A method for target positioning and error analysis based on a three-dimensional space multi-static sonar

Abstract

The present invention discloses a method for target positioning and error analysis based on a three-dimensional space multi-static sonar. Multiple base stations are allocated in different horizontal planes to construct a three-dimensional positioning model of the multi-static sonar system, and the error distribution of the three-dimensional space multi-static sonar under corresponding configuration conditions is given. The planar positioning of the multi-static sonar system is extended to three-dimensional space positioning, and a three-dimensional error distribution diagram is given, providing a novel and effective solution for further research on multi-static sonar positioning methods and error analysis. The present invention can accurately and efficiently describe the positioning accuracy characteristics of the three-dimensional space, effectively solving the problem that the original method and simulation can only display two-dimensional positioning accuracy data.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater target detection, and particularly relates to a method for target positioning and error analysis. Background Technique

[0002] With the development of underwater acoustic stealth technology, the research on multi-static sonar positioning technology has become a hot topic in the field of sonar technology. A multi-static sonar system can use multiple sonars with different functions for array arrangement, detect targets simultaneously from different directions, and utilize the reflected energy in each direction to detect stealth targets, having strong anti-target stealth ability and being an effective means for anti-submarine warfare.

[0003] In recent years, scholars at home and abroad have conducted a large number of studies on the optimal site layout, positioning methods, optimization algorithms of multi-static sonar, and the preprocessing method of measurement results combined with neural networks, and have achieved numerous results. The multi-static sonar system obtains measurement information such as the distance, azimuth angle, and elevation angle of the target, and determines the estimated position of the target by calculating using the positioning algorithm based on the geometric relationship between these measurement quantities and the spatial geometry of each transceiver base station. Patent CN 110837086 A discloses a method and system for underwater target positioning based on side-scan sonar. By obtaining the longitude and latitude information of the side-scan sonar and the height information of the sonar from the seabed plane, the position information of the sonar is obtained, and then the attitude correction matrix is calculated to estimate the target position. It combines the GPS coordinates of the sonar, the water depth information, and the hull attitude parameters to correct the positions of the underwater target and the sonar, so as to obtain the accurate target position coordinates. Patent CN 113406645 A uses the least squares method of average sound speed for target positioning, modifies the average sound speed value and repeats the above process until the best average sound speed makes the result meet the error requirements, and establishes a new average sound speed positioning model based on the incident angle of the sound ray, which solves the problem of low positioning accuracy caused by using a single sound speed. Patent CN 112946574 A controls the data quality by preprocessing multi-source data, takes into account the change of the transducer position during the propagation of the sound signal, corrects the sound ray bending through sound ray tracking, weakens the error influence, and improves the positioning accuracy. The above several sonar positioning methods all involve repeated correction of the measurement data or calculation results to achieve the purpose of reducing error factors and improving positioning accuracy, and belong to the algorithm optimization scheme based on the traditional multi-static positioning model. Patent CN110346802 A is also based on the conventional multi-static sonar positioning algorithm. At the same time, it calculates the parameters of the frequency modulation signal of the underwater acoustic channel and uses the state recognition method to determine the target. If the signal energy weakens or spreads to other channels, there is a target. This target positioning method makes full use of the characteristics of large detection range, good concealment, and strong anti-interference ability of the multi-static sonar. However, the traditional multi-static sonar system generally consists of sonar buoys or airborne dipping sonars, which is reflected in the positioning algorithm model that the transmitting station, receiving station of the sonar system, and the target position are on the same horizontal plane. Therefore, the traditional multi-static sonar positioning algorithm has the drawback of lacking three-dimensional space positioning ability. Patent CN 110907936 A discloses an underwater terrain matching positioning and navigation sonar. According to the calculated horizontal angle of the echo, the elevation angle of the echo, and the distance between the sonar and the target, the distance corresponding to each echo sample of the target can be obtained. For the continuous echo on the seabed, a continuous sequence can be obtained, and thus a continuous three-dimensional underwater terrain can be obtained. The base stations of the multi-static sonar system are distributed on different underwater horizontal planes to achieve the positioning of targets within a certain three-dimensional space underwater, solve the problem of target detection on different horizontal planes, and then construct a three-dimensional space multi-static sonar positioning model, and simulate and give the error distribution in the three-dimensional space. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, the present invention provides a method for target positioning and error analysis based on a three-dimensional space multi-static sonar. Multiple base stations are allocated in different horizontal planes, thereby constructing a three-dimensional multi-static sonar system positioning model, and giving the error distribution of the three-dimensional space multi-static sonar under corresponding configuration conditions. It extends the plane positioning of the multi-static sonar system to three-dimensional space positioning, and gives a three-dimensional error distribution map, providing a novel and effective solution for further research on multi-static sonar positioning methods and error analysis. The present invention can accurately and efficiently describe the positioning accuracy characteristics of the three-dimensional space, and effectively solves the problem that the original method and simulation can only display two-dimensional positioning accuracy data.

[0005] The technical solution adopted by the present invention to solve its technical problems includes the following steps:

[0006] Step 1: According to the co-planar multi-static sonar positioning model, place each base station of the multi-static sonar on different horizontal planes, construct a three-dimensional space multi-static sonar system configuration model, draw a three-dimensional space sonar system topology diagram, and determine the actual physical meaning of each parameter;

[0007] Step 2: Determine the positional relationship of each base station of the three-dimensional multi-static sonar system, utilize its geometric relationship and the distance measurement information of each base station, analyze the target positioning principle of the three-dimensional space multi-static sonar, further give the target positioning equation, and calculate the three-dimensional space target estimated value, specifically as follows;

[0008] Suppose S represents the target position, r T is the distance from the receiving station to the target, r R1 , r R2 , … r RN are the distances from the target to each receiving station of the sonar respectively; the sum of distances r Σi is the product of the time for the sound wave to travel from the transmitting station through the target to the i-th receiving station and the speed of sound in water; write the following target positioning equation for the three-dimensional space multi-static sonar:

[0009]

[0010] In the formula, x T , y T , z T represent the x, y, and z coordinates of the position of the T station respectively, x R1 … x RN represent the x coordinates of the i-th receiving station respectively, y R1 … y RN represent the y coordinates of the i-th receiving station respectively, z R1 … z RNrespectively represent the z coordinate of the i-th receiving station, and x, y, and z respectively represent the x, y, and z coordinates of the target position;

[0011] From the above equations, we can obtain:

[0012]

[0013] Write the above equations in matrix form: AX = f;

[0014] where: X = [x, y, z] T , f = [g1, g2,..., g N T

[0015]

[0016] Then the estimated value of the target can be obtained as:

[0017] Step 3: Considering the time measurement error and the station location measurement error, give the calculation equation for the error distribution of the three-dimensional multi-static sonar system;

[0018] Differentiate both sides of the target positioning equation (1) to obtain the error equation of the three-dimensional multi-static sonar:

[0019]

[0020] In the formula, c 11 ... c N1 respectively represent the ratio of the difference in the x coordinate between the target and the j-th receiving station to the distance, that is c 12 ... c N2 respectively represent the ratio of the difference in the y coordinate between the target and the j-th receiving station to the distance, that is c 13 ... c N3 respectively represent the ratio of the difference in the z coordinate between the target and the j-th receiving station to the distance, that is c T1 、c T2 、c T3 respectively represent k R1 ... k RN is represented as k Ri =-(c j1 dx j +c j2 dy j +c j3 dz j ), k T =-(c T1 dx T +c T2 dyT +c T3 dz T );

[0021] Write Equation (2) in matrix form and use the pseudo-inverse method to solve for the estimated positioning error of the target:

[0022] dV = CdX + dX S

[0023] dX = (C T C) -1 C T [dV - dX S T

[0024] where dV = [dr ∑1 dr ∑2 … dr ∑N dr T T , dX = [dx dy dz] T ,dX S =[k R1 +k T k R2 +k T … k RN +k T k T T ;

[0025] Therefore, the covariance of the positioning error is:

[0026] P dx =E[dXdX T =(C T C) -1 C T {E[dVdV T +E[dX S dX S T}((C T C) -1 C T ) T

[0027] The positioning accuracy is expressed as:

[0028] Step 4: Use MATLAB software to build a three-dimensional multi-static sonar error distribution simulation environment, select the number of base stations, and obtain a three-dimensional space error distribution map.

[0029] The beneficial effects of the present invention are as follows:

[0030] ​​​By adopting the method of distributing the base stations of the multi-static sonar in different underwater horizontal planes, the multi-static sonar positioning method is expanded to realize the target detection and positioning accuracy analysis in the underwater three-dimensional space, and the simulation calculation is completed. This changes the current situation where each transceiver base station in the original positioning model is in the same horizontal plane. Moreover, combined with the simulation software, the simulation of three-dimensional space positioning and error distribution is realized, resulting in a three-dimensional distribution map of the three-dimensional space positioning accuracy data. Using colors to reflect the GDOP size of a certain point in space effectively solves the problem that the original method and simulation can only display two-dimensional positioning accuracy data. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is the topology diagram of the three-dimensional space multi-static sonar system configuration of the present invention.

[0032] Figure 2 This is the topology diagram of the three-dimensional space four-receiver sonar system configuration of the embodiment of the present invention.

[0033] Figure 3 This is the two-dimensional data expansion schematic diagram of the three-dimensional space GDOP of the four-receiver in the embodiment of the present invention at the cross-sections of z = -1, 1, 3 km.

[0034] Figure 4 This is the three-dimensional schematic diagram of the two-dimensional data of the three-dimensional space GDOP of the embodiment of the present invention at the cross-section of z = -1 km on the xy plane.

[0035] Figure 5 This is the three-dimensional schematic diagram of the two-dimensional data of the three-dimensional space GDOP of the embodiment of the present invention at the cross-section of z = 1 km on the xy plane.

[0036] Figure 6 This is the three-dimensional schematic diagram of the two-dimensional data of the three-dimensional space GDOP of the embodiment of the present invention at the cross-section of z = 3 km on the xy plane. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] The present invention will be further described below in conjunction with the drawings and embodiments.

[0038] The object of the present invention is to propose a multi-static sonar positioning and error analysis method based on the three-dimensional space. On the basis of constructing a three-dimensional positioning model, numerical simulation is carried out to obtain the spatial GDOP distribution map around the three-dimensional multi-static sonar, thereby providing a new three-dimensional positioning and error analysis method for the multi-static sonar system.

[0039] Currently, for the underwater target localization method of multi-static sonar, most of them calculate and estimate the target position by using the measurement quantities and geometric position relationships of the transceiver base stations on the same underwater plane. However, the present invention proposes a three-dimensional underwater multi-static sonar localization and error analysis method, which distributes multiple base stations in different horizontal planes, thereby constructing a three-dimensional multi-static sonar system localization model. The advantage of this method is that it can localize targets within a certain space and give the error distribution of the three-dimensional multi-static sonar under corresponding configuration conditions, which can reflect the system localization accuracy in the three-dimensional space of a sea area, extend the planar localization of the multi-static sonar system to three-dimensional space localization, and give a three-dimensional error distribution map, providing a novel and effective solution for further research on the multi-static sonar localization method and error analysis.

[0040] Step 1: Starting from the traditional co-planar multi-static sonar localization model, build a three-dimensional multi-static sonar system configuration model, analyze the geometric relationships between each base station, and determine the actual physical meanings of each parameter.

[0041] Based on the traditional multi-static sonar system localization principle, place each base station of the multi-static sonar on different horizontal planes, construct a three-dimensional multi-static sonar system configuration model, draw a topological diagram of the three-dimensional sonar system, and determine the actual meanings of each parameter to prepare for establishing the three-dimensional multi-static sonar localization principle.

[0042] Step 2: Based on the distance measurement information of the three-dimensional multi-static sonar base stations, use each observation quantity and the geometric relationship of the base stations to give the three-dimensional multi-static sonar localization principle.

[0043] Determine the position relationships of each base station in the three-dimensional multi-static sonar system, use its geometric relationship and the distance measurement information of each base station, analyze the target localization principle of the three-dimensional multi-static sonar, further give the target localization equation, and perform a series of calculations to give the three-dimensional space target estimated value.

[0044] Step 3: Analyze the influence of each measurement error on the localization error, such as: site measurement error, time measurement error, and base station site layout error, and further calculate to give the three-dimensional multi-static sonar error distribution equation.

[0045] Combined with the error analysis of the traditional multi-static sonar system, discuss the factors that cause system localization errors, and further analyze the actual influence of each influencing factor on the localization error. Under the condition of only considering the time measurement error and the site measurement error, we give the three-dimensional multi-static sonar system error distribution calculation equation.

[0046] Step 4: Use MATLAB software to build a simulation environment for the error distribution of a three-dimensional multi-static sonar. Select an appropriate number of base stations. Taking the three-dimensional multi-static sonar system configuration model with a single transmitting station and four receiving stations as an example, present its three-dimensional space error distribution diagram.

[0047] Taking the multi-static system configuration model with a single transmitting station and four receiving stations as an example, select the target sea area range: ±20 km in the x direction, ±20 km in the y direction, and ±20 km in the z direction. Use MATLAB simulation: Assume the coordinates of the transmitting station and receiving stations are T(x T , y T ), R1(x R1 , y R1 ), R2(x R2 , y R2 ), R3(x R3 , y R3 ), and R4(x R4 , y R4 ) respectively, and perform simulation calculations on the error distribution of the three-dimensional multi-static sonar under this configuration condition. Specific embodiments:

[0049] 1. Build a three-dimensional space multi-static sonar configuration model. The topology diagram is as shown in the appendix Figure 1 , analyze the geometric relationship between each base station, and determine the actual physical meaning of each parameter;

[0050] Specifically, use a three-dimensional modeling tool to build the three-dimensional multi-static sonar system configuration. In the figure, T / R is the transceiver station, which emits an active acoustic detection signal to irradiate the target, and R1, R2,...R N are receiving stations that receive the target echo. It can be seen that each transceiver station is not in the same plane at the same time, and this cluster has a wide coverage range in the three-dimensional space of a certain water area.

[0051] 2. Based on the distance measurement information of the multi-static sonar base stations, use each observation quantity and the geometric relationship of the base stations to give the positioning principle of the three-dimensional space multi-static sonar;

[0052] Specifically, assume that S represents the target position, r T is the distance from the receiving station to the target, and r R1 , r R2 , … r RN are the distances from the target to each receiving station of the sonar respectively. The sum of distances r Σi is the product of the time for the sound wave to travel from the transmitting station through the target and be reflected to the i-th receiving station and the sound speed in water. Combining the above coordinate information of the transmitting station and receiving stations, the following target positioning equation for the three-dimensional space multi-static sonar can be written:

[0053]

[0054] It can be obtained from the above equation that:

[0055]

[0056] Write the above equation in matrix form: AX = f

[0057] where: X = [x, y, z] T , f = [g1, g2, …, g N T

[0058]

[0059] The estimated value of the target can be obtained as:

[0060] 3. Analyze the influence of each measurement error on the positioning error, such as: site measurement error, time measurement error, and base station site layout error, and further calculate and give the error distribution equation of the three-dimensional multi-static sonar;

[0061] Specifically, it can be known from reading the literature that there are many factors affecting the system positioning error, such as: the measurement information of each base station, the site layout, the different sound speeds at different sea depths, and the complex ocean environment, etc. In this paper, we focus on studying the influence of the errors of several measured quantities. We can obtain the error equation of the three-dimensional multi-static sonar by differentiating both sides of the target positioning equation:

[0062]

[0063] Write the above equation in matrix form and use the pseudo-inverse method to solve the estimated value of the target positioning error:

[0064] dV = CdX + dX S

[0065] dX = (C T C) -1 C T [dV - dX S T

[0066] Therefore, the covariance of the positioning error is:

[0067] P dx = E[dXdX T = (C T C) -1 C T {E[dVdV T + E[dX S dX S T}((C T C) -1 ​​C T ) T

[0068] For this three-dimensional multi-static sonar system, its positioning accuracy can be expressed as:

[0069] 4. Use MATLAB software to build a simulation environment for the error distribution of the three-dimensional multi-static sonar, select an appropriate number of base stations. Taking the multi-static system configuration model of a single transmitting station and four receiving stations as an example, give the error distribution diagrams of the four receiving stations.

[0070] Specifically, taking the three-dimensional multi-static sonar system with four receiving stations as an example, conduct 100 Monte-Carlo simulations. The simulation parameters are as follows: the target sea area range is ±20 km in the x direction, ±20 km in the y direction, and ±20 km in the z direction. The sound speed in water Vc = 1.5 km / s, and the time measurement error and station location measurement error are σ τ = 1 ms and σ S = 5 m respectively. The coordinates of the transmitting station and receiving stations are: the coordinates of the T station are (0, 0, 2.121) km, the coordinates of the R1 station are (-5.196, -3, 0) km, the coordinates of the R2 station are (5.196, -3, 0) km, the coordinates of the R3 station are (0, 6, 0) km, and the coordinates of the R4 station are (0, 0, 8.485) km. The multi-static sonar system configuration model is as Figure 2 shown.

[0071] According to the above three-dimensional space multi-static sonar positioning principle and error calculation principle, use MATLAB to conduct numerical simulation modeling of the three-dimensional multi-static sonar positioning algorithm and error for the four receiving stations. The GDOP distribution of this three-dimensional layout multi-static sonar is as Figure 3 shown. The result of the three-dimensional multi-static sonar error analysis method of the present invention is reflected in the GDOP entity distribution in three-dimensional space. Therefore, any cross-section in any direction can be selected for two-dimensional data display. Here, the cross-sections at z = -1, 1, 3 km are selected for two-dimensional data extended display. And a three-dimensional display schematic diagram of the GDOP two-dimensional data on the corresponding cross-section in the cross-section direction is given, as Figures 4 to 6 , which can more stereoscopically observe the three-dimensional schematic diagram of the two-dimensional data of any cross-section in the three-dimensional space in the cross-section direction.

[0072] It should be noted that under the conditions of the three-dimensional multi-static sonar of the present invention, the GDOP distribution in the three-dimensional space can be clearly observed. This embodiment simultaneously conducts three-dimensional display of the two-dimensional data on the cross-section, only to conveniently observe the distribution of errors in a certain direction.

Claims

1. A method for target positioning and error analysis based on a three-dimensional space multi-static sonar, characterized in that Including the following steps: Step 1: According to the co-planar multi-static sonar positioning model, place each base station of the multi-static sonar on different horizontal planes, construct a three-dimensional space multi-static sonar system configuration model, draw a three-dimensional space sonar system topology diagram, and determine the actual physical meaning of each parameter; Step 2: Determine the positional relationship of each base station of the three-dimensional multi-static sonar system. Utilize its geometric relationship and the distance measurement information of each base station to analyze the target positioning principle of the three-dimensional space multi-static sonar, further give the target positioning equation, and calculate the three-dimensional space target estimated value, specifically as follows; Suppose S represents the target position, r T is the distance from the receiving station to the target, r R1 , r R2 , … r RN are the distances from the target to each sonar receiving station respectively; the sum of distances r Σi is the product of the time for the sound wave to travel from the transmitting station, reflect off the target and reach the i-th receiving station and the speed of sound in water; the target location equation for the three-dimensional multi-static sonar is written as follows: where x T , y T , z T represent the x, y, and z coordinates of the T station position respectively, x R1 …x RN represent the x coordinates of the i-th receiving station respectively, y R1 …y RN represent the y coordinates of the i-th receiving station respectively, z R1 …z RN represent the z coordinates of the i-th receiving station respectively, and x, y, and z represent the x, y, and z coordinates of the target position; It can be obtained from the above equation: (x T -x Ri )x+(y T -y Ri )y+(z T -z Ri )z = g i Write the above equation in matrix form: AX = f; where: X = [x, y, z] T , f = [g1, g2, …, g N T ​ The estimated value of the target can be obtained as follows: Step 3: Considering the time measurement error and the station location measurement error, give the calculation equation of the error distribution of the three-dimensional multi-static sonar system; Differentiate both sides of the target positioning equation (1) to obtain the error equation of the three-dimensional multi-static sonar: where c 11 …c N1 respectively represent the ratio of the difference in the x - coordinate between the target and the j - th receiving station to the distance, that is c 12 …c N2 respectively represent the ratio of the difference in the y - coordinate between the target and the j - th receiving station to the distance, that is c 13 …c N3 respectively represent the ratio of the difference in the z - coordinate between the target and the j - th receiving station to the distance, that is c T1 、c T2 、c T3 respectively represent k R1 …k RN is expressed as k Ri =-(c j1 dx j +c j2 dy j +c j3 dz j ), k T =-(c T1 dx T +c T2 dy T +c T3 dz T ); Write Equation (2) in matrix form and use the pseudo-inverse method to solve the estimated value of the target positioning error: dV = CdX + dX S dX = (C T C) -1 C T [dV - dX S T ​ where dV = [dr ∑1 dr ∑2 … dr ∑N dr T T , dX = [dx dy dz] T ,dX S =[k R1 +k T k R2 +k T … k RN +k T k T T ;​​ Therefore, the covariance of the positioning error is: P dx = E[dXdX T = (C T C) -1 C T {E[dVdV T + E[dX S dX S T}((C T C) -1 C T ) T The positioning accuracy is expressed as: Step 4: Use MATLAB software to build a three-dimensional multi-static sonar error distribution simulation environment, select the number of base stations, and obtain the three-dimensional space error distribution diagram.

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