Three-dimensional passive positioning method

Abstract

The present invention provides a three-dimensional passive positioning method, which is used for positioning a target by an N+1 hybrid base station positioning system, and includes the following steps: S1, obtaining the TDOA and AOA of the target, and performing time alignment; S2, constructing the geometric relationship between the monitoring station, the reference station and the target position, using the geometric relationship and the definition of TDOA and AOA, establishing the linear equation of TDOA and AOA about the target position, and simultaneously obtaining the linear matrix equation about the target position; S3, solving the estimated value of the target position by weighted least squares method, and analyzing the influence of measurement noise on the positioning result. The present invention requires at least two base stations to realize positioning of the target, and only one base station used to measure the target TDOA can observe the target AOA, and the closed-form solution of the target position can be obtained, the calculation complexity is low, and the positioning performance can reach CRLB accuracy.

Description

Technical Field

[0001] The present invention relates to the field of passive positioning technology, and specifically provides a three-dimensional passive positioning method applied in a scenario where an N+1 hybrid base station positioning system is used to position a target, wherein N represents N monitoring stations, 1 represents a reference station, the monitoring station and the reference station are collectively referred to as base stations, the N+1 base stations are all used to measure the time difference of arrival, i.e., TDOA, and only the reference station is used to measure the angle of arrival, i.e., AOA. Background Art

[0002] Passive target localization is a basic problem in passive detection systems such as radar, sonar, wireless sensor networks, and optoelectronic detection systems. The localization process is to obtain different types of measurement values ​​of the target through stations with known positions, and use the positioning algorithm to solve the target position. Since the relationship between the target position and the TDOA and AOA measurements from it is nonlinear and non-convex, the target localization problem is usually difficult. Maximum likelihood estimation (MLE) is a general method to solve this type of problem. MLE has asymptotic unbiasedness, and its performance can reach the Cramer-Rao lower bound (CRLB) when there are enough observations. However, MLE requires iterative calculations, has high requirements on the accuracy of the initial value of the iteration, and is prone to local convergence. Therefore, it is more inclined to use a source position estimation algorithm with a closed-form solution.

[0003] Within a small error range under Gaussian noise conditions, the performance of the existing closed-form positioning algorithm based on TDOA can reach CRLB accuracy. However, it requires at least four base stations to participate in positioning, and when the number of base stations is small, these methods may produce ghost points. The existing positioning algorithm based on AOA uses multiple pairs of azimuth and elevation angles for triangulation positioning, and can determine the source position in the form of a closed solution. It is well known that the more measurement values, the higher the positioning accuracy of the target. The existing positioning method based on hybrid TDOA and AOA measurement has higher positioning accuracy and only requires at least two stations to locate the target. However, it requires that each base station used to measure the target TDOA can observe the target's AOA. In fact, due to factors such as multipath effects and non-line-of-sight propagation, the observation station sometimes cannot use infrared sensors or antenna arrays to obtain the source's AOA. In addition, due to the high cost of antenna array receivers and infrared sensors, the feasibility of large-scale use is very low. These factors will cause the above algorithms to fail. Therefore, the present invention provides an effective three-dimensional passive positioning method, which requires at least two base stations to participate in the positioning and only one of the base stations used to measure the target TDOA can observe the target's AOA, so as to obtain a closed-form solution to the target position, that is, an estimated value of the target position. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a three-dimensional passive positioning method, which mainly uses the geometric relationship between the base station and the target position, utilizes the measurement equation to establish the linear matrix equation between TDOA and AOA and the unknown target position, and obtains the estimated value of the target position by solving the matrix equation through the weighted least squares method.

[0005] The three-dimensional passive positioning method provided by the present invention is used for positioning a target in an N+1 hybrid base station positioning system, wherein N represents N monitoring stations, and N is an integer greater than 0; 1 represents a reference station, and the N+1 base stations are all used to measure the time difference of arrival, i.e., TDOA, and only the reference station is used to measure the angle of arrival, i.e., AOA, and comprises the following steps:

[0006] S1. Obtain the TDOA and AOA of the target and perform time alignment;

[0007] S2, construct the geometric relationship between the monitoring station, the reference station and the target position, and use the geometric relationship and the definition of TDOA and AOA to establish the linear equations of TDOA and AOA about the target position, and jointly obtain the linear matrix equation about the target position;

[0008] S3. The estimated value of the target position is solved by weighted least squares method, and the influence of measurement noise on the positioning result is analyzed.

[0009] Preferably, the geometric relationship is expressed as:

[0010] u-s0=r0b;

[0011] in, Represents the three-dimensional spatial position of the target, which is an unknown number. Represents the dimension, represents the unit vector pointing from the reference station to the target, α and β represent the azimuth and elevation angle of the target relative to the reference station, r0 = ||u-s0|| is the distance between the reference station and the target, represents the three-dimensional spatial position of N+1 base stations. When i=0, s0 represents the three-dimensional spatial position of the reference station. When i=1,2,3,…,N, s1,s2,s3,…,s N Represents the three-dimensional spatial position of N monitoring stations.

[0012] Preferably, the definition of TDOA is used: i,0 =r i -r0 and geometric relationship, TDOA is expressed as a linear equation:

[0013]

[0014] in, T is the matrix transpose operator, ||s i|| means s i The Euclidean norm of i,0 Indicates monitoring stations i and the distance difference between the reference station s0 and the target, r i Indicates monitoring stations i The distance to the target.

[0015] Preferably, AOA is defined as:

[0016]

[0017] Where arctan represents the inverse tangent function;

[0018] Using the definition and geometric relationship of AOA, AOA is expressed as a linear equation:

[0019] γ T s0=γ T u;

[0020] in,

[0021] Preferably, the linear equation represented by TDOA and the linear equation represented by AOA are combined to obtain the linear matrix equation as follows:

[0022] h m =G m u;

[0023] in,

[0024] Preferably, the process of analyzing the influence of measurement noise on the positioning result is as follows: perform a first-order Taylor expansion on each TDOA and AOA, remove the noise terms above the second order, obtain the measurement error, substitute the TDOA and AOA containing the measurement error into the measurement equation, obtain the error component of the measurement equation, express the error component as the estimated deviation of the target position, and the estimated deviation is expressed as: in, represents the estimated value of the target position;

[0025] The covariance matrix of the target position obtained based on the estimated deviation is expressed as: in, represents G affected by measurement noise m , Δm represents the measurement noise that obeys Gaussian white distribution, Q m represents the covariance matrix of Δm, W = (HQ m H T ) -1 represents the weighting matrix, where H = diag([2r1,2r2,...,2r N,r0cosβ,r0]).

[0026] Preferably, the estimated value of the target position is obtained using the weighted least squares method as follows:

[0027]

[0028] Among them, argmin() is a mathematical function, which means to find the value of the independent variable when the function value is minimum. represents h affected by measurement noise m .

[0029] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0030] The present invention requires at least two base stations to locate the target, and only one base station for measuring the target TDOA is required to observe the target AOA, so as to obtain a closed-form solution for the target position, with low computational complexity and positioning performance that can achieve CRLB accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of positioning a target by an N+1 hybrid base station positioning system provided in an embodiment of the present invention;

[0032] Figure 2 is a schematic diagram of a three-dimensional passive positioning method provided according to an embodiment of the present invention;

[0033] Figure 3 This is a comparison chart of the positioning performance of the present invention and the traditional algorithm affected by TDOA measurement noise;

[0034] Figure 4 This is a comparison chart of the positioning performance of the present invention and the traditional algorithm affected by AOA measurement noise. DETAILED DESCRIPTION

[0035] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0036] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0037] The application scenario of the present invention is an N+1 hybrid base station positioning system, where N represents N monitoring stations and N is a positive integer greater than 0; 1 represents a reference station, and the monitoring station and the reference station are collectively referred to as a base station. The three-dimensional spatial position of the base station is represented by in Indicates latitude information, that is, here it means s i is the three-dimensional information. When i=0, it indicates the three-dimensional spatial position of the reference station; when i≠0, it indicates the three-dimensional spatial position of the monitoring station; the target at an unknown position is represented by Reference station s0 and any monitoring station s i Both are used to determine the TDOA value of the target, but only reference station s0 can determine the AOA value of the target.

[0038] Figure 1 The mathematical model of the N+1 hybrid base station positioning system for positioning a target according to an embodiment of the present invention is shown.

[0039] like Figure 1 As shown, X, Y, and Z represent the corresponding coordinate axes of the coordinate system, O is the origin of the coordinate system, and r i represents any base station s i The three-dimensional spatial position of the target When i=0, it indicates the distance between the reference station and the target; when i≠0, it indicates the distance between the monitoring station and the target, s i and j represents the three-dimensional spatial position of any two monitoring stations, α and β represent the azimuth and elevation angle of the target relative to the reference station, respectively.

[0040] It should be noted that this embodiment is verified by numerical simulation experiment, and all steps are successfully simulated on Matlab2019a.

[0041] It should be noted that: in the N+1 hybrid base station positioning system in this embodiment, the value of N is 7, and the position coordinates of the 8 base stations used in the simulation are as follows:

[0042]

[0043] It should be noted that the actual position of the target is u = [1000, 1000, 1000] T m, this data is used for comparison and calculation with the final estimated value of the target position, and for drawing a curve to illustrate the effect. In the process of solving the estimated value of the target position, this data is not required to participate in the calculation and is regarded as an unknown number.

[0044] Figure 2 The flowchart of the three-dimensional passive positioning method provided according to an embodiment of the present invention is shown.

[0045] like Figure 1 , Figure 2 As shown, the steps of the three-dimensional passive positioning method are as follows:

[0046] S1. Establish a scenario in which a 7+1 hybrid base station positioning system is used to locate the target and initialize the system parameters. Any two base stations can collaborate to measure the TDOA of the target, but only the reference station can measure the AOA of the target. Obtain the TDOA and AOA of the target and perform time alignment.

[0047] S2. Construct the geometric relationship between the monitoring station, the reference station and the target position. Use the geometric relationship and the definitions of TDOA and AOA to establish the linear equations of TDOA and AOA about the target position. Combine the linear equations of TDOA and AOA about the target position to obtain the linear matrix equation about the target position.

[0048] The geometric relationship is expressed as:

[0049] u-s0=r0b;

[0050] in, represents the unit vector pointing from the reference station to the target, r0=||u-s0|| is the distance between the reference station and the target, It represents the three-dimensional spatial position of 7+1 base stations. When i=0, s0 represents the three-dimensional spatial position of the reference station. When i=1,2,3,…,Ν, s1,s2,s3,…,s7 represent the three-dimensional spatial position of the 7 monitoring stations.

[0051] Using the definition of TDOA: r i,0 =r i -r0 and geometric relationship, TDOA is expressed as a linear equation as follows:

[0052]

[0053] in, T is the matrix transpose operator, ||s i || means s i The Euclidean norm of i,0 Indicates monitoring stations i The difference between the distance between the reference station s0 and the target, r i Indicates monitoring stations i The distance to the target.

[0054] AOA is defined as:

[0055]

[0056] Where arctan represents the inverse tangent function;

[0057] Using the definition and geometric relationship of AOA, the AOA is expressed as a linear equation as follows:

[0058] γ Ts0=γ T u;

[0059] in α and β represent the azimuth and elevation angles of the target relative to the reference station, respectively.

[0060] The linear equation of TDOA and the linear equation of AOA are combined to obtain the measurement equation as follows:

[0061] h m =G m u;

[0062] in,

[0063] S3. Since there will be measurement noise in the actual positioning process that affects the positioning results, the process of analyzing the impact of measurement noise on the positioning results is as follows: perform a first-order Taylor expansion on each TDOA and AOA, remove the noise terms above the second order, and obtain the measurement error. Substitute the TDOA and AOA containing the measurement error into the measurement equation to obtain the error component of the measurement equation. The error component is used to represent the estimated deviation of the target position. The estimated deviation is expressed as:

[0064]

[0065] in, Represents an estimate of the target location.

[0066] The covariance matrix of the target position obtained based on the estimated deviation is expressed as:

[0067]

[0068] in, represents G affected by measurement noise m , Δm represents the measurement noise that obeys Gaussian white distribution, Q m represents the covariance matrix of Δm, W = (HQ m H T ) -1 is a weighting matrix, where H = diag([2r1,2r2,...,2r7,r0cosβ,r0]).

[0069] Based on the above analysis, the Monte Carlo method is used to introduce the same distribution of TDOA and AOA white noise as measurement noise in the simulation process, and their covariance matrices are: and Among them, I represents the identity matrix, and the subscript represents the dimension of the identity matrix. and In this case, the TDOA measurement value and AOA measurement value of the target observed by each base station are obtained by initializing the system parameters.

[0070] The measurement equation after introducing TDOA and AOA white noise with the same distribution is as follows:

[0071]

[0072] Substitute the measured values ​​of the target observed by each base station into the vector and matrix In the expression of , we get the following formula:

[0073]

[0074]

[0075] First, the estimated deviation and covariance matrix of the target position are used to calculate the weighting matrix W = (TQ m T T ) -1 , where T = diag([2r1,2r2,...,2r7,r0cosβ,r0]), the covariance matrix of the measurement noise

[0076] Since the matrix T depends on the actual position u of the target, we can first use the identity matrix instead of W or let W = Q m -1 , solve for an initial position estimate of the target, and then use the initial position estimate to calculate a more accurate weighting matrix W, and then get the final solution, which is the estimate of the target position.

[0077] The estimated value of the target position solved by weighted least squares method is as follows:

[0078]

[0079] It should be noted that the estimated value of the target position, the deviation of the estimated value of the target position and the covariance matrix are directly generated by the simulation software. A single experiment is accidental and not convincing, so a large number of simulation operations are required. The number of estimated values ​​of the target position affected by noise is too large to be listed one by one. This embodiment will compare the following performances, namely Figure 3 , Figure 4 To illustrate the effectiveness of the present invention.

[0080] The following will verify the results obtained by the present invention:

[0081] This embodiment also compares the operation time of the traditional least square method (LSE), IMLE and the present invention (IMLE refers to the maximum likelihood estimation with the true target position as the initial value for iteration), and roughly estimates the computational complexity of these algorithms through the running time of Intel Core-i7 CPU. The specific data are shown in the following table:

[0082]

[0083] The three-dimensional passive positioning method proposed in the present invention only needs one or two iterations to obtain an accurate weighting matrix, and its computational complexity is slightly higher than that of LSE, but still much lower than that of IMLE. It is worth noting that the average number of iterations of IMLE is 11.2 times.

[0084] The following is a comparison of the positioning performance of LSE, IMLE and the present invention in this embodiment:

[0085] Figure 3 The comparison of positioning performance between the present invention and the traditional algorithm affected by TDOA measurement noise is shown.

[0086] Figure 4 The comparison of positioning performance between the present invention and the traditional algorithm affected by AOA measurement noise is shown.

[0087] exist Figure 3 , Figure 4 In the figure, × represents the performance curve of locating the target using the LSE method. represents the performance curve of using the LSE method to locate the target, ◇ represents the performance curve of using the method of the present invention to locate the target, and + represents the estimated deviation data curve of using the method of the present invention to locate the target.

[0088] like Figure 3 As shown, the horizontal axis is 10 times the TDOA standard deviation σ r The natural logarithm of the position is in degrees; the ordinate is the natural logarithm of 10 times the root mean square error and variance in meters, which is used to describe the impact of TDOA measurement noise on the positioning performance of each positioning method. The choice of logarithmic operation here can represent the performance comparison of different algorithms under a larger dynamic range error.

[0089] observe Figure 3It can be obtained that: when the TDOA measurement noise is small, the performance of the method of the present invention and IMLE are better than LSE, and can achieve CRLB accuracy. Compared with IMLE, the estimation deviation of the method of the present invention is smaller, which is approximately an unbiased estimate. As the measurement noise increases, the root mean square error of the method of the present invention gradually increases. When the standard deviation of the TDOA measurement noise is about 90 meters, that is, the horizontal coordinate, the IMLE has a threshold effect. This situation may be due to the irregular observation error surface near the real target position, which is easily interfered by noise. However, at this time, the method of the present invention still has good performance.

[0090] like Figure 4 As shown, the horizontal axis is 10 times the AOA standard deviation The natural logarithm of is in degrees; the ordinate is the natural logarithm of 10 times the root mean square error and variance in meters, which is used to describe the influence of AOA measurement noise on the positioning performance of each positioning method.

[0091] observe Figure 4 It can be obtained that when the AOA measurement noise is small, the performance of the method of the present invention and IMLE is better than that of LSE, and can achieve CRLB accuracy. Compared with IMLE, the estimation bias of the method of the present invention is smaller and is approximately an unbiased estimate. At the same time, since the number of AOA measurement values ​​is much less than that of TDOA measurement values, the weight of AOA measurement values ​​on the results is lower, and the positioning performance of each positioning method is less affected by AOA measurement noise.

[0092] In summary, the comparison of operation time and the effect of noise on performance are sufficient to show that the method of the present invention is effective and superior to the traditional method.

[0093] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

[0094] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A three-dimensional passive positioning method is applied to an N+1 hybrid base station positioning system to locate a target, comprising N monitoring stations and one reference station, where N is an integer greater than 0; the N+1 base stations are all used to measure the time difference of arrival, i.e., TDOA, and only the reference station is used to measure the angle of arrival, i.e., AOA, characterized in that: The following steps are involved: S1. Acquire the TDOA and the AOA of the target and perform time alignment; S2. Construct a geometric relationship between the monitoring station, the reference station and the target position. Use the geometric relationship and the definitions of the TDOA and the AOA to establish linear equations of the TDOA and the AOA with respect to the target position, and obtain a linear matrix equation with respect to the target position by combining the linear equations. The geometric relationship is expressed as: u-s0=r0b; in, Represents the three-dimensional spatial position of the target, which is an unknown number. Represents the dimension, represents the unit vector pointing from the reference station to the target, α and β represent the azimuth and elevation angle of the target relative to the reference station, r0=‖u-s0‖ is the distance between the reference station and the target, represents the three-dimensional spatial position of N+1 base stations. When i=0, s0 represents the three-dimensional spatial position of the reference station. When i=1,2,3,...,N, s1,s2,s3,...,s N Represents the three-dimensional spatial position of N monitoring stations; Using the definition of TDOA: r i,0 =r i -r0 and geometric relationship, the TDOA is expressed as a linear equation: in, T is the matrix transpose operator, ||s i || means s i The Euclidean norm of i,0 Indicates the monitoring station s i and the distance difference between the reference station s0 and the target, r i Indicates the monitoring station s i Distance to target; S3. The estimated value of the target position is solved by weighted least squares method, and the influence of measurement noise on the positioning result is analyzed.

2. The three-dimensional passive positioning method according to claim 1, characterized in that: AOA is defined as: Where arctan represents the inverse tangent function; Using the definition and geometric relationship of AOA, the AOA is expressed as a linear equation: γ T s0=γ T u; in, 3. The three-dimensional passive positioning method according to claim 2, characterized in that: The linear matrix equation obtained by combining the linear equation represented by TDOA and the linear equation represented by AOA is as follows: h m =G m u; in, 4. The three-dimensional passive positioning method according to claim 3, characterized in that: The process of analyzing the influence of measurement noise on positioning results is as follows: perform first-order Taylor expansion on each TDOA and AOA, remove the noise terms above the second order, obtain the measurement error, substitute the TDOA and AOA containing the measurement error into the measurement equation, obtain the error component of the measurement equation, express the error component as the estimated deviation of the target position, and the estimated deviation is expressed as: in, represents the estimated value of the target position; The covariance matrix of the target position obtained according to the estimated deviation is expressed as: in, represents G affected by measurement noise m , Δm represents the measurement noise that obeys Gaussian white distribution, Q m represents the covariance matrix of Δm, W = ( HQ m H T ) -1 represents the weighting matrix, where H = diag([2r1,2r2,...,2r N ,r0cosβ,r0]).

5. The three-dimensional passive positioning method according to claim 4, characterized in that: The estimated value of the target position is obtained using the weighted least squares method as follows: Among them, argmin() is a mathematical function, which means to find the value of the independent variable when the function value is minimum. represents h affected by measurement noise m .

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