Combined positioning method based on bistatic distance and distance difference measurement value

Abstract

The invention discloses a combined positioning method based on a bistatic distance and a distance difference measured value, positioning is carried out by combining BR and RD measured values, and the BR method measures the total time of a signal reflected to a receiver through a target after emission through time synchronization of a transceiver, and further calculates the sum of the distances between the target and the transceiver; each transceiver pair can perform ellipse positioning by taking the transceiver as a focus and taking the distance sum as a long axis according to the measured distance information, so that the ellipse positioning is also called as ellipse positioning; according to the RD method, a reference receiver is selected, a TDoA measurement value is obtained according to the difference between the time when a signal reaches different receivers and the arrival time of the reference receiver, each receiver and the reference receiver can form a hyperbolic curve with the two receivers as focuses, and therefore hyperbolic curve positioning is also achieved; the method directly constructs the target position linear equation through the weighted least square model, eliminates the redundancy calculation step, improves the positioning efficiency of the multi-static radar system, and gives consideration to the high precision of positioning.

Description

Technical Field

[0001] The present invention relates to the field of target positioning, and in particular to a single-step weighted least squares fast positioning method based on the combination of dual-base distance and distance difference measurement values. Background Art

[0002] A multistatic radar system utilizes a coordinated configuration of one or more transmitters and multiple receivers, leveraging time synchronization between the nodes to precisely measure parameters such as signal transmission time. This flexible deployment of receivers enables the system to acquire richer target information than a single-base radar, significantly improving target positioning accuracy. Furthermore, the ability to acquire target information from multiple directions offers significant advantages in anti-interference capabilities and stealth target detection.

[0003] Current mainstream positioning algorithms include methods based on bistatic distance (BR), distance difference (RD), Doppler shift (DS), and angle of arrival (AoA). BR and RD positioning methods rely solely on time information for positioning. BR positioning requires system-wide time synchronization. The sum of the distances between the target and the transmitting and receiving nodes is calculated by calculating the time delay between the transmission and reception times. Each pair of transmitting and receiving nodes forms an elliptical positioning surface centered on the reference receiver and the other receivers. Multiple ellipse intersections determine the target's position. RD positioning requires synchronization between receivers. The time difference of arrival (TDoA) constructs a hyperbolic positioning surface centered on the reference receiver and the other receivers. Target location is achieved through multiple hyperbolic intersections.

[0004] Some existing studies are listed in the following table:

[0005] Among them, Liyang Rui compared the accuracy of synchronous and asynchronous elliptical positioning and hyperbolic positioning, and derived the optimal receiver layout for elliptical positioning; Ali Noroozi compared the BR-based method and the RD-based method, and simulation verified that the positioning accuracy of BR-based positioning is significantly better than that of RD-based positioning, where BR and RD methods correspond to elliptical positioning and hyperbolic positioning, respectively; Rouhollah Amiri proposed to use dual-base distance measurement values ​​and arrival angle measurement values ​​to jointly estimate the target position, providing a high-precision and efficient positioning method; Qin, Z. positioned the target by combining dual-base distance and range difference measurement values, and proposed an efficient closed-form solution algorithm based on the two-step weighted least squares method.

[0006] Liu Yang combined bistatic range, Doppler shift, and angle of arrival measurements to obtain a closed-form solution for the target position and velocity using a two-step weighted least squares method. Lijuan Yang proposed a two-step weighted least squares method based on the combination of bistatic range, range difference, and Doppler shift measurements to estimate the target position and velocity. In another paper, he proposed a three-dimensional joint estimation algorithm based on a variable step-size hill climbing algorithm and a two-step weighted least squares algorithm. This algorithm combines bistatic range, range difference, and Doppler shift measurements to estimate and optimize the three-dimensional position and velocity of a moving target. Reena Mamgain proposed an improved positioning algorithm based on the least squares method. This method calculates the SNR of each receiver based on the multistatic radar range equation, selects the receiver with the highest SNR as the reference receiver, and uses the RD measurements of some receivers closest to the reference receiver to estimate the target position. On this basis, a two-step iterative weighted least squares estimator is constructed to further improve positioning accuracy.

[0007] Dong Qing measured signal transmission delay and target angle, and achieved target positioning using active positioning constraints and arrival time difference. He also analyzed the impact of different numbers of receivers, different geometric configurations, and different target altitudes on positioning accuracy, providing a theoretical basis for selecting the appropriate number of receivers and station layout methods according to positioning index requirements in actual engineering applications. Siavash Bayat proposed a solution for elliptical positioning under asynchronous transmission, and expanded it to scenarios with uncertainty in the transmitter position. He proposed a semi-closed estimator through three consecutive stages: clock offset elimination, offset estimation and joint target positioning, and offset refinement.

[0008] References 3 to 7, respectively, report on joint positioning or velocity measurement using different measurements. They generally employ a two-step weighted least squares method to construct the joint equation. This two-step weighted least squares algorithm consists of two stages. In the first stage, pseudo-linear equations are constructed based on the measured parameters and geometric relationships. Nonlinear equations such as BR and RD are linearized by introducing auxiliary variables, and a joint least squares solution is established. In the second stage, the error term is solved by associating the auxiliary variables with the target parameters. While this method linearizes nonlinear equations by introducing auxiliary variables, it requires additional steps to correct the estimated values, increasing computational complexity. Summary of the Invention

[0009] The current mainstream method uses a two-step weighted least squares approach to locate targets. The first step involves constructing a pseudo-linear equation based on the relationship between measured parameters and geometrical relationships. This nonlinear equation is linearized by introducing auxiliary variables, and a joint least squares solution is established. The second step involves solving for the error term by correlating the auxiliary variables with the target parameters. This process increases algorithm complexity and computational resource consumption.

[0010] To address these issues, the present invention aims to improve the computational efficiency of existing algorithms. By deeply exploring the correlation between the BR and RD measurement parameters and leveraging the geometric constraints of RD and BR to construct a linear equation containing only the target position vector as an unknown parameter, the auxiliary variables introduced in the two-step weighted least squares algorithm are eliminated, compressing the traditional two-step weighted least squares algorithm into a single-step weighted least squares operation.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is: positioning by combining BR and RD measurements. The BR method uses time synchronization between the transceiver and the receiver to measure the total time it takes for the signal to be reflected from the target to the receiver, and then calculates the sum of the distances between the target and the transceiver. Each transceiver can use the distance information obtained from the measurement to create an ellipse with the transceiver as the focus and the above distance sum as the major axis, so it is also called elliptical positioning. The RD method selects a reference receiver and subtracts the arrival time of the signal at different receivers from the arrival time of the reference receiver to obtain the TDoA measurement value. Each receiver can form a hyperbola with the reference receiver as the focus, so it is also called hyperbola positioning.

[0012] The technical solution of the present invention comprises the following steps: Step 1: In a multi-base radar system with multiple receivers, a three-dimensional rectangular coordinate system is constructed with the transmitter as the origin. The positions of all receivers are known and all receivers are synchronized with the transmitter. The position of the target to be located is recorded as , construct a three-dimensional spatial model of the multi-base radar system based on the position relationship of the transceiver, the receiver coordinates ,by is the reference receiver; Step 2: Through time synchronization between multiple bases, the distance difference and the dual-base distance measurement value can be obtained, where the distance difference measurement value is the difference between the distance from the target to receiver i and the distance from the target to the reference receiver, the bistatic distance measurement value is the total distance that the transmitted signal is reflected by the target to the receiver i; definition , , then the two measurements can be described as: , , in , is the true value of its corresponding measurement value, , is the measurement error; define the measurement value Error value , , ; Assuming that all measurements are independent of each other and the error vector is zero-mean Gaussian, its covariance matrix is ,in , .

[0013] Step 3: Construct a weighted least squares problem with the target position as the vector to be solved in the model based on the combined positioning of the two-base distance and the range difference. The specific process is as follows: Step 3.1: From bistatic distance measurements , by Moving to the left side of the equation and squaring both sides, ignoring the second-order noise terms, we get: ; then you can get Expression , substitute it into ,get , Rewritten in matrix form ,in , ,

[0014] Step 3.2: Measure the value from the distance difference , by Moving to the left side of the equation and squaring both sides, ignoring the second-order noise terms, we get: ; can obtain Expression , which is substituted into step 3.1 to obtain ,get , rewritten into matrix form ,in , , .

[0015] Step 3.3: Combine the equations obtained in the previous two steps to get ,in , , .

[0016] Step 4: Estimate the initial target positioning solution using the least squares algorithm , ,calculate And substitute into the weight calculation formula , use weighted least squares method to calculate the target position .

[0017] Compared with the prior art, the technical solution adopted by the present invention has the following beneficial effects: 1. Traditional methods rely on auxiliary variables and iterative correction processes, resulting in high computational complexity. This invention directly constructs the target position linear equation through a weighted least squares model, eliminating redundant calculation steps, improving the positioning efficiency of the multi-base radar system while also ensuring high positioning accuracy.

[0018] 2. Simulation results show that, under conventional scenarios, the positioning accuracy of the method proposed in the present invention is at the same level as that of the two-step weighted least squares method, and the operation time of the method proposed in the present invention is only about one-fourth of that of the two-step weighted least squares method. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of a method for joint positioning based on dual-base distance and distance difference measurements in this embodiment.

[0020] Figure 2 Schematic diagram of the geometric model of a multi-base radar with one transmitter and multiple receivers in this embodiment.

[0021] Figure 3 This is a schematic diagram comparing the noise power and positioning accuracy of different algorithms in the one-transmit-four-receive multi-base radar system in this embodiment.

[0022] Figure 4 This is a schematic diagram comparing the noise power and positioning accuracy of different algorithms in the one-transmit-five-receive multi-base radar system in this embodiment.

[0023] Figure 5 This is a schematic diagram comparing the noise power and positioning accuracy of different algorithms in the one-transmit-six-receive multi-base radar system in this embodiment.

[0024] Figure 6 This is a schematic diagram comparing the noise power and positioning accuracy of different algorithms in the one-transmit, seven-receive multi-base radar system of this embodiment.

[0025] Figure 7 3 is a schematic diagram comparing the average positioning accuracy and noise power changes of the two-step weighted least squares algorithm in this embodiment in a one-transmitter, six-receiver multistatic radar system when the target appears at a random position. DETAILED DESCRIPTION

[0026] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Any modifications made based on the technical solutions in accordance with the technical ideas proposed by the present invention shall fall within the scope of protection of the present invention.

[0027] like Figure 1As shown in FIG, a joint efficient positioning method based on bistatic range and range difference measurements is proposed. The BR and RD measurements are effectively combined by variable substitution to obtain a linear equation containing only the target position as an unknown parameter. The method includes the following steps: Step 1: In a multistatic radar system with multiple receivers and one transmitter, a three-dimensional rectangular coordinate system is constructed with the transmitter as the origin. The positions of all receivers are known, and all receivers are synchronized with the transmitter. Step 2: Obtain distance difference measurements through time synchronization between multiple bases Distance measurement to bistatic base ; Step 3: Construct a weighted least squares problem with the target position as the vector to be solved in the model based on the joint positioning of the two-base distance and the range difference; Step 4: Estimate the initial target positioning solution using the least squares algorithm , according to the initial solution ,calculate And substitute into the weight calculation formula , use weighted least squares method to calculate the target position .

[0028] Example 1 Step 1: Use Matlab to model the multi-base radar system. In the multi-base radar system with one transmitter and four receivers, the transmitter position Establish a rectangular coordinate system for the coordinate origin. The coordinates of the four receivers are known to be , , , , the target position to be located ; Unit: km.

[0029] Step 2: Based on the geometric relationship between the transceivers, such as Figure 2 , get the distance from the target to the transmitter , target to receiver distance and receiver Distance to transmitter . RD measurement value and BR measurements The true values ​​of and The actual measurement value is and ,in , is the measurement error, subject to , Distribution. Let the standard deviation of the noise in the measurement be , , assuming that all measurements are independent of each other, the covariance matrix of the measurements is ,in , .

[0030] Step 3: Substitute the formula to derive the result , , , , , , , , ,

[0031] because contains unknown parameters, which are also the coefficients of the error vector. Therefore, the error vector can be ignored first and the least squares algorithm can be used to estimate the initial solution of target positioning. , according to the initial solution ,calculate And substitute into the weight calculation formula , use weighted least squares method to calculate the target position .

[0032] Step 4: Change the noise standard deviation of the measured value, let represents the noise level, The root mean square error (RMSE) is calculated using 10,000 Monte Carlo simulations from -10 to 10, and compared with the two-step weighted least squares method and the BR positioning algorithm. The results are as follows: Figure 3 shown.

[0033] Example 2 Step 1: Consider a multi-base radar system with one transmitter and five receivers. The five receivers are located at , , , , (All units are km), other conditions remain unchanged.

[0034] Step 2 to step 4: the same as in Example 1, the results are as follows Figure 4 shown.

[0035] Example 3 Step 1: Consider a multi-base radar system with one transmitter and six receivers. The six receivers are located at , , , , , (All units are km), other conditions remain unchanged.

[0036] Step 2 to step 4: the same as in Example 1, the results are as follows Figure 5 shown.

[0037] Example 4 Step 1: Consider a multi-base radar system with one transmitter and seven receivers. The seven receivers are located at , , , , , , (All units are km), other conditions remain unchanged.

[0038] Step 2 to step 4: the same as in Example 1, the results are as follows Figure 6 shown.

[0039] When the number of receivers is small, the positioning accuracy of this method is superior to the traditional two-step weighted least squares method. As the number of receivers increases, the performance of the original algorithm gradually catches up with and surpasses the improved algorithm, but the overall accuracy difference is small. Furthermore, when the number of receivers increases from 4 to 6, the positioning accuracy improves significantly, but with further increases in the number of receivers, the accuracy improvement is less significant. Considering both system cost and performance, the number of receivers should be six or fewer.

[0040] Example 5 Step 1: Consider a multi-base radar system with one transmitter and six receivers. The six receivers are located at , , , , , , target location (All units are km). y and They obey the uniform distribution of [10,400] respectively to simulate the expectation of positioning accuracy when the target appears at random positions.

[0041] Step 2 to step 3: the same as in Example 1, no further details will be given; Step 4: Use 10,000 Monte Carlo simulations to calculate the root mean square error and compare it with the two-step weighted least squares method. The results are as follows Figure 7 shown.

[0042] It can be seen that the target positioning accuracy of the present invention is comparable to that of the traditional two-step weighted least squares algorithm.

[0043] It should be noted that the positioning accuracy of the present invention in three-dimensional space is not completely superior to that of traditional algorithms. The specific accuracy difference depends on many factors, such as the geometric layout and target position. The above illustrations are only intended to illustrate that the positioning accuracy of the present invention is comparable to that of traditional algorithms. However, the advantage of the present invention over the traditional two-step weighted least squares algorithm lies in improved computational efficiency.

[0044] We evaluated the execution time (in seconds) of the proposed algorithm on an Intel Core i7-9750H CPU (6 cores, 2.6 GHz base frequency). Simulations were performed using MATLAB, and the total runtime for 10,000 iterations is shown in the table below.

[0045]

[0046] The improved algorithm proposed in this paper achieves a computational speed improvement of more than four times that of the traditional algorithm, and the advantage becomes more significant as the system scales up. Notably, the improved algorithm's computational time remains essentially stable when the number of receiving stations exceeds five, demonstrating good scalability.

[0047] Although the present invention has been disclosed above with reference to preferred embodiments, the embodiments and accompanying drawings are not intended to limit the present invention. Any person skilled in the art will readily be able to make various changes or modifications without departing from the spirit and scope of the present invention, and such changes and modifications are within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the scope of protection of the claims of this application.

Claims

1. A method for joint positioning based on bistatic range and range difference measurements, characterized by: The BR and RD measurements are effectively combined by variable substitution to obtain a linear equation containing only the target position as an unknown parameter, including the following steps: Step 1: In a multistatic radar system with multiple receivers and one transmitter, a three-dimensional rectangular coordinate system is constructed with the transmitter as the origin. The positions of all receivers are known, and all receivers are synchronized with the transmitter. Step 2: Obtain distance difference measurements through time synchronization between multiple bases Distance measurement to bistatic base ; Step 3: Construct a weighted least squares problem with the target position as the vector to be solved in the model based on the joint positioning of the two-base distance and the range difference; Step 4: Estimate the initial target positioning solution using the least squares algorithm , according to the initial solution ,calculate And substitute into the weight calculation formula , use weighted least squares method to calculate the target position .

2. The method for joint positioning based on bistatic distance and range difference measurements according to claim 1, characterized in that: In step 1: The target position to be located is recorded as , construct a three-dimensional spatial model of the multi-base radar system based on the position relationship of the transceiver, the receiver coordinates ,by is the reference receiver.

3. The method for joint positioning based on bistatic distance and range difference measurements according to claim 1, characterized in that: In step 2: The distance difference measurement is the difference between the distance from the target to receiver i and the distance from the target to the reference receiver, the bistatic distance measurement value is the total distance that the transmitted signal is reflected by the target to the receiver i; definition , , then the two measurements can be described as: ， ， in , is the true value of its corresponding measurement value, , is the measurement error; define the measurement value Error value , , ; Assuming that all measurements are independent of each other and the error vector is zero-mean Gaussian, its covariance matrix is ,in , .

4. The method for joint positioning based on bistatic distance and range difference measurements according to claim 1, characterized in that: The step 3 specifically includes: Step 3.1: From bistatic distance measurements , by Moving to the left side of the equation and squaring both sides, ignoring the second-order noise terms, we get: ; then you can get Expression , substitute it into ,get , Rewritten in matrix form ,in ， ， ； Step 3.2: Measure the value from the distance difference , by Moving to the left side of the equation and squaring both sides, ignoring the second-order noise terms, we get: ; can obtain Expression , which is substituted into step 3.1 to obtain ,get , rewritten into matrix form ,in , , ; Step 3.3: Combine the equations obtained in the previous two steps to get ,in , , .

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