Linear base station array positioning method based on geometric modeling

Abstract

The invention discloses a linear base station array positioning method based on geometric modeling, and aims to solve the technical problems in the aspects of positioning precision, calculation efficiency and convergence of an existing method under a linear base station. The method comprises the following steps: receiving signals based on a linear base station array with known position coordinates, and collecting a signal time difference of arrival (TDOA) between a target and each base station in real time; by selecting a base station combination and combining geometric characteristics of a linear base station array, a dynamic correction model for ranging errors is constructed, and errors caused by equipment deviation and signal interference are reduced; based on linear base station array environment characteristics, creatively combining a triangular cosine theorem and an inequality relation to generate a preliminary positioning result corresponding to each base station combination; by designing an improved Cramer-Rao lower bound (CRLB) weighting strategy, a fusion method of multi-combination positioning results is optimized, and finally a positioning result with higher robustness is obtained. The algorithm provided by the invention has relatively high error resistance, and has a wide application prospect in target positioning of the linear base station array.

Description

Technical Field

[0001] The present invention relates to the field of positioning and navigation technology, and in particular to a linear base station array positioning method based on geometric modeling. Background Art

[0002] In modern wireless communication and positioning technology, positioning accuracy is mainly affected by the combined effects of geometric configuration and measurement error variance. When the geometric configuration is poor, the influence of the error source is easily amplified, thus significantly reducing the final positioning accuracy.

[0003] With the development of smart cities, smart street lights have been widely popularized as an important urban infrastructure. These smart street lights not only undertake traditional lighting tasks, but also integrate a variety of sensors and cellular micro base stations to support a variety of smart city applications. The large-scale deployment of smart street lights has laid the foundation for the comprehensive coverage of cellular signals and has become an effective means to achieve high-precision target positioning in complex urban environments. Especially in urban densely built areas or densely treed street environments, traditional GNSS positioning has greatly reduced positioning accuracy due to the obstruction or weakening of satellite signals, making it difficult to meet actual needs. The smart street light system can make up for the shortcomings of traditional GNSS technology and provide reliable positioning support for applications such as mobile device tracking, unmanned vehicle management, and drone delivery.

[0004] In this context, the positioning method based on time difference of arrival (TDOA) is widely used in smart cities and the Internet of Things because it does not require global time synchronization and only relies on the relative time difference between base stations. The TDOA method not only reduces the dependence on precise time synchronization, but also has high reliability in practical applications. However, the special layout of the linear base station array brings new challenges to the TDOA positioning algorithm.

[0005] The traditional linear least squares (LLS) method is widely used due to its high computational efficiency. However, the LLS method faces multiple challenges when the base stations are unevenly distributed or the signal quality is poor. First, in a linear base station layout, the coefficient matrix of the positioning model is prone to singularity, which makes the algorithm unable to converge or solve, directly affecting the reliability of the positioning results. Secondly, when the geometric structure is poor (for example, the positioning precision factor PDOP is high) or the environmental noise is large, the positioning accuracy of the LLS method will drop significantly, making it difficult to meet the high-precision requirements in practical applications. Its optimized version, such as the weighted linear least squares (WLS), has a significantly increased computational complexity and a slow solution speed due to the introduction of a complex weight adjustment process. It is difficult to apply in scenarios with a large number of base stations or where real-time response is required. In addition, there are some low-complexity optimization algorithms that reduce the computational cost, but the positioning accuracy in a high-noise environment is still not ideal.

[0006] In response to the above problems, the present invention proposes a linear base station array positioning method based on geometric modeling. Compared with the existing methods, the present invention innovatively combines the trigonometric cosine theorem and inequality relationships in geometry, and uses these geometric characteristics to generate preliminary positioning results, avoiding the reliance on matrix inversion, thereby effectively avoiding the convergence problem caused by the singularity of the coefficient matrix in the linear base station layout. At the same time, by designing an improved Cramer-Rao lower bound (CRLB) weighting strategy, this method weightedly combines multiple preliminary positioning results to further improve the positioning accuracy and robustness. As a closed-form solution method, this method has significant computational efficiency advantages and can quickly complete the positioning solution. It is particularly suitable for intelligent street light positioning systems in smart cities and complex application scenarios such as mines and tunnels, meeting the requirements of real-time and high precision. Summary of the invention

[0007] In the TDOA positioning model, the matrix A and vector b are composed of sensor coordinates and distance differences respectively. The target variable is X, and m represents the measurement error. There are N base stations, (x i ,y i ,h i ) represents the position coordinates of the ith base station, (x, y, 0) represents the position coordinates of the 2D target to be determined, and only the case where the target is on the ground is considered, and the ground height is assumed to be 0.

[0008] AX=b+m,

[0009] in

[0010]

[0011] X=[x-x1 y-y1 R1] T .

[0012] In view of the problem that the traditional LLS and WLS coefficient matrix A cannot converge or be solved when the rank is not full or the matrix is ​​singular in the linear base station scenario, and the shortcomings of the existing methods in positioning accuracy and computational efficiency, the present invention provides a TDOA positioning method suitable for linearly arranged base station arrays. By optimizing geometric modeling and algorithm design, the positioning accuracy can be improved and the robustness of the system can be enhanced, which is suitable for various complex scenarios such as smart street light systems, mines, tunnels, etc. in smart cities.

[0013] The method includes:

[0014] Step 1: Based on a linear base station array with known position coordinates, signal reception is performed to collect the signal arrival time difference between the target and each base station in real time;

[0015] Step 2: By selecting a base station combination and combining the geometric characteristics of the linear base station array, a dynamic correction model for ranging errors is constructed to reduce errors caused by equipment deviation and signal interference; wherein the base station combination refers to selecting three base stations from all base stations as different combinations, thereby calculating a positioning solution under each combination to provide a basis for subsequent optimization;

[0016] Step 3: Based on the linear base station array environment characteristics, the trigonometric cosine theorem and inequality relationship are innovatively combined to generate the corresponding preliminary positioning results for each base station combination;

[0017] Step 4: By designing an improved Cramer-Rao lower bound weighting strategy, the fusion method of multiple combination positioning results is optimized, and finally a more robust positioning result is obtained.

[0018] Preferably, a combination of three base stations is selected from all base stations in the linear base station array, based on optimizing the relative positions of the base stations and the signal quality, thereby avoiding the calculation instability caused by the base station positions to a certain extent. In the process of selecting base stations, the present invention selects a combination of base stations for error correction through a weighted evaluation algorithm, combined with actual measurement values ​​and the distance between base stations, thereby significantly improving the reliability of positioning.

[0019] Preferably, when using the trigonometric cosine theorem and the inequality theorem, the angle between each base station combination and the measured distance relationship are modeled to obtain the preliminary positioning results for each combination.

[0020] Preferably, the positioning accuracy is mainly affected by three factors: base station coordinates, target position and measurement noise variance. The influence of these three factors can be reflected by the Cramer-Rao lower bound formula. The CRLB weighted average method is adopted to weight each preliminary positioning result to ensure that high-quality positioning results are given priority. By optimizing the weighted results, the present invention can effectively improve the positioning accuracy and reduce the error caused by low-quality signals.

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] In the case of linear arrangement of base stations, the present invention significantly improves the positioning accuracy through innovative geometric modeling and algorithm optimization, and effectively avoids the defects of inaccurate positioning and system instability caused by singular matrix problems. At the same time, the improved Cramer-Rao lower bound weighted average method is used to weighted optimize the positioning results, further improving the positioning accuracy. Compared with the traditional method, the present invention significantly enhances the stability and reliability of the system in various environments by dynamically selecting base station combinations and combining weighted evaluation, especially in environments with limited GNSS signals such as urban canyons and densely treed areas, and can fully utilize the cellular signals in the intelligent street light system for accurate positioning. As a closed-form solution method, the present invention has significant computational efficiency advantages over traditional iterative methods and can quickly complete positioning solutions. In addition, the present invention has strong adaptability. In addition to the application of intelligent street light systems in smart cities, it can also be widely used in special environments such as mines and tunnels, showing good environmental adaptability and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a block diagram of the TDOA positioning principle under the linear base station array provided by the present invention;

[0024] Figure 2 It is a TDOA positioning flow chart under the linear base station array provided by the present invention;

[0025] Figure 3 is a schematic diagram of TDOA of a linear base station array provided by the present invention;

[0026] Figure 4 It is a schematic diagram when the base station 1 provided by the present invention is located in the middle position of the selected three-base station combination;

[0027] Figure 5 The present invention provides Figure 4 Enlarged schematic diagram of the orange part;

[0028] Figure 6 It is a schematic diagram when the base station 1 provided by the present invention is located at any end of the selected three-base station combination; DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0030] In this embodiment, a TDOA positioning method applicable to a linear base station array is provided. Figure 1 , algorithm flow chart see Figure 2 , the following are the specific implementation steps of this method:

[0031] 1. Signal reception and TDOA measurement:

[0032] In this embodiment, multiple base stations are arranged along a straight line, and the target device can receive signals from these base stations. The signal arrival time difference between each base station and the target is measured and recorded. The relative position of each base station is known, and the positioning information of the target can be estimated through these known positions.

[0033] 2. Select three base station combinations and perform error correction:

[0034] Due to the particularity of the base station arrangement, the linear base station array TDOA positioning diagram is shown in Figure 3 , this embodiment randomly selects three base stations from N base stations for combination, that is, M indicates that there are M combinations in total, and the preliminary positioning results of the target are calculated through different combinations of three base stations. Combined with the known geometric relationship, the measured distance difference is corrected for measurement errors.

[0035]

[0036] where b 12 ,b 13 Respectively represent the distances between base station 1 and base station 2 and base station 3; R1 represents the distance between the target and base station 1, d 21 , d 31 They represent the distance difference respectively, and H is the height of the base station.

[0037]

[0038] where d 21 ω1 and d 31 ω2 represents the measured value D 21 and D 31 The noise component in . We get the following results:

[0039]

[0040] d2′1 represents the distance difference after calibration error, where δ is an adjustable hyperparameter.

[0041] 3. Geometric modeling and positioning result calculation:

[0042] The trigonometric cosine theorem and trigonometric inequality theorem are used for geometric modeling. According to the relative position relationship between the target position and the base station (see Figure 4 , Figure 5 ), and calculate the positioning results for each combination of three base stations.

[0043]

[0044] cosθ1+cosθ2=0,

[0045] Get an estimate of R1

[0046]

[0047] When the base station BS1 is located at either end of the linear array, Figure 6 As shown in the previous scenario, Estimated

[0048]

[0049] According to the obtained The relationship with other distances is

[0050]

[0051] Based on the above formula, the initial positioning result under this combination is obtained

[0052]

[0053] 4. Weighted average method to optimize positioning results:

[0054] When the number of base stations is greater than 3, the weighted average method of the combined Cramer-Rao lower bound is used to weight the preliminary positioning results obtained from multiple base station combinations to ensure that more accurate and reliable results are given priority.

[0055]

[0056] The weight is set to

[0057]

[0058] When the jth combination When it is greater than the threshold T, the weight is set to 0 to filter This method eliminates base stations with too large errors and improves the robustness of the results.

[0059] in From the above, we can get the distance between base station 2, base station 3 and the target

[0060]

[0061] is the covariance matrix of the empirical measurement errors.

[0062] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A linear base station array positioning method based on geometric modeling, characterized in that: The following steps are involved: Step 1: Based on a linear base station array with known position coordinates, signal reception is performed to collect the signal time difference of arrival (TDOA) between the target and each base station in real time; Step 2: By selecting a base station combination and combining the geometric characteristics of the linear base station array, a dynamic correction model for ranging errors is constructed to reduce errors caused by equipment deviation and signal interference; wherein the base station combination refers to selecting three base stations from all base stations as different combinations, thereby calculating a positioning solution under each combination to provide a basis for subsequent optimization; Step 3: Based on the linear base station array environment characteristics, the trigonometric cosine theorem and inequality relationship are innovatively combined to generate the corresponding preliminary positioning results for each base station combination; Step 4: By designing an improved Cramer-Rao lower bound (CRLB) weighting strategy, the fusion method of multiple combination positioning results is optimized, and finally a more robust positioning result is obtained.

2. The method according to claim 1, characterized in that The linear base station array with known position coordinates described in step 1, that is, the base stations are arranged in a straight line or approximately in a straight line, and the number of base stations is not less than three, to ensure that the measurement result based on the time difference has a unique solution in the positioning process.

3. The method according to claim 1, characterized in that Three base stations are selected from all base stations to form different combinations. The ranging error correction step uses the relationship between the three sides of a triangle to build a geometric model for estimation and correction to eliminate the influence of equipment deviation and signal interference.

4. The method according to claim 1, characterized in that Combining the trigonometric cosine theorem and the inequality theorem, a corresponding preliminary positioning result is generated for each base station combination (see Figure 5). cosθ1+cosθ2=0, According to the calculated R1, the corresponding preliminary positioning result is obtained.

5. The method according to claim 1, characterized in that The Cramer-Rao lower bound weighted average method is used to calculate all the preliminary positioning results. Perform weighted combination to obtain the final positioning result Set up a Threshold T, where w j Expressed as

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