is The smoothed value of the sound velocity profile data point, is the counting parameter, It is The sound velocity value of a sound velocity profile.

5. The multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible according to claim 4 is characterized in that: Perform consistency checks on all sound velocity profiles to ensure that the rate of change of adjacent depth points is consistent. In the preset range: 。 6. The multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible according to claim 5 is characterized in that: The sound velocity profile calculated using the temperature-salinity-depth instrument data includes: the mother ship carrying the manned submersible arrives at the working sea area, the mother ship performs fixed-point operations to obtain the temperature-salinity-depth instrument data and calculates the sound velocity profile as follows: ； In the formula, represents the speed of sound, Indicates temperature, Indicates salinity, Indicates depth.

7. The multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible according to claim 6 is characterized in that: Obtaining the sensor observation noise index includes querying the observation noise index of different sensors. The sensor observation noise index of the historical multi-source sound velocity profile is The sensor observation noise index of the sound velocity profile calculated using the temperature-salinity-depth instrument data is The sensor observation noise index of the multi-source sound velocity profile observed in the manned submersible is , the accuracy of the sound velocity profile is determined based on the sensor observation noise index; The noise variance is calculated based on the sensor observation noise index.

8. The multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible according to claim 7 is characterized in that: The accurate sound velocity profile after fusion processing is processed to obtain the full-sea depth sound velocity profile, including extrapolating the sound velocity profile according to the method of calculating the sound velocity profile using the temperature-salinity-depth instrument data, and setting the fitting function after extrapolation. for: ； In the formula, is the initial temperature value, is the temperature variation coefficient, is a natural constant, is the initial depth value, To fit the power exponent, a feedback-assisted grid search is used to find and The optimal value of is obtained by using the least squares solution of 70% of the known accurate sound velocity profile after fusion processing. and , is the full-sea-depth sound velocity profile of the extrapolated part.

9. The multi-source data fusion quasi-real-time high-precision positioning method based on a manned submersible according to claim 8, characterized in that: When the fusion processing is performed based on the sound velocity profile of the diving area on the day and the historical multi-source sound velocity profile, the The same sound velocity profile fusion method.

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