A method for three-dimensional positioning by a RIS-assisted two-coordinate radar

Abstract

The application discloses a method for three-dimensional positioning of a two-coordinate radar assisted by RIS, comprising the following steps: a direct receiving channel and an auxiliary receiving channel of a target echo signal are constructed by combining the RIS with the two-coordinate radar; a measurement information error equation of a target is constructed according to the two-coordinate radar assisted by the RIS; and a value of the target position is estimated according to the measurement information error equation of the target. In the application, a single or multiple RIS is introduced into a same detection beam, the characteristics of a wide-beam in the elevation direction of a two-coordinate radar station are combined, a virtual multi-station receiving channel in the elevation direction is constructed, the spatial diversity gain of the two-coordinate radar is explored, and the three-dimensional positioning of a target is realized by using the redundant information. The RIS has low power consumption and low cost, can be carried by a UAV to be moved at any time, can change the electromagnetic wave propagation direction by phase shifting, does not need data transmission for fusing information, and is easier to realize high-precision phase alignment.

Description

Technical Field

[0001] This invention relates to a method for three-dimensional positioning using a RIS-assisted two-coordinate radar, belonging to the field of radar technology. Background Technology

[0002] Two-coordinate radar is the earliest radar system, capable of providing range and azimuth information for aerial targets. After years of development, two-coordinate radar technology has matured. Due to its small equipment size, low cost, simplicity, and reliability, it remains widely used in battlefield surveillance. However, the antenna elevation plane of a two-coordinate radar typically has only one channel, making it difficult to obtain target altitude using conventional sum-difference beamforming methods. When the target is far from the radar, inaccurate target altitude estimation can cause it to shift horizontally, reducing detection and tracking accuracy and affecting intelligence quality. Modern warfare demands high target detection accuracy, making target altitude estimation for two-coordinate radar a pressing problem that needs to be solved.

[0003] Currently, there are two methods for measuring the three-dimensional coordinates of a target: (1) using a two-coordinate radar in conjunction with an altimeter radar; and (2) directly measuring the three-dimensional information of the target using a three-coordinate radar. Each of these methods has its advantages and disadvantages. For the first method, since two-coordinate radar was developed earlier and is technically mature, using a two-coordinate radar to measure the target's azimuth and distance, and then using an altimeter radar for specialized height measurement, has the advantages of high accuracy, simple operation, easy technical implementation, and low cost. Therefore, it is the method widely used in the current air defense system. However, this method requires a dedicated altimeter radar for the two-coordinate radar, which makes the measurement process complex and increases the processing steps for intelligence data. It also results in poor real-time performance and is not conducive to the mobility of radar sites. For the second method, the three-coordinate radar directly measures the three-dimensional information of the target, which has higher accuracy and better real-time performance. However, due to the high production, training, and maintenance costs and technical complexity of the three-coordinate radar, it is not widely used at present. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for three-dimensional positioning using RIS-assisted two-coordinate radar. Compared with dedicated altimeter radar, RIS has low power consumption and low cost. It can be carried by UAVs for easy movement and can change the propagation direction of electromagnetic waves by phase shifting. The radar then uses multi-beam to receive target echo signals at different elevation angles. It does not require data transmission of fused information and is easier to achieve high-precision phase alignment.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] This invention provides a method for 3D positioning using RIS-assisted two-coordinate radar, comprising:

[0007] By combining RIS with a two-coordinate radar, a direct reception channel and an auxiliary reception channel for target echo signals are constructed.

[0008] The measurement information error equation F(x,y,z) of the target is constructed based on the RIS-assisted two-coordinate radar.

[0009] The target position (x, y, z) is estimated based on the error equation F(x, y, z) of the target's measurement information.

[0010] Furthermore, the method of combining RIS with a two-coordinate radar to construct a direct reception channel and an auxiliary reception channel for the target echo signal includes:

[0011] The RIS is mounted on the drone, and the drone is set to always be within the radar's transmission beam during flight. The echo channel from the target directly to the radar is the direct receiving channel, and the echo channel from the target to the RIS and then from the RIS back to the radar is the auxiliary receiving channel.

[0012] Furthermore, one or more RIS are arranged within the same detection beam, and the distribution of the RIS ensures that the observation angles of the target by the direct receiving channel and each auxiliary receiving channel are different.

[0013] Furthermore, the formula for the measurement information error equation F(x,y,z) of the target is as follows:

[0014]

[0015] In the formula: (x,y,z) are the three-dimensional spatial coordinates of the target Z = (x,y,z), (x... ri ,y ri ,z ri ), i = 1, ..., N are the three-dimensional spatial coordinates of the i-th RIS, (x R ,y R ,z R () represents the three-dimensional spatial coordinates of a two-coordinate radar;

[0016] r and θ are the range and azimuth of the target measured by the radar in the direct receiving channel, respectively, denoted as:

[0017]

[0018] θ = arctan((yy) R ) / (xx R ))+ω2;

[0019] d_sum i The sum of distances measured in the i-th indirect receiving channel from the radar to the target and then to the i-th RIS is expressed as:

[0020]

[0021] Where: ω1 follows a normal distribution σ r The radar ranging error; ω2 follows a normal distribution. σ θ This represents the radar angle measurement error.

[0022] Furthermore, estimating the target position (x,y,z) based on the target measurement information error equation F(x,y,z) includes:

[0023] Calculate the Hessian matrix of the measurement information error equation F(x,y,z) of the target;

[0024] Prove that the measurement information error equation F(x,y,z) is a convex function;

[0025] The target position (x, y, z) is estimated using a convex optimization method.

[0026] Furthermore, the Hessian matrix of the measurement information error equation F(x,y,z) of the target is:

[0027] in:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] in, α3=2x-2x R α4=2y-2y R α5=2z-2z R α6=2x-2x ri α7=2y-2yri α8=2z-2z ri .

[0038] Furthermore, the proof that the measurement information error equation F(x,y,z) is a convex function includes:

[0039] Using the Symbolic Math Toolbox in MATLAB to compute the Hessian matrix, prove that for any (x, y, z) and non-zero vector v = [a, b, c], v T *H*v≥0, which proves that the Hessian matrix is ​​positive semi-definite and F(x,y,z) is a convex function.

[0040] Furthermore, the method of estimating the target position (x, y, z) using convex optimization includes:

[0041] The minimum value of the measurement information error equation F(x,y,z) of the target is obtained by using the convex optimization method, and the estimated target position (x,y,z) is obtained as follows:

[0042] Wherein, Ω represents the three-dimensional space of the target detected by the RIS-assisted monostation radar.

[0043] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0044] The method described in this invention introduces one or more RIS (Radio Receiving Systems) within the same detection beam. Combining this with the wide-beam elevation dimension of a two-coordinate radar station, a virtual multi-station receiving channel in the elevation dimension is constructed. This explores the multi-view spatial diversity gain of the two-coordinate radar and utilizes its redundant information for three-dimensional target localization. Compared to dedicated altimeter radars, RIS are low-power and low-cost. They can be carried by UAVs for easy mobility and can change the electromagnetic wave propagation direction through phase shifting. The radar then uses multi-beam reception to receive target echo signals at different elevation angles. Data transmission without fusion information is not required, making high-precision phase alignment easier to achieve. Attached Figure Description

[0045] Figure 1 This is a flowchart of a method for three-dimensional positioning using a RIS-assisted two-coordinate radar, as provided in Embodiment 1 of the present invention.

[0046] Figure 2 It is the RIS-assisted two-coordinate radar three-dimensional positioning model described in Example 1;

[0047] Figure 3 This is a graph showing the variation of GDOP with distance and angle measurement errors as described in Example 2;

[0048] Figure 4This is a graph showing the change in GDOP as the distance between the UAV and the radar changes, as described in Example 2. Detailed Implementation

[0049] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0050] Example 1

[0051] Figure 1 This is a flowchart illustrating a method for 3D positioning using a RIS-assisted two-coordinate radar according to Embodiment 1 of the present invention. This flowchart merely shows the logical sequence of the method described in this embodiment. Without conflict, different methods may be used in other possible embodiments of the present invention. Figure 1 Complete the steps shown or described in the order indicated.

[0052] The RIS-assisted two-coordinate radar 3D positioning method provided in this embodiment can be applied to a terminal and can be executed by a RIS-assisted two-coordinate radar 3D positioning device. This device can be implemented in software and / or hardware and can be integrated into the terminal, such as any smartphone, tablet, or computer device with communication capabilities. See also... Figure 1 The method implemented in this way specifically includes the following steps:

[0053] S1: Using a UAV carrying a RIS (Radio Router Array) to construct a virtual receiving channel for a two-coordinate radar on the same azimuth beam, receiving information at different elevation angles, and exploring the multi-view spatial diversity gain of the radar in terms of altitude information, as follows:

[0054] Two-coordinate radar can measure the radial distance and azimuth of a target, and can continuously observe the target for a period of time. The horizontal beam of a two-coordinate radar is typically narrow to achieve high azimuth resolution and positioning accuracy, while the vertical beam is a wide-angle beam, covering a wide vertical angle range. Its measurement can only measure the distance from the target to the radar and the target's azimuth relative to the radar, but cannot measure the target's altitude. To achieve three-dimensional positioning with two-coordinate radar, we propose to introduce a Resonant Array (RIS), mounted on a UAV. The UAV will be programmed to always be within the radar's transmitted beam during flight, meaning its azimuth relative to the radar and the azimuth of the target measured by the radar will always be within a certain range. Due to the wide elevation-dimensional beam characteristic of the two-coordinate radar, the radar can receive both the target's direct scattered echo and the target echo signal reflected through the RIS. Figure 2As shown, taking a single RIS auxiliary as an example, the radar system is constructed from a single-station two-coordinate radar and a RIS auxiliary. The radar transmit beam points to the target, and the two receive beams point to the target and the RIS, respectively.

[0055] The radar transmits a beam directed at the target. The received target echo signal consists of two parts: one is the radar direct receiving channel, which receives the echo directly from the target to the radar; the other is the RIS auxiliary receiving channel, which receives the echo signal from the target to the RIS and then reflected back to the radar receiving channel. The distributed deployment of RIS and radar stations ensures sufficient spectral differences between the radar direct receiving channel and the RIS auxiliary receiving channel to guarantee the spatial diversity characteristics of the target across different receiving channels.

[0056] S2: Construct the target measurement information error equation based on the RIS-assisted two-coordinate radar.

[0057] S2.1 Suppose that in three-dimensional space, the coordinates of a two-coordinate radar are (x... R ,y R ,z R A radar system employs N drones to assist in detecting a target Z = (x, y, z). Each drone is equipped with a smart reflector RIS, and the drones and RIS are considered as a single unit. The drones move in tandem with the radar's scanning beam. In the direct channel, the radar measures the target's range and azimuth as r and θ, respectively.

[0058] The distance r measured by the direct channel can be expressed as:

[0059]

[0060] Wherein, ω1 follows a normal distribution. σ r This represents radar ranging error.

[0061] The measured azimuth angle θ can be expressed as:

[0062] θ = arctan((yy) R ) / (xx R ))+ω2 (2)

[0063] Wherein, ω2 follows a normal distribution. σ θ This represents the radar angle measurement error.

[0064] Let the coordinates of the i-th RIS be (x ri ,y ri ,z ri Let i = 1, ..., N. Since we can know the drone's position in real time, we can also obtain the distance between the drone and the radar. Therefore, the distance sum that can be measured in the i-th indirect channel is d_sum.i σ represents the total distance the signal travels from the radar to the target and then to the i-th RIS. r σ θ These represent the ranging and azimuth errors of the two coordinate radars, respectively.

[0065] The sum of distances measured in the i-th indirect channel is d_sum i It can be represented as

[0066]

[0067] S2.2 Based on the distance measurements of each channel of the target obtained from the above formula, the measurement information error equation formula for the target is as follows:

[0068]

[0069] S3: Calculate the Hessian matrix of F(x,y,z) and prove that F(x,y,z) is a convex function.

[0070] S3.1 Taking the difference twice from equation (4) yields the Hessian matrix H of the objective function, as shown in equation (5):

[0071]

[0072] The formulas for each row and column are shown below:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] in, α3=2x-2x R α4=2y-2y R α5=2z-2z R α6=2x-2x riα7=2y-2y ri α8=2z-2z ri .

[0083] S3.2 Using the Symbolic Math Toolbox in MATLAB to calculate the Hessian matrix, it is proved that for any (x,y,z) and non-zero vector v = [a,b,c], v T *H*v≥0, meaning the Hessian matrix is ​​positive semi-definite and the function F(x,y,z) is a convex function.

[0084] S4: The minimum value of the target measurement information error equation F(x,y,z) is obtained using the convex optimization method, thus yielding the estimated target position (x,y,z). Wherein, Ω represents the three-dimensional space of the target detected by the RIS-assisted monostation radar.

[0085] Example 2

[0086] The detection area contains a real target with coordinates [20, 40, 6] km, and two radars with coordinates [0, 0, 0] km. An UAV carrying a RIS-assisted radar locates the target. The radar's ranging error is assumed to be 10 m, and its angular measurement error 0.1°. 10,000 measurements were taken in the experiment, resulting in 10,000 optimization results. GDOP (Geometric Dilution of Precision) is an indicator of the geometrical accuracy of a positioning system. It represents the impact of a positioning system on the accuracy of a target's positioning in different directions under a given satellite configuration. The smaller the target error, the lower the GDOP, and the higher the positioning accuracy.

[0087] Experiment 1: The Influence of Ranging and Angle Measurement Errors of Two-Coordinate Radar on Positioning

[0088] Assume there are three UAV-assisted radars. The coordinates of the UAVs are x = 3 km (x-axis), y = x * tan(θ + Δθ) km (y-axis), and z = 100 m, 800 m, and 1500 m (z-axis). Here, Δθ represents a random azimuth angle within the beam range, ensuring that all three UAVs are within the detection beams of the two-coordinate radars. After changing the ranging and angle measurement errors of the two-coordinate radars, the target position is obtained using a convex optimization method. Then, the variance of the target coordinates on the x, y, and z axes is calculated to obtain the GDOP (Gross Target Position). The result is as follows: Figure 3 As shown.

[0089] from Figure 3 It is evident that the smaller the ranging error of the two-coordinate radar, the better the performance of the algorithm and the higher the accuracy of 3D positioning. Relatively speaking, ranging error has a greater impact on the system than angular measurement error.

[0090] Experiment 2: The impact of the number of drones and radar distance on positioning.

[0091] The distance between the drones and the radar was varied, ensuring that all three drones were within the detection beam of the two-coordinate radar. Multiple positioning results were obtained after employing a convex optimization method. The final result after calculating GDOP is as follows: Figure 4 As shown.

[0092] from Figure 4 It can be seen that the farther the UAV is from the radar, the greater the difference in the echo angle between the target's direct channel and the auxiliary channel, and the smaller the GDOP becomes, indicating a smaller positioning error. Compared to two RIS, the more RIS there are, the higher the positioning accuracy.

[0093] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0094] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0095] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0096] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0097] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for three-dimensional positioning using RIS-assisted two-coordinate radar, characterized in that, include: By combining RIS with a two-coordinate radar, a direct reception channel and an auxiliary reception channel for target echo signals are constructed. The target measurement information error equation is constructed based on the RIS-assisted two-coordinate radar. ; Error equation based on target measurement information Estimate the target location The value; The measurement information error equation of the target The formula is as follows: ； In the formula: (x, y, z) represent the target being detected. Three-dimensional spatial coordinates, Let i be the three-dimensional spatial coordinates of the i-th RIS. The three-dimensional spatial coordinates of the two-coordinate radar; r and Here, represents the range and azimuth of the target measured by the radar in the direct receiving channel, respectively, and is expressed as: ； ； The sum of distances measured in the i-th indirect receiving channel from the radar to the target and then to the i-th RIS is expressed as: ； in: Follows a normal distribution , This refers to radar ranging error; Follows a normal distribution , This refers to radar angle measurement error; The error equation based on the target's measurement information Estimate the target location The values ​​include: Calculate the measurement information error equation of the target. The Hessian matrix; Prove the measurement information error equation It is a convex function; The target position is estimated using a convex optimization method. The value; The measurement information error equation of the target The Hessian matrix is: ； in: ； ； ； ； ； ； ； ； ； in, , , , , , , , .

2. The method for three-dimensional positioning using RIS-assisted two-coordinate radar according to claim 1, characterized in that, The method of combining RIS with a two-coordinate radar to construct a direct reception channel and an auxiliary reception channel for target echo signals includes: The RIS is mounted on the drone, and the drone is set to always be within the radar's transmission beam during flight. The echo channel from the target directly to the radar is the direct receiving channel, and the echo channel from the target to the RIS and then from the RIS back to the radar is the auxiliary receiving channel.

3. The method for three-dimensional positioning using RIS-assisted two-coordinate radar according to claim 2, characterized in that, The RIS are arranged in one or more within the same detection beam. The distribution of the RIS ensures that the observation angle of the target is different for both the direct receiving channel and each auxiliary receiving channel.

4. The method for three-dimensional positioning using RIS-assisted two-coordinate radar according to claim 1, characterized in that, The proof measurement information error equation It is a convex function, including: Using the Symbolic Math Toolbox in MATLAB to compute the Hessian matrix, it is proved that for any... Non-zero vectors , That is, to prove that the Hessian matrix is ​​positive semi-definite. It is a convex function.

5. The method for three-dimensional positioning using RIS-assisted two-coordinate radar according to claim 1, characterized in that, The target position is estimated using a convex optimization method. The values ​​include: The measurement information error equation of the target is obtained by using convex optimization method. The minimum value is used to obtain the estimated target location. The value is: ; in, This represents the three-dimensional space of a target detected by a RIS-assisted monostation radar.

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