Underwater single beacon virtual long baseline positioning method and system considering sound propagation refraction

Abstract

The invention belongs to the technical field of underwater positioning, and discloses an underwater single beacon virtual long baseline positioning method and system considering sound propagation refraction. After the AUV receives the underwater acoustic signal emitted by the underwater acoustic beacon, the known underwater acoustic signal emission time is combined to obtain the underwater acoustic signal propagation time; when the AUV receives a certain number of underwater acoustic signals, constructing a virtual long baseline array in combination with the stored dead reckoning data; constructing a virtual long baseline positioning problem by combining the relationship between the underwater sound propagation time and the AUV position under the linear sound profile; auxiliary variables are introduced, a pseudo-linear positioning equation is obtained based on algebraic conversion, and an AUV position initial solution is obtained based on a weighted least square method; and a second-step linear estimation problem is constructed by exploring the relationship between the auxiliary variable and the position of the AUV. According to the method, the refraction of the underwater sound propagation channel is considered, and the practical application capability of single beacon positioning is enhanced.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater positioning, and in particular relates to an underwater single-beacon virtual long baseline positioning method and system taking into account sound propagation refraction. Background Art

[0002] When performing underwater operations, underwater vehicles (AUVs) need to obtain their own position coordinates in real time to ensure the accuracy of motion control and the validity of the collected data. Since electromagnetic wave signals attenuate rapidly underwater, hydroacoustic positioning has become the most widely used positioning method in underwater environments. Compared with the common underwater long baseline positioning and ultra-short baseline positioning technologies, the positioning method that combines a single hydroacoustic beacon with dead reckoning information only requires a single hydroacoustic beacon with a known position to provide positioning assistance, which can greatly reduce the time and economic cost of long baseline positioning and obtain greater positioning flexibility. Therefore, it has attracted widespread attention from researchers.

[0003] Most of the current underwater single beacon positioning methods assume that the water acoustic speed is constant, and directly correct the dead reckoning data based on the distance between the AUV and the beacon. In actual underwater positioning applications, affected by factors such as seawater temperature, salinity, and depth, the water acoustic speed varies with space, especially in the depth direction, where the sound speed value has a large gradient, which can cause obvious sound propagation refraction. Ignoring the influence of sound propagation refraction will cause a large ranging error, which will in turn lead to errors in single beacon positioning, affecting the actual application capabilities of the single beacon system. Studies have shown that for deep-sea environments, the water acoustic speed profile can be approximated as linear, that is, the sound speed value can be approximated as a linear function of depth. In other words, single beacon positioning under linear sound speed profile conditions has broad application prospects.

[0004] Through the above analysis, the problems and defects of the existing technology are as follows: for the common sound profile form of linear sound velocity profile, the existing single beacon positioning method does not take into account the influence of sound propagation refraction, which will cause a large ranging error, and then lead to the low accuracy of the obtained position solution result, and the practical application capability of single beacon positioning is weak. Summary of the invention

[0005] In order 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 taking into account the refraction of sound propagation.

[0006] The technical solution is as follows: an underwater single beacon virtual long baseline positioning method considering sound propagation refraction is designed for a linear sound velocity profile. A single beacon positioning position solution method based on two-step weighted least squares is designed under the framework of a virtual long baseline to obtain the final single beacon positioning position of the AUV, specifically including:

[0007] The hydroacoustic beacon periodically emits hydroacoustic signals, and the hydrophone carried by the AUV measures the propagation time of the hydroacoustic signals. The sound velocity profile is modeled as a linear sound profile. Combining the known hydroacoustic profile parameter information with the hydroacoustic beacon position coordinates, a hydroacoustic observation model under the linear sound profile condition is constructed to obtain the relationship between the signal propagation time and the AUV position.

[0008] The AUV dead reckoning information is integrated and all the acoustic signal propagation time observations within the time window width N are used to construct a virtual long baseline positioning model under the condition of linear acoustic profile.

[0009] Auxiliary variables are introduced for algebraic transformation to obtain the pseudo-linear equation solution of virtual long baseline positioning, and the positioning problem is preliminarily solved based on weighted least squares;

[0010] Combining the relationship between the auxiliary variables and the unknown variables, taking the square of the AUV position coordinates as the unknown variable, a new linear estimation equation is constructed based on the results of the preliminary solution, and an accurate estimation solution is obtained through the weighted least squares method;

[0011] The obtained preliminary solution to the positioning problem is combined with the weighted least squares method to obtain an accurate estimation solution, and the final single beacon positioning position estimate of the AUV is calculated.

[0012] Furthermore, the hydroacoustic beacon periodically emits hydroacoustic signals. Before the hydrophone carried by the AUV measures the propagation time of the hydroacoustic signal, the following operations need to be performed:

[0013] Take any point in the positioning area as the origin, set the east, north and sky directions as X, Y and Z axes respectively, and establish the underwater single beacon positioning geodetic coordinate system; take the AUV centroid as the origin, set the front, right and bottom directions as x, y and z axes respectively, and establish the AUV body coordinate system;

[0014] The dead reckoning model is constructed based on the AUV velocity in the body coordinate system detected by the DVL and the AUV attitude detected by the attitude sensor.

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

[0016]

[0017] In the formula, 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, and 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.

[0018] Furthermore, a hydroacoustic observation model under the condition of linear acoustic profile is constructed, including:

[0019] The coordinates of the hydroacoustic beacon are fixed and known, recorded as:

[0020]

[0021] Where P b is the coordinate vector of the hydroacoustic beacon position, x b is the east coordinate of the hydroacoustic beacon, y b is the north coordinate of the hydroacoustic beacon, z b The celestial coordinates of the hydroacoustic beacon;

[0022] The sound velocity profile is modeled as linear, that is, the sound velocity value is a linear function of the depth, which can be specifically expressed as:

[0023] c=az+b

[0024] Where z is the depth, a is the sound velocity gradient, b is the sound velocity at sea level, and c is the sound velocity at depth z;

[0025] When the sound velocity profile is known, the sound velocity at the beacon is also known and is denoted as c b , the speed of sound at the AUV position at time k is recorded as c k , the propagation time of the underwater acoustic signal measured at time k is recorded as t k , then the relationship between horizontal distance and signal propagation time is:

[0026]

[0027] In the formula, e is a natural constant, r k is the horizontal distance between the AUV and the beacon, and its geometric calculation formula is:

[0028]

[0029] Squaring both sides of the above equation yields:

[0030]

[0031] Simplifying, we get:

[0032]

[0033] Substituting the sound velocity profile parameters into the equation:

[0034]

[0035] definition:

[0036]

[0037] is a virtual observation, all parameters are known, m k The value depends on the signal propagation time observation value and the acoustic profile parameters at the current moment, so the relationship between the AUV position and the underwater acoustic signal propagation time is:

[0038] 0=(x k -x b ) 2 +(y k -y b ) 2 +(z k -z b ) 2 -m k (az k +b).

[0039] Furthermore, a virtual long baseline positioning model under the condition of linear acoustic profile is constructed, including:

[0040] Define the time window width as N, and use the propagation time of the underwater acoustic signal received from kN to k to solve the position coordinates of the AUV at time k. For time ki, the observation equation established by applying the relationship between the AUV position and the propagation time of the underwater acoustic signal is: k-i -x b ) 2 +(y k-i -y b ) 2 +(z k-i -z b ) 2 -m k-i (az k-i + b), for i=1,2…N

[0041] Substitute the AUV’s dead reckoning model, that is, the position relationship between time k and time ki, and we get:

[0042] 0=(x k -x b，i ) 2 +(y k -y b,i ) 2 +(z k -z b,i ) 2-m k-i (az k +b i ), for i=1,2…N

[0043] in,

[0044]

[0045]

[0046] In the formula, x b,i ,y b，i , z b,i , b i Respectively represent the x, y, z axis position coordinates of the ith virtual beacon and the virtual surface sound speed corresponding to the ith beacon, record:

[0047] x b,0 =x b

[0048] y b,0 =y b

[0049] z b,0 =z b

[0050] b0=b

[0051] Combining the observation equation at time k, we get all N+1 observation equations, which can be expressed as follows:

[0052] 0=(x k -x b，i ) 2 +(y k -y b，i ) 2 +(z k -z b，i ) 2 -m k-i (az k +b i ), for i=0,1,2…N

[0053] In real applications, the propagation time of the underwater acoustic signal contains observation noise, and the observed value of the propagation time of the underwater acoustic signal is recorded as for:

[0054]

[0055] Where, t k is the actual underwater acoustic signal propagation time, v k is the observation noise of the underwater acoustic signal propagation time, which is modeled as having a mean of 0 and a variance of A Gaussian random variable Performing Taylor expansion and ignoring higher-order terms, we obtain:

[0056]

[0057] Then we have:

[0058]

[0059] Substituting the above equation into the virtual observation quantity, we get:

[0060]

[0061] For the ki-th observation, we have:

[0062]

[0063] The virtual observation containing noise is defined as:

[0064]

[0065] Then we have:

[0066]

[0067] Substituting the above formula into the observation equation, we get:

[0068]

[0069] Moving the noise term to the left side of the equal sign gives:

[0070]

[0071] in,

[0072]

[0073] Where η i is the noise coefficient of the virtual long baseline positioning equation.

[0074] Furthermore, the positioning problem is initially solved based on weighted least squares, including:

[0075] Expand the right side of the virtual long baseline positioning equation to obtain:

[0076]

[0077] definition:

[0078]

[0079] Then we have:

[0080]

[0081] All N+1 equations are integrated into a vector matrix form:

[0082]

[0083] In the formula, 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 system model parameters, is the unknown quantity to be estimated, and the definitions of each variable are as follows:

[0084]

[0085] get The weighted least squares solution of is:

[0086]

[0087] Among them, the weight matrix W 1，k Defined as:

[0088]

[0089] In the formula, E(·) represents 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 observed variance matrix of the underwater acoustic signal propagation time, defined as The specific form is:

[0090]

[0091] The weighted least squares method The estimated variance of is:

[0092]

[0093] Where D(·) represents the variance of the random variable.

[0094] Furthermore, the noise coefficient matrix B k The calculation of 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

[0095] Furthermore, the steps of obtaining a more accurate weighted least squares solution include:

[0096] The estimated value that will be obtained Expressed as the true value and the estimated error:

[0097]

[0098] in, To estimate the error, define a new unknown quantity χ k as follows:

[0099]

[0100] according to The first three elements of k The relationship between them is:

[0101]

[0102] 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:

[0103]

[0104] Combining the above two equations, we get:

[0105]

[0106] in,

[0107]

[0108] χ k The weighted least squares estimation solution of is:

[0109]

[0110] Weight matrix W 2，k Set to:

[0111]

[0112] Furthermore, the final single beacon positioning position estimate of the AUV is calculated, including:

[0113] The estimated value obtained Take the square root and combine the estimated values The sign corresponding to the position variable is used to obtain the estimated position of the AUV. The calculation formula is as follows:

[0114]

[0115] Where sign(a) represents the sign of each element of vector a. If b = sign(a), then

[0116]

[0117] Another object of the present invention is to provide an underwater single beacon virtual long baseline positioning system considering sound propagation and refraction, the system comprising an underwater single beacon virtual long baseline positioning method considering sound propagation and refraction, the system comprising an AUV; the AUV is equipped with a hydrophone, a DVL, a posture sensor and a CTD; the AUV detects the sound velocity profile parameters of the experimental area through the CTD; the hydroacoustic beacon periodically broadcasts a hydroacoustic signal, the AUV periodically observes its velocity in the body coordinate system through the carried DVL, calculates the velocity of the AUV in the geodetic coordinate system in combination with the AUV posture angle observed by the posture sensor, performs dead reckoning, and records and stores the dead reckoning data; the AUV is connected to the After receiving the hydroacoustic signal emitted by the hydroacoustic beacon, the propagation time of the hydroacoustic signal is obtained in combination with the known emission time of the hydroacoustic signal; when the AUV receives a certain number of hydroacoustic signals, a virtual long baseline array is constructed in combination with the stored dead reckoning data; a virtual long baseline positioning problem is constructed in combination with the relationship between the hydroacoustic propagation time and the AUV position under the linear acoustic profile; auxiliary variables are introduced, and a pseudo-linear positioning equation is obtained based on algebraic transformation, and a preliminary solution to the AUV position is obtained based on the weighted least squares method; and then by exploring 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 AUV position estimation solution.

[0118] Combining all the above-mentioned technical solutions, the beneficial effects of the present invention are as follows: the present invention focuses on the common linear sound velocity profile, and designs a single beacon positioning position solution method under the condition of linear sound profile based on two-step weighted least squares. The AUV is equipped with a hydrophone, a DVL (Doppler velocimeter), an attitude sensor, and a temperature-salinity-depth meter; the AUV detects the sound velocity profile parameters of the experimental area through a CTD or a sound velocity profiler; the hydroacoustic beacon periodically broadcasts hydroacoustic signals, and the AUV periodically observes its velocity in the body coordinate system through the DVL it carries, and calculates the AUV velocity 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; after receiving the hydroacoustic signal emitted by the hydroacoustic beacon, the AUV obtains the water velocity in combination with the known emission time of the hydroacoustic signal. Acoustic signal propagation time; when the AUV receives a certain number of hydroacoustic signals, a virtual long baseline array is constructed in combination with the stored dead reckoning data; a virtual long baseline positioning problem is constructed in combination with the relationship between the hydroacoustic propagation time and the AUV position under the linear acoustic profile; an auxiliary variable is introduced, a pseudo-linear positioning equation is obtained based on algebraic transformation, and a preliminary solution to the AUV position is obtained based on the weighted least squares method; and then, by exploring the relationship between the auxiliary variable and the AUV position, a second-step linear estimation problem is constructed, and the weighted least squares method is used to solve the problem, thereby obtaining a more accurate AUV position estimation solution. Compared with other single beacon positioning methods that do not consider the refraction of acoustic propagation, the method of the present invention can obtain more accurate position solution results and enhance the practical application capability of single beacon positioning.

[0119] The method of the present invention takes into account the refraction of the water acoustic propagation channel that is widely present in real water acoustic positioning applications, adopts a more reasonable and accurate water acoustic observation model, can obtain better ranging accuracy and positioning accuracy, improve the effectiveness and value of the data collected by the AUV, and enhance the operation and application value of the AUV itself. The present invention takes into account the problem of water acoustic propagation channel refraction that is widely present in single beacon positioning. At present, there is no related technology, which fills the gap in the single beacon positioning technology that considers the refraction of sound propagation. Affected by the temperature, salinity and depth changes of seawater, the gradient of the water acoustic sound velocity in the depth direction is large, which will cause obvious refraction of the sound propagation channel. This problem is widely present in all underwater positioning methods based on water acoustic ranging, including single beacon positioning. At present, the common processing method in the field of single beacon positioning is to ignore the refraction of the channel, or introduce the concept of effective sound velocity, and directly regard the effective sound velocity as unknown. Ignoring the refraction of the channel will cause ranging error and positioning error, while directly considering the effective sound velocity as unknown will ignore the valuable physical information of the water acoustic sound velocity profile, which will also cause performance loss and positioning error. It is urgent to study the single beacon positioning method considering the refraction of sound propagation. The present invention directly and accurately describes the underwater acoustic observation model under the linear acoustic profile, and directly processes the observation model taking into account propagation and refraction, so as to obtain better position estimation performance and solve the technical problems that people are eager to solve. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0121] Figure 1 It is a flow chart of an underwater single beacon virtual long baseline positioning method considering sound propagation and refraction provided by an embodiment of the present invention;

[0122] Figure 2 It 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;

[0123] Figure 3 The motion trajectory of the AUV obtained by simulation;

[0124] Figure 4 The sound velocity profile used for the simulation;

[0125] Figure 5 Positioning error diagram of the four methods. DETAILED DESCRIPTION

[0126] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0127] The innovation of the present invention is that the present invention innovatively introduces the relationship between horizontal distance and signal propagation time under the condition of linear sound velocity profile, and innovatively derives the hydroacoustic observation model under the condition of linear sound profile. The present invention integrates the dead reckoning information of AUV (autonomous underwater vehicle), and constructs a virtual long baseline positioning method under the condition of linear sound profile under the framework of virtual long baseline positioning. Furthermore, the present invention designs an AUV position solution method based on two-step weighted least squares: by introducing auxiliary variables, constructing a pseudo-linear positioning equation, and obtaining a preliminary estimate of the AUV position based on weighted least squares, and then by exploring the relationship between the auxiliary variables and the AUV position, the linear estimation model of the second step is constructed with the square of the AUV position as a variable, and a more accurate AUV position solution is obtained based on weighted least squares. The method of the present invention takes into account the refraction of the hydroacoustic propagation channel in single beacon positioning, and can obtain more accurate position estimation results, thereby enhancing the practical application capability of AUV.

[0128] Aiming at the problem of refraction of the sound propagation channel caused by the change of water acoustic velocity with depth in underwater single beacon positioning, a single beacon positioning method considering the refraction of sound propagation is proposed. In particular, for the common sound profile form of linear sound velocity profile, a single beacon positioning position solution method based on two-step weighted least squares is proposed under the framework of virtual long baseline positioning.

[0129] Embodiment 1, as Figure 1 As shown, an underwater single beacon virtual long baseline positioning method considering sound propagation refraction is provided in an embodiment of the present invention, comprising the following steps:

[0130] S1, take any point in the positioning area as the origin, set the east, north and sky directions as X, Y and Z axes respectively, and establish the underwater single beacon positioning geodetic coordinate system; take the centroid of the underwater autonomous vehicle (AUV) as the origin, and set the front, right and bottom directions as x, y and z axes respectively, and establish the AUV body coordinate system;

[0131] S2, constructing a dead reckoning model based on the velocity of the AUV in the body coordinate system detected by the Doppler velocimeter (DVL) and the attitude of the AUV detected by the attitude sensor;

[0132] S3, the hydroacoustic beacon periodically emits hydroacoustic signals, the beacon position coordinates are known, and the AUV is equipped with a hydrophone, which can measure the propagation time of the hydroacoustic signal; the sound velocity profile is modeled as a linear sound profile, and the known hydroacoustic profile parameter information and the hydroacoustic beacon position coordinates are combined to construct a hydroacoustic observation model under the linear sound profile condition, that is, the relationship between the signal propagation time and the AUV position;

[0133] S4, integrating AUV dead reckoning information and using all acoustic signal propagation time observations within the time window width N, constructs a virtual long baseline positioning model under linear acoustic profile conditions;

[0134] S5, by introducing auxiliary variables and performing algebraic transformation, the pseudo-linear equation solution of virtual long baseline positioning is obtained, and the positioning problem is preliminarily solved based on weighted least squares;

[0135] S6, combining the relationship between the auxiliary variables and the unknown variables, taking the square of the AUV position coordinates as the unknown quantity, constructing a new linear estimation equation based on the preliminary solution results, and obtaining a more accurate estimation solution through the weighted least squares method;

[0136] S7, combining the obtained estimated solution, calculating the final single beacon positioning position estimate of the AUV.

[0137] It can be understood that, for a scenario where the sound speed profile is known, the present invention models the sound speed profile as a linear function of depth for processing.

[0138] Exemplarily, in step S1, the established geodetic coordinate system and body coordinate system are as follows: Figure 2 shown.

[0139] Exemplarily, in step S2, the dead reckoning model constructed is as follows:

[0140] The coordinates of the AUV at time k are expressed as:

[0141]

[0142] In the formula, x k is the x-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 velocity of the AUV detected by DVL at time k in the body coordinate system is recorded as:

[0143]

[0144] The AUV attitude angle detected by the attitude sensor is recorded as:

[0145]

[0146] In the formula, are the forward, rightward and downward speeds of the AUV respectively, 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 geodetic coordinate system at time k can be obtained as

[0147]

[0148] Among them, R k is the rotation matrix, defined as:

[0149]

[0150] According to the position and speed of AUV at time k-1, the position coordinates of AUV at time k are obtained as follows:

[0151] P k =P k-1 +v k-1 Δt

[0152] Where Δt represents the discrete time interval of dead reckoning;

[0153] Expressing the above in component form is:

[0154] x k =x k-1 +v x，k-1 Δt

[0155] y k =y k-1 +v y,k-1 Δt

[0156] z k =z k-1 +v z，k-1 Δt

[0157] Then the relationship between the AUV position variables at time k and time ki (i ≥ 1) is obtained as follows:

[0158]

[0159] In the formula, 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, and 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.

[0160] Exemplarily, in step S3, the constructed hydroacoustic observation model under the linear acoustic profile condition is as follows:

[0161] The coordinates of the hydroacoustic beacon are fixed and known, which can be recorded as:

[0162]

[0163] Where P b is the coordinate vector of the hydroacoustic beacon position, x b is the east coordinate of the hydroacoustic beacon, y b is the north coordinate of the hydroacoustic beacon, z b The celestial coordinates of the hydroacoustic beacon;

[0164] The sound velocity profile is modeled as linear, that is, the sound velocity value is a linear function of the depth, which is specifically expressed as:

[0165] c=az+b

[0166] Where z is the depth, a is the sound velocity gradient, b is the sound velocity at sea level, and c is the sound velocity at depth z;

[0167] When the sound velocity profile is known, the sound velocity at the beacon is also known and is denoted as c b , the speed of sound at the AUV position at time k is recorded as c k , the propagation time of the underwater acoustic signal at time k is recorded as t k , the relationship between horizontal distance and signal propagation time is:

[0168]

[0169] In the formula, r k is the horizontal distance between the AUV and the beacon, and its geometric calculation formula is: e is a natural constant; squaring both sides of the above equation yields:

[0170]

[0171] Simplifying, we get:

[0172]

[0173] Substituting the sound velocity profile parameters into the equation:

[0174]

[0175] definition:

[0176]

[0177] is a virtual observation, where all parameters are known, m k The value depends on the signal propagation time observation value and the acoustic profile parameters at the current moment, so the relationship between the AUV position and the underwater acoustic signal propagation time is:

[0178] 0=(x k -x b ) 2 +(y k -y b ) 2 +(z k -z b ) 2 -m k (az k +b)

[0179] It can be understood that the above calculation formula proposed in the present invention is used to construct the relationship between the position coordinates and the propagation time of the underwater acoustic signal under the condition of linear sound velocity profile.

[0180] Exemplarily, in step S4, the constructed virtual long baseline positioning model under the linear acoustic profile condition is as follows:

[0181] The time window width is defined as N, that is, the propagation time of the hydroacoustic signal received from time kN to k is used to solve the position coordinates of the AUV at time k. For time ki, the time observation equation established by applying the relationship between the AUV position and the propagation time of the hydroacoustic signal is as follows:

[0182] 0=(x k-i -x b ) 2 +(y k-i -y b ) 2 +(z k-i -z b ) 2 -m k-i (az k-i + b), for i=1,2…N

[0183] Substitute the AUV’s dead reckoning model, that is, the position relationship between time k and time ki, and we get:

[0184] 0=(x k -x b，i ) 2 +(y k -y b，i ) 2 +(z k -z b,i ) 2 -m k-i (az k +bi ), for i=1,2…N

[0185] in,

[0186]

[0187] x b,i ,y b，i , z b,i , b i Represents the x, y, z axis position coordinates of the ith virtual beacon and the virtual surface sound velocity corresponding to the ith position.

[0188] x b,0 =x b

[0189] y b,0 =y b

[0190] z b,0 =z b

[0191] b0=b

[0192] Combined with the observation equation at time k, all N+1 observation equations are expressed as follows:

[0193] 0=(x k -x b，i ) 2 +(y k -y b，i ) 2 +(z k -z b，i ) 2 -m k-i (az k +b i ), for i=0,1,2…N

[0194] In real applications, the propagation time of the underwater acoustic signal contains observation noise, and the observed value of the propagation time of the underwater acoustic signal is recorded as for:

[0195]

[0196] Where, t k is the actual underwater acoustic signal propagation time, v k is the observation noise of the underwater acoustic signal propagation time, which is modeled as having a mean of 0 and a variance of A Gaussian random variable Performing Taylor expansion and ignoring higher-order terms, we obtain:

[0197]

[0198] That is:

[0199]

[0200] Substituting the above equation into the virtual observation quantity, we get:

[0201]

[0202] For the ki-th observation, we have:

[0203]

[0204] The virtual observation containing noise is defined as:

[0205]

[0206] Then we have:

[0207]

[0208] Substituting the above formula into the observation equation, we get:

[0209]

[0210] Moving the noise term to the left side of the equal sign gives:

[0211]

[0212] in,

[0213]

[0214] Where η i is the noise coefficient of the virtual long baseline positioning equation.

[0215] Exemplarily, in step S5, the steps of obtaining the preliminary weighted least squares solution are as follows:

[0216] The present invention innovatively proposes to expand the right side of the virtual long baseline positioning equation to obtain:

[0217]

[0218] definition:

[0219]

[0220] Then we have:

[0221]

[0222] All N+1 equations are integrated into a vector matrix form:

[0223]

[0224] In the formula, 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 system model parameters, is the unknown quantity to be estimated, and the definitions of each variable are as follows:

[0225]

[0226]

[0227] get The weighted least squares solution of is:

[0228]

[0229] Among them, the weight matrix W 1，k Defined as:

[0230]

[0231] In the formula, E(·) represents the expected value of the random variable, and the superscript -1 represents the inverse of the matrix. It is approximately equal to, Qk is the observation variance matrix of the underwater acoustic signal propagation time, defined as The specific form is:

[0232]

[0233] The weighted least squares method The estimated variance of is:

[0234]

[0235] Where D(·) represents the variance of the random variable.

[0236] Noise coefficient matrix B k The calculation of 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

[0237] Exemplarily, in step S6, the more accurate weighted least squares solution step obtained includes:

[0238] The estimated value that will be obtained Expressed as the true value and the estimated error:

[0239]

[0240] in, To estimate the error, define a new unknown quantity χ k as follows:

[0241]

[0242] according to The first three elements of k The relationship between them is:

[0243]

[0244] 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:

[0245]

[0246] Combining the above two equations, we get:

[0247]

[0248] in,

[0249]

[0250] χ k The weighted least squares estimation solution of is:

[0251]

[0252] Weight matrix W 2，k Set to:

[0253]

[0254] Exemplarily, in step S7, calculating the final single beacon positioning position estimate of the AUV includes:

[0255] The estimated value obtained Take the square root and combine the estimated values The sign corresponding to the position variable is used to obtain the estimated position of the AUV. The calculation formula is as follows:

[0256]

[0257] Where sign(a) represents the sign of each element of vector a. If b = sign(a), then

[0258]

[0259] The pseudo code of the underwater single beacon virtual long baseline positioning method considering sound propagation and refraction is shown in Table 1.

[0260] Table 1 Pseudo code of underwater single beacon virtual long baseline positioning method

[0261]

[0262]

[0263] First embodiment 2, the first embodiment of the present invention provides an underwater single beacon virtual long baseline positioning system taking into account sound propagation refraction, comprising:

[0264] The AUV is equipped with a hydrophone, a DVL, an attitude sensor and a CTD. The AUV detects the sound velocity profile parameters of the experimental area through the CTD. The hydroacoustic beacon broadcasts hydroacoustic signals periodically. The AUV periodically observes its velocity in the body coordinate system through the DVL it carries, and 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. After receiving the hydroacoustic signal emitted by the hydroacoustic beacon, the AUV obtains the propagation time of the hydroacoustic signal in combination with the known emission time of the hydroacoustic signal. When the AUV receives a certain number of hydroacoustic signals, it constructs a virtual long baseline array in combination with the stored dead reckoning data. The virtual long baseline positioning problem is constructed in combination with the relationship between the hydroacoustic propagation time under the linear sound profile and the AUV position. Auxiliary variables are introduced, and a pseudo-linear positioning equation is obtained based on algebraic transformation, and a preliminary solution of 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, 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 estimation solution.

[0265] The method of the present invention takes into account the refraction of the underwater acoustic propagation channel existing in real applications, and can more accurately model the relationship between the propagation time of the underwater acoustic signal and the position of the AUV. Compared with the method that does not take into account the refraction of sound propagation, the method of the present invention can obtain more accurate position estimation accuracy.

[0266] For comparison, this embodiment simultaneously demonstrates the positioning performance of three single beacon positioning methods that do not consider the refraction of sound propagation. The sound velocity value is calculated using the average value of the entire linear sound velocity profile. Combined with the observed propagation time of the hydroacoustic signal, the distance observation value between the AUV and the beacon can be calculated, and the distance is used to estimate the AUV position coordinates. Method 1 is based on weighted least squares to solve the virtual long baseline positioning problem (denoted as R-WLS), method 2 is based on the semidefinite programming method in the literature Yanshen Du, Ping Wei, and Huaguo Zhang. Semidefinite programming approaches for source localization problems. In 2014 IEEE International Conference on Communiction Problem-solving, pages 339-342, 2014. to solve the virtual long baseline positioning problem (denoted as R-SDR1), and method 3 is based on the semidefinite programming method in the literature KW Cheung, WK Ma, and HC So. Accurate approximational algorithm for to a-based maximum like|ihood mobile location using semidefinite programming. In 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing, volume 2, pages ii-145, 2004. to solve the virtual long baseline positioning problem (denoted as R-SDR2). The method of the present invention directly uses the underwater acoustic propagation time as the observed quantity and is based on a two-step weighted least squares solution, which is abbreviated as T-TSWLS.

[0267] The simulation parameters are set as follows: AUV dead reckoning interval is 0.1 seconds, acoustic signal transmission interval is 15 seconds, and acoustic beacon is fixed at [0 0 100] f m, and the total simulation time is 500 seconds. The AUV dynamics model is used to generate the spiral diving motion trajectory of the AUV. The control input of the AUV is horizontal rudder 8°, vertical rudder -8°, and propeller speed 1000 rpm. The initial position of the AUV is [100100 10] T m, the forward initial velocity is 1.2 m / s, and the initial velocity in other directions is 0. The AUV motion trajectory obtained by simulation is as follows Figure 3 shown.

[0268] 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 angle and pitch angle observation 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 100us. The simulated linear sound velocity profile function is c = -0.22z + 1542m / s, and its profile shape is as follows Figure 4 shown.

[0269] The Bellhop hydroacoustic simulation toolbox is used to generate the hydroacoustic sound lines and the real hydroacoustic signal propagation time during the AUV movement. The parameters of the Bellhop model used are shown in Table 2.

[0270] Table 2 Bellhop environmental parameters

[0271] Signal transmission frequency 10KHz depth 200m Seafloor modeling Acoustic elastic half space Minimum and maximum sound angle -90°，90° Maximum sound line distance 1.6 km Maximum sound depth 200 meters Number of beams 9001

[0272] For all methods, the width of the sliding window is set to 15, that is, the current moment and the 15 hydroacoustic 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 are solved by using the CVX toolbox of Matlab software, using the sedumi solver, and the solution accuracy is set to the highest, see the reference Michael Grant and Stephen Boyd. CVX: Matlab software for disciplined convex programming, version 2.0beta. https: / / cvxr.com / cvx, September 2013. and the reference 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 positioning error and average positioning error of the four methods are used as performance evaluation criteria, and the calculation formulas of positioning error and average positioning error are:

[0273]

[0274] Among them, K represents the number of single beacon positioning settlements. The positioning errors of the four methods are as follows: Figure 5 The average positioning error is shown in Table 3.

[0275] according to Figure 5 As shown in Table 3, the method proposed in the present invention can obtain better positioning accuracy than the traditional single beacon positioning method that does not consider the refraction of sound propagation, and its positioning error is lower than that of other comparison methods at most times. This shows that considering the refraction of the sound propagation channel has a certain degree of influence on the performance of single beacon positioning, and the method proposed in the present invention can eliminate this influence.

[0276] Table 3 Comparison of average positioning errors of different methods

[0277] Positioning method Average error (meters) T-TSWLS 0.724656 R-WLS 2.379559 R-SDR1 1.676759 R-SDR2 2.349435

[0278] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. An underwater single beacon virtual long baseline positioning method considering sound propagation refraction, characterized in that: This method is aimed at the linear sound velocity profile. Under the framework of virtual long baseline, a single beacon positioning position solution method based on two-step weighted least squares is designed to obtain the final single beacon positioning position of the AUV, which specifically includes: The hydroacoustic beacon periodically emits hydroacoustic signals, and the hydrophone carried by the AUV measures the propagation time of the hydroacoustic signals. The sound velocity profile is modeled as a linear sound profile. Combining the known hydroacoustic profile parameter information with the hydroacoustic beacon position coordinates, a hydroacoustic observation model under the linear sound profile condition is constructed to obtain the relationship between the signal propagation time and the AUV position. The AUV dead reckoning information is integrated and all the acoustic signal propagation time observations within the time window width N are used to construct a virtual long baseline positioning model under the condition of linear acoustic profile. Auxiliary variables are introduced for algebraic transformation to obtain the pseudo-linear equation solution of virtual long baseline positioning, and the positioning problem is preliminarily solved based on weighted least squares; Combining the relationship between the auxiliary variables and the unknown variables, taking the square of the AUV position coordinates as the unknown variable, a new linear estimation equation is constructed based on the results of the preliminary solution, and an accurate estimation solution is obtained through the weighted least squares method; The obtained preliminary solution to the positioning problem is combined with the weighted least squares method to obtain an accurate estimation solution, and the final single beacon positioning position estimate of the AUV is calculated.

2. The underwater single beacon virtual long baseline positioning method considering sound propagation and refraction according to claim 1 is characterized in that: The hydroacoustic beacon periodically emits hydroacoustic signals. Before the hydrophone carried by the AUV measures the propagation time of the hydroacoustic signal, the following operations must be performed: Take any point in the positioning area as the origin, set the east, north and sky directions as X, Y and Z axes respectively, and establish the underwater single beacon positioning geodetic coordinate system; take the AUV centroid as the origin, and set the front, right and bottom directions as x, y and z axes respectively, and establish the AUV body coordinate system; The dead reckoning model is constructed based on the speed of the AUV in the body coordinate system detected by the DVL and the attitude of the AUV detected by the attitude sensor.

3. The underwater single beacon virtual long baseline positioning method considering sound propagation and refraction according to claim 2 is characterized in that: Constructing a dead reckoning model includes: obtaining the relationship between the AUV position variables at time k and time ki, where i ≥ 1; specifically: In the formula, 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 the AUV at time kt.

4. The underwater single beacon virtual long baseline positioning method considering sound propagation and refraction according to claim 3 is characterized in that: Construct a hydroacoustic observation model under linear acoustic profile conditions, including: The coordinates of the hydroacoustic beacon are fixed and known, recorded as: Where P b is the coordinate vector of the hydroacoustic beacon position, x b is the east coordinate of the hydroacoustic beacon, y b is the north coordinate of the hydroacoustic beacon, z b The celestial coordinates of the hydroacoustic beacon; The sound velocity profile is modeled as linear, that is, the sound velocity value is a linear function of the depth, which can be specifically expressed as: c=az+b Where z is the depth, a is the sound velocity gradient, b is the sound velocity at sea level, and c is the sound velocity at depth z; When the sound velocity profile is known, the sound velocity at the beacon is also known and is denoted as c b , the speed of sound at the AUV position at time k is recorded as c k , the propagation time of the underwater acoustic signal at time k is recorded as t k , then the relationship between horizontal distance and signal propagation time is: In the formula, e is a natural constant, r k is the horizontal distance between the AUV and the beacon, and its geometric calculation formula is: Squaring both sides of the above equation yields: Simplifying, we get: Substituting the sound velocity profile parameters into the equation: definition: is a virtual observation, all parameters are known, m k The value depends on the signal propagation time observation value and the acoustic profile parameters at the current moment, so the relationship between the AUV position and the underwater acoustic signal propagation time is: 0=(x k -x b ) 2 +(y k -y b ) 2 +(z k -z b ) 2 -m k (a) k +b)。 5. The underwater single beacon virtual long baseline positioning method considering sound propagation and refraction according to claim 4 is characterized in that: Construct a virtual long baseline positioning model under linear acoustic profile conditions, including: Define the time window width as N, and use the propagation time of the underwater acoustic signal received from kN to k to solve the position coordinates of the AUV at time k. For time ki, the observation equation established by applying the relationship between the AUV position and the propagation time of the underwater acoustic signal is: 0=(x k-i -x b ) 2 +(y k-i -y b ) 2 +(z k-i -z b ) 2 -m k-i (az k-i +b),for i=1,2…N Substitute the AUV’s dead reckoning model, that is, the position relationship between time k and time ki, and we get: 0=(x k -x b，i ) 2 +(y k -y b，i ) 2 +(z k -z b,i ) 2 -m k-i (az k +b i ),for i=1,2…N in, In the formula, x b,i ,y b，i , z b,i , b i Respectively represent the x, y, z axis position coordinates of the ith virtual beacon and the virtual surface sound speed corresponding to the ith beacon, record: x b,0 =x b and b,0 =and b With b,0 =from b b0=b Combining the observation equation at time k, we get all N+1 observation equations, which can be expressed as follows: 0=(x k -x b，i ) 2 +(y k -y b，i ) 2 +(z k -z b，i ) 2 -m k-i (az k +b i ),for i=0,1,2…N In real applications, the propagation time of the underwater acoustic signal contains observation noise, and the observed value of the propagation time of the underwater acoustic signal is recorded as for: Where, t k is the actual underwater acoustic signal propagation time, v k is the observation noise of the underwater acoustic signal propagation time, which is modeled as having a mean of 0 and a variance of A Gaussian random variable; Performing Taylor expansion and ignoring higher-order terms, we obtain: Then we have: Substituting the above equation into the virtual observation quantity, we get: For the ki-th observation, we have: The virtual observation containing noise is defined as: Then we have: Substituting the above formula into the observation equation, we get: Moving the noise term to the left side of the equal sign gives: in, Where η i is the noise coefficient of the virtual long baseline positioning equation.

6. The underwater single beacon virtual long baseline positioning method considering sound propagation and refraction according to claim 5 is characterized in that: The positioning problem is initially solved based on weighted least squares, including: Expand the right side of the virtual long baseline positioning equation to obtain: definition: Then we have: All N+1 equations are integrated into a vector matrix form: In the formula, 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 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(·) represents 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 observed 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.

7. The underwater single beacon virtual long baseline positioning method considering sound propagation and refraction according to claim 6 is characterized in that: Noise coefficient matrix B k The calculation of 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 8. The underwater single beacon virtual long baseline positioning method considering sound propagation and refraction according to claim 1 is 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: Combining the above two equations, we get: in, χ k The weighted least squares estimate solution of is: Weight matrix W 2，k Set to:

9. The underwater single beacon virtual long baseline positioning method considering sound propagation and refraction according to claim 1 is characterized in that: The final single beacon positioning position estimate of the AUV is calculated, including: The estimated value obtained Take the square root and combine the estimated values The sign 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 10. An underwater single beacon virtual long baseline positioning system considering sound propagation and refraction, characterized in that: The system implements the underwater single beacon virtual long baseline positioning method considering sound propagation and refraction as described in any one of claims 1 to 9, and the system is provided with an AUV; the AUV is equipped with a hydrophone, a DVL, a posture sensor and a CTD; the AUV detects the sound velocity profile parameters of the experimental area through the CTD; the hydroacoustic beacon periodically broadcasts a hydroacoustic signal, and the AUV periodically observes its velocity in the body coordinate system through the carried DVL, calculates the velocity of the AUV in the geodetic coordinate system in combination with the AUV attitude angle observed by the posture sensor, performs dead reckoning, and records and stores the dead reckoning data; After receiving the acoustic signal emitted by the acoustic beacon, the AUV obtains the acoustic signal propagation time based on the known acoustic signal emission time; When the AUV receives a certain number of hydroacoustic signals, it constructs a virtual long baseline array in combination with the stored dead reckoning data; Combining the relationship between the acoustic propagation time and the AUV position under the linear acoustic profile, a virtual long baseline positioning problem is constructed; auxiliary variables are introduced, and the pseudo-linear positioning equation is obtained based on algebraic transformation, and the preliminary solution of 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, 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 estimation solution.

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