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

Abstract

The application provides a water three-dimensional target fusion positioning method using only linear array AOA measurement, only needs to obtain the pitching angle information of the target relative to the array to realize positioning, and greatly reduces the positioning cost in the three-dimensional scene. Compared with the existing estimation method, the SDR estimation avoids the increase of unknown items and constraints caused by regarding the item containing the distance between the target and the array as an unknown quantity in the existing algorithm, and further reduces the calculation amount. Through some 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 the robust target positioning is realized.

Description

Technical Field

[0001] This invention relates to the field of underwater target localization, and in particular to a target localization method in a three-dimensional scene, especially a sensor network convex optimization localization method that uses only linear array measurement information in a three-dimensional scene. Background Technology

[0002] Since the beginning of the 21st century, countries have intensified their research and development in marine science and technology, primarily to enhance their competitiveness and influence in global maritime affairs. The ocean is not only a vital source of resources, such as oil, natural gas, and minerals, but also plays a crucial role in global climate regulation, ecological balance, and international security. Therefore, countries are actively investing resources to promote marine science and technology advancements to safeguard their maritime rights and strategic interests. This trend has made marine science and technology research increasingly important, particularly with the growing demand for applications in deep-sea exploration, marine environmental monitoring, and resource development.

[0003] Multi-sensor information fusion target localization technology plays a crucial role in marine science and technology research and development. In underwater target localization, we typically aim to obtain the target's three-dimensional position information. Most existing research focuses on obtaining both pitch and azimuth angles simultaneously. However, obtaining both pitch and azimuth angles in underwater scenarios requires planar arrays, which are far more expensive than linear arrays. Theoretical analysis shows that three-dimensional target localization can be achieved using only pitch angle information relative to a linear array; generally, four or more linear arrays are sufficient. Some papers have also proposed AOA (Angle-of-Arrival) three-dimensional localization methods using only linear arrays, but the convex optimization methods employed are not optimal and do not reach the theoretical performance limits.

[0004] In summary, AOA-based target localization methods have better performance than other localization methods. However, existing AOA-based target localization methods still have many imperfections, so it is necessary to conduct in-depth research on AOA-based target localization methods. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a method for fusion localization of three-dimensional targets in water using only linear array AOA measurements. It employs a more rigorous convex optimization method than existing schemes and considers the impact of node position errors on localization. Simulation results show a significant improvement in localization performance compared to existing schemes.

[0006] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0007] Step 1: Establish a Cartesian coordinate system as the reference coordinate system in the wireless sensor network. There are N sensor nodes with position drift and one target with an unknown position. The position coordinates of the i-th sensor node at the time of deployment are v. i =(x i ,y i ,z i ) T i = 1, ..., N, sensor orientation 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 passively acquires the AOA measurement between itself and the target. The node position error term follows a zero-mean Gaussian distribution, and the position drift of the i-th sensor is modeled as follows: in For the unknown but real sensor node location after drift, s i =(sx i ,sy i ,sz i ) is the covariance Φ i =δ i 2 I3 is zero-mean Gaussian white noise, where I3 represents a 3×3 unit diagonal matrix;

[0008] Step 2: After the target node transmits the signal, the sensor nodes acquire the measurements. The AOA measurement acquired by the i-th sensor is... Modeling (the angular information of the target relative to the array) yields the sensor measurement equations.

[0009] Step 3: Transform the acquired sensor measurement equations;

[0010] Step 4: Separate the noise-related quantities from 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, use maximum likelihood estimation to locate the target;

[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 specific value of the vector g obtained by solving is: the first part is the x-coordinate of the target position, the second part is the y-coordinate of the target position, and the third part is the vertical coordinate of the target position.

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

[0015]

[0016] θ represents the AOA measurement value acquired by the sensor node. i Represents the true value of AOA, ε i ε represents the AOA measurement error. i Model as a function with a mean of zero and a variance of . Gaussian white noise, n i Let ε be the error caused by node position drift. i and s i They are independent of each other.

[0017] In step three, the obtained sensor measurement equations are transformed:

[0018]

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

[0020]

[0021] Squaring both sides of the equation:

[0022]

[0023] Modeling node position errors The equation obtained by substituting and squaring

[0024]

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

[0026]

[0027] in

[0028] In step four, the noise-related and noise-independent quantities in the omitted polynomial obtained in step three are separated:

[0029]

[0030] make According to the properties of the normal distribution, η follows a distribution with a mean of zero and a variance of β.i 2 The normal distribution, where

[0031]

[0032] After sorting, we can obtain:

[0033]

[0034] in:

[0035]

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

[0037]

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

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

[0040]

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

[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 the non-convex constraint G = gg still exists. T Therefore, by using semidefinite relaxation, G = gg T Transformed into the following convex constraint conditions

[0051] By definition of 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 vector g is not a convex constraint, but through the relationship between g and G, G = gg T Transform 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 obtained as follows:

[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 includes: 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 perform the methods described above.

[0083] A computer-readable storage medium storing program code that can be invoked by a processor to perform the method described above.

[0084] The beneficial effect of this invention is that it only requires obtaining the target's elevation angle information relative to the array to achieve localization, greatly reducing the cost of localization in 3D scenes. Compared with existing estimation methods, the proposed SDR estimation avoids the increase in unknowns and constraints caused by treating this term as an unknown quantity in existing algorithms by moving the term containing the target-array distance to the same side and then squaring it, thereby reducing the computational load. By performing some mathematical equivalent transformations on the node position error, the impact of node position error on localization performance is minimized, achieving robust target localization. Attached Figure Description

[0085] Figure 1 This is a general implementation block diagram of the present invention.

[0086] Figure 2 This diagram illustrates the changes in the root mean square error of the method of this invention, the existing AOA convex optimization target localization method, and the Cramer-Rao lower bound corresponding to the method of this invention as the standard deviation of the azimuth measurement noise increases, assuming no node position errors.

[0087] Figure 3 This diagram illustrates the changes in the root mean square error of the method of this invention, the existing AOA convex optimization target localization method, and the Cramer-Rao lower bound corresponding to the method of this invention as the standard deviation of the node position error increases, under the condition of no azimuth measurement noise. Detailed Implementation

[0088] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0089] The present invention proposes a target localization method for wireless sensor networks based on AoA measurement, the overall implementation block diagram of which is shown below. Figure 1 As shown, it includes the following steps:

[0090] Step 1: Establish a Cartesian coordinate system as the reference coordinate system in the wireless sensor network. There are N sensor nodes with position drift and one target with an unknown position. The position coordinates of the i-th sensor node at the time of deployment are v. i =(x i ,y i ,z i ) T i = 1, ..., N, sensor orientation 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 passively acquires the AOA measurement between itself and the target. The node position error term follows a zero-mean Gaussian distribution, and the position drift of the i-th sensor is modeled as follows: in For the unknown but real sensor node location after drift, s i =(sx i ,sy i ,sz i ) is the covariance Φ i =δ i 2 I3 is zero-mean Gaussian white noise, where I3 represents a 3×3 unit diagonal matrix;

[0091] Step 2: After the target node transmits the signal, the sensor nodes acquire the measurements. The AOA measurement acquired by the i-th sensor is... (The angular information of the target relative to the array) is modeled as follows:

[0092]

[0093] θ represents the AOA measurement value acquired by the sensor node. i Represents the true value of AOA, ε i ε represents the AOA measurement error. i Model as a function with a mean of zero and a variance of . Gaussian white noise, n i Let ε be the error caused by node position drift. i and s i They are independent of each other;

[0094] Step 3: Transform the acquired sensor measurement equations:

[0095]

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

[0097]

[0098] Squaring both sides of the equation:

[0099]

[0100] Modeling node position errors The equation obtained by substituting and squaring

[0101]

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

[0103]

[0104] in

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

[0106]

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

[0108]

[0109] After sorting, we can obtain:

[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 sum matrix

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

[0117]

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

[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 the non-convex constraint G = gg still exists. T Therefore, by using semidefinite relaxation, G = gg T Transformed into the following convex constraint conditions

[0128] By definition of 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 vector g are not convex constraints, but through the relationship between g and G, G = gg T This can be transformed into the following equation 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] Thus, we obtain the final convex optimization expression as follows:

[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 specific value of the vector g obtained by solving is: the first part is the x-coordinate of the target position, the second part is the y-coordinate of the target position, and the third part is the vertical coordinate of the target position.

[0160] The following simulation experiments are used to verify the feasibility, effectiveness, and positioning performance of the method of the present invention.

[0161] Assume there are N=8 sensor nodes and one target in the wireless sensor network. 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 The diagram illustrates the changes in the root mean square error (RMSE) of the proposed method, existing AOA convex optimization target localization methods, and the corresponding Cramer-Rao lower bound of the proposed method as the standard deviation of the azimuth measurement noise increases, under the condition of no node position errors. Figure 2 As can be seen, the RMSE of both methods increases with the increase of the standard deviation of pitch angle measurement noise. However, the method of this 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 to see how it changes as the standard deviation of the node position error increases.

[0165] Figure 3 A schematic diagram is provided illustrating the changes in the root mean square error of the proposed method and existing AOA convex optimization target localization methods, along with the corresponding Cramer-Rao lower bound, as the standard deviation of the node position error increases, under the condition of no pitch angle measurement noise. From Figure 3 As can be seen, as the node position error increases, the method of this invention is always better than the existing methods. Moreover, the existing algorithms are not ideal in terms of accuracy because they are overly relaxed and do not take into account the influence of node position error when the noise is small.

[0166] In summary, the algorithm proposed in this invention outperforms existing methods in all situations and exhibits good stability. Furthermore, compared to existing algorithms, the computational complexity of this invention is significantly reduced.

[0167] From the above Figure 2 and Figure 3The simulation results show that the method of the present invention has good performance and can well meet the requirements of high positioning accuracy.

Claims

1. A method for underwater three-dimensional target fusion localization using only linear array AOA measurements, characterized in that... Includes the following steps: Step 1: Establish a Cartesian coordinate system as the reference coordinate system in the wireless sensor network. There are N sensor nodes with position drift and one target with an unknown position. The position coordinates of the i-th sensor node at the time of deployment are... Sensor orientation vector The location coordinates of the target to be located are Each sensor passively acquires the AOA measurement between itself and the target; the node position error term follows a Gaussian distribution with zero mean, and the position drift of the i-th sensor is modeled as... ,in This represents the unknown but actual location of the sensor node after drift. The covariance is Zero-mean Gaussian white noise, where Represents a 3×3 unit diagonal matrix; Step 2: After the target node transmits the signal, the sensor node acquires the measurement. AOA measurements acquired by each sensor Modeling is performed to obtain the sensor measurement equations; Step 3: Transform the acquired sensor measurement equations; In step three, the obtained sensor measurement equations are transformed: ， Taking a first-order Taylor expansion of the above equation, we get: ， Squaring both sides of the equation: ， Modeling node position errors The equation obtained by substituting and squaring ； After simplification and ignoring second-order terms, we obtain the omitted polynomial: ； in ; Step 4: Separate the noise-related quantities from the noise-independent quantities in the omitted polynomial obtained in Step 3; Step 5: Based on the AOA measurement model obtained in Step 4, use maximum likelihood estimation to locate the target; 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. The specific value, the vector obtained by solving The first digit is the x-coordinate of the target position, the second digit is the y-coordinate of the target position, and the third digit is the vertical coordinate of the target position.

2. The underwater three-dimensional target fusion localization method using only linear array AOA measurement as described in claim 1, characterized in that: In step two, the sensor measurement equation is obtained as follows: ， This represents the AOA measurement value acquired by the sensor node. This represents the actual value of AOA. For AOA measurement error, Model as a function with a mean of zero and a variance of . Gaussian white noise, Assuming the error caused by node position drift, and They are independent of each other.

3. The underwater three-dimensional target fusion localization method using only linear array AOA measurement as described in claim 1, characterized in that: In step four, the noise-related and noise-independent quantities in the omitted polynomial obtained in step three are separated: ； make From the properties of the normal distribution, we know It follows a pattern with a mean of zero and a variance of . The normal distribution, where After sorting, we can obtain: ； in: ； ； ； ； ， ； ， ； ， 。 4. The underwater three-dimensional target fusion localization method using only linear array AOA measurement as described in claim 1, characterized in that: In step five, the formula for maximum likelihood estimation of the target location is: 。 5. The underwater three-dimensional target fusion localization method using only linear array AOA measurement as described in claim 4, characterized in that: In step six, a new vector is defined. sum matrix ,in: ； ； ； ； ； ； ； ； ； The formula for locating the target using maximum likelihood estimation in step five can be rewritten as follows: ； in: ； The objective function is further transformed into: ； Where: C=C i C i T , ; At this point, the objective function has been transformed into a convex function, but non-convex constraints still exist. Therefore, semidefinite relaxation is used to... This is transformed into the following convex constraint conditions. ; From vector By definition, the following equality constraint holds: ； The constraint on vector g is not a convex constraint, but the relationship between g and G is used to determine its convexity. Transform into the following equality constraint: ； The final convex optimization expression is obtained as follows: ； ； ， C=C i C i T 。 6. 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, the one or more programs being configured to perform the method as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program code that can be invoked by a processor to execute the method as described in any one of claims 1-5.

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