Underwater fusion positioning method based on Bayesian inversion

Abstract

The present invention relates to the technical field of underwater positioning, and in particular to an underwater fusion positioning method based on Bayesian inversion that can effectively improve positioning accuracy. The method is characterized by comprising the following steps: obtaining depth information by using a depth gauge DG, obtaining seawater temperature and salinity by using a temperature-salinity-depth instrument CTD, and further obtaining real-time sound velocity information in the seawater; inverting three-dimensional position information of an autonomous underwater vehicle (AUV) by combining time delay information obtained by four transponders of a long baseline LBL with the sound velocity information and depth information obtained in the previous step; measuring the speed information of the AUV by using a DVL; obtaining the north, east and celestial position and velocity information of the AUV by using an INS; and performing Bayesian inversion on the difference between the position information obtained by an inertial navigation system INS and the position information obtained by the LBL, and the difference between the velocity information of the inertial navigation system INS and the velocity information obtained by the DVL as observation data. The target position coordinates are finally obtained by fusing the observation data with a priori model.

Description

Technical Field

[0001] The present invention relates to the field of underwater positioning technology, and in particular to an underwater fusion positioning method based on Bayesian inversion that can effectively improve positioning accuracy. Background Art

[0002] Underwater positioning is a technology that provides information such as the attitude, speed, and position of autonomous underwater vehicles (AUVs). It is a prerequisite for AUVs to successfully complete various underwater tasks.

[0003] Currently, common positioning methods for underwater navigation include inertial navigation systems (INS), hydroacoustic positioning technology, and Doppler velocity logs (DVLs). These methods, combined with extended Kalman filters (EKFs), can be used to localize individual sensor nodes. However, due to the complex and changing underwater environment, a single positioning technology often cannot meet the requirements for long-range, multi-target, and high-precision navigation. Therefore, fusion positioning, combining multiple technologies, will become the mainstream trend in future AUV positioning. This fusion positioning system typically employs two or more position sensors to achieve multi-source fusion positioning. This fusion positioning system can combine multiple sensors, such as INS, DVLs, conductivity temperature depth (CTDs), and magnetic compasses, containing information such as time delay, velocity, and depth. Based on this information, the underwater vehicle's velocity, acceleration, depth, and other multi-source data are fused to achieve positioning. However, since the measurement noise generated by various measurement signals in the ocean will also change continuously, the measurement results of various measurement signals will have some uncertainties to a greater or lesser extent. Therefore, the fusion method of multi-source information is a key scientific problem that needs to be solved.

[0004] Bayesian theory is a statistically based inversion method that offers unique advantages in solving inversion problems and can effectively promote the integration of multiple fields. Bayesian inversion has applications in geophysics, electromagnetics, fluid mechanics, and other fields. For example, Chinese patent application number 202210307474.5, entitled "A Joint Bayesian Inversion Method and System for Reservoir Lithology and Physical Property Parameters," combines the concepts of lithology classification and physical property estimation to develop a new joint Bayesian inversion method for reservoir lithology and physical property parameters. This method enables quantitative prediction of subsurface reservoir properties, providing reliable support for refined oil and gas exploration and development. Chinese patent application number 202111102996.3, entitled "Micro-nanoprobe Dynamic Characteristics Compensation Method Based on Bayesian Inversion Modeling," implements dynamic characteristic compensation for micro-nanoprobe systems. This method can quickly and effectively reduce the overshoot of the probe step output, shorten the probe response time, and improve the dynamic characteristics of the micro-nanoprobe system at a low cost. Because the statistical model of the inverse problem is very flexible, it can greatly improve all aspects of scientific and technological production and life, promote the combination of theoretical knowledge and practical applications, and has great research significance and practical value.

[0005] Bayesian inversion, based on randomness and mathematical statistics, employs an optimal integral approach to quantitatively analyze the model's posterior probability distribution, statistically reflecting the uncertainty of the inversion. The Bayesian inversion method is used for multi-source fusion position estimation. During the inversion process, conventional methods are used to build on existing information to bring the estimated information closer to the actual information. Finally, existing observational data is used to correct the obtained information to obtain the fused information. However, due to the complex and changing marine environment, its positioning accuracy is still constrained by various factors and is subject to significant uncertainty. Summary of the Invention

[0006] In view of the shortcomings and deficiencies in the existing technology, the present invention proposes an underwater fusion positioning method based on Bayesian inversion theory, which integrates INS, DVL, long baseline line (LBL), CTD and depth gauge (DG), makes full use of ranging information and AUV multi-sensor information, effectively improves positioning accuracy, and has adaptive capability.

[0007] The present invention is obtained by the following measures:

[0008] An underwater fusion positioning method based on Bayesian inversion, characterized by comprising the following steps:

[0009] Step 1: Use the depth gauge DG to obtain depth information, and use the temperature and salinity meter CTD to obtain seawater temperature and salinity, and then obtain real-time sound speed information in the seawater;

[0010] Step 2: Use the time delay information obtained by the four transponders of the long baseline LBL and combine it with the sound speed information and depth information obtained in the previous step to invert the three-dimensional position information of the AUV;

[0011] Step 3: Use the Doppler velocimeter (DVL) to measure the AUV's velocity information; use the INS to calculate the AUV's position and velocity information in the north, east, and sky directions using the measurements of the accelerometer and gyroscope;

[0012] Step 4: The difference between the position information obtained by the inertial navigation system INS and the position information obtained by the long baseline LBL, and the difference between the velocity information of the inertial navigation system INS and the velocity information obtained by the Doppler velocimeter DVL are used as observation data for Bayesian inversion. After fusing the observation data and the model prior, the target position coordinates are finally obtained.

[0013] Step 2 of the present invention specifically includes:

[0014] Step 2-1: Since the DG measurement value is relatively accurate and the error does not accumulate, the LBL positioning method with known depth is used to obtain the forward model based on the geometric relationship: the model formula is as follows:

[0015]

[0016]

[0017] The model parameters are is the two-dimensional position information of the AUV in the carrier coordinate system, and the observation information is:

[0018]

[0019] Among them, (x i ,y i ,z i ), i = 1, 2, 3, 4 are the three-dimensional position information of the four transponders, and (x, y, z) is the three-dimensional position information of the AUV, and the depth information of the AUV is z=z obtained in the first step. DG , d i is the distance between the i-th transponder and the AUV, and c is the underwater sound speed, τ i is the time difference between the AUV sending the sound wave and receiving the sound wave from the i-th transponder;

[0020] Step 2-2: Using the coordinates of the four transponders and the AUV depth information as background information, implement the "delay-distance-coordinate" transformation and obtain the position coordinates using the maximum a posteriori estimation algorithm. The formula is as follows:

[0021]

[0022]

[0023] Among them, m0 takes the position coordinate of the previous moment, is the posterior covariance matrix of the model at the previous moment, m MAP To obtain the position information, the data covariance matrix C d Let it be the identity matrix, C m is the covariance matrix of the model posterior;

[0024] In step 3 of the present invention, after the three-dimensional position of the AUV is obtained in step 2, the position information in the navigation coordinate system is obtained after coordinate transformation. The formula is as follows:

[0025]

[0026]

[0027] in is the AUV three-dimensional position obtained in step 2, pos LBL is the three-dimensional position of the AUV obtained after coordinate transformation, x LBL is the x-axis coordinate obtained by LBL Bayesian inversion, y LBL is the y-axis coordinate obtained by LBL Bayesian inversion, z DG is the depth information obtained by DG, L LBL ,λ LBL 、h LBL They are After the coordinate transformation, the AUV's position in the east, north and sky directions is: is the transformation matrix between the carrier coordinate system and the navigation coordinate system.

[0028] In step 3 of the present invention, the three-dimensional velocity of the AUV is obtained by combining the two-dimensional velocity information obtained by the DVL and the z-axis velocity information obtained by differentiating the depth meter. Coordinate transformation is also required to obtain the three-dimensional velocity in the navigation coordinate system. The formula is as follows:

[0029]

[0030]

[0031] The velocity of the sound wave is c, θ is the incident angle of the sound wave, and f0 is the signal frequency emitted by the DVL. are the x-axis, y-axis, and z-axis speeds respectively, They are the north axis, east axis and celestial velocity respectively.

[0032] Step 4 of the present invention specifically includes:

[0033] Step 4-1: Take the difference between the INS position and the LBL position and the difference between the INS velocity and the DVL velocity information as the EKF measurement value:

[0034] For INS, in addition to selecting attitude error, velocity error, and position error as state variables, the zero bias of the gyroscope and accelerometer are also selected as extensions of the state variables, and the state vector is obtained as follows:

[0035]

[0036] Using EKF as the state update algorithm, the continuous-time system can be expressed as:

[0037]

[0038] Where Z represents the observation quantity, H is the observation matrix, Φ is the state transfer matrix, W and V are random noises;

[0039]

[0040] Among them, L INS ,λ INS 、h INS Indicates the AUV's position in the east, north, and sky directions measured by INS. Indicates the speed of the AUV in the east, north, and sky directions measured by INS. δL, δλ, and δh represent the actual error of the INS output position, and δv N ,δv E ,δv U They represent the actual errors of the INS output velocity, δL1, δλ2, and δh3 are the observation noises of the position measured by LBL in the east, north, and sky directions, and δv1, δv2, and δv3 are the observation noises of the velocity measured by DVL in the east, north, and sky directions, respectively; H is the LBL position observation and DVL velocity observation matrix, X is the state matrix, and V is the random noise;

[0041] Step 4-2: The relationship between the state vectors before and after the EKF prediction is used as the forward model. Based on this, Bayesian inversion is performed and the model is corrected according to the observations obtained in the previous step. The specific formula is as follows:

[0042]

[0043]

[0044]

[0045] in, is the estimated value of X at time k-1, It uses the k-1 state matrix to calculate X at time k. yes The covariance matrix of is the prior covariance matrix of the model parameters, is the prior value of the model parameter, K k is the filter gain reflecting the prediction and update weights;

[0046] Step 4-3: After the fusion of observation data and model priors, the target position coordinates are finally obtained: the specific formula is as follows:

[0047]

[0048] Among them L INS ,λ INS 、h INS are the north, east and sky position information of the AUV obtained by INS in step 3, are the position errors in the north, east and sky directions obtained in the previous step respectively.

[0049] The multi-source fusion positioning method of Bayesian inversion proposed in this paper integrates INS, DVL, LBL, CTD and DG, expands the difference between the INS position and LBL position and the difference between the INS velocity and DVL velocity information as measurement values, performs Bayesian inversion, and then obtains position information. This method can effectively improve positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Attachment Figure 1 It is a multi-source fusion block diagram of the present invention.

[0051] Attachment Figure 2 This is the Bayesian inversion method process used in the present invention.

[0052] Attachment Figure 3 3 is a comparison chart of the predicted trajectory in an embodiment of the present invention, the actual trajectory, and the trajectory predicted by other methods.

[0053] Attachment Figure 4 3 is a graph showing the mean square error of the embodiment of the present invention and the mean square error of other methods. DETAILED DESCRIPTION

[0054] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0055] Current single-source positioning technologies suffer from numerous drawbacks, such as low positioning accuracy and cumulative errors. Therefore, the present invention utilizes multi-source fusion positioning technology to combine these technologies, leveraging their strengths to overcome their weaknesses and provide more reliable positioning information. This invention proposes an underwater fusion positioning method based on Bayesian inversion to address the shortcomings of single-source positioning and effectively improve positioning accuracy.

[0056] The multi-source fusion technology used in the present invention is as follows Figure 1 As shown in the figure, the fusion of INS, DVL, LBL, CTD and DG is an underwater fusion positioning algorithm that covers more positioning sources and has wider application value. The specific steps are:

[0057] (1) Use DG to obtain depth information z = z DG ,Using the seawater temperature and salinity obtained by CTD, the temperature (T℃), salinity (S‰, thousandths) and depth h (m) data are combined with the sound speed empirical model to obtain the real-time sound speed information in seawater;

[0058] (2) The time delay information obtained by the four transponders of LBL is combined with the sound speed information and depth information obtained in the previous step to invert the three-dimensional position information of the AUV; the Bayesian inversion algorithm used in the present invention is as follows Figure 2 shown.

[0059] Since the DG measurement value is relatively accurate and the error does not accumulate, the LBL positioning method with known depth is used to obtain the forward model based on the geometric relationship. The formula is as follows:

[0060]

[0061]

[0062] The model parameters are is the two-dimensional position information of the AUV in the carrier coordinate system. The observation information is:

[0063]

[0064] Among them, (x i ,y i ,z i ), i = 1, 2, 3, 4 are the three-dimensional position information of the four transponders, and (x, y, z) is the three-dimensional position information of the AUV, and the depth information of the AUV is z=z obtained in the first step. DG .d i is the distance between the i-th transponder and the AUV, and c is the underwater sound speed, τ iIt is the time difference between the AUV sending the sound wave and receiving the sound wave from the i-th transponder.

[0065] Then, the coordinates of the four transponders and the AUV depth information are used as background information to implement the "delay-distance-coordinate" transformation. According to the maximum a posteriori estimation algorithm, the position coordinates of the target are obtained. The formula is as follows:

[0066]

[0067]

[0068] Among them, m0 takes the position coordinate of the previous moment, is the posterior covariance matrix of the model at the previous moment, m MAP To obtain the position information, the data covariance matrix C d Let it be the identity matrix, C m is the covariance matrix of the model posterior.

[0069] The above steps can be used to obtain the three-dimensional position of the AUV, and after coordinate transformation, the position information in the navigation coordinate system can be obtained. The formula is as follows:

[0070]

[0071]

[0072] in is the AUV three-dimensional position obtained in the previous step, pos LBL is the three-dimensional position of the AUV obtained after coordinate transformation, x LBL is the x-axis coordinate obtained by LBL Bayesian inversion, y LBL is the y-axis coordinate obtained by LBL Bayesian inversion, z DG is the depth information obtained by DG, L LBL ,λ LBL 、h LBL They are After the coordinate transformation, the AUV's position in the east, north and sky directions is: is the transformation matrix between the carrier coordinate system and the navigation coordinate system.

[0073] (3) Use the DVL to measure the AUV's velocity information; use the INS to calculate the AUV's position and velocity information in the north, east, and sky directions using the measurements of the accelerometer and gyroscope;

[0074] The three-dimensional velocity of the AUV can be obtained by the two-dimensional velocity information obtained by the DVL and the z-axis velocity information obtained by the differentiation of the depth meter. Coordinate transformation is also required to obtain the three-dimensional velocity in the navigation coordinate system. The formula is as follows:

[0075]

[0076]

[0077] The velocity of the sound wave is c, θ is the incident angle of the sound wave, and f0 is the signal frequency emitted by the DVL. are the x-axis, y-axis, and z-axis speeds respectively, They are the north axis, east axis and celestial velocity respectively.

[0078] (4) The difference between the position information obtained by INS and the position information obtained by LBL and the difference between the speed information obtained by INS and the speed information obtained by DVL are used as the observation data of EKF, and then Bayesian inversion is performed to finally obtain the position information of the target. Specifically:

[0079] For INS, in addition to selecting attitude error, velocity error, and position error as state variables, the zero bias of the gyroscope and accelerometer are also selected as extensions of the state variables, and the state vector is obtained as follows:

[0080]

[0081] Using EKF as the state update algorithm, the continuous-time system can be expressed as:

[0082]

[0083] Where Z represents the observation quantity, H is the observation matrix, Φ is the state transfer matrix, and W and V are random noises.

[0084]

[0085] Among them, L INS ,λ INS 、h INS Indicates the AUV's position in the east, north, and sky directions measured by INS. Indicates the speed of the AUV in the east, north, and sky directions measured by INS. δL, δλ, and δh represent the actual error of the INS output position, and δv N ,δv E ,δv U denote the actual error in the INS output velocity, δL1, δλ2, and δh3 are the observation noises of the LBL position in the east, north, and sky directions, and δv1, δv2, and δv3 are the observation noises of the DVL velocity in the east, north, and sky directions. H is the matrix of LBL position observations and DVL velocity observations, X is the state matrix, and V is the random noise.

[0086] Then, the relationship between the state vectors before and after EKF prediction is used as the forward model, and Bayesian inversion is performed on this basis, and it is corrected according to Z obtained in the previous step. The specific formula is as follows:

[0087]

[0088]

[0089]

[0090] in, is the estimated value of X at time k-1, It uses the k-1 state matrix to estimate X at time k. yes The covariance matrix of is the prior covariance matrix of the model parameters, is the prior value of the model parameter. k is the filter gain that reflects the prediction and update weights.

[0091] After the fusion of observation data and model priors, the final position coordinates are obtained. The specific formula is as follows:

[0092]

[0093] Among them L INS ,λ INS 、h INS are the north, east and sky position information of the AUV obtained by INS in step 3, are the position errors in the north, east and sky directions obtained in the previous step respectively.

[0094] The performance of the technical solution of the present invention is analyzed below, specifically through simulation verification, and the simulation results are as follows:

[0095] The AUV is equipped with an INS, a four-beam DVL, an LBL positioning system, a CTD, and a DG. The INS data update cycle is 0.005 seconds, the DVL data update cycle is 0.1 seconds, the LBL data update cycle is 0.15 seconds, and the motion time is 250 seconds. The trajectory comparison curves obtained using INS alone, INS / DVL fusion positioning, INS / DVL, EKF, and multi-source fusion positioning methods are shown in the figure below. Figure 3 As shown, when the method of the present invention is used, the predicted curve is always closer to the true curve.

[0096] according to Figure 3 The following is an analysis of the relationship between error and time. Figure 4As shown in the figure, it can be seen that the method of the present invention has smaller errors than using INS, INS / DVL fusion positioning, INS / DVL, and using EKF to estimate the position alone, which shows that the performance of the fusion positioning method is better than single positioning source positioning and fusion positioning. The positioning result of the Bayesian inversion algorithm is better than that of EKF, and the fluctuation of the inversion positioning method is smaller than that of EKF positioning, and the stability of the positioning result is also better than that of EKF, which shows that the Bayesian inversion multi-source fusion method proposed in the present invention is better than the EKF algorithm. Moreover, the error curve trend of the other three algorithms is still rising, while the upward trend of the error curve of multi-source fusion positioning is not obvious. As time goes by, this difference becomes more obvious, which shows that the multi-source fusion positioning method is better at suppressing the cumulative error of inertial navigation.

[0097] The present invention adopts a multi-source fusion positioning method of Bayesian inversion, which integrates INS, DVL, LBL, CTD and DG, and expands the use of the position difference between INS and LBL and the velocity difference between INS and DVL as EKF observation information for Bayesian inversion. Compared with the traditional single-source positioning method, the present invention can effectively improve positioning accuracy.

Claims

1. An underwater fusion positioning method based on Bayesian inversion, characterized in that: The following steps are involved: Step 1: Use the depth gauge DG to obtain depth information, and use the temperature and salinity meter CTD to obtain seawater temperature and salinity, and then obtain real-time sound speed information in the seawater; Step 2: Use the time delay information obtained by the four transponders of the long baseline LBL and combine it with the sound speed information and depth information obtained in the previous step to invert the three-dimensional position information of the AUV; Step 3: Use the Doppler velocimeter (DVL) to measure the AUV's velocity information; use the INS to calculate the AUV's position and velocity information in the north, east, and sky directions using the measurements of the accelerometer and gyroscope; Step 4: The difference between the position information obtained by the inertial navigation system INS and the position information obtained by the long baseline LBL, and the difference between the velocity information of the inertial navigation system INS and the velocity information obtained by the Doppler velocimeter DVL are used as observation data for Bayesian inversion. After fusing the observation data and the model prior, the target position coordinates are finally obtained.

2. The underwater fusion positioning method based on Bayesian inversion according to claim 1 is characterized in that: The step 2 specifically includes: Step 2-1: Since the DG measurement value is relatively accurate and the error does not accumulate, the LBL positioning method with known depth is used to obtain the forward model based on the geometric relationship: the model formula is as follows: The model parameters are is the two-dimensional position information of the AUV in the carrier coordinate system, and the observation information is: Among them, (x i ,y i ,z i ), i = 1, 2, 3, 4 are the three-dimensional position information of the four transponders, and i = 1, 2, 3, 4, (x, y, z) is the three-dimensional position information of the AUV, and the depth information of the AUV is z = z obtained in the first step. DG , d i is the distance between the i-th transponder and the AUV, and i=1,2,3,4, c is the underwater sound speed, τ i is the time difference between the AUV sending the sound wave and receiving the sound wave from the i-th transponder; Step 2-2: Using the coordinates of the four transponders and the AUV depth information as background information, implement the "delay-distance-coordinate" transformation and obtain the position coordinates using the maximum a posteriori estimation algorithm. The formula is as follows: Among them, m0 takes the position coordinate of the previous moment, is the posterior covariance matrix of the model at the previous moment, m MAP To obtain the position information, the data covariance matrix C d Let it be the identity matrix, C m is the covariance matrix of the model posterior.

3. The underwater fusion positioning method based on Bayesian inversion according to claim 1 is characterized in that: Step 3: After obtaining the three-dimensional position of the AUV in step 2, the position information in the navigation coordinate system is obtained after coordinate transformation. The formula is as follows: in is the AUV three-dimensional position obtained in step 2, pos LBL is the three-dimensional position of the AUV obtained after coordinate transformation, x LBL is the x-axis coordinate obtained by LBL Bayesian inversion, y LBL is the y-axis coordinate obtained by LBL Bayesian inversion, z DG is the depth information obtained by DG, L LBL ,λ LBL 、h LBL They are After the coordinate transformation, the AUV's position in the east, north and sky directions is: is the transformation matrix between the carrier coordinate system and the navigation coordinate system.

4. The underwater fusion positioning method based on Bayesian inversion according to claim 1 is characterized in that: In step 3, the three-dimensional velocity of the AUV is obtained by the two-dimensional velocity information obtained by the DVL and the z-axis velocity information obtained by the differentiation of the depth meter. Coordinate transformation is also required to obtain the three-dimensional velocity in the navigation coordinate system. The formula is as follows: The velocity of the sound wave is c, θ is the incident angle of the sound wave, and f0 is the signal frequency emitted by the DVL. are the x-axis, y-axis, and z-axis speeds respectively, They are the north axis, east axis and celestial velocity respectively.

5. The underwater fusion positioning method based on Bayesian inversion according to claim 1 is characterized in that: The step 4 specifically includes: Step 4-1: Take the difference between the INS position and the LBL position and the difference between the INS velocity and the DVL velocity information as the EKF measurement value: For INS, in addition to selecting attitude error, velocity error, and position error as state variables, the zero bias of the gyroscope and accelerometer are also selected as extensions of the state variables, and the state vector is obtained as follows: Using EKF as the state update algorithm, the continuous-time system can be expressed as: Where Z represents the observation quantity, H is the observation matrix, Φ is the state transfer matrix, W and V are random noises; Among them, L INS ,λ INS 、h INS Indicates the AUV's position in the east, north, and sky directions measured by INS. It represents the speed of the AUV in the east, north and sky directions measured by INS, δL, δλ and δh represent the actual error of the position output by INS, and δv N ,δv E ,δv U They represent the actual errors of the INS output velocity, δL1, δλ2, and δh3 are the observation noises of the position measured by LBL in the east, north, and sky directions, and δv1, δv2, and δv3 are the observation noises of the velocity measured by DVL in the east, north, and sky directions, respectively; H is the LBL position observation and DVL velocity observation matrix, X is the state matrix, and V is the random noise; Step 4-2: The relationship between the state vectors before and after the EKF prediction is used as the forward model. Based on this, Bayesian inversion is performed and the model is corrected according to the observations obtained in the previous step. The specific formula is as follows: in, is the estimated value of X at time k-1, It uses the k-1 state matrix to calculate X at time k. yes The covariance matrix of is the prior covariance matrix of the model parameters, is the prior value of the model parameter, K k is the filter gain reflecting the prediction and update weights; Step 4-3: After the fusion of observation data and model priors, the target position coordinates are finally obtained: the specific formula is as follows: Among them L INS ,λ INS 、h INS are the north, east and sky position information of the AUV obtained by INS in step 3, are the position errors in the north, east and sky directions obtained in the previous step respectively.

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