A linear base station array localization method based on geometric modeling

Abstract

This invention discloses a linear base station array positioning method based on geometric modeling, aiming to solve the technical challenges of existing methods in terms of positioning accuracy, computational efficiency, and convergence under linear base station conditions. The method includes: receiving signals from a linear base station array with known location coordinates and real-time acquisition of the time difference of arrival (TDOA) between the target and each base station; selecting base station combinations and, considering the geometric characteristics of the linear base station array, constraining the rationality of geometric distance measurements based on the trigonometric inequality to construct a dynamic correction model for ranging errors, reducing errors caused by equipment deviations and signal interference; generating preliminary positioning results for each base station combination based on the environmental characteristics of the linear base station array using the trigonometric cosine theorem; and optimizing the fusion method of multiple combination positioning results by designing an improved Cramer-Rao lower bound (CRLB) weighting strategy, ultimately obtaining a more robust positioning result. The algorithm proposed in this invention has strong error resistance and broad application prospects in target positioning of linear base station arrays.

Description

Technical Field

[0001] This invention relates to the field of positioning and navigation technology, and specifically to a linear base station array positioning method based on geometric modeling. Background Technology

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

[0003] With the development of smart cities, smart streetlights have become widely used as an important urban infrastructure. These smart streetlights not only perform traditional lighting tasks but also integrate various sensors and cellular micro base stations, supporting diverse smart city applications. The large-scale deployment of smart streetlights has laid the foundation for comprehensive cellular signal coverage, becoming an effective means of achieving high-precision target positioning in complex urban environments. Especially in densely built-up urban areas or tree-lined streets, traditional GNSS positioning suffers a significant drop in accuracy due to satellite signal blockage or weakening, making it difficult to meet practical needs. Smart streetlight systems can compensate for the shortcomings of traditional GNSS technology, providing reliable positioning support for applications such as mobile device tracking, autonomous vehicle management, and drone delivery.

[0004] Against this backdrop, positioning methods based on Time Difference of Arrival (TDOA) are widely used in smart cities and the Internet of Things (IoT) due to their ability to operate without global time synchronization and rely solely on the relative time difference between base stations. TDOA methods not only reduce the dependence on precise time synchronization but also offer high reliability in practical applications. However, the unique layout of linear base station arrays presents new challenges to TDOA positioning algorithms.

[0005] Traditional linear least squares (LLS) is widely used due to its high computational efficiency. However, it faces multiple challenges in situations with uneven base station distribution or poor signal quality. First, in linear base station layouts, the coefficient matrix of the positioning model is prone to singularities, leading to algorithm non-convergence or inability to solve, directly affecting the reliability of the positioning results. Second, when the geometry is poor (e.g., high positioning accuracy factor PDOP) or environmental noise is high, the positioning accuracy of LLS decreases significantly, making it difficult to meet the high-accuracy requirements of practical applications. Its optimized versions, such as weighted linear least squares (WLS), introduce complex weight adjustment processes, significantly increasing computational complexity and slowing down the solution speed, making them unsuitable for scenarios with a large number of base stations or requiring real-time response. Furthermore, some low-complexity optimization algorithms, while reducing computational costs, still suffer from unsatisfactory positioning accuracy in high-noise environments.

[0006] To address the aforementioned problems, this invention proposes a linear base station array positioning method based on geometric modeling. Compared with existing methods, this invention innovatively combines the trigonometric cosine theorem and inequalities from geometry, utilizing these geometric properties to generate preliminary positioning results. This avoids dependence on matrix inversion, effectively circumventing the convergence problem caused by the singularity of the coefficient matrix in linear base station layout. Furthermore, by designing an improved Cramer-Rao lower bound (CRLB) weighting strategy, this method weights and combines multiple preliminary positioning results, further improving positioning accuracy and robustness. As a closed-form solution method, this method has significant computational efficiency advantages, enabling rapid positioning solutions. It is particularly suitable for intelligent streetlight positioning systems in smart cities and complex application scenarios such as mines and tunnels, meeting the requirements for real-time performance and high accuracy. Summary of the Invention

[0007] In the TDOA positioning model, 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 (x, y, 0) represents the location coordinates of the i-th base station, and (x, y, 0) represents the location coordinates of the 2D target to be determined. 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] To address the issues of convergence or inability to solve traditional LLS and WLS methods when the coefficient matrix A is not of full rank or is singular in linear base station scenarios, and the shortcomings of existing methods in terms of positioning accuracy and computational efficiency, this invention provides a TDOA positioning method suitable for base station arrays with linear arrangements. By optimizing geometric modeling and algorithm design, positioning accuracy can be improved and system robustness enhanced, making it applicable to various complex scenarios such as smart street light systems in smart cities, mines, and tunnels.

[0013] The method includes:

[0014] Step 1: Based on the linear base station array with known location coordinates, receive signals and collect the signal arrival time difference between the target and each base station in real time;

[0015] Step 2 involves selecting different base station combinations and, based on the geometric characteristics of the linear base station array, constraining the rationality of geometric distance measurement using the triangle inequality. This constructs a dynamic correction model for ranging errors, thereby reducing the impact of equipment deviations and signal interference. Specifically, a base station combination refers to randomly selecting three base stations from all available base stations to form a group. Each combination yields a positioning solution, providing a foundation for subsequent optimization and improvement of positioning accuracy.

[0016] Step 3: Based on the environmental characteristics of the linear base station array, geometric modeling is performed for each base station combination using the trigonometric cosine theorem. Based on the relative positional relationship between the target location and the base stations, preliminary positioning results are generated for each base station combination.

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

[0018] Preferably, three base stations are selected from all base stations in the linear base station array, based on optimization of the relative positions and signal quality of the base stations, thereby avoiding computational instability caused by base station positions to a certain extent. During the base station selection process, this invention uses a weighted evaluation algorithm, combining actual measurements and distances between base stations, to select base station combinations for error correction, thus significantly improving the reliability of positioning.

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

[0020] Preferably, 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 formula for the Cramer-Rao lower bound. A CRLB weighted average method is used to weight each preliminary positioning result to ensure that high-quality positioning results are given priority. By optimizing the weighted results, this invention can effectively improve positioning accuracy while reducing errors caused by low-quality signals.

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

[0022] When base stations are linearly arranged, this invention significantly improves positioning accuracy through innovative geometric modeling and algorithm optimization, effectively avoiding the defects of inaccurate positioning and system instability caused by singular matrix problems. Simultaneously, an improved Cramer-Rao lower bound weighted average method is used to weight and optimize the positioning results, further improving positioning accuracy. Compared with traditional methods, this invention significantly enhances the stability and reliability of the system in various environments by dynamically selecting base station combinations and combining them with weighted evaluation. Especially in environments with limited GNSS signals, such as urban canyons and densely wooded areas, it can fully utilize the cellular signals in the smart streetlight system for accurate positioning. As a closed-form solution method, this invention has a significant computational efficiency advantage compared to traditional iterative methods, enabling rapid positioning solutions. Furthermore, this invention has strong adaptability; besides its application in smart streetlight systems in smart cities, it can also be widely applied in special environments such as mines and tunnels, demonstrating good environmental adaptability and broad application prospects. Attached Figure Description

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

[0024] Figure 2 This is a flowchart of TDOA positioning under a linear base station array provided by the present invention;

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

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

[0027] Figure 5 This invention provides Figure 4 Enlarged view of the orange section;

[0028] Figure 6 This is a schematic diagram of the base station 1 provided by the present invention located at any end of a selected combination of three base stations; Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0030] In this embodiment, a TDOA positioning method suitable for linear base station arrays is provided. The positioning principle block diagram is shown below. Figure 1 See the algorithm flowchart. 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 in a straight line, and the target device can receive signals from these base stations. The time difference of arrival of the signal between each base station and the target is measured and recorded. The relative position of each base station is known, and the target's positioning information can be estimated using these known positions.

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

[0034] Due to the unique arrangement of base stations, a schematic diagram of the TDOA positioning for a linear base station array is shown below. Figure 3 In this embodiment, three base stations are randomly selected from N base stations for combination, i.e. M represents a total of M possible combinations. The initial target location is calculated using different combinations of three base stations. Based on known geometric relationships, and according to the triangle inequality theorem (the sum of any two sides is greater than the third side) and the Pythagorean theorem (the hypotenuse is greater than the legs), the following system of inequalities can be obtained.

[0035]

[0036] Where b 12 b 13 R1 represents the distance between base station 1 and base station 2, and base station 3 respectively; R1 represents the distance between the target and base station 1, and d 21 d 31 These represent the distance difference, 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 [the image]. We obtain the following results:

[0039]

[0040] d′ 21 This represents the distance difference after calibration error, where δ is an adjustable hyperparameter.

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

[0042] Geometric modeling is performed using the trigonometric cosine theorem, based on the relative positional relationship between the target location and the base station (see...). Figure 4 , Figure 5 ), calculate the positioning results for each three-base station combination.

[0043]

[0044] Obtain the estimated value of R1.

[0045]

[0046] When base station BS1 is located at either end of the linear array, such as Figure 6 As shown. Similar to the previous scenario, at this time... Estimated as

[0047]

[0048] Based on the obtained The relationship with other distances can be obtained

[0049]

[0050] Based on the above formula, the initial positioning result for this combination is obtained.

[0051]

[0052] 4. Weighted average method optimization of positioning results:

[0053] When the number of base stations is greater than 3, a weighted average method with 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.

[0054]

[0055] Weights set to

[0056]

[0057] When the j-th combination When the value is greater than the threshold T, the weight is set to 0 to filter the data. Base station combinations with excessively large values ​​are excluded. This method helps to eliminate base stations with excessively large errors, improving the robustness of the results.

[0058] in The distances between base stations 2 and 3 and the target can be calculated from the previous information.

[0059] Let be the covariance matrix of empirical measurement errors.

[0060] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A linear base station array positioning method based on geometric modeling, characterized in that, Includes the following steps: Step 1: Based on the linear base station array with known location coordinates, receive signals and collect the time difference of arrival (TDOA) between the target and each base station in real time. Step 2: By selecting different base station combinations and combining the geometric characteristics of the linear base station array, a dynamic correction model for ranging error is constructed to reduce the impact of equipment deviation and signal interference. Here, base station combination refers to randomly selecting three base stations from all base stations to form a group. Under each combination, a positioning solution can be obtained, which provides a basis for subsequent optimization and improvement of positioning accuracy. Step 3: Based on the environmental characteristics of the linear base station array, geometric modeling is performed for each base station combination using the trigonometric cosine theorem. According to the relative positional relationship between the target location and the base stations, preliminary positioning results are generated for each base station combination. Step 4: By designing an improved Cramer-Rao lower bound (CRLB) weighting strategy, the fusion method of multiple combined localization results is optimized, and finally a more robust localization result is obtained.

2. The method according to claim 1, characterized in that, The linear base station array with known location coordinates mentioned in step 1 means that 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 results based on the time difference have a unique solution in the positioning process.

3. The method according to claim 1, characterized in that, Different base station combinations, based on modified ranging, yield corresponding preliminary positioning results using the trigonometric cosine theorem: cosθ1+cosθ2=0, Among them, b 12 b 13 d represents the distance between base station 1 and base station 2 and base station 3, respectively; 21 d 31 θ1 represents the distance difference between the target and base stations 1 and 2, and between base stations 1 and 3, respectively; θ2 represents the angle between the direction from base station 1 to base station 2 and the direction from base station 1 to the target; based on the calculated distance R1 between the target and base station 1, a preliminary positioning result is obtained.

4. The method according to claim 1, characterized in that, The Cramer-Rao lower bound weighted average method was used to analyze all preliminary positioning results. By performing weighted combinations, the final positioning result is obtained. Set one Threshold T, where w j Represented as

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