Long baseline system time delay correction positioning method based on radial speed information

Abstract

The invention discloses a long baseline system time delay correction positioning method based on radial speed information, belongs to the field of underwater positioning and navigation, and particularly relates to the long baseline system time delay correction positioning method based on the radial speed information. The invention aims to solve the problems of large calculation amount and low positioning precision of the existing navigation positioning algorithm. The method comprises the following steps of: 1, acquiring one-way propagation time delay between a target and a transponder; 2, calculating a horizontal distance and propagation time of sound ray propagation, and generating a time delay-distance table based on the horizontal distance and the propagation time; 3, finding a corresponding horizontal propagation distance in the time delay-distance table according to the one-way propagation time delay, and resolving the position of the target to be positioned by using a positioning algorithm according to the horizontal propagation distance; assigning the calculated target position coordinate, the target initial position and the initial speed as parameters to a target state to obtain [X1,..., Xm,..., XM]; and 4, processing the target state by using a Kalman filtering algorithm to obtain a target trajectory.

Description

Technical Field

[0001] The present invention belongs to the field of underwater positioning and navigation, and in particular relates to a long baseline system delay correction positioning method based on radial velocity information. Background Art

[0002] As marine development progresses towards higher speeds and deeper submersion, unmanned submersibles (UUVs) are experiencing higher speeds and deeper operating depths, placing greater demands on the positioning accuracy and response speed of autonomous underwater navigation systems. UUVs require the support of underwater navigation and positioning systems, which use high-precision underwater positioning algorithms to calculate parameters such as the submersible's spatial position and motion state in real time.

[0003] However, because unmanned underwater vehicles (UUVs) constantly move underwater, the signal transmission and reception positions of navigation systems in interrogation-response mode are inconsistent. Therefore, traditional positioning algorithms must solve the elliptical confocal point problem within a short period of time. Existing underwater long-baseline positioning systems primarily employ the elliptical confocal point algorithm with nonlinear least-squares optimization. However, these methods often have limitations: they are computationally intensive and complex, failing to meet the real-time requirements of navigation systems with limited computing and storage resources; they are also sensitive to initial conditions, resulting in large errors in the calculated results.

[0004] Furthermore, sound speed, a key parameter in navigation and positioning systems, is affected by the temperature, salinity, and depth of the water medium. According to ray acoustics theory, sound rays bend in water toward decreasing speed. Therefore, if only a fixed sound speed is used in underwater environments, the target position calculated by the positioning algorithm will have significant errors. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems of large computational complexity and low positioning accuracy of existing navigation and positioning algorithms, and to propose a long baseline system delay correction positioning method based on radial velocity information.

[0006] A long baseline system delay correction positioning method based on radial velocity information has the following specific process:

[0007] Step 1: Obtain the one-way propagation delay between the target and the transponder. The specific process is as follows:

[0008] Step 1: Construct the two-way distance R of the signal propagation of the i-th synchronization period i Expressions of

[0009] Step 1 and 2: The round-trip distance R based on the signal propagation of the i-th synchronization cycle i The expression of the corrected slope distance D is obtained ri ;

[0010] Step 13: Based on the round-trip propagation delay ti , t j Construct an expression for the radial velocity v of the target relative to the transponder;

[0011] Step 14: Substitute the expression of the target's radial velocity v relative to the transponder into the corrected slant distance D obtained in step 12. ri , and obtain the new corrected slope distance D ri ;

[0012] Step 15: Based on the new corrected slant distance D from step 14 ri , and obtain the corrected one-way propagation delay t ri ;

[0013] Step 2: Use ray tracing technology to calculate the horizontal distance and propagation time of the sound ray, and generate a time delay-distance table based on the horizontal distance and propagation time;

[0014] Step 3: The corrected one-way propagation delay t obtained in step 15 ri Find the corresponding horizontal propagation distance in the delay-distance table obtained in step 2, and use the positioning algorithm to calculate the position of the target to be located based on the horizontal propagation distance;

[0015] The calculated target position coordinates, target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m ,…,X M ];

[0016] Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ;

[0017] The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ;

[0018] The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ;

[0019] (v x (1),v y (1)) represents the x-axis velocity component and the y-axis velocity component of the target at time 1;

[0020] (v x (m),v y (m)) represents the x-axis velocity and y-axis velocity of the target at time m;

[0021] (v x (M),v y (M)) represents the x-axis velocity and y-axis velocity of the target at time M;

[0022] The superscript T means to find the transpose;

[0023] Step 4: Use the Kalman filter algorithm to process the target state and obtain the target trajectory; the specific process is:

[0024] 1) Input the initial target state X1=[x(1),v x (1),y(1),v y (1)] T ;

[0025] 2) Let m = 2;

[0026] If the target state X m If it is a null value, Kalman filter is used to filter the target state X m Make a prediction and use the predicted value to fill the empty value as the updated target position to be located;

[0027] If the target state X m If it is a non-null value, Kalman filtering is used to filter the target state X m Make predictions and updates, and use the updated value as the updated target position to be located;

[0028] 3) Set m = m + 1, repeat 2) until m = M, and obtain the target trajectory.

[0029] Preferably, in the step one, the round-trip distance R of the propagation of the i-th synchronous periodic signal is constructed. i Expressions of

[0030] R i =r i1 +r i2 =r i1 +[r i1 +(t i +τ)v]=2r i1 +(t i +τ)v

[0031] Where,

[0032] r i1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period;

[0033] r i2 Indicates the distance from the transponder to the target when the target receives the response signal returned by the transponder in the i-th synchronization cycle;

[0034] t i represents the round-trip propagation delay of the signal between the target and the transponder in the i-th synchronization period;

[0035] τ represents the response delay of the transponder;

[0036] v represents the radial velocity of the target relative to the seabed transponder.

[0037] Preferably, the round-trip distance R based on the propagation of the i-th synchronization period signal in steps one and two is i The expression of the corrected slope distance D is obtained ri ; The expression is:

[0038]

[0039] Where c is the speed of sound in water.

[0040] Preferably, in the steps 1 and 3, the round-trip propagation delay t i , t j Construct an expression for the radial velocity v of the target relative to the transponder; the specific process is:

[0041] Step 131. Calculate the distance r between the target and the transponder when the target transmits the interrogation signal in the kth synchronization period k1 The distance r from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period i1 The difference; expressed as:

[0042] r k1 -r i1 =(r k1 -r j1 )+(r j1 -r i1 )

[0043] ≈(r j2 -r i2 )+(r j1 -r i1 )

[0044] =(r j1 +r j2 )-(r i1 +r i2 )

[0045] =R j -R i

[0046] Where, j = i + 1, k = i + 2;

[0047] r i1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period;

[0048] r j1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the jth synchronization period;

[0049] r k1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the kth synchronization period;

[0050] r i2 represents the distance between the target and the transponder when the target receives the response signal returned by the transponder in the i-th synchronization cycle;

[0051] r j2 represents the distance between the target and the transponder when the target receives the response signal returned by the transponder in the jth synchronization cycle;

[0052] R i represents the two-way distance of signal propagation in the i-th synchronization cycle;

[0053] R j represents the two-way distance of signal propagation in the jth synchronization cycle;

[0054] Step 132: Based on the round-trip distance R of the signal propagation in the i-th synchronization cycle i and the round-trip distance R of the signal propagation in the jth synchronization cycle j , calculate the radial velocity v of the target relative to the transponder; the expression is:

[0055]

[0056] in,

[0057] t j represents the round-trip propagation delay of the signal between the target and the transponder in the jth synchronization cycle;

[0058] t i represents the round-trip propagation delay of the signal between the target and the transponder in the i-th synchronization cycle;

[0059] T is the synchronization period.

[0060] Preferably, in step 14, the expression of the radial motion speed v of the target relative to the transponder is substituted into the corrected slant distance D obtained in step 12. ri , and obtain the new corrected slope distance D ri ; The specific process is:

[0061] Substitute the expression of the radial velocity v of the target relative to the transponder into the corrected slant distance D obtained in steps 1 and 2. ri The expression of the new corrected slope distance D is obtained ri ; The expression is:

[0062]

[0063] Preferably, the step 15 is based on the new corrected slant distance D in step 14. ri , and obtain the corrected one-way propagation delay t ri ; The specific process is:

[0064] Based on the new corrected slope distance D in step 1 and 4 ri The expression of the corrected one-way propagation delay t ri ; The expression is:

[0065]

[0066] Preferably, in step 2, the horizontal distance and propagation time of the sound ray are calculated using the sound ray tracing technology, and a time delay-distance table is generated based on the horizontal distance and propagation time. The specific process is as follows:

[0067] Step 21: Obtain the sound velocity gradient distribution c(z) of the water area through hydrological measurement;

[0068] Step 2: Set l eigenvalues in the Bellhop sound field model, and the initial grazing angle of each ray is θ ω (ω=1,2,…l), set the sound source depth to z s , the depth of the receiving point is z r , the horizontal distance between the sound source and the receiving point is s;

[0069] Select the first arriving eigenvalue from all the sound rays at the receiving point, and obtain the initial grazing angle α0 and the sound speed c0 at the sound source corresponding to the first arriving eigenvalue;

[0070] Step 2 and 3: Distribute the sound velocity gradient distribution c(z) of the water area along the z-axis from the depth z s to z r Divided into E layers, the sound velocity gradient g in each layer of water medium e Approximately constant value:

[0071]

[0072] in,

[0073] g e represents the constant sound velocity gradient in the e-th layer of medium;

[0074] ze Indicates the depth of the lower interface of the e-th layer of medium;

[0075] z e-1 represents the depth of the lower interface of the e-1th layer of medium;

[0076] c(z e ) indicates the depth is z e The speed of sound at 1000 s;

[0077] c(z e-1 ) indicates the depth is z e-1 The speed of sound at 1000 s;

[0078] During the propagation of sound rays, the speed of sound and the grazing angle at different positions satisfy Snell's law:

[0079]

[0080] Calculate the horizontal propagation distance s and propagation time t of the first arriving eigenvalue ray;

[0081]

[0082]

[0083] Among them, α e represents the grazing angle of the first eigenvalue ray arriving at the lower boundary of the e-th layer of medium, α e+1 represents the grazing angle of the first arriving eigenvalue ray at the lower boundary of the e+1th layer of medium;

[0084] Step 24: Obtain the delay-distance table.

[0085] Preferably, the delay-distance table is obtained in step 24; the specific process is:

[0086] 1) Let n = 0;

[0087] 2) Set the horizontal distance between the sound source and the receiving point to s+nds;

[0088] Where s is the minimum horizontal distance between the sound source and the receiving point, and ds is the horizontal distance step size;

[0089] 3) Repeat steps 22 to 23 to obtain the propagation time corresponding to the horizontal distance s+nds;

[0090] 4) Let n = n + 1;

[0091] Repeat 2) to 3) until n = N, and obtain the propagation time corresponding to all horizontal distances;

[0092] In this way, the corresponding relationship between the horizontal distance between the sound source and the receiving point and the propagation time is established, and the time delay-distance table is obtained.

[0093] Preferably, the corrected one-way propagation delay t obtained in step 3 according to step 15 is ri Find the corresponding horizontal propagation distance in the delay-distance table obtained in step 2, and use the positioning algorithm to calculate the position of the target to be located based on the horizontal propagation distance;

[0094] The calculated target position coordinates, target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m ,…,X M ];

[0095] Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ;

[0096] The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ;

[0097] The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ;

[0098] (v x (1),v y (1)) represents the x-axis velocity component and the y-axis velocity component of the target at time 1;

[0099] (v x (m),v y (m)) represents the x-axis velocity and y-axis velocity of the target at time m;

[0100] (v x (M),v y (M)) represents the x-axis velocity and y-axis velocity of the target at time M;

[0101] The superscript T means to find the transpose;

[0102] The specific process is:

[0103] 1) If the delay data of more than 3 transponders is received in a synchronization period, the target position is calculated using a linear solution algorithm. The specific process is as follows:

[0104]

[0105]

[0106]

[0107] in,

[0108] (x t ,y t ,z t ) is the target position to be solved;

[0109] (x1, y1, z1) are the coordinates of the first transponder; (x2, y2, z2) are the coordinates of the second transponder; (x3, y3, z3) are the coordinates of the third transponder;

[0110] s1 is the propagation distance from the underwater target to the first transponder; s2 is the propagation distance from the underwater target to the second transponder; s3 is the propagation distance from the underwater target to the third transponder;

[0111] The above three formulas can be organized as follows:

[0112]

[0113]

[0114] Rewrite the above formula as:

[0115] AX=B

[0116] Among them, A and B are matrices, and X is the target position coordinate;

[0117]

[0118] When the inverse matrix of matrix A exists, vector X has a unique solution, that is, the target position is uniquely determined;

[0119] 2) If the time delay data of two transponders is received in a synchronization period, the target position is calculated using a nonlinear solution algorithm; the specific process is as follows:

[0120]

[0121]

[0122] When two sets of solutions are obtained by combining the two equations, the points far from the historical trajectory are discarded and the points close to the historical trajectory are selected as the target positions.

[0123] When two equations are solved together to obtain a set of solutions, the set of solutions is directly used as the target position;

[0124] When no solution is obtained for the two equations, the target position is set to a null value;

[0125] 3): If the delay data of 0 or 1 transponder is received in a certain synchronization period, the target position corresponding to the synchronization period is set to a null value;

[0126] 4): The calculated target position coordinates and the target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m ,…,X M ];

[0127] Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ;

[0128] The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ;

[0129] The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ;

[0130] (v x (1),v y (1)) represents the x-axis velocity component and the y-axis velocity component of the target at time 1;

[0131] (v x (m),v y (m)) represents the x-axis velocity and y-axis velocity of the target at time m;

[0132] (v x (M),v y (M)) represents the x-axis velocity and y-axis velocity of the target at time M;

[0133] The superscript T means transpose.

[0134] Preferably, in step 4, if the target state X m If it is a null value, Kalman filter is used to filter the target state X mMake a prediction and use the predicted value to fill the empty value as the updated target position to be located;

[0135] If the target state X m If it is a non-null value, Kalman filtering is used to filter the target state X m Make predictions and updates, and use the updated value as the updated target position to be located;

[0136] The specific process is:

[0137] 1. Target state vector X at time m m =[x(m),v x (m),y(m),v y (m)] T ;

[0138] Among them, x(m),v x (m),y(m),v y (m) represents the x-axis coordinate, x-axis velocity component, y-axis coordinate, and y-axis velocity component of the target at time m.

[0139] The superscript T means to find the transpose;

[0140] Second, the state space model is:

[0141]

[0142] in,

[0143] X m =FX m-1 +w m-1 is the equation of state;

[0144] Z m =HX m +v m is the observation equation;

[0145] F is the state transfer matrix, w m-1 is the process noise, Z m is the observed value of the system at time m, H is the observation matrix, v m is the observation noise; X m-1 is the state vector at time m-1;

[0146] The state equation of the Kalman filter is a uniform velocity model. In the state equation:

[0147]

[0148] In the observation equation

[0149]

[0150] 3. Process the target state:

[0151] State prediction equation:

[0152]

[0153] in, represents the state vector updated at time m-1, Represents the predicted value of the state vector at time m;

[0154] Covariance prediction equation:

[0155]

[0156] in, represents the posterior estimated covariance at time m-1, represents the prior estimated covariance at time m, and Q represents the process noise covariance;

[0157] Prior estimated covariance based on k moments Calculate the Kalman gain:

[0158]

[0159] Among them, K m represents the Kalman gain, R represents the observation noise covariance;

[0160] State update equation:

[0161] If the target state X m If it is null, the predicted value Fill in the empty value as the updated target position to be located;

[0162] If the target state X m Is a non-null value, then As the updated target position to be located;

[0163]

[0164] Covariance update equation:

[0165]

[0166] in, represents the posterior estimated covariance at time m.

[0167] The beneficial effects of the present invention are:

[0168] The purpose of the method of the present invention is to improve the positioning accuracy of the autonomous navigation system in the query-response working scenario. The present invention derives a one-way delay correction method based on the radial velocity of the moving target relative to the seabed transponder, which reduces the slant range error caused by the target movement in the intersection positioning model. Afterwards, the sound ray tracking technology is used to calculate the horizontal distance of the sound ray propagation and locate the target to overcome the influence of the sound ray bending in the underwater environment. The post-processing part uses the Kalman filter algorithm to process the target motion trajectory to further improve the accuracy of the navigation trajectory. The method of the present invention can be applied to the field of underwater positioning and navigation.

[0169] In the navigation system, the one-way delay correction algorithm calculates the one-way delay of the interrogation signal to the transponder based on the radial velocity of the target relative to the transponder, and aligns the target positioning solution point of each synchronization cycle to the time when the interrogation signal is transmitted, avoiding the solution of the elliptical confocal point problem, greatly reducing the computational complexity of the positioning algorithm, improving the calculation speed, reducing the error of the positioning result, and improving the positioning accuracy, thus meeting the real-time requirements of the autonomous navigation system.

[0170] Ray acoustics theory shows that sound rays bend when propagating underwater. Therefore, the actual distance traveled by the ray is not the straight-line distance between the target and the transponder. Using a fixed sound speed solution across the entire water area can introduce significant positioning errors. Ray tracking technology can correct the distance between the target and the transponder, calculating the horizontal distance between them based on the laws of underwater sound propagation, thereby reducing positioning errors.

[0171] Furthermore, underwater acoustic propagation typically exhibits multipath effects, time-varying characteristics, and absorption attenuation. Uncertainty in the underwater acoustic channel can lead to failures in the transmission of response signals. When insufficient transponder delay data is received by the target, the positioning algorithm cannot determine the target's position. Using a Kalman filter in post-processing can interpolate missing portions of the target's trajectory and reduce overall navigation trajectory errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0172] Figure 1 This is the basic flow chart of the delay correction positioning algorithm;

[0173] Figure 2 This is a schematic diagram of the navigation system working in the interrogation-response mode;

[0174] Figure 3 This is a schematic diagram of the derivation of the one-way delay correction algorithm;

[0175] Figure 4 This is a typical deep-sea sound velocity profile used in the simulation process;

[0176] Figure 5 Navigate simulation result graphs for traditional algorithms;

[0177] Figure 6 This is the positioning error map of the traditional algorithm;

[0178] Figure 7 This is a diagram of the simulation results of the algorithm navigation of the present invention;

[0179] Figure 8 This is the positioning error diagram of the algorithm of the present invention. DETAILED DESCRIPTION

[0180] Specific embodiment 1: This embodiment is a long baseline system delay correction positioning method based on radial velocity information. The specific process is as follows:

[0181] Step 1: Obtain the one-way propagation delay between the target and the transponder;

[0182] In the interrogation-response mode of the long-baseline positioning and navigation model, when the target's velocity is negligibly low, the system can directly use half of the total delay from transmission to reception as the one-way propagation delay and use this delay to solve the intersection positioning equation. However, when the target's velocity is high or the system's synchronization period is long, this algorithm introduces non-negligible systematic errors. To address this issue and improve the accuracy of signal propagation delay estimation, a one-way delay correction algorithm is derived below.

[0183] The specific process is:

[0184] Step 1: Construct the round-trip distance R of the signal propagation in the i-th synchronization period (fixed time interval) i Expressions of

[0185] Step 1 and 2: The round-trip distance R of the signal propagation based on the i-th synchronization period (fixed time interval) i The expression of the corrected slope distance D is obtained ri ;

[0186] Step 13: Based on the round-trip propagation delay t i , t j Construct an expression for the radial velocity v of the target relative to the transponder;

[0187] Step 14: Substitute the expression of the target's radial velocity v relative to the transponder into the corrected slant distance D obtained in step 12. ri , and obtain the new corrected slope distance D ri ;

[0188] Step 15: Based on the new corrected slant distance D from step 14 ri , and obtain the corrected one-way propagation delay t ri ;

[0189] Step 2: Use ray tracing technology to calculate the horizontal distance and propagation time of the sound ray, and generate a time delay-distance table based on the horizontal distance and propagation time;

[0190] Step 3: The corrected one-way propagation delay t obtained in step 15 ri Find the corresponding horizontal propagation distance in the delay-distance table obtained in step 2, and use the positioning algorithm to calculate the position of the target to be located based on the horizontal propagation distance;

[0191] The calculated target position coordinates, target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m ,…,X M ];

[0192] Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ;The initial coordinates of the target are known;

[0193] The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ;

[0194] The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ; Target position solution from time 2 to time M;

[0195] (v x (1),v y (1)) represents the x-axis component velocity and y-axis component velocity of the target at time 1 (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis); the initial velocity (v x (1),v y (1) Obtained through existing technical means, such as a speed meter;

[0196] (v x (m),v y (m)) represents the x-axis velocity component and the y-axis velocity component of the target at time m (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis), which is obtained by the Kalman filter algorithm in step 4;

[0197] (vx (M),v y (M)) represents the x-axis velocity component and the y-axis velocity component of the target at time M (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis), which is obtained by the Kalman filter algorithm in step 4;

[0198] The superscript T means to find the transpose;

[0199] 2. The x-axis velocity and y-axis velocity of the target at time 2 (v x (2),v y (2)) to the target's x-axis velocity and y-axis velocity (v x (M),v y In (M), the x-axis velocity component and the y-axis velocity component are obtained by the Kalman filter algorithm;

[0200] Step 4: Use the Kalman filter algorithm to process the target state and obtain the target trajectory; the specific process is:

[0201] 1) Input the initial target state X1=[x(1),v x (1),y(1),v y (1)] T ;

[0202] 2) Let m = 2;

[0203] If the target state X m If it is a null value, Kalman filter is used to filter the target state X m Make a prediction and use the predicted value to fill the empty value as the updated target position to be located;

[0204] If the target state X m If it is a non-null value, Kalman filtering is used to filter the target state X m Make predictions and updates, and use the updated value as the updated target position to be located;

[0205] 3) Set m = m + 1, repeat 2) until m = M, and obtain the target trajectory.

[0206] Only one filtering can achieve two goals (filling the voids + reducing the trajectory error).

[0207] Specific embodiment 2: The difference between this embodiment and specific embodiment 1 is that the round-trip distance R of the signal propagation in the i-th synchronization period (fixed time interval) is constructed in step 1. i Expressions of

[0208] R i =r i1 +r i2 =ri1 +[r i1 +(t i +τ)v]=2r i1 +(t i +τ)v

[0209] Where,

[0210] r i1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period;

[0211] r i2 Indicates the distance from the transponder to the target when the target receives the response signal returned by the transponder in the i-th synchronization cycle;

[0212] t i represents the round-trip propagation delay (from transmission to reception) of the signal between the target and the transponder in the i-th synchronization period;

[0213] τ represents the response delay of the transponder;

[0214] v represents the radial motion speed of the target relative to the seabed transponder (in the spatial rectangular coordinate system, due north is the Y axis, due east is the X axis, and the vertical sea surface is the Z axis).

[0215] Other steps and parameters are the same as those in the first embodiment.

[0216] Specific embodiment 3: This embodiment differs from specific embodiment 1 or 2 in that the round-trip distance R of the signal propagation based on the i-th synchronization cycle (fixed time interval) in steps 1 and 2 is i The expression of the corrected slope distance D is obtained ri ; The expression is:

[0217]

[0218] Where c is the speed of sound in water.

[0219] Other steps and parameters are the same as those in the first or second embodiment.

[0220] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the round-trip propagation delay t i , t j Construct an expression for the radial velocity v of the target relative to the transponder; the specific process is:

[0221] The formula for the radial velocity of the target relative to the transponder is:

[0222]

[0223] However, in actual application scenarios, it is impossible for the system to predict the distance between the target and the transponder after two synchronization cycles, that is, r in the above formula k1 It cannot be obtained and needs to be approximated based on known quantities.

[0224] r k1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the kth synchronization period;

[0225] Step 131. Calculate the distance r between the target and the transponder when the target transmits the interrogation signal in the kth synchronization period k1 The distance r from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period i1 The difference; expressed as:

[0226] Considering the relatively low speed of underwater targets, r j2 -r i2 With r k1 -r j1 Approximately equal, the approximate process of the radial velocity v of the target relative to the transponder is given below;

[0227] r k1 -r i1 =(r k1 -r j1 )+(r j1 -r i1 )

[0228] ≈(r j2 -r i2 )+(r j1 -r i1 )

[0229] =(r j1 +r j2 )-(r i1 +r i2 )

[0230] =R j -R i

[0231] Where, j = i + 1, k = i + 2;

[0232] r i1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period;

[0233] r j1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the jth synchronization period;

[0234] r k1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the kth synchronization period;

[0235] r i2 Indicates the distance from the target to the transponder when the target receives the response signal returned by the transponder in the i-th synchronization cycle;

[0236] r j2 represents the distance between the target and the transponder when the target receives the response signal returned by the transponder in the jth synchronization cycle;

[0237] R i represents the two-way distance of signal propagation in the i-th synchronization cycle;

[0238] R j represents the two-way distance of signal propagation in the jth synchronization cycle;

[0239] Step 132: Based on the round-trip distance R of the signal propagation in the i-th synchronization cycle i and the round-trip distance R of the signal propagation in the jth synchronization cycle j , calculate the radial velocity v of the target relative to the transponder; the expression is:

[0240]

[0241] in,

[0242] t j represents the round-trip propagation delay (from transmission to reception) of the signal between the target and the transponder in the jth synchronization cycle;

[0243] t i represents the round-trip propagation delay (from transmission to reception) of the signal between the target and the transponder in the i-th synchronization cycle;

[0244] T is the synchronization period.

[0245] The radial velocity of the moving target relative to the transponder is approximately deduced based on the geometric relationship between the target motion trajectory and the transponder. This approximation method can reduce the slant range error of the positioning algorithm while making full use of known parameters.

[0246] The other steps and parameters are the same as those in the first to third embodiments.

[0247] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that in step 14, the expression of the radial motion velocity v of the target relative to the transponder is substituted into the corrected slant distance D obtained in step 12. ri , and obtain the new corrected slope distance D ri ; The specific process is:

[0248] Substitute the expression of the radial velocity v of the target relative to the transponder into the corrected slant distance D obtained in steps 1 and 2.ri The expression of the new corrected slope distance D is obtained ri ; The expression is:

[0249]

[0250] The other steps and parameters are the same as those in the first to fourth embodiments.

[0251] Specific embodiment 6: This embodiment differs from any one of the specific embodiments 1 to 5 in that the step 15 is based on the newly corrected slant distance D in step 14. ri , and obtain the corrected one-way propagation delay t ri ; The specific process is:

[0252] Based on the new corrected slope distance D in step 1 and 4 ri The expression of the corrected one-way propagation delay t ri ; The expression is:

[0253]

[0254] The other steps and parameters are the same as those in the first to fifth embodiments.

[0255] Specific embodiment seven: This embodiment differs from any one of specific embodiments one to six in that, in step two, the horizontal distance and propagation time of the sound ray are calculated using the sound ray tracing technology, and a time delay-distance table is generated based on the horizontal distance and propagation time. The specific process is as follows:

[0256] In an ideal positioning and navigation model, the speed of sound in the water medium is approximately constant, and the acoustic signal propagates in a straight line in the water. The distance between the target and the transponder can be obtained by multiplying the speed of sound by the propagation delay of the signal. According to the theory of ray acoustics, the sound line will bend in the direction of lower sound speed during underwater propagation. Therefore, in the actual underwater environment, the sound line does not propagate in a straight line. The solution equation of the long baseline positioning system needs to obtain the distance between the two based on the signal propagation delay from the target to the transponder and the speed of sound in the water. If a constant sound speed is used for positioning in all test sea areas, the calculated slant range error will be large, resulting in a large deviation between the positioning result and the actual position.

[0257] The following uses sound ray tracing technology to calculate the horizontal distance of sound ray propagation to reduce the error caused by sound ray bending.

[0258] Step 21: Obtain the sound velocity gradient distribution c(z) of the water area through hydrological measurement;

[0259] Step 2: Use Bellhop to build a sound field model and simulate the propagation path of the eigenvalue line. Set l eigenvalue lines in the Bellhop sound field model, and the initial grazing angle of each line is θ ω (ω=1,2,…l), set the sound source depth to z s (The sound source position can be changed each cycle), the depth of the receiving point is z r (The transponder position remains unchanged in each cycle), the horizontal distance between the sound source and the receiving point is s;

[0260] Select the first arriving eigenvalue from all the sound rays at the receiving point, and obtain the initial grazing angle α0 and the sound speed c0 at the sound source corresponding to the first arriving eigenvalue;

[0261] Step 2 and 3: calculate the sound velocity gradient distribution c(z) of the water area along the z-axis (vertical to the water surface) from the depth z s to z r Divided into E layer (including z s and z r ), the sound velocity gradient g in each layer of water medium e Approximately constant value:

[0262]

[0263] in,

[0264] g e represents the constant sound velocity gradient in the e-th layer of medium;

[0265] z e Indicates the depth of the lower interface of the e-th layer of medium;

[0266] z e-1 represents the depth of the lower interface of the e-1th layer of medium;

[0267] c(z e ) indicates the depth is z e The speed of sound at 1000 s;

[0268] c(z e-1 ) indicates the depth is z e-1 The speed of sound at 1000 s;

[0269] During the propagation of sound rays, the speed of sound and the grazing angle at different positions satisfy Snell's law:

[0270]

[0271] Calculate the horizontal propagation distance s and propagation time t of the first arriving eigenvalue ray;

[0272]

[0273]

[0274] Among them, α e represents the grazing angle of the first eigenvalue ray arriving at the lower boundary of the e-th layer of medium, α e+1 represents the grazing angle of the first arriving eigenvalue ray at the lower boundary of the e+1th layer of medium;

[0275] Step 24: Obtain the delay-distance table.

[0276] The other steps and parameters are the same as those in the first to sixth embodiments.

[0277] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the delay-distance table is obtained in step 24; the specific process is as follows:

[0278] 1) Let n = 0;

[0279] 2) Set the horizontal distance between the sound source and the receiving point to s+nds;

[0280] Where s is the minimum horizontal distance between the sound source and the receiving point, and ds is the horizontal distance step size;

[0281] 3) Repeat steps 22 to 23 to obtain the propagation time corresponding to the horizontal distance s+nds;

[0282] 4) Let n = n + 1;

[0283] Repeat 2) to 3) until n = N, and obtain the propagation time corresponding to all horizontal distances;

[0284] In this way, the corresponding relationship between the horizontal distance between the sound source and the receiving point and the propagation time is established, and the time delay-distance table is obtained.

[0285] When the sound source depth changes, reset the sound source depth in step 22 and obtain the delay-distance table at the current depth.

[0286] The other steps and parameters are the same as those in the first to seventh embodiments.

[0287] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the corrected one-way propagation delay t obtained in step 3 according to step 15 is ri Find the corresponding horizontal propagation distance in the delay-distance table obtained in step 2;

[0288] For delay values that do not appear in the delay-distance table, use linear interpolation to calculate the corresponding horizontal distance:

[0289]

[0290] Among them, t p and t q is the one-way propagation delay t in the delay-distance table ri The two closest delays, s p and s q is the delay t p and t q Corresponding horizontal distance, s a is the horizontal distance calculated by linear interpolation;

[0291] Use the positioning algorithm to calculate the position of the target to be located based on the horizontal propagation distance;

[0292] The calculated target position coordinates, target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m ,…,X M ];

[0293] Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ;

[0294] The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ;

[0295] The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ;

[0296] (v x (1),v y (1)) represents the x-axis component velocity and y-axis component velocity of the target at time 1 (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis); the initial velocity (v x (1),v y (1) Obtained through existing technical means, such as a speed meter;

[0297] (v x (m),v y(m)) represents the x-axis velocity component and the y-axis velocity component of the target at time m (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis), which is obtained by the Kalman filter algorithm in step 4;

[0298] (v x (M),v y (M)) represents the x-axis velocity component and the y-axis velocity component of the target at time M (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis), which is obtained by the Kalman filter algorithm in step 4;

[0299] The superscript T means to find the transpose;

[0300] 2. The x-axis velocity and y-axis velocity of the target at time 2 (v x (2),v y (2)) to the target's x-axis velocity and y-axis velocity (v x (M),v y In (M), the x-axis velocity component and the y-axis velocity component are obtained by the Kalman filter algorithm;

[0301] The specific process is:

[0302] 1) If the delay data (round-trip propagation delay) of three or more transponders is received in a synchronization period, the target position is calculated using a linear solution algorithm. The specific process is as follows:

[0303]

[0304]

[0305]

[0306] in,

[0307] (x t ,y t ,z t ) is the target position to be solved;

[0308] (x1, y1, z1) are the coordinates of the first transponder; (x2, y2, z2) are the coordinates of the second transponder; (x3, y3, z3) are the coordinates of the third transponder;

[0309] s1 is the propagation distance from the underwater target to the first transponder; s2 is the propagation distance from the underwater target to the second transponder; s3 is the propagation distance from the underwater target to the third transponder;

[0310] In this model, only the time delay data of three transponders are needed to uniquely determine the target location;

[0311] In the actual processing process, when the delay data of three or more transponders are obtained, a linear solution algorithm can be used.

[0312] The above three formulas can be organized as follows:

[0313]

[0314]

[0315] Rewrite the above formula as:

[0316] AX=B

[0317] Among them, A and B are matrices, and X is the target position coordinate;

[0318]

[0319] When the inverse matrix of matrix A exists, vector X has a unique solution, that is, the target position is uniquely determined;

[0320] 2) If the delay data (round-trip propagation delay) of two transponders is received in a synchronization period, a nonlinear solution algorithm is used to solve the target position. The specific process is as follows:

[0321] In the actual processing, only the time delay data of two transponders is obtained, and a nonlinear solution algorithm is used;

[0322]

[0323]

[0324] When two sets of solutions are obtained by combining the two equations (two circles intersect), the points far from the historical trajectory are discarded and the points close to the historical trajectory are selected as the target position.

[0325] When two equations are solved together to obtain a set of solutions (two circles are tangent), the set of solutions is directly used as the target position;

[0326] When the two equations are not solved simultaneously (the two circles are separated), the target position is set to a null value;

[0327] 3): If the delay data (round-trip propagation delay) of 0 or 1 transponder is received in a synchronization period, the target position cannot be solved at this time, and the target position corresponding to the synchronization period is set to a null value;

[0328] 4): The calculated target position coordinates and the target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m,…,X M ];

[0329] Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ;

[0330] The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ;

[0331] The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ;

[0332] (v x (1),v y (1)) represents the x-axis component velocity and y-axis component velocity of the target at time 1 (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis); the initial velocity (v x (1),v y (1) Obtained through existing technical means, such as a speed meter;

[0333] (v x (m),v y (m)) represents the x-axis velocity component and the y-axis velocity component of the target at time m (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis), which is obtained by the Kalman filter algorithm in step 4;

[0334] (v x (M),v y (M)) represents the x-axis velocity component and the y-axis velocity component of the target at time M (in the spatial rectangular coordinate system, the north is the Y axis, the east is the X axis, and the vertical sea surface is the Z axis), which is obtained by the Kalman filter algorithm in step 4;

[0335] The superscript T means transpose.

[0336] 2. The x-axis velocity and y-axis velocity of the target at time 2 (v x (2),v y (2)) to the target's x-axis velocity and y-axis velocity (v x (M),v y The x-axis velocity component and the y-axis velocity component in (M) are obtained by the Kalman filter algorithm.

[0337] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0338] Specific embodiment 10: This embodiment differs from any one of specific embodiments 1 to 9 in that in step 4, if the target state X m If it is a null value, Kalman filter is used to filter the target state X m Make a prediction and use the predicted value to fill the empty value as the updated target position to be located;

[0339] If the target state X m If it is a non-null value, Kalman filtering is used to filter the target state X m Make predictions and updates, and use the updated value as the updated target position to be located;

[0340] The specific process is:

[0341] 1. Target state vector X at time m m =[x(m),v x (m),y(m),v y (m)] T ;

[0342] Among them, x(m),v x (m),y(m),v y (m) represents the x-axis coordinate, x-axis velocity component, y-axis coordinate, and y-axis velocity component of the target at time m.

[0343] The superscript T means to find the transpose;

[0344] Second, the state space model is:

[0345]

[0346] in,

[0347] X m =FX m-1 +w m-1 is the equation of state;

[0348] Z m =HX m +v m is the observation equation;

[0349] F is the state transfer matrix, w m-1 is the process noise, Z m is the observed value of the system at time m, H is the observation matrix, v m is the observation noise; X m-1 is the state vector at time m-1;

[0350] The state equation of the Kalman filter is a uniform velocity model (CV model), in which:

[0351]

[0352] In the observation equation

[0353]

[0354] Since most underwater vehicles are non-maneuverable targets, a uniform speed model is set here.

[0355] 3. Process the target state:

[0356] State prediction equation:

[0357]

[0358] in, Represents the state vector updated at time m-1 (when m=2, The target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T , no update required), Represents the predicted value of the state vector at time m;

[0359] Covariance prediction equation:

[0360]

[0361] in, represents the posterior estimated covariance at time m-1, represents the prior estimated covariance at time m, Q represents the process noise covariance (settable);

[0362] Prior estimated covariance based on k moments Calculate the Kalman gain:

[0363]

[0364] Among them, K m represents the Kalman gain, R represents the observation noise covariance (known);

[0365] State update equation:

[0366] If the target state X m If it is null, the predicted value Fill in the empty value as the updated target position to be located;

[0367] If the target state X m Is a non-null value, then As the updated target position to be located;

[0368]

[0369] X m When X is a non-empty value, the prediction and update process are performed normally; m When it is a null value, the updated value is directly filled with the predicted value, so that the empty trajectory points can be filled.

[0370] Covariance update equation:

[0371]

[0372] in, represents the posterior estimated covariance at time m.

[0373] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0374] Example:

[0375] Simulation parameter settings

[0376] The system synchronization period is 2 seconds, the observation time is 160 seconds, the buoy depth is 4500 meters, the target depth is 300 meters, the buoys are arranged in a positive direction, and the coordinates of the four buoys are (0,0) (5000,0) (5000,5000) (0,5000). Assume the initial state of the target is: X1 = [150,8,200,6] T , the target moves in a uniform straight line. A time delay measurement error of 0.5ms, a sound speed error of 1m / s, and a transponder coordinate error of 0.5m are added to the simulation program. The sound speed profile is set to a typical sound speed profile of the deep sea. Among them, the traditional algorithm uses the elliptical confocal algorithm with nonlinear least squares optimization; the optimized algorithm of the present invention uses the modified time delay t ri As one-way delay. Figure 4-Figure 8 .

[0377] The present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A long baseline system delay correction positioning method based on radial velocity information, characterized by: The specific process of the method is: Step 1: Obtain the one-way propagation delay between the target and the transponder. The specific process is as follows: Step 1: Construct the two-way distance R of the signal propagation of the i-th synchronization period i Expressions of Step 1 and 2: The round-trip distance R based on the signal propagation of the i-th synchronization cycle i The expression of the corrected slope distance D is obtained ri ; Step 13: Based on the round-trip propagation delay t i , t j Construct an expression for the radial velocity v of the target relative to the transponder; Step 14: Substitute the expression of the target's radial velocity v relative to the transponder into the corrected slant distance D obtained in step 12. ri , and obtain the new corrected slope distance D ri ; Step 15: Based on the new corrected slant distance D from step 14 ri , and obtain the corrected one-way propagation delay t ri ; Step 2: Use ray tracing technology to calculate the horizontal distance and propagation time of the sound ray, and generate a time delay-distance table based on the horizontal distance and propagation time; Step 3: The corrected one-way propagation delay t obtained in step 15 ri Find the corresponding horizontal propagation distance in the delay-distance table obtained in step 2, and use the positioning algorithm to calculate the position of the target to be located based on the horizontal propagation distance; The calculated target position coordinates, target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m ,…,X M ]; Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ; The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ; The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ; (v x (1),v y (1)) represents the x-axis velocity component and the y-axis velocity component of the target at time 1; (v x (m),v y (m)) represents the x-axis velocity and y-axis velocity of the target at time m; (v x (M),v y (M)) represents the x-axis velocity and y-axis velocity of the target at time M; The superscript T means to find the transpose; Step 4: Use the Kalman filter algorithm to process the target state and obtain the target trajectory; The specific process is: 1) Input the initial target state X1=[x(1),v x (1),y(1),v y (1)] T ; 2) Let m = 2; If the target state X m If it is a null value, Kalman filter is used to filter the target state X m Make a prediction and use the predicted value to fill the empty value as the updated target position to be located; If the target state X m If it is a non-null value, Kalman filtering is used to filter the target state X m Make predictions and updates, and use the updated value as the updated target position to be located; 3) Set m = m + 1, repeat 2) until m = M, and obtain the target trajectory.

2. The long baseline system delay correction positioning method based on radial velocity information according to claim 1, characterized in that: In the step 1, the round-trip distance R of the i-th synchronous period signal propagation is constructed i Expressions of R i =r i1 +r i2 =r i1 +[r i1 +(t i +τ)v]=2r i1 +(t i +τ)v Where, r i1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period; r i2 Indicates the distance from the transponder to the target when the target receives the response signal returned by the transponder in the i-th synchronization cycle; t i represents the round-trip propagation delay of the signal between the target and the transponder in the i-th synchronization period; τ represents the response delay of the transponder; v represents the radial velocity of the target relative to the seabed transponder.

3. The long baseline system delay correction positioning method based on radial velocity information according to claim 2, characterized in that: The round-trip distance R based on the propagation of the i-th synchronization period signal in steps 1 and 2 i The expression of the corrected slope distance D is obtained ri ; The expression is: Where c is the speed of sound in water.

4. The long baseline system delay correction positioning method based on radial velocity information according to claim 3 is characterized by: In the steps 1 and 3, the round-trip propagation delay t i , t j Construct an expression for the radial velocity v of the target relative to the transponder; the specific process is: Step 131. Calculate the distance r between the target and the transponder when the target transmits the interrogation signal in the kth synchronization period k1 The distance r from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period i1 The difference; expressed as: r k1 -r i1 ＝(r k1 -r j1 )+(r j1 -r i1 ) ≈(r j2 -r i2 )+(r j1 -r i1 ) ＝(r j1 +r j2 )-(r i1 +r i2 ) =R j -R i Where, j = i + 1, k = i + 2; r i1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the i-th synchronization period; r j1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the jth synchronization period; r k1 represents the distance from the target to the transponder when the target transmits the interrogation signal in the kth synchronization period; r i2 Indicates the distance from the target to the transponder when the target receives the response signal returned by the transponder in the i-th synchronization cycle; r j2 represents the distance between the target and the transponder when the target receives the response signal returned by the transponder in the jth synchronization cycle; R i represents the two-way distance of signal propagation in the i-th synchronization cycle; R j represents the two-way distance of signal propagation in the jth synchronization cycle; Step 132: Based on the round-trip distance R of the signal propagation in the i-th synchronization cycle i and the round-trip distance R of the signal propagation in the jth synchronization cycle j , calculate the radial velocity v of the target relative to the transponder; the expression is: in, t j represents the round-trip propagation delay of the signal between the target and the transponder in the jth synchronization cycle; t i represents the round-trip propagation delay of the signal between the target and the transponder in the i-th synchronization cycle; T is the synchronization period.

5. The long baseline system delay correction positioning method based on radial velocity information according to claim 4, characterized in that: In step 14, the expression of the radial velocity v of the target relative to the transponder is substituted into the corrected slant distance D obtained in step 12. ri , and obtain the new corrected slope distance D ri ; The specific process is: Substitute the expression of the radial velocity v of the target relative to the transponder into the corrected slant distance D obtained in steps 1 and 2. ri The expression of the new corrected slope distance D is obtained ri ; The expression is:

6. The long baseline system delay correction positioning method based on radial velocity information according to claim 5, characterized in that: The step 15 is based on the newly corrected slant distance D in step 14. ri , and obtain the corrected one-way propagation delay t ri ; The specific process is: Based on the new corrected slope distance D in step 1 and 4 ri The expression of the corrected one-way propagation delay t ri ; The expression is:

7. The long baseline system delay correction positioning method based on radial velocity information according to claim 6, characterized in that: In step 2, the sound ray tracing technology is used to calculate the horizontal distance and propagation time of the sound ray propagation, and a time delay-distance table is generated based on the horizontal distance and propagation time. The specific process is as follows: Step 21: Obtain the sound velocity gradient distribution c(z) of the water area through hydrological measurement; Step 2: Set l eigenvalues in the Bellhop sound field model, and the initial grazing angle of each ray is θ ω (ω=1,2,…l), set the sound source depth to z s , the depth of the receiving point is z r , the horizontal distance between the sound source and the receiving point is s; Select the first arriving eigenvalue from all the sound rays at the receiving point, and obtain the initial grazing angle α0 and the sound speed c0 at the sound source corresponding to the first arriving eigenvalue; Step 2 and 3: Distribute the sound velocity gradient distribution c(z) of the water area along the z-axis from the depth z s to z r Divided into E layers, the sound velocity gradient g in each layer of water medium e Approximately constant value: in, g e represents the constant sound velocity gradient in the e-th layer of medium; z e Indicates the depth of the lower interface of the e-th layer of medium; z e-1 represents the depth of the lower interface of the e-1th layer of medium; c(z e ) indicates the depth is z e The speed of sound at 1000 s; c(z e-1 ) indicates the depth is z e-1 The speed of sound at 1000 s; During the propagation of sound rays, the speed of sound and the grazing angle at different positions satisfy Snell's law: Calculate the horizontal propagation distance s and propagation time t of the first arriving eigenvalue ray; Among them, α e represents the grazing angle of the first eigenvalue ray arriving at the lower boundary of the e-th layer of medium, α e+1 represents the grazing angle of the first arriving eigenvalue ray at the lower boundary of the e+1th layer of medium; Step 24: Obtain the delay-distance table.

8. The long baseline system delay correction positioning method based on radial velocity information according to claim 7, characterized in that: The delay-distance table is obtained in step 24; the specific process is: 1) Let n = 0; 2) Set the horizontal distance between the sound source and the receiving point to s+nds; Where s is the minimum horizontal distance between the sound source and the receiving point, and ds is the horizontal distance step size; 3) Repeat steps 22 to 23 to obtain the propagation time corresponding to the horizontal distance s+nds; 4) Let n = n + 1; Repeat 2) to 3) until n = N, and obtain the propagation time corresponding to all horizontal distances; In this way, the corresponding relationship between the horizontal distance between the sound source and the receiving point and the propagation time is established, and the time delay-distance table is obtained.

9. The long baseline system delay correction positioning method based on radial velocity information according to claim 8, characterized in that: The corrected one-way propagation delay t obtained in step 3 according to step 15 ri Find the corresponding horizontal propagation distance in the delay-distance table obtained in step 2, and use the positioning algorithm to calculate the position of the target to be located based on the horizontal propagation distance; The calculated target position coordinates, target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m ,…,X M ]; Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ; The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ; The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ; (v x (1),v y (1)) represents the x-axis velocity component and the y-axis velocity component of the target at time 1; (v x (m),v y (m)) represents the x-axis velocity and y-axis velocity of the target at time m; (v x (M),v y (M)) represents the x-axis velocity and y-axis velocity of the target at time M; The superscript T means to find the transpose; The specific process is: 1) If the delay data of more than 3 transponders is received in a synchronization period, the target position is calculated using a linear solution algorithm. The specific process is as follows: in, (x t ,y t ,z t ) is the target position to be solved; (x1, y1, z1) are the coordinates of the first transponder; (x2, y2, z2) are the coordinates of the second transponder; (x3, y3, z3) are the coordinates of the third transponder; s1 is the propagation distance from the underwater target to the first transponder; s2 is the propagation distance from the underwater target to the second transponder; s3 is the propagation distance from the underwater target to the third transponder; The above three formulas can be organized as follows: Rewrite the above formula as: AX=B Among them, A and B are matrices, and X is the target position coordinate; When the inverse matrix of matrix A exists, vector X has a unique solution, that is, the target position is uniquely determined; 2) If the time delay data of two transponders is received in a synchronization period, the target position is solved using a nonlinear solution algorithm; the specific process is as follows: When two sets of solutions are obtained by combining the two equations, the points far from the historical trajectory are discarded and the points close to the historical trajectory are selected as the target positions. When two equations are solved together to obtain a set of solutions, the set of solutions is directly used as the target position; When no solution is obtained for the two equations, the target position is set to a null value; 3): If the delay data of 0 or 1 transponder is received in a certain synchronization period, the target position corresponding to the synchronization period is set to a null value; 4): The calculated target position coordinates and the target initial position (x(1), y(1)) and initial velocity (v x (1),v y (1)) is assigned as a parameter to the target state, and [X1,…,X m ,…,X M ]; Among them, the target state at time 1 is X1=[x(1),v x (1),y(1),v y (1)] T ; The state of the target at time m is X m =[x(m),v x (m),y(m),v y (m)] T ; The state of the target at time M is X M =[x(M),v x (M),y(M),v y (M)] T ; (v x (1),v y (1)) represents the x-axis velocity component and the y-axis velocity component of the target at time 1; (v x (m),v y (m)) represents the x-axis velocity and y-axis velocity of the target at time m; (v x (M),v y (M)) represents the x-axis velocity and y-axis velocity of the target at time M; The superscript T means transpose.

10. The long baseline system delay correction positioning method based on radial velocity information according to claim 9, characterized in that: In step 4, if the target state X m If it is a null value, Kalman filter is used to filter the target state X m Make a prediction and use the predicted value to fill the empty value as the updated target position to be located; If the target state X m If it is a non-null value, Kalman filtering is used to filter the target state X m Make predictions and updates, and use the updated value as the updated target position to be located; The specific process is:

1. Target state vector X at time m m =[x(m),v x (m),y(m),v y (m)] T ; Among them, x(m),v x (m),y(m),v y (m) represents the x-axis coordinate, x-axis velocity component, y-axis coordinate, and y-axis velocity component of the target at time m. The superscript T means to find the transpose; Second, the state space model is: in, X m =FX m-1 +w m-1 is the equation of state; Z m =HX m +v m is the observation equation; F is the state transfer matrix, w m-1 is the process noise, Z m is the observed value of the system at time m, H is the observation matrix, v m is the observation noise; X m-1 is the state vector at time m-1; The state equation of the Kalman filter is a uniform velocity model. In the state equation: In the observation equation 3. Process the target state: State prediction equation: in, represents the state vector after the update at time m-1, Represents the predicted value of the state vector at time m; Covariance prediction equation: in, represents the posterior estimated covariance at time m-1, represents the prior estimated covariance at time m, and Q represents the process noise covariance; Prior estimated covariance based on k moments Calculate the Kalman gain: Among them, K m represents the Kalman gain, R represents the observation noise covariance; State update equation: If the target state X m If it is null, the predicted value Fill in the empty value as the updated target position to be located; If the target state X m Is a non-null value, then As the updated target position to be located; Covariance update equation: in, represents the posterior estimated covariance at time m.

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