Underwater three-dimensional target fusion positioning method only using linear array AOA measurement

Abstract

According to the underwater three-dimensional target fusion positioning method provided by the invention, only the linear array AOA measurement is used, the positioning can be realized only by obtaining the pitch angle information of the target relative to the array, and the positioning cost in a three-dimensional scene is greatly reduced. Compared with the existing estimation method, the provided SDR estimation has the advantages that the item containing the distance between the target and the array is moved to the same side and then squared, the increase of unknown items and constraints caused by the fact that the item is used as unknown quantity estimation in the existing algorithm is avoided, and the calculation amount is further reduced. Through carrying out mathematical equivalent transformation on the node position error, the influence of the node position error on the positioning performance is reduced as much as possible, and stable target positioning is realized.

Description

Technical Field

[0001] The present invention relates to the field of underwater target positioning, in particular to a target positioning method in a three-dimensional scene, and in particular to a sensor network convex optimization positioning method using only linear array measurement information in a three-dimensional scene. Background Art

[0002] Since the 21st century, countries have stepped up their research and development of marine science and technology, mainly to enhance their competitiveness and influence in global marine affairs. The ocean is not only an important source of resources, such as oil, natural gas and minerals, but also plays a vital role in global climate regulation, ecological balance and international security. Therefore, countries are actively investing resources to promote the advancement of marine science and technology in order to safeguard their marine rights and strategic interests. This trend makes the research of marine science and technology increasingly important, especially in the fields of deep-sea exploration, marine environmental monitoring and resource development, where the demand for applications is increasing.

[0003] Multi-sensor information fusion target positioning technology plays an important role in the research and development of marine science and technology. In underwater target positioning, we usually hope to obtain the three-dimensional position information of the target. Most of the existing research is aimed at the case where the pitch angle and azimuth angle can be obtained at the same time. However, in underwater scenes, obtaining the pitch angle and azimuth angle at the same time requires a planar array to obtain, and its cost is much higher than that of a linear array. Theoretical analysis shows that only using the pitch angle information relative to the linear array can also achieve three-dimensional target positioning. Generally speaking, more than four linear arrays can be used to complete the positioning of the target. At present, there are also papers that give the AOA (Angle-of-Arrival) three-dimensional positioning method using only linear arrays, but the convex optimization method used is not good enough and cannot reach the theoretical performance limit.

[0004] In summary, the target positioning method based on AOA has better performance than other positioning methods, but the existing target positioning method based on AOA still has many imperfections, so it is necessary to conduct in-depth research on the target positioning method based on AOA. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a method for fusion positioning of underwater three-dimensional targets using only linear array AOA measurement. A more rigorous convex optimization method than the existing scheme is adopted, and the influence of node position error on positioning is considered at the same time. Simulation shows that the positioning performance is significantly improved compared with the existing scheme.

[0006] The technical solution adopted by the present invention to solve the technical problem comprises the following steps:

[0007] Step 1: Establish a rectangular coordinate system as a reference coordinate system in the wireless sensor network. There are N sensor nodes with position drift and a target with unknown position. The position coordinate of the i-th sensor node is v i =(x i ,y i ,z i ) T ,i=1,…,N, sensor direction vector dv i =(dx i ,dy i ,dz i ) T , the position coordinates of the target to be located are u 0 =(x 0 ,y 0 ,z 0 ) T , each sensor acquires the AOA measurement between it and the target in a passive way. The node position error term follows a zero-mean Gaussian distribution, and the position drift of the i-th sensor is modeled as in is the unknown but true sensor node position after drift, s i =(sx i ,sy i ,sz i ) is the covariance Φ i =δ i 2 Zero-mean Gaussian white noise of I3, where I3 represents a 3×3 unit diagonal matrix;

[0008] Step 2: After the target node transmits a signal, the sensor node obtains the measurement. The AOA measurement obtained by the i-th sensor (angle information of the target relative to the array) model and obtain the sensor measurement equation

[0009] Step 3: Transform the obtained sensor measurement equation;

[0010] Step 4: Separate the noise-related quantities and the noise-independent quantities in the omitted polynomial obtained in step 3;

[0011] Step 5: Based on the AOA measurement model obtained in step 4, the target is located using maximum likelihood estimation;

[0012] Step 6: Obtain the convex optimization expression through calculation;

[0013] Step 7: Use the CVX solver (interior point method) to solve the final convex optimization expression obtained in step 6 to obtain the vector g = [x, y, x 2 ,y2 ,xy] T The first digit of the vector g obtained is the horizontal coordinate of the target position, the second digit is the vertical coordinate of the target position, and the third digit is the vertical coordinate of the target position.

[0014] In step 2, the sensor measurement equation is obtained as follows:

[0015]

[0016] represents the AOA measurement value obtained by the sensor node, θ i represents the true value of AOA, ε i is the AOA measurement error, ε i Modeled as a function with mean zero and variance Gaussian white noise, n i is the error caused by node position drift, assuming ε i and i Are independent of each other.

[0017] In step three, the obtained sensor measurement equation is transformed:

[0018]

[0019] Taking the first-order Taylor expansion of the above formula, we get:

[0020]

[0021] Square both sides of the equation:

[0022]

[0023] Modeling the node position error Substitute the squared equation into

[0024]

[0025] After rearranging and ignoring the second-order terms, we get the omitted polynomial:

[0026]

[0027] in

[0028] In the step 4, the noise-related quantity and the noise-independent quantity in the omitted polynomial obtained in the step 3 are separated:

[0029]

[0030] make According to the properties of normal distribution, η has a mean of zero and a variance of βi 2 The normal distribution of

[0031]

[0032] After finishing, we can get:

[0033]

[0034] in:

[0035]

[0036] In step 5, the formula for maximum likelihood estimation of the target location is:

[0037]

[0038] In step 6, define a new vector g = [x, y, z, x 2 ,y 2 ,z 2 ,xy,xz,yz] T and matrix

[0039] B=[L1,L2,L3,L4,L5,L6,L7,L8,L9], where:

[0040]

[0041] The objective function in step 5 is rewritten as:

[0042] (c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz) T

[0043] W(c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz)

[0044] =Trace{W(c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz)}

[0045] (c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2+L6×z 2 +L7×xy+L8×xz+L9×yz) T

[0046] in:

[0047] The objective function is further transformed into:

[0048] Trace{W(c+Bg)(c+Bg) T}=Trace{W(C+BGB T +2Bgc T )}

[0049] Where: θ = θθ T ,C=cc T ,G=gg T .

[0050] At this point, the objective function has been transformed into a convex function, but there is still a non-convex constraint G = gg T , so using semi-positive definite relaxation G = gg T Transformed into the following convex constraint

[0051] Defined by the vector g, the following equality constraints hold:

[0052] g(1)g(1)=g(4),

[0053] g(2)g(2)=g(5),

[0054] g(3)g(3)=g(6),

[0055] g(1)g(2)=g(7),

[0056] g(1)g(3)=g(8),

[0057] g(2)g(3)=g(9)

[0058] The constraint on the vector g is not a convex constraint, but through the relationship between g and G G = gg T Transformed into the following equality constraint:

[0059] G(1,1)=g(4),

[0060] G(2,2)=g(5),

[0061] G(3,3)=g(6),

[0062] G(1,2)=g(7),

[0063] G(1,3)=g(8),

[0064] G(2,3)=g(9),

[0065] G(2,1)=g(7),

[0066] G(3,1)=g(8),

[0067] G(3,2)=g(9)

[0068] The final convex optimization expression is:

[0069]

[0070] st

[0071] G(1,1)=g(4),

[0072] G(2,2)=g(5),

[0073] G(3,3)=g(6),

[0074] G(1,2)=g(7),

[0075] G(1,3)=g(8),

[0076] G(2,3)=g(9),

[0077] G(2,1)=g(7),

[0078] G(3,1)=g(8),

[0079] G(3,2)=g(9)

[0080]

[0081] θ=θθ T ,C=cc T .

[0082] An electronic device comprises: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to execute the method as described above.

[0083] A computer-readable storage medium stores program codes, and the program codes can be called by a processor to execute the method as described above.

[0084] The beneficial effect of the present invention is that the present invention can achieve positioning only by obtaining the pitch angle information of the target relative to the array, which greatly reduces the cost of positioning in three-dimensional scenes. Compared with the existing estimation method, the proposed SDR estimation avoids the increase of unknown terms and constraints caused by treating this term as an unknown quantity in the existing algorithm by moving the term containing the distance between the target and the array to the same side and then squaring it, thereby reducing the amount of calculation. By performing some mathematical equivalent transformations on the node position error, the impact of the node position error on the positioning performance is minimized, and robust target positioning is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is an overall implementation block diagram of the present invention.

[0086] Figure 2 It is a schematic diagram of the change of the root mean square error of the method of the present invention, the existing AOA convex optimization target positioning method and the Cramer-Rao lower bound corresponding to the method of the present invention as the standard deviation of the azimuth measurement noise increases under the condition that there is no node position error.

[0087] Figure 3 It is a schematic diagram of the change of the root mean square error of the method of the present invention, the existing AOA convex optimization target positioning method and the Cramer-Rao lower bound corresponding to the method of the present invention as the standard deviation of the node position error increases under the condition that there is no azimuth measurement noise. DETAILED DESCRIPTION

[0088] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0089] The present invention proposes a wireless sensor network target positioning method based on AoA measurement, and its overall implementation block diagram is as follows: Figure 1 As shown, it includes the following steps:

[0090] Step 1: Establish a rectangular coordinate system as a reference coordinate system in the wireless sensor network. There are N sensor nodes with position drift and a target with unknown position. The position coordinate of the i-th sensor node is v i =(x i ,y i ,z i ) T ,i=1,…,N, sensor direction vector dv i =(dx i ,dy i ,dz i ) T , the position coordinates of the target to be located are u 0 =(x 0 ,y 0 ,z 0 )T , each sensor acquires the AOA measurement between it and the target in a passive way. The node position error term follows a zero-mean Gaussian distribution, and the position drift of the i-th sensor is modeled as in is the unknown but true sensor node position after drift, s i =(sx i ,sy i ,sz i ) is the covariance Φ i =δ i 2 Zero-mean Gaussian white noise of I3, where I3 represents a 3×3 unit diagonal matrix;

[0091] Step 2: After the target node transmits a signal, the sensor node obtains the measurement. The AOA measurement obtained by the i-th sensor (The angle information of the target relative to the array) is modeled as:

[0092]

[0093] represents the AOA measurement value obtained by the sensor node, θ i represents the true value of AOA, ε i is the AOA measurement error, ε i Modeled as a function with mean zero and variance Gaussian white noise, n i is the error caused by node position drift, assuming ε i and i are independent of each other;

[0094] Step 3: Transform the obtained sensor measurement equation:

[0095]

[0096] Taking the first-order Taylor expansion of the above formula, we get:

[0097]

[0098] Square both sides of the equation:

[0099]

[0100] Modeling the node position error Substitute the squared equation into

[0101]

[0102] After rearranging and neglecting the second-order terms we get:

[0103]

[0104] in

[0105] Step 4: Separate the noise-related quantities from the noise-independent quantities in the formula obtained in step 3:

[0106]

[0107] make According to the properties of normal distribution, η has a mean of zero and a variance of β i 2 Here

[0108]

[0109] After finishing, we can get:

[0110]

[0111] in:

[0112]

[0113] Step 5: Based on the AoA measurement model obtained in step 4, use maximum likelihood estimation to locate the target:

[0114]

[0115] Step 6: Define a new vector g = [x, y, z, x 2 ,y 2 ,z 2 ,xy,xz,yz] T and matrix

[0116] B=[L1,L2,L3,L4,L5,L6,L7,L8,L9]where:

[0117]

[0118] The objective function in step 5 is rewritten as:

[0119] (c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz) T

[0120] W(c+L1×x+L2×y+L3×z+L4×x 2 +L5×y2 +L6×z 2 +L7×xy+L8×xz+L9×yz)

[0121] =Trace{W(c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz)}

[0122] (c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz) T

[0123] in:

[0124] The objective function is further transformed into:

[0125] Trace{W(c+Bg)(c+Bg) T}=Trace{W(C+BGB T +2Bgc T )}

[0126] Where: θ = θθ T ,C=cc T ,G=gg T .

[0127] At this point, the objective function has been transformed into a convex function, but there is still a non-convex constraint G = gg T , so using semi-positive definite relaxation G = gg T Transformed into the following convex constraint

[0128] Defined by the vector g, the following equality constraints hold:

[0129] g(1)g(1)=g(4),

[0130] g(2)g(2)=g(5),

[0131] g(3)g(3)=g(6),

[0132] g(1)g(2)=g(7),

[0133] g(1)g(3)=g(8),

[0134] g(2)g(3)=g(9)

[0135] These constraints on the vector g are not convex constraints, but through the relationship between g and G G = gg T It can be transformed into the following equality constraint:

[0136] G(1,1)=g(4),

[0137] G(2,2)=g(5),

[0138] G(3,3)=g(6),

[0139] G(1,2)=g(7),

[0140] G(1,3)=g(8),

[0141] G(2,3)=g(9),

[0142] G(2,1)=g(7),

[0143] G(3,1)=g(8),

[0144] G(3,2)=g(9)

[0145] In this way, we get the final convex optimization expression:

[0146]

[0147] st

[0148] G(1,1)=g(4),

[0149] G(2,2)=g(5),

[0150] G(3,3)=g(6),

[0151] G(1,2)=g(7),

[0152] G(1,3)=g(8),

[0153] G(2,3)=g(9),

[0154] G(2,1)=g(7),

[0155] G(3,1)=g(8),

[0156] G(3,2)=g(9)

[0157]

[0158] θ=θθ T ,C=cc T .

[0159] Step 7: Use the CVX solver (interior point method) to solve the final convex optimization expression obtained in step 6 to obtain the vector g = [x, y, x 2 ,y 2 ,xy] T The first digit of the vector g obtained is the horizontal coordinate of the target position, the second digit is the vertical coordinate of the target position, and the third digit is the vertical coordinate of the target position.

[0160] The feasibility, effectiveness and positioning performance of the method of the present invention are verified by simulation experiments as follows.

[0161] Assume that there are N=8 sensor nodes and one target in the wireless sensor network, and all nodes (including anchor nodes and target nodes) are randomly deployed in a three-dimensional space of 40×40×40 square meters.

[0162] The performance of the method of the present invention was tested as the standard deviation of the azimuth measurement noise increased.

[0163] Figure 2 A schematic diagram of the change of the root mean square error of the method of the present invention and the existing AOA convex optimization target positioning method and the Cramer-Rao lower bound corresponding to the method of the present invention as the standard deviation of the azimuth measurement noise increases is given under the condition that there is no node position error; Figure 2 It can be seen that as the standard deviation of the pitch angle measurement noise increases, the RMSE of the two methods both show an upward trend, but the method of the present invention is always better than the existing method. This is because the existing algorithm introduces some errors due to excessive relaxation.

[0164] The performance of the method of the present invention was tested as the standard deviation of the node position error increased.

[0165] Figure 3 A schematic diagram of the change of the root mean square error of the method of the present invention and the existing AOA convex optimization target positioning method and the corresponding Cramer-Rao lower bound as the standard deviation of the node position error increases is given under the condition that there is no pitch angle measurement noise. Figure 3 It can be seen that as the node position error increases, the method of the present invention is always better than the existing method. In addition, the existing algorithm is overly relaxed when the noise is small and does not take into account the influence of the node position error, so the accuracy is not ideal.

[0166] In summary, the algorithm proposed by the present invention is superior to the existing method in any case and has good stability. In addition, compared with the existing algorithm, the computational complexity of the algorithm of the present invention is greatly reduced.

[0167] From the above Figure 2 and Figure 3It can be seen from the simulation results that the method of the present invention has good performance and can well meet the demand for high-precision positioning.

Claims

1. A method for underwater three-dimensional target fusion positioning using only linear array AOA measurement, characterized in that The steps include: Step 1: Establish a rectangular coordinate system as a reference coordinate system in the wireless sensor network. There are N sensor nodes with position drift and a target with unknown position. The position coordinate of the i-th sensor node is v i =(x i ,y i ,z i ) T ,i=1,…,N, sensor direction vector dv i =(dx i ,dy i ,dz i ) T , the position coordinates of the target to be located are u 0 =(x 0 ,y 0 ,z 0 ) T , each sensor acquires the AOA measurement between it and the target in a passive way. The node position error term follows a zero-mean Gaussian distribution, and the position drift of the i-th sensor is modeled as in is the unknown but true sensor node position after drift, s i =(sx i ,sy i ,sz i ) is the covariance Φ i =δ i 2 Zero-mean Gaussian white noise of I3, where I3 represents a 3×3 unit diagonal matrix; Step 2: After the target node transmits a signal, the sensor node obtains the measurement. The AOA measurement obtained by the i-th sensor Modeling and obtaining the sensor measurement equation; Step 3: Transform the obtained sensor measurement equation; Step 4: Separate the noise-related quantities and the noise-independent quantities in the omitted polynomial obtained in step 3; Step 5: Based on the AOA measurement model obtained in step 4, the target is located using maximum likelihood estimation; Step 6: Obtain the convex optimization expression through calculation; Step 7: Use the CVX solver to solve the final convex optimization expression obtained in step 6 to obtain the vector g = [x, y, x 2 ,y 2 ,xy] T The first digit of the vector g obtained is the horizontal coordinate of the target position, the second digit is the vertical coordinate of the target position, and the third digit is the vertical coordinate of the target position.

2. The underwater three-dimensional target fusion positioning method using only linear array AOA measurement according to claim 1, characterized in that: In step 2, the sensor measurement equation is obtained as follows: represents the AOA measurement value obtained by the sensor node, θ i represents the true value of AOA, ε i is the AOA measurement error, ε i Modeled as a function with mean zero and variance Gaussian white noise, n i is the error caused by node position drift, assuming ε i and i Are independent of each other.

3. The underwater three-dimensional target fusion positioning method using only linear array AOA measurement according to claim 2, characterized in that: In step three, the obtained sensor measurement equation is transformed: Taking the first-order Taylor expansion of the above formula, we get: Square both sides of the equation: Modeling the node position error Substitute the squared equation into After rearranging and ignoring the second-order terms, we get the omitted polynomial: in 4. The underwater three-dimensional target fusion positioning method using only linear array AOA measurement according to claim 3, characterized in that: In the step 4, the noise-related quantity and the noise-independent quantity in the omitted polynomial obtained in the step 3 are separated: make According to the properties of normal distribution, η has a mean of zero and a variance of β i 2 The normal distribution of After finishing, we can get: in:

5. The underwater three-dimensional target fusion positioning method using only linear array AOA measurement according to claim 4, characterized in that: In step 5, the formula for maximum likelihood estimation of the target location is:

6. The underwater three-dimensional target fusion positioning method using only linear array AOA measurement according to claim 5, characterized in that: In step 6, define a new vector g = [x, y, z, x 2 ,y 2 ,z 2 ,xy,xz,yz] T And the matrix B = [L1, L2, L3, L4, L5, L6, L7, L8, L9], where: The objective function in step 5 is rewritten as: (c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz) T W(c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz) =Trace{W(c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz)}(c+L1×x+L2×y+L3×z+L4×x 2 +L5×y 2 +L6×z 2 +L7×xy+L8×xz+L9×yz) T in: The objective function is further transformed into: Trace{W(c+Bg)(c+Bg) T }=Trace{W(C+BGB T +2Bgc T )} Where: Θ=θθ T ,C=cc T ,G=gg T 。 At this point, the objective function has been transformed into a convex function, but there is still a non-convex constraint G = gg T , so using semi-positive definite relaxation G = gg T Transformed into the following convex constraint Defined by the vector g, the following equality constraints hold: g(1)g(1)=g(4), g(2)g(2)=g(5), g(3)g(3)=g(6), g(1)g(2)=g(7), g(1)g(3)=g(8), g(2)g(3)=g(9) The constraint on the vector g is not a convex constraint, but through the relationship between g and G G = gg T Transformed into the following equality constraint: G(1,1)=g(4), G(2,2)=g(5), G(3,3)=g(6), G(1,2)=g(7), G(1,3)=g(8), G(2,3)=g(9), G(2,1)=g(7), G(3,1)=g(8), G(3,2)=g(9) The final convex optimization expression is: st G(1,1)=g(4), G(2,2)=g(5), G(3,3)=g(6), G(1,2)=g(7), G(1,3)=g(8), G(2,3)=g(9), G(2,1)=g(7), G(3,1)=g(8), G(3,2)=g(9) Θ=θθ T ,C=cc T 。 7. An electronic device, characterized in that: include: one or more processors; Memory; One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to execute the method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program codes, and the program codes can be called by a processor to execute the method according to any one of claims 1 to 6.

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