A long baseline system time delay correction positioning method based on radial velocity information

Abstract

This invention relates to a long baseline system time-delay correction positioning method based on radial velocity information. The invention belongs to the field of underwater positioning and navigation, specifically involving a long baseline system time-delay correction positioning method based on radial velocity information. The purpose of this invention is to solve the problems of high computational load and low positioning accuracy in existing navigation and positioning algorithms. The process is as follows: 1. Obtain the one-way propagation delay between the target and the transponder; 2. Calculate the horizontal distance and propagation time of the sound ray propagation, and generate a time-delay-distance table based on the horizontal distance and propagation time; 3. Find the corresponding horizontal propagation distance in the time-delay-distance table according to the one-way propagation delay, and use the positioning algorithm to calculate the position of the target to be located based on the horizontal propagation distance; assign the calculated target position coordinates, the target's initial position, and the initial velocity as parameters to the target state to obtain [X1,…,X]. m ,…,X M Fourth, the Kalman filter algorithm is used to process the target state to obtain the target trajectory.

Description

Technical Field

[0001] This invention belongs to the field of underwater positioning and navigation, specifically relating to a time-delay correction positioning method for long baseline systems based on radial velocity information. Background Technology

[0002] As marine environmental development moves towards higher speeds and deeper depths, unmanned underwater vehicles (UUVs) are reaching greater speeds and operating depths, placing higher demands on the positioning accuracy and response speed of autonomous underwater navigation systems. UUVs require the support of underwater navigation and positioning systems that use high-precision underwater positioning algorithms to calculate parameters such as the UUV's spatial position and motion status in real time.

[0003] However, because unmanned underwater vehicles (UUVs) are constantly moving underwater, the signal transmission and reception positions of the navigation system are inconsistent in the interrogation-response mode. Therefore, traditional positioning algorithms need to solve the elliptic confoci problem in a short time. Existing underwater long baseline positioning systems mainly use nonlinear least squares optimized elliptic confoci algorithms. However, these methods usually have some limitations: they are computationally intensive and complex, and cannot meet the real-time requirements of navigation systems when computing and storage resources are limited; they are also sensitive to the initial conditions, resulting in large errors in the calculation results.

[0004] Furthermore, the speed of sound, as 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 in the direction of decreasing sound speed. If only a fixed sound speed is used for calculation in an underwater environment, the target position calculated by the positioning algorithm will have a large error. Summary of the Invention

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

[0006] The specific process of a time delay correction positioning method for long baseline systems based on radial velocity information is as follows:

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

[0008] Step 11: Construct the two-way distance R for the propagation of the i-th synchronization cycle signal. i The expression;

[0009] Steps 1 and 2: The two-way distance R based on the propagation of the i-th synchronization cycle signal. i The expression is used to obtain the corrected slope distance D. ri ;

[0010] Step 13: Based on the two-way 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 for the radial velocity v of the target relative to the transponder into the corrected slant range D obtained in Step 12. ri The new corrected slope distance D is obtained. ri ;

[0012] Step 15: Based on the new corrected slope distance D from Step 14 ri The corrected one-way propagation delay t is obtained. 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: Based on the corrected one-way propagation delay t obtained in Step 15 ri Find the corresponding horizontal propagation distance in the time delay-distance table obtained in step two, and use the positioning algorithm to calculate the location of the target to be located based on the horizontal propagation distance.

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

[0016] Wherein, 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 X at time m m =[x(m),v x (m),y(m),v y (m)] T ;

[0018] The state of the target X at time M 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 y-axis velocity component of the target at time 1;

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

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

[0022] The superscript T indicates transpose;

[0023] Step 4: Process the target state using the Kalman filter algorithm to obtain the target trajectory; the specific process is as follows:

[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 the value is null, then Kalman filtering is used to evaluate the target state X. m Make predictions and fill in the missing values ​​with the predicted values ​​to update the target location to be located.

[0027] If the target state X m If the value is non-null, then Kalman filtering is used to evaluate the target state X. m The prediction and update are performed, and the updated value is used as the updated location of the target to be located.

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

[0029] Preferably, in step one, the two-way distance R for constructing the propagation of the i-th synchronization period signal is... i The expression;

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

[0031] In the formula,

[0032] r i1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the i-th synchronization period.

[0033] r i2 This represents the distance between the transponder and the target when the target receives the response signal returned by the transponder during the i-th synchronization cycle.

[0034] t i This represents the two-way propagation delay of the signal between the target and the transponder during the i-th synchronization cycle.

[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, in steps one and two, the two-way distance R based on the propagation of the i-th synchronization cycle signal is... i The expression is used to obtain the corrected slope distance D. ri The expression is:

[0038]

[0039] In the formula, c is the speed of sound in the water medium.

[0040] Preferably, in steps one and three, the propagation delay t is used as the basis for... i t j Construct an expression for the radial velocity v of the target relative to the transponder; the specific process is as follows:

[0041] Step 131: Calculate the distance r from the target to the transponder when the target transmits the interrogation signal during the k-th synchronization cycle. k1 When the target transmits an interrogation signal during the i-th synchronization period, the distance r from the target to the transponder i1 The difference is 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] In the formula, j = i + 1, k = i + 2;

[0047] r i1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the i-th synchronization period.

[0048] r j1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the j-th synchronization cycle.

[0049] r k1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the k-th synchronization cycle.

[0050] r i2 This represents the distance from the target to the transponder when the target receives the response signal returned by the transponder during the i-th synchronization cycle.

[0051] r j2 This represents the distance from the target to the transponder when the target receives the response signal returned by the transponder during the j-th synchronization cycle.

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

[0053] R j This represents the two-way distance of signal propagation during the j-th synchronization cycle;

[0054] Step 1, Step 3, Step 2: Based on the two-way distance R of signal propagation in the i-th synchronization cycle. i The two-way distance R of signal propagation in the j-th synchronization period j Calculate the radial velocity v of the target relative to the transponder; the expression is:

[0055]

[0056] in,

[0057] t j This represents the two-way propagation delay of the signal between the target and the transponder during the j-th synchronization cycle;

[0058] t i This represents the two-way propagation delay of the signal between the target and the transponder during the i-th synchronization cycle;

[0059] T is the synchronization period.

[0060] Preferably, in step one four, the expression for the radial velocity v of the target relative to the transponder is substituted into the corrected slant range D obtained in step one two. ri The new corrected slope distance D is obtained. ri The specific process is as follows:

[0061] Substitute the expression for the radial velocity v of the target relative to the transponder into the corrected slant range D obtained in steps one and two. ri The expression is used to obtain the new corrected slope distance D. ri The expression is:

[0062]

[0063] Preferably, in step one-five, the new corrected slope distance D from step one-four is used. ri The corrected one-way propagation delay t is obtained. ri The specific process is as follows:

[0064] Based on the new corrected slope distance D in step one four ri The expression yields the corrected one-way propagation delay t. ri The expression is:

[0065]

[0066] Preferably, in step two, sound ray tracing technology is used to calculate the horizontal distance and propagation time of sound rays, and a time delay-distance table is generated based on the horizontal distance and propagation time; the specific process is as follows:

[0067] Step 2: Obtain the sound velocity gradient distribution c(z) of the water area through hydrological measurements;

[0068] Step 22: In the Bellhop sound field model, set l intrinsic sound rays, with an initial grazing angle of θ for each ray. ω (ω=1,2,…l), setting the depth of the sound source as 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 eigenvalue from all the sound rays at the receiving point, and obtain the initial glancing angle α0 and the sound speed c0 at the source corresponding to the first eigenvalue.

[0070] Steps two and three: The sound velocity gradient distribution c(z) of the water body is shifted along the z-axis from depth z. s To z r Divided into E layers, the sound velocity gradient g in each water medium e Approximately a constant value:

[0071]

[0072] in,

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

[0074] ze This represents the depth of the interface beneath the e-th medium layer;

[0075] z e-1 This represents the depth of the interface beneath the (e-1)th medium layer;

[0076] c(z e ) represents a depth of z e The speed of sound at that time;

[0077] c(z e-1 ) represents a depth of z e-1 The speed of sound at that time;

[0078] During sound propagation, the speed of sound at different locations and the glancing angle satisfy Snell's Law:

[0079]

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

[0081]

[0082]

[0083] Where, α e α represents the glancing angle of the first arriving intrinsic sound ray at the lower boundary of the e-th layer of medium. e+1 This represents the glancing angle of the first arriving intrinsic sound 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 two or four; the specific process is as follows:

[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 steps 2) to 3) until n = N to obtain the propagation time for all horizontal distances;

[0092] This establishes the correspondence between the horizontal distance between the sound source and the receiving point and the propagation time, thus obtaining the time delay-distance table.

[0093] Preferably, in step three, the corrected one-way propagation delay t obtained in step one five is... ri Find the corresponding horizontal propagation distance in the time delay-distance table obtained in step two, and use the positioning algorithm to calculate the location of the target to be located based on the horizontal propagation distance.

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

[0095] Wherein, 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 X at time m m =[x(m),v x (m),y(m),v y (m)] T ;

[0097] The state of the target X at time M 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 y-axis velocity component of the target at time 1;

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

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

[0101] The superscript T indicates transpose;

[0102] The specific process is as follows:

[0103] 1) If delay data from three or more transponders is received during a synchronization cycle, the target position is calculated using a linear algorithm; the specific process is as follows:

[0104]

[0105]

[0106]

[0107] in,

[0108] (x t ,y t ,z t () represents the target location 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 reorganized as follows:

[0112]

[0113]

[0114] The above expression can be written as:

[0115] AX = B

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

[0117]

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

[0119] 2) If delay data from two transponders are received during a certain synchronization cycle, a nonlinear calculation algorithm is used to calculate the target position; the specific process is as follows:

[0120]

[0121]

[0122] When two equations are solved simultaneously to obtain two sets of solutions, the historical trajectory is used to make a judgment. Points that are far from the historical trajectory are discarded, and points that are close to the historical trajectory are selected as the target positions.

[0123] When a solution is obtained by solving two equations simultaneously, the solution is directly used as the target location.

[0124] If the solution to the two equations is not found, the target position is set to an empty value.

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

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

[0127] Wherein, 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 X at time m m =[x(m),v x (m),y(m),v y (m)] T ;

[0129] The state of the target X at time M 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 y-axis velocity component of the target at time 1;

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

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

[0133] The superscript T indicates transpose.

[0134] Preferably, in step four, if the target state X m If the value is null, then Kalman filtering is used to evaluate the target state X. mMake predictions and fill in the missing values ​​with the predicted values ​​to update the target location to be located.

[0135] If the target state X m If the value is non-null, then Kalman filtering is used to evaluate the target state X. m The prediction and update are performed, and the updated value is used as the updated location of the target to be located.

[0136] The specific process is as follows:

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

[0138] Where x(m),v x (m),y(m),v y (m) represents the target's x-axis coordinate, x-axis velocity component, y-axis coordinate, and y-axis velocity component at time m, respectively.

[0139] The superscript T indicates transpose;

[0140] II. The state-space model is as follows:

[0141]

[0142] in,

[0143] X m =FX m-1 +w m-1 The equations of state;

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

[0145] F is the state transition matrix, w m-1 It is process noise, Z m Here are the system observations at time m, H is the observation matrix, and v m For observation noise; X m-1 This is the state vector at time m-1;

[0146] The state equation of the Kalman filter is a uniform model, in which:

[0147]

[0148] In the observation equation

[0149]

[0150] III. Processing the target state:

[0151] State prediction equation:

[0152]

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

[0154] Covariance prediction equation:

[0155]

[0156] in, This represents the posterior estimated covariance at time m-1. Let m represent the prior estimate covariance at time m, and Q represent the process noise covariance.

[0157] Prior estimate of covariance at time k Calculate the Kalman gain:

[0158]

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

[0160] State update equation:

[0161] If the target state X m If it is a null value, then the predicted value is... Fill in the empty values ​​to get the updated target location;

[0162] If the target state X m If it is a non-null value, then As the updated target location;

[0163]

[0164] Covariance update equation:

[0165]

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

[0167] The beneficial effects of this invention are as follows:

[0168] The purpose of this invention is to improve the positioning accuracy of autonomous navigation systems in interrogation-response scenarios. Based on the radial velocity of a moving target relative to a seabed transponder, this invention derives a one-way time delay correction method, reducing the slant range error caused by target motion in convergence positioning models. Subsequently, ray tracing technology is used to calculate the horizontal distance of sound ray propagation and locate the target, overcoming the influence of sound ray bending in the underwater environment. The post-processing section employs a Kalman filter algorithm to process the target's trajectory, further improving the accuracy of the navigation trajectory. This invention can be applied to the field of underwater positioning and navigation.

[0169] In navigation systems, the one-way delay correction algorithm calculates the one-way delay of the interrogation signal propagating to the transponder based on the radial velocity of the target relative to the transponder. It aligns the target positioning solution points of each synchronization cycle to the time of the interrogation signal transmission, avoiding the solution of the elliptical confoci problem. This greatly reduces the computational load of the positioning algorithm, improves the calculation speed, reduces the error of the positioning result, improves the positioning accuracy, and meets the real-time requirements of autonomous navigation systems.

[0170] As ray acoustics theory shows, sound rays bend when propagating underwater, so the actual distance sound rays travel is not a straight line between the target and the transponder. Using a fixed sound velocity for calculation across the entire water area introduces significant positioning errors. Ray tracking technology can correct for the distance between the target and the transponder by calculating the horizontal distance based on the underwater sound propagation laws, thereby reducing positioning errors.

[0171] Furthermore, underwater acoustic propagation generally exhibits multipath effects, time-varying characteristics, and absorption attenuation. The uncertainty of the underwater acoustic channel can lead to the failure of the response signal transmission. When the target receives insufficient transponder delay data, the positioning algorithm cannot calculate the target's position. Using a Kalman filter algorithm in the post-processing stage can interpolate the missing parts of the target trajectory and reduce the overall error of the navigation trajectory. Attached Figure Description

[0172] Figure 1 A basic flowchart of the time-delay correction positioning algorithm;

[0173] Figure 2 This is a schematic diagram of the navigation system operating in query-response mode.

[0174] Figure 3 This is a schematic diagram illustrating the derivation of the single-pass delay correction algorithm;

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

[0176] Figure 5 The image shows the simulation results of traditional algorithm navigation.

[0177] Figure 6 A localization error map for traditional algorithms;

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

[0179] Figure 8 This is a diagram showing the positioning error of the algorithm in this invention. Detailed Implementation

[0180] Specific Implementation Method 1: The specific process of this implementation method for a long baseline system time delay correction positioning method based on radial velocity information 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 speed is negligible, the system can directly use half of the total time delay from signal transmission to reception as the one-way propagation delay and apply it to the rendezvous positioning solution equation. However, when the target's speed is high or the system's synchronization period is long, this algorithm introduces a non-negligible system error. 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 as follows:

[0184] Step 1: Construct the two-way distance R for signal propagation during the i-th synchronization period (fixed time interval). i The expression;

[0185] Steps 1 and 2: Calculate the two-way distance R based on the signal propagation during the i-th synchronization period (fixed time interval). i The expression is used to obtain the corrected slope distance D. ri ;

[0186] Step 13: Based on the two-way 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 for the radial velocity v of the target relative to the transponder into the corrected slant range D obtained in Step 12. ri The new corrected slope distance D is obtained. ri ;

[0188] Step 15: Based on the new corrected slope distance D from Step 14 ri The corrected one-way propagation delay t is obtained. 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: Based on the corrected one-way propagation delay t obtained in Step 15 ri Find the corresponding horizontal propagation distance in the time delay-distance table obtained in step two, and use the positioning algorithm to calculate the location of the target to be located based on the horizontal propagation distance.

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

[0192] Wherein, 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 X at time m m =[x(m),v x (m),y(m),v y (m)] T ;

[0194] The state of the target X at time M M =[x(M),v x (M),y(M),v y (M)] T The required solution for the location of the target to be located from time 2 to time M;

[0195] (v x (1),v y (1) represents the x-axis and y-axis velocities of the target at time 1 (in a Cartesian coordinate system, north is the Y-axis, east is the X-axis, and perpendicular to the sea surface is the Z-axis); initial velocity (v x (1),v y (1) Obtain it through existing technical means, such as speed measuring instruments;

[0196] (v x (m),v y (m) represents the x-axis and y-axis velocities of the target at time m (in a rectangular coordinate system, north is the y-axis, east is the x-axis, and perpendicular to the sea surface is the z-axis), obtained by the Kalman filter algorithm in step four;

[0197] (vx (M),v y (M) represents the x-axis and y-axis velocities of the target at time M (in a spatial rectangular coordinate system, north is the y-axis, east is the x-axis, and perpendicular to the sea surface is the z-axis), obtained by the Kalman filter algorithm in step four;

[0198] The superscript T indicates transpose;

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

[0200] Step 4: Process the target state using the Kalman filter algorithm to obtain the target trajectory; the specific process is as follows:

[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 the value is null, then Kalman filtering is used to evaluate the target state X. m Make predictions and fill in the missing values ​​with the predicted values ​​to update the target location to be located.

[0204] If the target state X m If the value is non-null, then Kalman filtering is used to evaluate the target state X. m The prediction and update are performed, and the updated value is used as the updated location of the target to be located.

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

[0206] A single filtering operation can achieve two objectives: filling in missing values ​​and reducing trajectory errors.

[0207] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that, in step one, the two-way distance R for constructing the signal propagation of the i-th synchronization period (fixed time interval) is... i The expression;

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

[0209] In the formula,

[0210] r i1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the i-th synchronization period.

[0211] r i2 This represents the distance between the transponder and the target when the target receives the response signal returned by the transponder during the i-th synchronization cycle.

[0212] t i This represents the two-way propagation delay (from transmission to reception) of the signal between the target and the transponder during the i-th synchronization period.

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

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

[0215] The other steps and parameters are the same as in Specific Implementation Method 1.

[0216] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the two-way distance R propagated based on the signal of the i-th synchronization period (fixed time interval) in steps one and two is... i The expression is used to obtain the corrected slope distance D. ri The expression is:

[0217]

[0218] In the formula, c is the speed of sound in the water medium.

[0219] Other steps and parameters are the same as in specific implementation method one or two.

[0220] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that, in steps one and three, the two-way propagation delay t is used... i t j Construct an expression for the radial velocity v of the target relative to the transponder; the specific process is as follows:

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

[0222]

[0223] However, in practical applications, the system cannot predict in advance the distance from the target to the transponder after two synchronization cycles, i.e., r in the above formula. k1 It cannot be obtained directly; it needs to be approximated based on known quantities.

[0224] r k1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the k-th synchronization cycle.

[0225] Step 131: Calculate the distance r from the target to the transponder when the target transmits the interrogation signal during the k-th synchronization cycle. k1 When the target transmits an interrogation signal during the i-th synchronization period, the distance r from the target to the transponder i1 The difference is 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] In the formula, j = i + 1, k = i + 2;

[0232] r i1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the i-th synchronization period.

[0233] r j1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the j-th synchronization cycle.

[0234] r k1 This represents the distance from the target to the transponder when the target transmits an interrogation signal during the k-th synchronization cycle.

[0235] r i2 This represents the distance from the target to the transponder when the target receives the response signal returned by the transponder during the i-th synchronization cycle.

[0236] r j2 This represents the distance from the target to the transponder when the target receives the response signal returned by the transponder during the j-th synchronization cycle.

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

[0238] R j This represents the two-way distance of signal propagation during the j-th synchronization cycle;

[0239] Step 1, Step 3, Step 2: Based on the two-way distance R of signal propagation in the i-th synchronization cycle. i The two-way distance R of signal propagation in the j-th synchronization period j Calculate the radial velocity v of the target relative to the transponder; the expression is:

[0240]

[0241] in,

[0242] t j This represents the two-way propagation delay (from transmission to reception) of the signal between the target and the transponder during the j-th synchronization cycle.

[0243] t i This represents the two-way propagation delay (from transmission to reception) of the signal between the target and the transponder during the i-th synchronization period.

[0244] T is the synchronization period.

[0245] The radial velocity of the moving target relative to the transponder can be approximately derived by considering the geometric relationship between the target's 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 one of the specific implementation methods one to three.

[0247] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that, in step one to four, the expression for the radial velocity v of the target relative to the transponder is substituted into the corrected slant range D obtained in step one to two. ri The new corrected slope distance D is obtained. ri The specific process is as follows:

[0248] Substitute the expression for the radial velocity v of the target relative to the transponder into the corrected slant range D obtained in steps one and two.ri The expression is used to obtain the new corrected slope distance D. ri The expression is:

[0249]

[0250] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0251] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that, in step one-five, the new corrected slant distance D based on step one-four is used. ri The corrected one-way propagation delay t is obtained. ri The specific process is as follows:

[0252] Based on the new corrected slope distance D in step one four ri The expression yields the corrected one-way propagation delay t. ri The expression is:

[0253]

[0254] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0255] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that, in step two, sound ray tracing technology is used to calculate the horizontal distance and propagation time of sound rays, 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 water is approximately constant, and the sound signal propagates in a straight line. Multiplying the speed of sound by the propagation delay yields the distance between the target and the transponder. However, according to ray acoustics, sound rays bend towards lower speeds during underwater propagation. Therefore, in actual underwater environments, sound rays do not propagate in a straight line. The solution equations for long-baseline positioning systems require calculating the distance between the target and the transponder based on the signal propagation delay and the speed of sound in water. If a constant speed of sound is used for positioning in all test areas, the calculated slant range error is large, leading to a significant deviation between the positioning result and the actual location.

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

[0258] Step 2: Obtain the sound velocity gradient distribution c(z) of the water area through hydrological measurements;

[0259] Step 2: Use Bellhop to build a sound field model to simulate the propagation path of intrinsic sound rays. In the Bellhop sound field model, set l intrinsic sound rays, with an initial grazing angle of θ for each ray. ω (ω=1,2,…l), setting the depth of the sound source as z s (The location of the sound source changes with each cycle), and the depth of the receiving point is z. r (The transponder position remains unchanged in each cycle), and the horizontal distance between the sound source and the receiver is s;

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

[0261] Steps two and three: The sound velocity gradient distribution c(z) of the water body is calculated along the z-axis (perpendicular to the water surface) from 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 a constant value:

[0262]

[0263] in,

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

[0265] z e This represents the depth of the interface beneath the e-th medium layer;

[0266] z e-1 This represents the depth of the interface beneath the (e-1)th medium layer;

[0267] c(z e ) represents a depth of z e The speed of sound at that time;

[0268] c(z e-1 ) represents a depth of z e-1 The speed of sound at that time;

[0269] During sound propagation, the speed of sound at different locations and the glancing angle satisfy Snell's Law:

[0270]

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

[0272]

[0273]

[0274] Where, α e α represents the glancing angle of the first arriving intrinsic sound ray at the lower boundary of the e-th layer of medium. e+1 This represents the glancing angle of the first arriving intrinsic sound 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 one of the specific implementation methods one to six.

[0277] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the delay-distance table is obtained in step two-four; 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 steps 2) to 3) until n = N to obtain the propagation time for all horizontal distances;

[0284] This establishes the correspondence between the horizontal distance between the sound source and the receiving point and the propagation time, thus obtaining the time delay-distance table.

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

[0286] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0287] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that, in step three, the corrected one-way propagation delay t obtained in step one through five is... ri Find the corresponding horizontal propagation distance in the delay-distance table obtained in step two;

[0288] For time delay values ​​not appearing in the time delay-distance table, the corresponding horizontal distance is calculated using linear interpolation.

[0289]

[0290] Among them, t p and t q For the time delay-distance table, compare the one-way propagation time delay t ri The two closest delays, s p and s q For the delay t p and t q The corresponding horizontal distance, s a The horizontal distance is calculated using linear interpolation.

[0291] The location of the target to be located is calculated using a positioning algorithm based on the horizontal propagation distance.

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

[0293] Wherein, 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 X at time m m =[x(m),v x (m),y(m),v y (m)] T ;

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

[0296] (v x (1),v y (1) represents the x-axis and y-axis velocities of the target at time 1 (in a Cartesian coordinate system, north is the Y-axis, east is the X-axis, and perpendicular to the sea surface is the Z-axis); initial velocity (v x (1),v y (1) Obtain it through existing technical means, such as speed measuring instruments;

[0297] (v x (m),v y(m) represents the x-axis and y-axis velocities of the target at time m (in a rectangular coordinate system, north is the y-axis, east is the x-axis, and perpendicular to the sea surface is the z-axis), obtained by the Kalman filter algorithm in step four;

[0298] (v x (M),v y (M) represents the x-axis and y-axis velocities of the target at time M (in a spatial rectangular coordinate system, north is the y-axis, east is the x-axis, and perpendicular to the sea surface is the z-axis), obtained by the Kalman filter algorithm in step four;

[0299] The superscript T indicates transpose;

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

[0301] The specific process is as follows:

[0302] 1) If delay data from 3 or more transponders is received during a certain synchronization cycle (two-way propagation delay), 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 () represents the target location 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] This model only requires the time delay data of three transponders to uniquely determine the target location;

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

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

[0313]

[0314]

[0315] The above expression can be written as:

[0316] AX = B

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

[0318]

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

[0320] 2) If delay data from two transponders is received during a certain synchronization cycle (two-way propagation delay), a nonlinear solution algorithm is used to calculate the target position; the specific process is as follows:

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

[0322]

[0323]

[0324] When two equations are solved simultaneously and two sets of solutions are obtained (the two circles intersect), the historical trajectory is used to make a judgment. Points that are far from the historical trajectory are discarded, and points that are close to the historical trajectory are selected as the target position.

[0325] When a solution is obtained by solving two equations simultaneously (the two circles are tangent), the solution is directly used as the target position.

[0326] If the two equations are not solved simultaneously (the two circles are separated), the target position is set to an empty value;

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

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

[0329] Wherein, 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 X at time m m =[x(m),v x (m),y(m),v y (m)] T ;

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

[0332] (v x (1),v y (1) represents the x-axis and y-axis velocities of the target at time 1 (in a Cartesian coordinate system, north is the Y-axis, east is the X-axis, and perpendicular to the sea surface is the Z-axis); initial velocity (v x (1),v y (1) Obtain it through existing technical means, such as speed measuring instruments;

[0333] (v x (m),v y (m) represents the x-axis and y-axis velocities of the target at time m (in a rectangular coordinate system, north is the y-axis, east is the x-axis, and perpendicular to the sea surface is the z-axis), obtained by the Kalman filter algorithm in step four;

[0334] (v x (M),v y (M) represents the x-axis and y-axis velocities of the target at time M (in a spatial rectangular coordinate system, north is the y-axis, east is the x-axis, and perpendicular to the sea surface is the z-axis), obtained by the Kalman filter algorithm in step four;

[0335] The superscript T indicates transpose.

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

[0337] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0338] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that, in step four, if the target state X... m If the value is null, then Kalman filtering is used to evaluate the target state X. m Make predictions and fill in the missing values ​​with the predicted values ​​to update the target location to be located.

[0339] If the target state X m If the value is non-null, then Kalman filtering is used to evaluate the target state X. m The prediction and update are performed, and the updated value is used as the updated location of the target to be located.

[0340] The specific process is as follows:

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

[0342] Where x(m),v x (m),y(m),v y (m) represents the target's x-axis coordinate, x-axis velocity component, y-axis coordinate, and y-axis velocity component at time m, respectively.

[0343] The superscript T indicates transpose;

[0344] II. The state-space model is as follows:

[0345]

[0346] in,

[0347] X m =FX m-1 +w m-1 The equations of state;

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

[0349] F is the state transition matrix, w m-1 It is process noise, Z m Here are the system observations at time m, H is the observation matrix, and v m For observation noise; X m-1 This 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 underwater vehicles are mostly non-maneuvering targets, they are set to a uniform speed model here.

[0355] III. Processing the target state:

[0356] State prediction equation:

[0357]

[0358] in, This represents the updated state vector 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) This represents the predicted value of the state vector at time m;

[0359] Covariance prediction equation:

[0360]

[0361] in, This represents the posterior estimated covariance at time m-1. The prior estimate covariance at time m is represented by Q, which represents the process noise covariance (which can be set).

[0362] Prior estimate of covariance at time k Calculate the Kalman gain:

[0363]

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

[0365] State update equation:

[0366] If the target state X m If it is a null value, then the predicted value is... Fill in the empty values ​​to get the updated target location;

[0367] If the target state X m If it is a non-null value, then As the updated target location;

[0368]

[0369] X m When X is a non-null value, the prediction and update process is executed normally; m When the value is empty, the updated value is filled directly with the predicted value, which can fill in the empty trajectory points.

[0370] Covariance update equation:

[0371]

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

[0373] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0374] Example:

[0375] Simulation parameter settings

[0376] The system synchronization period is 2 seconds, the observation duration is 160 seconds, the mooring depth is 4500m, the target depth is 300m, and the moorings are arranged in a positive orientation. The coordinates of the four moorings are (0,0), (5000,0), (5000,5000), and (0,5000). Assume the initial state of the target: X1 = [150,8,200,6]. T The target moves at a constant velocity in a straight line. The simulation program incorporates a time delay measurement error of 0.5 ms, a sound velocity error of 1 m / s, and a transponder coordinate error of 0.5 m. The sound velocity profile is set as a typical deep-sea sound velocity profile. The traditional algorithm uses a nonlinear least-squares optimized elliptic confocal algorithm; the optimized algorithm of this invention uses a modified time delay t. ri As a one-way delay. For example Figures 4-8 .

[0377] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A time-delay correction positioning method for a long baseline system based on radial velocity information, characterized in that: The specific process of the method is as follows: Step 1: Obtain the one-way propagation delay between the target and the transponder; the specific process is as follows: Step 11: Construct the first Two-way distance of a synchronous period signal propagation The expression; Steps one and two, based on the first Two-way distance of a synchronous period signal propagation The expression is used to obtain the corrected slope distance. ; Step 13: Based on the two-way propagation delay , Construct the radial velocity of the target relative to the transponder The expression; Step 14: Adjust the radial velocity of the target relative to the transponder. Substituting the expression into the corrected slope distance obtained in steps one and two The new corrected slope distance is obtained. ; Step 15: Based on the new corrected slope distance from Step 14 The corrected one-way propagation delay is obtained. ; 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: Based on the corrected one-way propagation delay obtained in Step 15 Find the corresponding horizontal propagation distance in the time delay-distance table obtained in step two, and use the positioning algorithm to calculate the location of the target to be located based on the horizontal propagation distance. The calculated target position coordinates and the target initial position and initial velocity Assign it as a parameter to the target state to obtain ; Among them, the target state at time 1 ; The state of the target at any time ; The state of the target at any time ; express The goal at all times Axis coordinates express The goal at all times Axis coordinates; Represents the target at time 1 axial velocity component Component of velocity in the axial direction; express The goal at all times axial velocity component Component of velocity in the axial direction; express The goal at all times axial velocity component Component of velocity in the axial direction; The superscript T indicates transpose; Step 4: Process the target state using the Kalman filter algorithm to obtain the target trajectory; the specific process is as follows: 1) Input the initial target state ; 2) Order ; If the target state If the value is empty, then Kalman filtering is used to evaluate the target state. Make predictions and fill in the missing values ​​with the predicted values ​​as the updated target location; If the target state If the value is non-null, then Kalman filtering is used to evaluate the target state. The prediction and update are performed, and the updated value is used as the updated location of the target to be located. 3) Order Repeat step 2) until... , thus obtaining the target trajectory.

2. The time delay correction positioning method for a long baseline system based on radial velocity information according to claim 1, characterized in that: In each of the steps, the first step is constructed. Two-way distance of a synchronous period signal propagation The expression; In the formula, Indicates the first One synchronization cycle, the distance from the target to the transponder when the target transmits an interrogation signal; Indicates the first One synchronization cycle, the distance between the transponder and the target when the target receives the response signal returned by the transponder; Indicates the first One synchronization cycle, the two-way propagation delay of the signal between the target and the transponder; Indicates the response delay of the transponder; This indicates the radial velocity of the target relative to the seabed transponder.

3. The time-delay correction positioning method for a long baseline system based on radial velocity information according to claim 2, characterized in that: The steps one and two are based on the first... Two-way distance of a synchronous period signal propagation The expression is used to obtain the corrected slope distance. The expression is: In the formula, The velocity of sound in water.

4. The time delay correction positioning method for a long baseline system based on radial velocity information according to claim 3, characterized in that: In steps one and three, the two-way propagation delay is used as a basis. , Construct the radial velocity of the target relative to the transponder The expression; the specific process is as follows: Step 131, Calculate the first... The distance between the target and the transponder when the target transmits an interrogation signal during a synchronous cycle With the The distance between the target and the transponder when the target transmits an interrogation signal during a synchronous cycle The difference is expressed as: In the formula, , ; Indicates the first One synchronization cycle, the distance from the target to the transponder when the target transmits an interrogation signal; Indicates the first One synchronization cycle, the distance from the target to the transponder when the target transmits an interrogation signal; Indicates the first One synchronization cycle, the distance from the target to the transponder when the target transmits an interrogation signal; Indicates the first One synchronization cycle, the distance from the target to the transponder when the target receives the response signal returned by the transponder; Indicates the first One synchronization cycle, the distance from the target to the transponder when the target receives the response signal returned by the transponder; Indicates the first The two-way distance of signal propagation during each synchronization cycle; Indicates the first The two-way distance of signal propagation during each synchronization cycle; Steps 1, 3, and 2, based on the first... Two-way distance of signal propagation in each synchronization cycle and the Two-way distance of signal propagation in each synchronization cycle Calculate the radial velocity of the target relative to the transponder. The expression is: in, Indicates the first The two-way propagation delay of the signal between the target and the transponder during each synchronization cycle; Indicates the first The two-way propagation delay of the signal between the target and the transponder during each synchronization cycle; For synchronization period.

5. The time delay correction positioning method for a long baseline system based on radial velocity information according to claim 4, characterized in that: In step one four, the radial velocity of the target relative to the transponder is... Substituting the expression into the corrected slope distance obtained in steps one and two The new corrected slope distance is obtained. The specific process is as follows: The radial velocity of the target relative to the transponder Substituting the expression into the corrected slope distance obtained in steps one and two The expression yields the new corrected slope distance. The expression is: 。 6. The time-delay correction positioning method for a long baseline system based on radial velocity information according to claim 5, characterized in that: The slope distance in step one-five is based on the new correction from step one-four. The corrected one-way propagation delay is obtained. ; The specific process is as follows: Based on the new corrected slope distance in step one four The expression yields the corrected one-way propagation delay. The expression is: 。 7. The time delay correction positioning method for a long baseline system based on radial velocity information according to claim 6, characterized in that: In step two, sound ray tracing technology is used to calculate the horizontal distance and propagation time of sound rays, and a time-delay-distance table is generated based on the horizontal distance and propagation time; the specific process is as follows: Step 2: Obtain the sound velocity gradient distribution of the water area through hydrological measurements. ; Step 22: Setting up the Bellhop sound field model There are 10 intrinsic sound rays, and the initial glancing angle of each ray is 100°. Set the sound source depth to The depth of the receiving point is The horizontal distance between the sound source and the receiver is ; Select the first arriving eigenray ray from all rays at the receiving point, and obtain the initial grazing angle corresponding to the first arriving eigenray ray. and the speed of sound at the sound source ; Steps two and three: Distribute the sound velocity gradient across the water. along Axial direction from depth arrive Divided into Layers, the sound velocity gradient in each layer of water medium Approximately a constant value: in, Indicates the first A constant sound velocity gradient in a layered medium; Indicates the first The depth of the interface beneath the medium layer; Indicates the first The depth of the interface beneath the medium layer; Indicates depth as The speed of sound at that time; Indicates depth as The speed of sound at that time; During sound propagation, the speed of sound at different locations and the glancing angle satisfy Snell's Law: Calculate the horizontal propagation distance of the first arriving intrinsic sound ray. With the time of transmission ; in, This indicates that the first arriving intrinsic sound ray is in the [number]th position. The grazing angle at the lower boundary of the layer medium. This indicates that the first arriving intrinsic sound ray is in the [number]th position. The glancing angle at the lower boundary of the layer medium; Step 24: Obtain the delay-distance table.

8. The time delay correction positioning method for a long baseline system based on radial velocity information according to claim 7, characterized in that: In step two, the time delay-distance table is obtained; the specific process is as follows: 1) Order ; 2) Set the horizontal distance between the sound source and the receiver as... ; in, This is the minimum horizontal distance between the sound source and the receiver. The horizontal distance step size; 3) Repeat steps 2.2 to 2.3 to obtain the horizontal distance. The corresponding propagation time; 4) Order ; Repeat steps 2) to 3) until... , thus obtaining the propagation time corresponding to all horizontal distances; This establishes the correspondence between the horizontal distance between the sound source and the receiving point and the propagation time, thus obtaining the time delay-distance table.

9. A time-delay correction positioning method for a long baseline system based on radial velocity information according to claim 8, characterized in that: In step three, the corrected one-way propagation delay obtained in step one five is used. Find the corresponding horizontal propagation distance in the time delay-distance table obtained in step two, and use the positioning algorithm to calculate the location of the target to be located based on the horizontal propagation distance. The calculated target position coordinates and the target initial position and initial velocity Assign it as a parameter to the target state to obtain ; Among them, the target state at time 1 ; The state of the target at any time ; The state of the target at any time ; Represents the target at time 1 axial velocity component Component of velocity in the axial direction; express The goal at all times axial velocity component Component of velocity in the axial direction; express The goal at all times axial velocity component Component of velocity in the axial direction; The superscript T indicates transpose; The specific process is as follows: 1) If delay data from three or more transponders is received during a synchronization cycle, the target position is calculated using a linear algorithm; the specific process is as follows: in, The target location to be solved; The coordinates of the first transponder; The coordinates of the second transponder; The coordinates of the third transponder; The propagation distance from the underwater target to the first transponder; The propagation distance from the underwater target to the second transponder; The propagation distance from the underwater target to the third transponder; The above three formulas can be reorganized as follows: The above expression can be written as: in, , For a matrix, The target location coordinates; When matrix When the inverse matrix exists, the vector There is a unique solution, meaning the target location is uniquely determined; 2) If delay data from two transponders are received during a certain synchronization cycle, a nonlinear calculation algorithm is used to calculate the target position; the specific process is as follows: When two equations are solved simultaneously to obtain two sets of solutions, the historical trajectory is used to make a judgment. Points that are far from the historical trajectory are discarded, and points that are close to the historical trajectory are selected as the target positions. When a solution is obtained by solving two equations simultaneously, the solution is directly used as the target location. If the solution to the two equations is not found, the target position is set to an empty value. 3): If delay data from 0 or 1 transponders is received in a certain synchronization cycle, the target position corresponding to the synchronization cycle is set to a null value; 4): Calculate the target position coordinates and the target's initial position. and initial velocity Assign it as a parameter to the target state to obtain ; Among them, the target state at time 1 ; The state of the target at any time ; The state of the target at any time ; Represents the target at time 1 axial velocity component Component of velocity in the axial direction; express The goal at all times axial velocity component Component of velocity in the axial direction; express The goal at all times axial velocity component Component of velocity in the axial direction; The superscript T indicates transpose.

10. A time-delay correction positioning method for a long baseline system based on radial velocity information according to claim 9, characterized in that: If the target state is in step four If the value is empty, then Kalman filtering is used to evaluate the target state. Make predictions and fill in the missing values ​​with the predicted values ​​as the updated target location; If the target state If the value is non-null, then Kalman filtering is used to evaluate the target state. The prediction and update are performed, and the updated value is used as the updated location of the target to be located. The specific process is as follows: one, Target state vector at time step ; in, In order to represent The goal of the moment Axis coordinates axial velocity component Axis coordinates Component of velocity in the axial direction; Superscript This indicates the transpose; II. The state-space model is as follows: in, The equation of state; The observation equation; Here is the state transition matrix. It's process noise. yes Observations of the time system For the observation matrix, To observe noise; for Time-state vector; The state equation of the Kalman filter is a uniform model, in which: In the observation equation III. Processing the target state: State prediction equation: in, express The updated state vector at each time step. express Predicted state vector value at time step; Covariance prediction equation: in, express The posterior estimate of the covariance at time t. express The prior estimate of covariance at time t, Represents the process noise covariance; based on Prior estimate of covariance at time Calculate the Kalman gain: in, Indicates Kalman gain, Represents the observation noise covariance; State update equation: If the target state If it is a null value, then the predicted value is... Fill in the empty values ​​to get the updated target location; If the target state If it is a non-null value, then As the updated target location; Covariance update equation: in, express The posterior estimate of the covariance at time t.

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