A method for real-time GNSS acoustic underwater positioning

Abstract

The application discloses a kind of sailing type real-time GNSS acoustic underwater positioning method, belong to underwater positioning technical field, for acoustic underwater positioning, including constructing extended Kalman filter solution model, the coordinate prior information of seabed transponder is regarded as constraint equation of constraint construction, initial state parameter and initial covariance matrix are solved;Using Tikhonov regularization method handles the ill-conditioned problem in the process of initial state parameter and initial covariance matrix solution, the initial state parameter and initial covariance matrix value are substituted into extended Kalman filter solution model, real-time GNSS acoustic underwater positioning is carried out to seabed transponder.The application solves the ill-conditioned problem possibly existing in the process of solution, has the good performance of short convergence time, high accuracy, can improve the real-time positioning efficiency of GNSS-acoustic seabed transponder, and is expected to provide strong technical support for seabed plate movement, geological disaster, disaster warning and seabed geodetic datum update.

Description

TECHNICAL FIELD

[0001] The application discloses a sailing real-time GNSS acoustic underwater positioning method and belongs to the technical field of underwater positioning. BACKGROUND

[0002] Due to flexibility and controllability, GNSS-acoustic positioning is mainly carried out by using a sailing ship to measure, and random errors, gross errors and systematic errors caused by observation instruments and complex marine environments inevitably exist in the measurement process, which seriously restricts the positioning accuracy of the seabed transponder. In view of the improvement of the underwater positioning model and error correction, the measurement track of the sailing ship is optimized, and the positioning accuracy of the seabed transponder is improved; the acoustic observation values are differentiated to weaken the common-mode error between the observation values; an elastic observation model with a periodic error term is constructed to effectively compensate the influence of the systematic error in acoustic observation; the sailing differential positioning algorithm based on selected weight iteration is proposed in view of the gross error existing in acoustic ranging; and the underwater positioning model based on double-path acoustic range is constructed in view of the error existing in the position of the signal transmitting and receiving time of the sea surface measurement ship. The above positioning methods are post-processing based on dynamic measurement data, and the real-time processing based on sailing ship observation information is not considered.

[0003] Unlike batch post-processing positioning, real-time GNSS-acoustic positioning is processed immediately after receiving observation data, and the positioning efficiency is improved. Real-time GNSS-acoustic underwater positioning is very important in aspects of instantaneous detection such as seabed seismic activity, crustal movement, rapid hydrological change and rapid updating of the geodetic datum. Considering the superiority of the filter theory algorithm in dynamic measurement data processing, Kalman filtering can be used for real-time GNSS-acoustic positioning; the influence of underwater acoustic signal propagation time modeling on GNSS-acoustic seabed point positioning under various acoustic measurement configurations is evaluated on the basis of the extended Kalman filter; the system error is taken as a random walk process, and Kalman filtering is used to estimate the position parameters at the same time, so as to weaken the influence of the system error on positioning; the equivalent gain matrix is constructed based on the principle of robust estimation, the weight of abnormal measurement values is reduced, the ability of the filter to resist abnormal value pollution is improved, and the reduction or even divergence of the filtering accuracy is prevented; a multi-mode GNSS-acoustic joint positioning model is constructed, and the Helmert variance component estimation is introduced into the filter model to improve the performance of the filter affected by the inaccuracy of the random model. The above research mainly focuses on the improvement of the filter algorithm itself, which improves the robustness and adaptability of the filter to a certain extent. However, the uncertainty of the initial value and its influence on the filter performance are not comprehensively considered and analyzed. In actual application, the convergence speed and stability of the filter are significantly affected by the initial state parameters and their covariance matrix. In the prior art, the initial value is usually determined according to experience or is arbitrarily assigned, and a large number of observation epochs are often required to reach convergence, which weakens the real-time performance of underwater positioning. Summary of the Invention

[0004] The object of the present invention is to provide a cruise-type real-time GNSS acoustic underwater positioning method to solve the problem in the prior art that the initial value of the state vector of acoustic underwater positioning is difficult to determine.

[0005] A cruise-type real-time GNSS acoustic underwater positioning method, comprising:

[0006] S1. Based on the observation data of the sailing ship, the nonlinear observation equation is expanded by Taylor series to establish the extended Kalman filter observation equation and state equation;

[0007] S2. According to the extended Kalman filter observation equation and state equation in S1, an extended Kalman filter solution model is constructed;

[0008] S3, using the coordinate prior information of the seabed transponder as a constraint to construct a constraint equation and solve the initial state parameters and initial covariance matrix;

[0009] S4. Use the Tikhonov regularization method to deal with the ill-posed problem in the process of solving the initial state parameters and initial covariance matrix;

[0010] S5. Substitute the initial state parameters and the initial covariance matrix values ​​into the extended Kalman filter solution model to perform real-time GNSS acoustic underwater positioning on the seabed transponder.

[0011] S1 includes, S1.1, an acoustic transducer installed on a sailing vessel transmits an interrogation signal to the seabed and receives corresponding response information, records the one-way propagation time of the acoustic signal, and calculates the propagation distance from the sea surface acoustic transducer to the seabed acoustic transponder with the help of sound velocity profile data:

[0012] ;

[0013] ;

[0014] ;

[0015] ;

[0016] ;

[0017] ;

[0018] Where, For the A moment, is the total number of observation epochs, for The acoustic distance measurement between the sea surface acoustic transducer and the seabed acoustic transponder at any time, for The theoretical distance between the sea surface acoustic transducer and the seabed acoustic transponder at any moment, for Time observation error, is the speed of sound, for The one-way propagation time of the acoustic signal at time instant, yes The coordinate matrix of the sea surface acoustic transducer at time t, 、 and yes The three-dimensional coordinates of the sea surface acoustic transducer at time t, is the coordinate matrix of the seabed acoustic transponder, 、 and is the three-dimensional coordinate of the seabed acoustic transponder.

[0019] S1 includes, S1.2, Perform a Taylor series expansion:

[0020] ;

[0021] ;

[0022] Where, is the linearized initial coordinate matrix of the seabed acoustic transponder, 、 and is the linearized initial three-dimensional coordinate of the seabed acoustic transponder;

[0023] S1.3, simplify the Taylor series result, The observation equation at time t is:

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] Where, for The observation vector at time t, for The estimated state vector matrix at time , 、 and for The estimated three-dimensional state vector at time , for The observation equation coefficient matrix at time , for The observation noise vector at time t.

[0030] S1 includes S1.4, and the state equation is:

[0031] ;

[0032] Where, for System status at all times, for Always The 3×3 state transition identity matrix at time t, for The moment process noise vector, and is Gaussian white noise with zero mean and is independent of each other:

[0033] ;

[0034] ;

[0035] Where, It means to find the mathematical expectation of the matrix. for The covariance matrix of for The covariance matrix of is the Kronecker function, For the A moment.

[0036] S2 includes the prediction update formula of the extended Kalman filter solution model:

[0037] ;

[0038] ;

[0039] Where, for Always The predicted state vector of the seabed acoustic transponder at time , for The predicted status of the seabed acoustic transponder at the moment, for The covariance matrix of for The covariance matrix of for Covariance matrix of process noise vector at time instant.

[0040] S2 includes, extending the measurement update formula of Kalman filter model as:

[0041] ;

[0042] ;

[0043] ;

[0044] In the formula, represents Gain matrix of Kalman filter at time instant, is a unit matrix of order 3.

[0045] Obtain the initial value of and the initial value of , , , recursively obtain and , is the initial state parameter, is the initial covariance matrix.

[0046] S3 includes, considering the positions of the front and rear epochs of the seabed acoustic transponder as the same, selecting the observation data of the initial stage of observation, dividing into groups, solving the position by acoustic ranging each group

[0047] ;

[0048] ;

[0049] ;

[0050] In the formula, represents Design matrix of constraint equation of rows columns, is a coordinate correction matrix, represents a zero vector with length , , respectively represent the horizontal, vertical and vertical component coordinate corrections of the th epoch.

[0051] S3 includes, the error equation of the constraint equation is:

[0052] ;

[0053] The observation equation corresponding to the constraint equation is:

[0054] ;

[0055] The error equation of the observation equation is:

[0056] ;

[0057] ;

[0058] wherein, is the coordinate correction of the position of the sea bottom transponder, is the correction matrix of the error equation of the observation equation, is the difference between the acoustic ranging observation value and the theoretical value between the sea surface acoustic transducer and the sea bottom acoustic transponder, and the vector length is , is the observation error, is the coefficient matrix, is the element of the coefficient matrix;

[0059] The coordinate correction of the position of the group of sea bottom transponders is:

[0060] ;

[0061] wherein, is a positive definite matrix;

[0062] The error variance matrix of the position parameter of the sea bottom transponder is :

[0063] ;

[0064] wherein, is the unit weight variance.

[0065] S4 comprises:

[0066] ;

[0067] ;

[0068] wherein, is the regularization parameter obtained by the L curve method, is the regularization unit matrix;

[0069] The average of and is and :

[0070] ;

[0071] ;

[0072] wherein, 、 and are the horizontal, vertical and vertical variance components of the group of is a block-diagonal matrix constructor, is the initial coordinates of the given sea bottom transponder.

[0073] Compared with the prior art, the application has the following beneficial effects: the application solves the ill-conditioned problem that may exist in the solving process, has good performance of short convergence time and high precision, can improve the real-time positioning efficiency of GNSS-acoustic sea bottom transponder, and is expected to provide strong technical support for sea bottom plate movement, geological disasters, disaster warning and sea bottom geodetic datum updating. BRIEF DESCRIPTION OF DRAWINGS

[0074] Figure 1 is an east direction positioning result graph;

[0075] Figure 2 is a north direction positioning result graph;

[0076] Figure 3 is a sky direction positioning result graph;

[0077] Figure 4 is a residual result comparison graph. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical scheme and advantages of the application clearer, the technical scheme in the application will be described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0079] A sailing type real-time GNSS acoustic underwater positioning method, comprising:

[0080] S1, according to the observation data of the sailing ship, Taylor series expansion is carried out on the nonlinear observation equation, and an extended Kalman filter observation equation and a state equation are established;

[0081] S2, according to the extended Kalman filter observation equation and the state equation in S1, an extended Kalman filter solving model is constructed;

[0082] ​S3, using the coordinate prior information of the seabed transponder as a constraint to construct a constraint equation and solve the initial state parameters and initial covariance matrix;

[0083] S4. Use the Tikhonov regularization method to deal with the ill-posed problem in the process of solving the initial state parameters and initial covariance matrix;

[0084] S5. Substitute the initial state parameters and the initial covariance matrix values ​​into the extended Kalman filter solution model to perform real-time GNSS acoustic underwater positioning on the seabed transponder.

[0085] S1 includes, S1.1, an acoustic transducer installed on a sailing vessel transmits an interrogation signal to the seabed and receives corresponding response information, records the one-way propagation time of the acoustic signal, and calculates the propagation distance from the sea surface acoustic transducer to the seabed acoustic transponder with the help of sound velocity profile data:

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] Where, For the A moment, is the total number of observation epochs, for The acoustic distance measurement between the sea surface acoustic transducer and the seabed acoustic transponder at any time, for The theoretical distance between the sea surface acoustic transducer and the seabed acoustic transponder at any moment, for Time observation error, is the speed of sound, for The one-way propagation time of the acoustic signal at time instant, yes The coordinate matrix of the sea surface acoustic transducer at time t, 、 and yes The three-dimensional coordinates of the sea surface acoustic transducer at time t, is the coordinate matrix of the seabed acoustic transponder, 、 and is the three-dimensional coordinate of the seabed acoustic transponder.

[0093] S1 includes, S1.2, Perform a Taylor series expansion:

[0094] ;

[0095] ;

[0096] Where, is the linearized initial coordinate matrix of the seabed acoustic transponder, 、 and is the linearized initial three-dimensional coordinate of the seabed acoustic transponder;

[0097] S1.3, simplify the Taylor series result, The observation equation at the moment is:

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] Where, for The observation vector at time t, for The estimated state vector matrix at time , 、 and for The estimated three-dimensional state vector at time , for The observation equation coefficient matrix at time , for The observation noise vector at time t.

[0104] S1 includes S1.4, and the state equation is:

[0105] ;

[0106] Where, for System status at all times, for Always The 3×3 state transition identity matrix at time t, for The moment process noise vector, and is Gaussian white noise with zero mean and is independent of each other:

[0107] ;

[0108] ;

[0109] Where, It means to find the mathematical expectation of the matrix. for The covariance matrix of for The covariance matrix of is the Kronecker function, For the A moment.

[0110] S2 includes the prediction update formula of the extended Kalman filter solution model:

[0111] ;

[0112] ;

[0113] Where, for Always The predicted state vector of the seabed acoustic transponder at time , for The predicted status of the seabed acoustic transponder at the moment, for The covariance matrix of for The covariance matrix of for The covariance matrix of the process noise vector at time t.

[0114] S2 includes the measurement update formula of the extended Kalman filter solution model:

[0115] ;

[0116] ;

[0117] ;

[0118] Where, express The gain matrix of the time-stamped Kalman filter, is the identity matrix of order 3.

[0119] get The initial value of and The initial value of , obtained by recursion and , is the initial state parameter, is the initial covariance matrix.

[0120] S3 includes considering the positions of the seabed acoustic transponders in the previous and next epochs to be the same, selecting the observation data in the initial stage of observation, and dividing them into Group, each group The constraint equation for solving the position using infraacoustic ranging is expressed as:

[0121] ;

[0122] ;

[0123] ;

[0124] Where, express OK The design matrix of the constraint equations is the column, is the coordinate correction matrix, Indicates the length is The zero vector of 、 、 Respectively represent The horizontal, vertical and vertical components of the coordinate correction for each epoch.

[0125] S3 includes the error equation of the constraint equation for:

[0126] ;

[0127] The observation equation corresponding to the constraint equation is:

[0128] ;

[0129] The error equation of the observation equation is:

[0130] ;

[0131] ;

[0132] Where, is the coordinate correction number of the seabed transponder position, is the correction matrix of the error equation of the observation equation, is the difference between the observed value and the theoretical value of the acoustic distance measurement between the sea surface acoustic transducer and the seabed acoustic transponder, and the vector length is , is the observation error, is the coefficient matrix, is the coefficient matrix element;

[0133] The coordinate corrections for the position of the group's seabed transponders are:

[0134] ;

[0135] Where, is a positive definite matrix;

[0136] Error variance matrix of seabed transponder position parameters for:

[0137] ;

[0138] Where, is the unit weight variance.

[0139] S4 includes:

[0140] ;

[0141] ;

[0142] Where, is the regularization parameter obtained by the L-curve method, is the regularized identity matrix;

[0143] Will and Taking the average, we get and :

[0144] ;

[0145] ;

[0146] Where, 、 and They are middle horizontal, vertical, and perpendicular variance components of the group, is a block diagonal matrix constructor, are the given initial coordinates of the seafloor transponder.

[0147] It can be seen from the filtering equation that the state estimate at the current moment is obtained by recursion from the state at the initial moment. Before filtering for real-time positioning, it is necessary not only to give the state noise covariance and observation noise covariance a priori, but also to know the initial state value and its covariance matrix. How the initial state vector and its covariance matrix affect the performance of the filter can be analyzed through the error dynamics equation and Lyapunov stability theory. In order to analyze the impact of the initial value error on the convergence of the system, the error dynamics equation can be introduced. Kalman filter in The state estimation error at time Expressed as:

[0148] ;

[0149] ;

[0150] The error dynamic equation is:

[0151] ;

[0152] Where, is the error propagation matrix. This equation shows that the current Not only depends on the current , is also affected by the state estimation error at the previous moment If Inaccurate selection, initial error will be larger, making the subsequent The filter will also be larger, and the filter will need more observations and time to correct this larger initial error, which will affect the convergence speed of the filter.

[0153] To ensure system convergence, the error propagation matrix The norm of must satisfy the following conditions:

[0154] ;

[0155] ;

[0156] Where, Represents the matrix norm operator.

[0157] when When it is larger, The value is closer to the identity matrix , The value of is closer to the zero matrix, will be smaller, speeding up the convergence of the filter and supporting the above conditions. However, it should be noted that It is not that the bigger the better, too big It will reduce the stability of the system.

[0158] Able to influence , which affects the system's trust in the observed and predicted values. If the initial state estimate is small, the filter believes that the initial state estimate is more accurate, the Kalman gain is small, and the filter will rely more on its own prediction. In this case, the filter is less sensitive to noise, but if the initial state estimate is inaccurate, the filter may correct the state more slowly, resulting in slower convergence. Larger, It will also be larger, resulting in If is large, the filter relies more on observation data to correct the state estimate. In this case, the filter may be overly sensitive to observation noise. Although the convergence speed is accelerated, the observation noise will also be amplified through the gain matrix, affecting the estimation stability of the filter.

[0159] Lyapunov stability theory is used to prove the influence of state parameters and their initial covariance values ​​on the stability of the filter. Assume that the error energy of the filter is expressed by the Lyapunov function To measure:

[0160] .

[0161] To ensure that the state vector estimate of the system converges over time, the Lyapunov stability condition needs to be satisfied:

[0162] ;

[0163] It shows that to achieve the convergence and stability of the filter, the error energy needs to decrease gradually over time.

[0164] Substituting the error dynamic equation into On the right side, we get:

[0165] ;

[0166] Expand and organize into:

[0167] ;

[0168] ;

[0169] ;

[0170] 、 is an intermediate variable, and the above formula shows that as well as It has a direct impact on the stability of the filtering system. If the initial value of the state parameter is inaccurate, If the deviation from the true value is large, even if the Kalman filter can eventually converge, the convergence speed will be significantly slowed down. Similarly, if If the initial value is selected reasonably, the Lyapunov function will gradually decrease, the error energy will gradually disappear, and the filter will converge to the true state. Optimizing the initial condition can improve the convergence speed of the filter and the accuracy of the final estimate. In practical applications, sufficient attention should be paid to the selection of the initial value to obtain better filtering effect.

[0171] As Figure 1 , Figure 2 , Figure 3 Compared with the traditional extended Kalman filter method, the initial coordinate error of the new method is smaller, and the initial coordinates of the seabed transponder obtained are significantly closer to the reference value. In addition, the new method achieves convergence with fewer observation epochs, and the convergence speed and stability are superior to the traditional method. Taking the three-dimensional positioning accuracy of the current epoch and the next ten epochs as the convergence condition, the new method uses 85 fewer epochs than the traditional method to reach the convergence state. Further verification shows that the initial value determination method proposed in the present application can obtain more accurate initial state parameters and covariance matrix.

[0172] Table 1 lists the positioning results of the seabed transponder after convergence and at the last epoch. T1 is the observation after convergence, and T2 is the observation at the last epoch. Table 1 shows that in both statistical methods, the coordinate error of the new method is smaller than that of the traditional method. Compared with the traditional method, the two-dimensional accuracy of the new method after convergence is improved by 31.8%, and the three-dimensional accuracy is improved by 38.6%. Compared with the traditional method, the final coordinate error of the seabed transponder of the new method is improved by 0.0063m, 0.0119m and 0.0494m in the horizontal and vertical directions, respectively. The above results further verify that the initial value determination method for filter can improve the convergence speed and positioning accuracy of the real-time GNSS-acoustic positioning of the moving ship, so as to obtain more reliable positioning results.

[0173] Table 1 Coordinate deviation and positioning accuracy statistics of two methods

[0174] .

[0175] Figure 4 The acoustic ranging residuals based on the new method and the traditional method are shown. The acoustic ranging residual results of the seabed transponder show that the acoustic ranging residual of the new method is more concentrated than that of the traditional method. This difference is particularly evident before the real-time positioning reaches convergence, which indicates that the real-time GNSS-acoustic seabed point positioning based on the filter initial value determination has good error compensation ability.

[0176] The above examples are only used for illustrating the technical solutions of the present application, and are not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing examples, it should be understood by those skilled in the art that the technical solutions recorded in the foregoing examples can be modified, or some or all of the technical features can be replaced by equivalent replacements, 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 application.

Claims

1. A real-time GNSS acoustic underwater positioning method underway, characterized in that: include: S1. Based on the observation data of the sailing ship, the nonlinear observation equation is expanded by Taylor series to establish the extended Kalman filter observation equation and state equation; S2. According to the extended Kalman filter observation equation and state equation in S1, an extended Kalman filter solution model is constructed; S3, using the coordinate prior information of the seabed transponder as a constraint to construct a constraint equation and solve the initial state parameters and initial covariance matrix; S4. Use the Tikhonov regularization method to deal with the ill-posed problem in the process of solving the initial state parameters and initial covariance matrix; S4 includes: ； ； Where, is the coordinate correction number of the seabed transponder position, is the coefficient matrix, is a positive definite matrix, express OK The design matrix of the constraint equations is the column, is the regularization parameter obtained by the L-curve method, is the regularized identity matrix, is the difference between the observed value and the theoretical value of the acoustic distance measurement between the sea surface acoustic transducer and the seabed acoustic transponder, and the vector length is , is the unit weight variance, is the error variance matrix of the seabed transponder position parameters; Will and Taking the average, we get and : ； ； Where, yes The initial value of yes The initial value of for The predicted status of the seabed acoustic transponder at the moment, for The covariance matrix of 、 and They are middle horizontal, vertical, and perpendicular variance components of the group, is a block diagonal matrix constructor, is the given initial coordinate of the seabed transponder, 、 、 Respectively represent The horizontal, longitudinal and vertical component coordinate corrections for each epoch; S5. Substitute the initial state parameters and the initial covariance matrix values ​​into the extended Kalman filter solution model to perform real-time GNSS acoustic underwater positioning on the seabed transponder.

2. The underway real-time GNSS acoustic underwater positioning method according to claim 1, characterized in that: S1 includes, S1.1, an acoustic transducer installed on a sailing vessel transmits an interrogation signal to the seabed and receives corresponding response information, records the one-way propagation time of the acoustic signal, and calculates the propagation distance from the sea surface acoustic transducer to the seabed acoustic transponder with the help of sound velocity profile data: ； ； ； ； ； ； Where, For the A moment, is the total number of observation epochs, for The acoustic distance measurement between the sea surface acoustic transducer and the seabed acoustic transponder at any time, for The theoretical distance between the sea surface acoustic transducer and the seabed acoustic transponder at any moment, for Time observation error, is the speed of sound, for The one-way propagation time of the acoustic signal at time instant, yes The coordinate matrix of the sea surface acoustic transducer at time t, 、 and yes The three-dimensional coordinates of the sea surface acoustic transducer at time t, is the coordinate matrix of the seabed acoustic transponder, 、 and is the three-dimensional coordinate of the seabed acoustic transponder.

3. The underway real-time GNSS acoustic underwater positioning method according to claim 2, characterized in that: S1 includes, S1.2, Perform a Taylor series expansion: ； ； Where, is the linearized initial coordinate matrix of the seabed acoustic transponder, 、 and is the linearized initial three-dimensional coordinate of the seabed acoustic transponder; S1.3, simplify the Taylor series result, The observation equation at the moment is: ； ； ； ； ； Where, for The observation vector at time t, for The estimated state vector matrix at time , 、 and for The estimated three-dimensional state vector at time , for The observation equation coefficient matrix at time , for The observation noise vector at time t.

4. The underway real-time GNSS acoustic underwater positioning method according to claim 3, characterized in that: S1 includes S1.4, and the state equation is: ； Where, for System status at all times, for Always The 3×3 state transition identity matrix at time t, for The moment process noise vector, and is zero-mean Gaussian white noise and is independent of each other: ； ； Where, It means to find the mathematical expectation of the matrix. for The covariance matrix of for The covariance matrix of is the Kronecker function, For the A moment.

5. The underway real-time GNSS acoustic underwater positioning method according to claim 4, characterized in that: S2 includes the prediction update formula of the extended Kalman filter solution model: ； ； Where, for Always The predicted state vector of the seabed acoustic transponder at time , for The predicted status of the seabed acoustic transponder at the moment, for The covariance matrix of for The covariance matrix of for The covariance matrix of the process noise vector at time t.

6. The underway real-time GNSS acoustic underwater positioning method according to claim 5, characterized in that: S2 includes the measurement update formula of the extended Kalman filter solution model: ； ； ； Where, express The gain matrix of the time-stamped Kalman filter, is the identity matrix of order 3.

7. The underway real-time GNSS acoustic underwater positioning method according to claim 6, characterized in that: Obtained by recursion and , is the initial state parameter, is the initial covariance matrix.

8. The underway real-time GNSS acoustic underwater positioning method according to claim 7, characterized in that: S3 includes considering the positions of the seabed acoustic transponders in the previous and next epochs to be the same, selecting the observation data in the initial stage of observation, and dividing them into Group, each group The constraint equation for solving the position using infraacoustic ranging is expressed as: ； ； ； Where, is the coordinate correction matrix, Indicates the length is The zero vector of 、 、 Respectively represent The horizontal, vertical and vertical components of the coordinate correction for each epoch.

9. The underway real-time GNSS acoustic underwater positioning method according to claim 8, characterized in that: S3 includes the error equation of the constraint equation for: ； The observation equation corresponding to the constraint equation is: ； The error equation of the observation equation is: ； ； Where, is the correction matrix of the error equation of the observation equation, is the observation error, is the coefficient matrix element; The coordinate corrections for the position of the group's seabed transponders are: ； Error variance matrix of seabed transponder position parameters for: 。

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