Underwater single-beacon virtual long baseline positioning method and system capable of estimating unknown sound speed

Abstract

The present invention belongs to the field of underwater positioning technology, and discloses an underwater single-beacon virtual long baseline positioning method and system that can estimate unknown sound speed. The method constructs a virtual long baseline array in combination with stored dead reckoning data; constructs a virtual long baseline positioning problem in combination with the relationship between the underwater acoustic signal propagation time and the AUV position and sound speed; introduces auxiliary variables, obtains a pseudo-linear positioning equation based on algebraic transformation, and obtains a preliminary solution to the AUV position based on the weighted least squares method; and then constructs a second-step linear estimation problem by exploring the relationship between the auxiliary variables and the AUV position, and solves it using weighted least squares to obtain a more accurate AUV position estimation solution. Compared to the single-beacon positioning method that does not consider the unknown sound speed, the method of the present invention can obtain more ideal position estimation performance and enhance the practical application capabilities of the underwater single-beacon positioning system.

Description

Technical Field

[0001] The present invention belongs to the field of underwater positioning technology, and in particular relates to an underwater single-beacon virtual long baseline positioning method and system capable of estimating unknown sound speed. Background Art

[0002] Underwater vehicles (AUVs) need to obtain accurate position feedback underwater to ensure the accuracy of their motion control and the smooth completion of underwater operations. Since electromagnetic wave signals attenuate rapidly underwater, acoustic signals are currently commonly used as the transmission medium for AUV underwater positioning. Compared with the more common underwater long baseline positioning and ultra-short baseline positioning methods, the underwater single beacon positioning method that combines a single hydroacoustic beacon with dead reckoning information has attracted widespread attention from researchers due to its advantages such as low cost, good flexibility and the ability to obtain bounded positioning errors. Among them, the single beacon positioning position solution method designed by constructing a virtual long baseline array has good flexibility and positioning accuracy, and therefore has good application prospects.

[0003] Current underwater single-beacon positioning methods typically treat the underwater acoustic velocity as known, directly multiplying the nominal velocity by the propagation time of the underwater acoustic signal detected by the hydrophone to obtain the distance between the AUV and the beacon as the observed value. However, in actual underwater positioning applications, the underwater acoustic velocity is usually time-varying and unknown due to factors such as seawater temperature, salinity, and depth. Errors in the velocity setting can cause errors in distance calculation, which in turn can lead to errors in navigation positioning, affecting the practical application capabilities of the single-beacon system. Therefore, research on single-beacon positioning methods that can simultaneously estimate the AUV position and underwater acoustic velocity is of great scientific and engineering significance.

[0004] Through the above analysis, the problems and defects of the existing technology are as follows: the existing single beacon positioning technology based on virtual long baseline cannot simultaneously estimate the AUV position and sound speed, and the positioning accuracy of the AUV position is poor, resulting in large errors in navigation positioning. Summary of the Invention

[0005] To overcome the problems existing in the related art, the embodiments disclosed in the present invention provide an underwater single-beacon virtual long baseline positioning method and system that can estimate unknown sound speed.

[0006] The technical solution is as follows: a single-beacon underwater virtual long baseline positioning method capable of estimating unknown sound speed. This method addresses the problem of unknown time-varying underwater sound speed in underwater single-beacon positioning. Based on the two-step weighted least squares principle, a single-beacon virtual long baseline positioning solution capable of estimating unknown sound speed is constructed to achieve joint estimation of AUV position and sound speed, including the following steps:

[0007] By integrating AUV dead reckoning information and utilizing all acoustic signal propagation time observations within a time window width N, a virtual long baseline positioning model is constructed.

[0008] By introducing auxiliary variables and performing algebraic transformation, the pseudo-linear equation for virtual long baseline positioning is obtained, which is solved based on the weighted least squares method to obtain preliminary estimates of the sound speed and AUV position.

[0009] Based on the relationship between the auxiliary variables and the AUV position, combined with the results of the preliminary estimation, the second-step linear estimation problem is constructed with the square of the AUV position and the square of the sound speed as unknowns. The solution is based on the weighted least squares method to obtain a more accurate least squares solution.

[0010] Combine the estimated value of the second step linear estimation problem with the preliminary estimate of the AUV position to calculate the final sound speed estimate and AUV position estimate.

[0011] Furthermore, before constructing the virtual long baseline positioning model, the following needs to be done:

[0012] With any point in the positioning area as the origin, the east, north, and sky directions are set as the X, Y, and Z axes respectively, and the underwater single beacon positioning geodetic coordinate system is established; with the AUV centroid as the origin, the front, right, and bottom directions are set as the X, Y, and Z axes respectively, and the AUV body coordinate system is established;

[0013] Construct a dead reckoning model based on the AUV velocity in the body coordinate system detected by the DVL and the AUV attitude detected by the attitude sensor;

[0014] The underwater acoustic beacon periodically emits underwater acoustic signals. The coordinates of the beacon position are known. The AUV is equipped with a hydrophone to measure the propagation time of the underwater acoustic signal. This is used as the observation quantity to construct the relationship between the propagation time of the underwater acoustic signal, the speed of sound, and the position of the AUV.

[0015] Furthermore, the dead reckoning model is constructed, i.e., the relationship between the AUV position variables at time k and time ki, where i ≥ 1; specifically:

[0016]

[0017]

[0018] Where x k ,y k ,z k is the real position coordinate of AUV at time k, x k-i is the x-direction position coordinate of the AUV at time ki, y k-i is the y-direction position coordinate of the AUV at time ki, z k-iis the z-direction position coordinate of the AUV at time ki, Δt is the discrete time interval, i is the time index variable, v x,k-t is the x-direction velocity of AUV at time kt, v y,k-t is the y-direction velocity of AUV at time kt, v z,k-t is the z-direction velocity of AUV at time kt;

[0019] Construct an underwater acoustic observation model under linear acoustic profile conditions, including:

[0020] The position coordinates of the underwater acoustic beacon are fixed and known, which can be expressed as:

[0021]

[0022] Where, P b is the coordinate vector of the underwater beacon position, x b is the east coordinate of the acoustic beacon, y b is the north coordinate of the acoustic beacon, z b The celestial coordinates of the hydroacoustic beacon;

[0023] The propagation time observation of the underwater acoustic signal obtained at time k is expressed as:

[0024]

[0025] Squaring both sides gives:

[0026]

[0027] Simplifying, we get:

[0028]

[0029] The propagation time of underwater acoustic signal contains observation noise, and the observed value of the propagation time of underwater acoustic signal is recorded as:

[0030]

[0031] Where, t k is the actual underwater acoustic signal propagation time, v k is the observation noise of the underwater acoustic signal propagation time;

[0032] Substituting it into the ranging equation, we get:

[0033]

[0034] Furthermore, the constructed virtual long baseline positioning model includes: combining the observation equation at time k, and obtaining all N+1 observation equations to be comprehensively expressed as:

[0035]

[0036] Substitute the AUV’s dead reckoning model, i.e. the position relationship between time k and time ki, and we get:

[0037]

[0038] in,

[0039]

[0040] Where x b,i ,y b,i ,z b,i Respectively represent the x, y, and z axis position coordinates of the i-th virtual beacon.

[0041] Furthermore, the method for calculating the sound speed and the preliminary estimate of the AUV position includes:

[0042] Expand all N+1 observation equations to obtain:

[0043]

[0044] All N+1 equations are integrated into a vector matrix form:

[0045]

[0046] Where B k is the noise coefficient matrix, v k is the noise vector of the underwater acoustic signal propagation time, h k ,G k are all system model parameters, is the unknown quantity to be estimated, and the definitions of each variable are as follows:

[0047]

[0048]

[0049] get The weighted least squares solution of is:

[0050]

[0051] Among them, the weight matrix W 1,k Defined as:

[0052]

[0053] Where E(·) is the expected value of the random variable, and the superscript -1 represents the inverse of the matrix. It is approximately equal to Q k is the observation variance matrix of the underwater acoustic signal propagation time, defined as The specific form is:

[0054]

[0055] The weighted least squares method The estimated variance of is:

[0056]

[0057] Where D(·) represents the variance of the random variable.

[0058] Furthermore, the method for calculating the initial estimate of the speed of sound and the position of the AUV further includes: firstly setting the weight W 1,k Set it as the unit matrix to calculate the preliminary least squares solution, and then bring the position coordinates corresponding to this solution into the noise coefficient matrix B k , calculate the weight W 1,k and the weighted least squares solution

[0059] Furthermore, the steps to obtain a more accurate weighted least squares solution include:

[0060] The estimated value that will be obtained Expressed as the true value and the estimated error:

[0061]

[0062] in, To estimate the error, define a new unknown quantity X k as follows:

[0063]

[0064] according to The first three elements of X k The relationship between them is:

[0065]

[0066] Among them, for any vector a, a[m:n] represents the subvector composed of the mth to nth elements of vector a, and a⊙b represents the vector formed by multiplying the corresponding elements of vector a and vector b; according to The fourth element of k The relationship between them is:

[0067]

[0068] according to The fifth element of k The relationship between them is:

[0069]

[0070] Combining the above three equations, we can get:

[0071]

[0072] in,

[0073]

[0074]

[0075] χ k The weighted least squares estimation solution of is:

[0076]

[0077] Weight matrix W 2,k Set to:

[0078]

[0079] Furthermore, the steps for calculating the estimated value of the AUV single beacon positioning position and the estimated value of the sound speed are as follows:

[0080] The estimated value obtained Take the square root and combine the estimated values The symbol corresponding to the position variable is used to obtain the estimated position of the AUV. The calculation formula is as follows:

[0081]

[0082] Where sign(a) represents the sign of each element of vector a. If b = sign(a), then

[0083]

[0084] Since the speed of sound should be a positive number, the estimated value of the speed of sound is as follows:

[0085]

[0086] Another object of the present invention is to provide an underwater single beacon virtual long baseline positioning system capable of estimating unknown sound speed, which is implemented by the underwater single beacon virtual long baseline positioning method capable of estimating unknown sound speed. The system includes an AUV, which is equipped with a hydrophone, a DVL and an attitude sensor; the hydrophone periodically broadcasts an acoustic signal, and the AUV periodically observes its velocity in the body coordinate system through the DVL carried by the AUV, calculates the velocity of the AUV in the geodetic coordinate system in combination with the AUV attitude angle observed by the attitude sensor, performs dead reckoning, and records and stores the dead reckoning data; the AUV receives the acoustic signal emitted by the hydrophone Finally, the propagation time of the underwater acoustic signal is obtained by combining the known emission time of the underwater acoustic signal; when the AUV receives a certain number of underwater acoustic signals, a virtual long baseline array is constructed in combination with the stored dead reckoning data; the virtual long baseline positioning problem is constructed by combining the relationship between the propagation time of the underwater acoustic signal and the AUV position and sound speed; auxiliary variables are introduced, and the pseudo-linear positioning equation is obtained based on algebraic transformation, and the preliminary solution of the AUV position and sound speed is obtained based on the weighted least squares method; then, through the relationship between the auxiliary variables and the AUV position, the second-step linear estimation problem is constructed, and the weighted least squares method is used to solve it to obtain a more accurate AUV position and sound speed estimation solution.

[0087] Furthermore, the underwater single beacon virtual long baseline positioning method for estimating an unknown sound speed operated by the underwater single beacon virtual long baseline positioning system for estimating an unknown sound speed is carried on a computer-readable storage medium, and the computer-readable storage medium stores a computer program. When the computer program is executed by the processor, the steps in the above-mentioned underwater single beacon virtual long baseline positioning method for estimating an unknown sound speed can be implemented.

[0088] In combination with all the above technical solutions, the beneficial effects of the present invention are as follows:

[0089] The AUV provided by the present invention is equipped with a hydrophone, a DVL, and an attitude sensor. The acoustic beacon periodically broadcasts an acoustic signal. The AUV periodically observes its velocity in the body coordinate system through the DVL carried by the AUV. Combined with the AUV attitude angle observed by the attitude sensor, the AUV velocity in the geodetic coordinate system is calculated to perform dead reckoning, and the dead reckoning data is recorded and stored. After receiving the acoustic signal transmitted by the acoustic beacon, the AUV obtains the acoustic signal propagation time in combination with the known acoustic signal transmission time. When the AUV receives a certain number of acoustic signals, it constructs a virtual long baseline array in combination with the stored dead reckoning data. A virtual long baseline positioning problem is constructed based on the relationship between the acoustic signal propagation time, the AUV position, and the sound speed. Auxiliary variables are introduced, a pseudo-linear positioning equation is obtained based on algebraic transformation, and a preliminary solution for the AUV position is obtained based on the weighted least squares method. Then, by exploring the relationship between the auxiliary variables and the AUV position, a second-step linear estimation problem is constructed and solved using the weighted least squares method to obtain a more accurate AUV position estimation solution. The method of the present invention can realize the joint estimation of AUV position and sound speed. Compared with the single beacon positioning method based on known sound speed, the method of the present invention can obtain more ideal position estimation performance and enhance the practical application capability of the underwater single beacon positioning system.

[0090] During application, the present invention eliminates the need for the AUV to use temperature, salinity, and depth sensors to monitor the sound velocity profile of the experimental area in real time, reducing the hardware cost of the AUV. Furthermore, compared to positioning methods based on nominal sound velocity, the present method can achieve better positioning accuracy, improve the validity and value of the data collected by the AUV, and enhance the operational and application value of the AUV itself. The present invention achieves simultaneous estimation of the AUV's position and sound velocity within the framework of virtual long-baseline positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure;

[0092] Figure 1 This is a flow chart of an underwater single-beacon virtual long baseline positioning method capable of estimating unknown sound speed provided by an embodiment of the present invention;

[0093] Figure 2 This is a schematic diagram of the underwater single beacon positioning geodetic coordinate system and the AUV body coordinate system provided by an embodiment of the present invention;

[0094] Figure 3 The AUV motion trajectory diagram obtained by simulation;

[0095] Figure 4 Comparison chart of positioning errors of different positioning methods;

[0096] Figure 5This is the sound speed estimation error diagram of the method proposed in this invention. DETAILED DESCRIPTION

[0097] To make the above-mentioned objects, features, and advantages of the present invention more readily apparent, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth numerous specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art may make similar modifications without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0098] The innovation of the present invention lies in: the present invention innovatively realizes the joint estimation of AUV position and sound speed in single beacon positioning under the framework of virtual long baseline positioning. By expanding the sound speed to the unknown quantity to be estimated, the virtual long baseline positioning equation is converted into a pseudo-linear equation form by introducing auxiliary variables; the preliminary estimate of the AUV position and sound speed is obtained by weighted least squares method; by exploring the relationship between the auxiliary variables and the AUV position, the second-step linear estimation problem is constructed, and the weighted least squares method is used to solve it to obtain more accurate estimates of the AUV position and sound speed. The method of the present invention can simultaneously estimate the position and sound speed of the AUV, enhancing the practical application capabilities of the AUV.

[0099] Aiming at the problem of unknown time-varying underwater sound velocity in single beacon positioning, the present invention constructs a single beacon virtual long baseline positioning solution based on the two-step weighted least squares principle to estimate the unknown sound velocity, thereby realizing the joint estimation of AUV position and sound velocity.

[0100] Example 1, as Figure 1 As shown, the underwater single-beacon virtual long baseline positioning method for estimating unknown sound speed provided by an embodiment of the present invention includes:

[0101] S1, with any point in the positioning area as the origin, the east, north, and sky directions are set as X, Y, and Z axes respectively, to establish the underwater single beacon positioning geodetic coordinate system; with the AUV centroid as the origin, the front, right, and bottom directions are set as X, Y, and Z axes respectively, to establish the AUV body coordinate system;

[0102] S2, constructing a dead reckoning model based on the AUV velocity in the body coordinate system detected by the DVL and the AUV attitude detected by the attitude sensor;

[0103] S3, the underwater acoustic beacon periodically emits underwater acoustic signals. The coordinates of the beacon position are known. The AUV is equipped with a hydrophone, which can measure the propagation time of the underwater acoustic signal. This is used as the observation quantity to construct the relationship between the propagation time of the underwater acoustic signal, the speed of sound, and the position of the AUV.

[0104] S4, integrating the AUV dead reckoning information and using all the acoustic signal propagation time observations within the time window width N to construct a virtual long baseline positioning model;

[0105] S5, by introducing auxiliary variables and performing algebraic transformation, the pseudo-linear equation of virtual long baseline positioning is obtained, which is solved based on the weighted least squares method to obtain preliminary estimates of the sound speed and AUV position;

[0106] S6, based on the relationship between the auxiliary variables and the AUV position, taking the preliminary estimation results as observations and the square of the AUV position and the square of the sound speed as unknowns, constructs the second-step linear estimation problem and solves it based on the weighted least squares method to obtain a more accurate least squares solution;

[0107] S7, combining the estimated value of the second step linear estimation problem with the preliminary estimated value of the AUV position to calculate the final sound speed estimate and the AUV position estimate.

[0108] For example, in step S1, the established geodetic coordinate system and the body coordinate system are as follows: Figure 2 shown.

[0109] Exemplarily, in step S2, the dead reckoning model constructed is as follows:

[0110] The coordinates of the AUV at time k are expressed as:

[0111]

[0112] Where x k is the x-direction coordinate at time k, y k is the y-direction coordinate at time k, z k is the z-direction coordinate at time k, and the speed of the AUV detected by DVL at time k in the body coordinate system is recorded as:

[0113]

[0114] The AUV attitude angle detected by the attitude sensor is recorded as:

[0115]

[0116] Where, are the forward, rightward and downward speeds of the AUV respectively, θ k ,ψ k are the roll angle, pitch angle and heading angle of the AUV respectively. Combining the velocity of the AUV in the body coordinate system and the AUV attitude angle, the velocity of the AUV in the earth coordinate system at time k can be obtained as:

[0117]

[0118] Among them, R k is the rotation matrix, defined as:

[0119]

[0120] According to the position and velocity of AUV at time k-1, the position coordinates of AUV at time k are obtained as follows:

[0121] P k =P k-1 +v k-1 Δt

[0122] Where Δt represents the discrete time interval of dead reckoning;

[0123] Expressing the above in component form is:

[0124] x k =x k-1 +v x,k-1 Δt

[0125] y k =y k-1 +v y,k-1 Δt

[0126] z k =z k-1 +v z,k-1 Δt

[0127] The relationship between the AUV position variables at time k and time ki (i ≥ 1) is obtained as follows:

[0128]

[0129]

[0130] Where x k-i is the x-direction position coordinate of the AUV at time ki, y k-i is the y-direction position coordinate of the AUV at time ki, z k-i is the z-direction position coordinate of the AUV at time ki, Δt is the discrete time interval, i is the time index variable, v x,k-t is the x-direction velocity of AUV at time kt, v y,k-t is the y-direction velocity of AUV at time kt, v z,k-t is the z-direction velocity of the AUV at time kt.

[0131] For example, in step S3, the underwater acoustic observation model constructed under the linear acoustic profile condition is as follows:

[0132] The coordinates of the underwater acoustic beacon are fixed and known, which can be recorded as:

[0133]

[0134] Where, P b is the coordinate vector of the underwater beacon position, x b is the east coordinate of the acoustic beacon, y b is the north coordinate of the acoustic beacon, z b The celestial coordinates of the hydroacoustic beacon;

[0135] The propagation time observation of the underwater acoustic signal obtained at time k is expressed as:

[0136]

[0137] Squaring both sides gives:

[0138]

[0139] Simplifying, we get:

[0140]

[0141] In real applications, the propagation time of underwater acoustic signals contains observation noise. The observed value of the propagation time of underwater acoustic signals is recorded as:

[0142]

[0143] Where, t k is the actual underwater acoustic signal propagation time, v k is the observation noise of the underwater acoustic signal propagation time;

[0144] Substituting it into the ranging equation, we get:

[0145]

[0146] Exemplarily, in step S4, the constructed virtual long baseline positioning model includes: combining the observation equation at time k to obtain a comprehensive expression of all N+1 observation equations:

[0147]

[0148] Substitute the AUV’s dead reckoning model, i.e. the position relationship between time k and time ki, and we get:

[0149]

[0150] in,

[0151]

[0152] Where x b,i ,y b,i,z b,i Respectively represent the x, y, and z axis position coordinates of the i-th virtual beacon.

[0153] For example, in step S5, the method for calculating the initial estimated value of the speed of sound and the position of the AUV is as follows:

[0154] Expand the observation equation in step S4 to obtain:

[0155]

[0156] All N+1 equations are integrated into a vector matrix form:

[0157]

[0158] Where B k is the noise coefficient matrix, v k is the noise vector of the underwater acoustic signal propagation time, h k ,G k are all system model parameters, is the unknown quantity to be estimated, and the definitions of each variable are as follows:

[0159]

[0160]

[0161] get The weighted least squares solution of is:

[0162]

[0163] Among them, the weight matrix W 1,k Defined as:

[0164]

[0165] Where E(·) is the expected value of the random variable, and the superscript -1 represents the inverse of the matrix. It is approximately equal to Q k is the observation variance matrix of the underwater acoustic signal propagation time, defined as The specific form is:

[0166]

[0167] The weighted least squares method The estimated variance of is:

[0168]

[0169] Where D(·) represents the variance of the random variable.

[0170] Noise figure matrix B k The calculation depends on the position estimation of AUV. In the application process, the weight W is first 1,k Set it as the unit matrix to calculate the preliminary least squares solution, and then bring the position coordinates corresponding to this solution into the noise coefficient matrix B k , calculate the weight W 1,k and the weighted least squares solution

[0171] Exemplarily, in step S6, the present invention innovatively proposes that the steps for obtaining a more accurate weighted least squares solution are as follows:

[0172] The estimated value obtained in step S5 Expressed as the true value and the estimated error:

[0173]

[0174] in, To estimate the error, define a new unknown quantity χ k as follows:

[0175]

[0176] according to The first three elements of k The relationship between them is:

[0177]

[0178] Among them, for any vector a, a[m:n] represents the subvector composed of the mth to nth elements of vector a, and a⊙b represents the vector formed by multiplying the corresponding elements of vector a and vector b; according to The fourth element of X k The relationship between them is:

[0179]

[0180] according to The fifth element of k The relationship between them is:

[0181]

[0182] Combining the above three equations, we can get:

[0183]

[0184] in,

[0185]

[0186]

[0187] χ k The weighted least squares estimation solution of is:

[0188]

[0189] Weight matrix W 2,k Set to:

[0190]

[0191] For example, in step S7, the steps of calculating the AUV single beacon positioning position estimate and the sound speed estimate are as follows:

[0192] The estimated value obtained Take the square root and combine the estimated values The symbols corresponding to the position variables can be used to obtain the estimated position of the AUV as follows:

[0193]

[0194] Where sign(a) represents the sign of each element of vector a. If b = sign(a), then

[0195]

[0196] Since the speed of sound should be a positive number, the estimated value of the speed of sound is as follows:

[0197]

[0198] It can be understood that the present invention constructs a relationship between auxiliary variables and unknown quantities and uses weighted least squares to correct the weighted least squares solution of the previous step.

[0199] Illustratively, the pseudo code flow of the underwater single-beacon virtual long baseline positioning method capable of estimating unknown sound speed provided by an embodiment of the present invention is shown in Table 1.

[0200] Table 1 Pseudo code flow of underwater single beacon virtual long baseline positioning method for estimating unknown sound speed

[0201]

[0202] In embodiment 2, an underwater single-beacon virtual long baseline positioning system capable of estimating unknown sound speed provided by an embodiment of the present invention includes:

[0203] The AUV is equipped with a hydrophone, a DVL and an attitude sensor. The acoustic beacon broadcasts acoustic signals periodically. The AUV periodically observes its velocity in the body coordinate system through the DVL it carries. Combined with the AUV attitude angle observed by the attitude sensor, the AUV velocity in the geodetic coordinate system is calculated to perform dead reckoning, and the dead reckoning data is recorded and stored. After receiving the acoustic signal transmitted by the acoustic beacon, the AUV obtains the acoustic signal propagation time based on the known acoustic signal transmission time. When the AUV receives a certain number of acoustic signals, it constructs a virtual long baseline array based on the stored dead reckoning data. Combining the relationship between the acoustic signal propagation time and the AUV position and sound speed, a virtual long baseline positioning problem is constructed. Auxiliary variables are introduced, and a pseudo-linear positioning equation is obtained based on algebraic transformation. The preliminary solution of the AUV position and sound speed is obtained based on the weighted least squares method. Then, by exploring the relationship between the auxiliary variables and the AUV position, a second-step linear estimation problem is constructed, which is solved using the weighted least squares method to obtain a more accurate AUV position and sound speed estimation solution.

[0204] To further illustrate the effects of the present invention, the following numerical simulations were performed. This example demonstrates the positioning performance of three single-beacon positioning methods using distance as an observation value. Because the underwater acoustic velocity is time-varying and unknown in real applications, the nominal velocity values ​​of the three comparison methods deviate from the true values. By multiplying the nominal velocity value by the observed underwater acoustic signal propagation time, the observed distance between the AUV and the beacon can be calculated, and this distance is used to estimate the AUV's position coordinates. Method 1 solves the virtual long baseline localization problem based on weighted least squares (R-WLS), method 2 solves the virtual long baseline localization problem based on the semidefinite programming method in the literature Yanshen Du, Ping Wei, and Huaguo Zhang.Semidefinite programming approaches for source localization problems.In 2014IEEE International Conference on Communiction Problem-solving, pages 339–342, 2014. (R-SDR1), and method 3 solves the virtual long baseline localization problem based on the semidefinite programming method in the literature KWCheung, WKMa, and H.C.So.Accurate approximation algorithm for toa-based maximum likelihood mobile location using semidefinite programming.In 2004IEEE International Conference on Acoustics, Speech, and Signal Processing, volume 2, pages ii–145, 2004. (R-SDR2). The method of the present invention directly uses the underwater sound propagation time as the observation quantity, and can estimate the unknown sound speed, and is solved based on a two-step weighted least squares solution.

[0205] The simulation parameters are set as follows: AUV dead reckoning interval is 0.1 seconds, acoustic signal transmission interval is 20 seconds, and acoustic beacon is fixed at [120 20 80] T m, and the total simulation time is 1000 seconds. The AUV dynamics model is used to generate the spiral dive trajectory of the AUV. The control inputs of the AUV are horizontal rudder 3°, vertical rudder -3°, and propeller speed 1000 rpm. The initial position of the AUV is [100 100 10] T m, the forward initial velocity is 1.2m / s, and the initial velocity in other directions is 0. The AUV motion trajectory obtained by simulation is as follows Figure 3 shown.

[0206] The standard deviation of the simulated DVL velocity observation noise in three directions is [0.01 0.01 0.01] T m / s, the standard deviation of the attitude sensor roll and pitch angle observations is 0.03°, the standard deviation of the heading angle observation is 0.3°, and the standard deviation of the underwater acoustic signal propagation time is 10us. The simulated sound speed value is 1530m / s, while the nominal sound speed value used by the three distance observation-based methods is 1500m / s.

[0207] For all methods, the width of the sliding window is set to 15, that is, the current moment and the 15 underwater acoustic ranging observations before the current moment are used to solve the position coordinates of the AUV at the current moment. The R-SDR1 and R-SDR2 methods were solved using the CVX toolbox in Matlab software, using the sedumi solver and setting the solution accuracy to the highest. References: Michael Grant and Stephen Boyd. CVX: Matlab software for disciplined convex programming, version 2.0beta. https: / / cvxr.com / cvx, September 2013. and Michael Grant and Stephen Boyd. Graph implementations for nonsmooth convex programs, Recent Advances in Learning and Control (a tribute to M. Vidyasagar), V. Blondel, S. Boyd, and H. Kimura, editors, pages 95-110, Lecture Notes in Control and Information Sciences, Springer, 2008. http: / / stanford.edu / ~boyd / graph_dcp.html. The localization error and average localization error of the four methods were used as performance evaluation criteria. The localization error and average localization error were calculated as follows:

[0208]

[0209] Among them, K represents the number of single beacon positioning settlements. The positioning errors of the four methods are as follows: Figure 4 The average positioning error is shown in Table 2.

[0210] according to Figure 4As shown in Table 2, the proposed method can achieve better positioning accuracy than the traditional single beacon positioning method based on distance observation, and its positioning error is lower than that of other comparison methods at most times. This shows that considering the unknown nature of the sound speed can improve the position estimation performance of single beacon positioning to a certain extent. Figure 5 The sound speed estimation error of the method proposed in the present invention is shown. It can be seen that at most positioning moments, the method proposed in the present invention can obtain better sound speed estimation accuracy, which further leads to better distance calculation accuracy and position estimation accuracy. The average sound speed estimation error of the method proposed in the present invention is 2.334561m / s, which is much better than the error corresponding to the nominal sound speed value (30m / s), that is, the method of the present invention can effectively eliminate the influence of the sound speed setting error. It should be noted that for the single beacon positioning of AUV, the spatial geometric relationship of the virtual long baseline beacon is directly related to the movement of the AUV itself. However, due to the weak maneuverability of most AUV bodies, the beacon arrangement of the virtual long baseline positioning is difficult to be as ideal as the real long baseline positioning system. This also leads to the instability of the results of solving the single beacon positioning problem based on the virtual long baseline positioning framework, that is, for certain specific moments, the positioning error suddenly becomes large, which is very important for Figure 4 This is particularly evident in the R-SDR1 method.

[0211] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made thereto. Therefore, such modifications and improvements, without departing from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

[0212] Table 2 Comparison of average positioning errors of different methods

[0213] Positioning method Average error (meters) Proposed method 0.351293 R-WLS 1.018677 R-SDR1 8.697602 R-SDR2 6.321329

[0214] The above description is only a preferred specific implementation method of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A single underwater beacon virtual long baseline positioning method capable of estimating unknown sound speed, characterized in that: This method addresses the problem of unknown time-varying underwater sound velocity in underwater single-beacon positioning. Based on the two-step weighted least squares principle, a single-beacon virtual long baseline positioning solution is constructed to estimate the unknown sound velocity. The method completes the joint estimation of the AUV position and sound velocity, including the following steps: By integrating AUV dead reckoning information and utilizing all acoustic signal propagation time observations within a time window width N, a virtual long baseline positioning model is constructed. By introducing auxiliary variables and performing algebraic transformation, the pseudo-linear equation for virtual long baseline positioning is obtained, which is solved based on the weighted least squares method to obtain preliminary estimates of the sound speed and AUV position. Based on the relationship between the auxiliary variables and the AUV position, combined with the results of the preliminary estimation, the second-step linear estimation problem is constructed with the square of the AUV position and the square of the sound speed as unknowns. The solution is based on the weighted least squares method to obtain a more accurate least squares solution. Combine the estimated value of the second step linear estimation problem with the preliminary estimate of the AUV position to calculate the final sound speed estimate and AUV position estimate.

2. The underwater single beacon virtual long baseline positioning method capable of estimating unknown sound speed according to claim 1 is characterized in that: Before constructing the virtual long baseline positioning model, the following steps must be performed: With any point in the positioning area as the origin, the east, north, and sky directions are set as the X, Y, and Z axes respectively, and the underwater single beacon positioning geodetic coordinate system is established; with the AUV centroid as the origin, the front, right, and bottom directions are set as the X, Y, and Z axes respectively, and the AUV body coordinate system is established; Construct a dead reckoning model based on the AUV velocity in the body coordinate system detected by the DVL and the AUV attitude detected by the attitude sensor; The underwater acoustic beacon periodically emits underwater acoustic signals. The coordinates of the beacon position are known. The AUV is equipped with a hydrophone to measure the propagation time of the underwater acoustic signal. This is used as the observation quantity to construct the relationship between the propagation time of the underwater acoustic signal, the speed of sound, and the position of the AUV.

3. The underwater single beacon virtual long baseline positioning method capable of estimating unknown sound speed according to claim 2, characterized in that: The constructed dead reckoning model, i.e., the relationship between the AUV position variables at time k and time ki, where i ≥ 1, is: Where x k ,y k , z k is the real position coordinate of AUV at time k, x k-i is the x-direction position coordinate of the AUV at time ki, y k-i is the y-direction position coordinate of the AUV at time ki, z k-i is the z-direction position coordinate of the AUV at time ki, Δt is the discrete time interval, i is the time index variable, v x，k-t is the x-direction velocity of AUV at time kt, v y，k-t is the y-direction velocity of AUV at time kt, v z，k-t is the z-direction velocity of AUV at time kt; Construct an underwater acoustic observation model under linear acoustic profile conditions, including: The position coordinates of the underwater acoustic beacon are fixed and known, which can be expressed as: Where, P b is the coordinate vector of the underwater beacon position, x b is the east coordinate of the acoustic beacon, y b is the north coordinate of the acoustic beacon, z b The celestial coordinates of the hydroacoustic beacon; The observed propagation time of the underwater acoustic signal obtained at time k is expressed as: Squaring both sides gives: Simplifying, we get: The propagation time of underwater acoustic signal contains observation noise, and the observed value of the propagation time of underwater acoustic signal is recorded as: Where, t k is the actual underwater acoustic signal propagation time, v k is the observation noise of the underwater acoustic signal propagation time; put it into the ranging equation, and we get:

4. The underwater single beacon virtual long baseline positioning method capable of estimating unknown sound speed according to claim 1, characterized in that: The constructed virtual long baseline positioning model includes: combining the observation equation at time k, and obtaining all N+1 observation equations to be expressed as follows: Substitute the AUV’s dead reckoning model, i.e. the position relationship between time k and time ki, and we get: in, Where x b，i ,y b，i , z b，i Respectively represent the x-, y-, and z-axis position coordinates of the i-th virtual beacon.

5. The underwater single beacon virtual long baseline positioning method capable of estimating unknown sound speed according to claim 1, characterized in that: Methods for calculating the speed of sound and a preliminary estimate of the AUV's position include: Expand all N+1 observation equations to obtain: All N+1 equations are integrated into a vector matrix form: Where B k is the noise coefficient matrix, v k is the noise vector of the underwater acoustic signal propagation time, h h , G k are all system model parameters, is the unknown quantity to be estimated, and the definitions of each variable are as follows: get The weighted least squares solution of is: Among them, the weight matrix W 1，k Defined as: In the formula, E(·) is the expected value of the random variable, the superscript -1 represents the inverse of the matrix, It is approximately equal to Q k is the observation variance matrix of the underwater acoustic signal propagation time, defined as The specific form is: The weighted least squares method The estimated variance of is: Where D(·) represents the variance of the random variable.

6. The underwater single beacon virtual long baseline positioning method capable of estimating unknown sound speed according to claim 5, characterized in that: The method for calculating the initial estimate of the speed of sound and the position of the AUV further includes: firstly setting the weight W 1，k Set it as the unit matrix to calculate the preliminary least squares solution, and then bring the position coordinates corresponding to this solution into the noise coefficient matrix B k , calculate the weight W 1，k and the weighted least squares solution 7. The underwater single beacon virtual long baseline positioning method capable of estimating unknown sound speed according to claim 1, characterized in that: The steps to obtain a more accurate weighted least squares solution include: The estimated value that will be obtained Expressed as the true value and the estimated error: in, To estimate the error, define a new unknown quantity χ k as follows: according to The first three elements of k The relationship between them is: Among them, for any vector a, a[m:n] represents the subvector composed of the mth to nth elements of vector a, and a⊙b represents the vector formed by multiplying the corresponding elements of vector a and vector b; according to The fourth element of k The relationship between them is: according to The fifth element of k The relationship between them is: Combining the above three equations, we can get: in, χ k The weighted least squares estimation solution of is: Weight matrix W 2,k Set to:

8. The underwater single beacon virtual long baseline positioning method capable of estimating unknown sound speed according to claim 1, characterized in that: The steps to calculate the AUV single beacon positioning position estimate and sound speed estimate are as follows: The estimated value obtained Take the square root and combine the estimated values The symbol corresponding to the position variable is used to obtain the estimated position of the AUV. The calculation formula is as follows: Where sign(a) represents the sign of each element of vector a. If b = sign(a), then Since the speed of sound should be a positive number, the estimated value of the speed of sound is as follows:

9. An underwater single-beacon virtual long baseline positioning system capable of estimating unknown sound speed, characterized in that: The system is implemented by the underwater single-beacon virtual long baseline positioning method capable of estimating unknown sound speed as described in any one of claims 1 to 8. The system includes an AUV equipped with a hydrophone, a DVL, and an attitude sensor; the hydrophone periodically broadcasts an underwater acoustic signal, and the AUV periodically observes its velocity in a body coordinate system through the DVL carried by the AUV. The velocity of the AUV in a geodetic coordinate system is calculated based on the AUV attitude angle observed by the attitude sensor, and dead reckoning is performed, and the dead reckoning data is recorded and stored; After receiving the underwater acoustic signal transmitted by the underwater acoustic beacon, the AUV obtains the underwater acoustic signal propagation time by combining the known underwater acoustic signal transmission time. When the AUV receives a certain number of underwater acoustic signals, it constructs a virtual long baseline array by combining the stored dead reckoning data. Combining the relationship between the propagation time of underwater acoustic signals and the AUV position and sound speed, a virtual long baseline positioning problem is constructed; auxiliary variables are introduced, and a pseudo-linear positioning equation is obtained based on algebraic transformation, and a preliminary solution of the AUV position and sound speed is obtained based on the weighted least squares method; then, based on the relationship between the auxiliary variables and the AUV position, a second-step linear estimation problem is constructed, and the weighted least squares method is used to solve it to obtain a more accurate estimation solution of the AUV position and sound speed.

10. The underwater single-beacon virtual long baseline positioning system capable of estimating unknown sound speed according to claim 9, characterized in that: The underwater single-beacon virtual long baseline positioning method for estimating an unknown sound speed, which is operated by the underwater single-beacon virtual long baseline positioning system for estimating an unknown sound speed, is carried on a computer-readable storage medium, and the computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps in the underwater single-beacon virtual long baseline positioning method for estimating an unknown sound speed can be implemented.

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