Wireless terminal positioning method based on multi-characteristic polynomial fitting

Abstract

The application relates to a wireless terminal positioning method based on multi-feature polynomial fitting. The method comprises the following steps: dividing a target area into a grid, acquiring multi-dimensional features such as propagation time delay, signal strength and angle of arrival for each grid center point, and constructing a multi-feature grid database. The measured multi-dimensional features of a terminal are collected, the joint distance of the terminal with each grid in the database is calculated, and the grid with the minimum distance is taken as an initial matching grid. A local neighborhood is selected with the grid as the center, and a polynomial fitting model is constructed by using the grid data in the neighborhood. The measured features are substituted into the model, a multi-feature joint target function is constructed and optimized, and finally continuous and high-precision estimated position coordinates are obtained. The method can realize high-precision and high-robustness user positioning.

Description

Technical Field

[0001] This application relates to the field of wireless communication positioning technology, and in particular to a wireless terminal positioning method based on multi-feature polynomial fitting. Background Technology

[0002] With the widespread adoption of 5G, the Internet of Things (IoT), and smart terminals, location-based services have become one of the core infrastructures of modern information society. Scenarios such as public safety, intelligent transportation, unmanned system control, industrial internet, and emergency search and rescue place increasingly higher demands on the accuracy, real-time performance, and reliability of user positioning. Current mainstream positioning technologies mainly include the following categories: Received Signal Strength (RSS)-based positioning, which uses a signal attenuation model to estimate distance; it is simple to implement but has low accuracy and is susceptible to environmental interference. Time of Arrival (TOA) / Time Difference of Arrival (TDOA)-based positioning, which determines distance by measuring signal propagation time or time difference; it has clear physical meaning, high theoretical accuracy, and is the mainstream method for cellular network positioning. Angle of Arrival (AOA)-based positioning, which uses an array antenna to measure the signal's angle of arrival; it requires dedicated hardware and has significant errors in multipath environments. Fingerprint matching positioning methods, which pre-collect location fingerprint features (such as time delay and signal strength) to build a database and achieve positioning through online matching; it has good environmental adaptability.

[0003] However, the aforementioned positioning methods still face the following technical shortcomings in practical deployment: traditional analytical / iterative methods suffer from high computational complexity, sensitivity to initial values, and poor robustness in non-line-of-sight environments; traditional grid fingerprinting methods suffer from difficulty in balancing grid granularity and accuracy, output dispersion due to quantization errors, and insufficient information utilization; existing interpolation methods typically assume that fingerprint features exhibit linear or simple weighted variations in space, failing to accurately characterize the nonlinear spatial distribution of actual propagation delay in complex environments; and most existing grid fingerprinting methods use only a single feature for positioning, making them susceptible to interference in complex environments, resulting in insufficient positioning robustness. Summary of the Invention

[0004] Therefore, it is necessary to provide a wireless terminal positioning method based on multi-feature polynomial fitting that can achieve high accuracy, high robustness, low complexity, and uncertainty estimation capability for user positioning, in order to address the above-mentioned technical problems.

[0005] A wireless terminal localization method based on multi-feature polynomial fitting, the method includes an offline database construction stage and an online localization stage; The offline database building phase includes: The target geographic area is divided into multiple grids, and the center point coordinates of each grid are determined. For each grid center point, obtain its own multidimensional feature value relative to each base station. The multidimensional feature value includes propagation delay feature value, signal strength feature value and angle of arrival feature value. Store the coordinates of all grid center points and their corresponding multidimensional feature values ​​as a multi-feature grid database. The online location phase includes: The measured multidimensional feature values ​​of the terminal to be located relative to each base station are collected. The measured multidimensional feature values ​​include the measured propagation delay feature value, the measured signal strength feature value, and the measured angle of arrival feature value. Calculate the joint distance between the measured multidimensional eigenvalues ​​and the multidimensional eigenvalues ​​of each grid in the multi-feature grid database, and determine the grid with the smallest joint distance as the initial matching grid; Centered on the initial matching grid, select multiple adjacent grids around the initial matching grid to form a local neighborhood; By utilizing the coordinates of each grid center point in the local neighborhood and the corresponding multidimensional feature values, a polynomial fitting model between the multidimensional features and the position coordinates is constructed. The measured multidimensional feature values ​​are substituted into the polynomial fitting model to construct a multi-feature joint objective function. The objective function is then optimized to obtain the estimated position coordinates of the terminal to be located.

[0006] The aforementioned wireless terminal positioning method based on multi-feature polynomial fitting achieves low-complexity real-time positioning by calculating only the joint distance between measured features and finite grid center point features in the coarse positioning stage and constructing a polynomial fitting model only in the local neighborhood in the fine positioning stage. This avoids the high computational overhead of global fine search. Simultaneously, the polynomial fitting model constructs a continuous functional relationship between features and position. Through local nonlinear fitting, a continuous multi-feature spatial surface is constructed within the initial matching grid, which can accurately characterize the spatial changes of each feature, thereby obtaining a more refined positioning result than the grid size. This breaks through the grid resolution limitation and eliminates the "step effect" of traditional grid methods, thus achieving both high accuracy and high efficiency. Secondly, the system deeply integrates three complementary physical features: propagation delay, signal strength, and angle of arrival. In the coarse matching stage, similarity is comprehensively evaluated through a weighted multi-feature joint distance. In the fine localization stage, the fitting error of all features is simultaneously optimized through a multi-feature joint objective function. This allows the system to automatically balance the contribution of each feature. Even if one feature is severely distorted in complex environments, other features can still provide effective constraints, significantly enhancing its resistance to interference such as multipath interference, occlusion, and NLOS. Furthermore, the system incorporates information from multiple neighboring grids for joint fitting, effectively reducing the impact of database construction errors or measurement noise from a single base station through least-squares smoothing. In addition, the multi-feature grid database generated offline in this application can be used long-term, requiring only table lookups and simple matrix operations in the online stage, making it suitable for embedded or cloud deployment. Feature weights and base station weights can be dynamically adjusted according to the environment, and grid size and fitting order can be adaptively selected based on regional characteristics. It supports expansion to 3D localization and has good engineering feasibility and scene adaptability. Attached Figure Description

[0007] Figure 1 This is a flowchart illustrating a wireless terminal positioning method based on multi-feature polynomial fitting in one embodiment. Figure 2 This is a flowchart illustrating the offline database creation phase in one embodiment; Figure 3 This is a schematic diagram illustrating the grid division method of the target region and the selection of local neighborhoods in one embodiment. Detailed Implementation

[0008] 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.

[0009] In one embodiment, such as Figure 1 As shown, a wireless terminal positioning method based on multi-feature polynomial fitting is provided, which includes an offline database construction stage and an online positioning stage. The offline database building phase includes: Step 102: Divide the target geographic area into multiple grids and determine the center point coordinates for each grid.

[0010] like Figure 2 As shown, this is the offline database construction stage, where the target geographic area to be located is divided into a uniform grid according to a preset granularity. The grid shape can be square, rectangular, or hexagonal; a square grid is preferred for simplifying calculations and facilitating spatial indexing. The grid side length is set to... Divide the area into There are 1 grid, each grid is defined by the coordinates of its center point. Identification. For scenarios requiring 3D positioning (such as drones, indoor floors), it can be expanded into a 3D cubic mesh, with the center point being... .

[0011] Step 104: For each grid center point, obtain its multidimensional feature value relative to each base station. The multidimensional feature value includes propagation delay feature value, signal strength feature value and angle of arrival feature value. Store the coordinates of all grid center points and their corresponding multidimensional feature values ​​as a multi-feature grid database.

[0012] Obtain the location coordinates of all base stations in this area, assuming there are a total of There are 1 base station, and their coordinates are as follows: , For each grid center point Collect or calculate the following multidimensional features: Propagation Time Delay (TOA): Calculates the distance from the grid center point to each base station. Theoretical propagation delay: ; in, For Euclidean distance, It is the speed of light.

[0013] Signal Strength Characteristics (RSSI): Obtain the signal received from each base station at the grid center point using propagation models (such as the Cost-231 Hata model, ray tracing simulation) or actual drive tests. signal strength value (Unit: dBm). Theoretical formulas combined with environmental correction factors can also be used for calculation.

[0014] Angle of Arrival (AOA): If the base station is equipped with an array antenna, the grid center point relative to each base station can be calculated. The angle of arrival. For two-dimensional positioning, this includes the azimuth angle. For three-dimensional positioning, pitch angle is also included. It can be derived through geometric relationships: ; Considering the periodicity of the angle, normalize to or .

[0015] Other optional features include: statistics of channel state information (CSI) such as delay spread, angle spread, channel correlation, etc., round-trip time (RTT), and reference signal reception quality (RSRQ).

[0016] The above calculation results are structured and stored to form a "multi-feature spatiotemporal grid fingerprint database". Each data record includes: grid ID, grid center point coordinates. Delay feature vector Signal strength feature vector , Angle of arrival eigenvector This database can be generated offline and used long-term, and supports regular updates to reflect environmental changes.

[0017] The online location phase includes: Step 106: Collect the measured multidimensional feature values ​​of the terminal to be located relative to each base station. The measured multidimensional feature values ​​include the measured propagation delay feature value, the measured signal strength feature value, and the measured angle of arrival feature value.

[0018] When a base station system needs to locate a user device, it obtains various characteristics of the user signal reaching each base station through measurement reports submitted by the user or measurements taken by the base station: Time of Arrival (TOA) or Time Difference of Arrival (TDOA); Received Signal Strength (RSSI); Angle of Arrival (AOA) (if supported by the terminal or base station), and other available characteristics. After acquisition, the delay measurement values ​​are time-synchronized and error-corrected; the RSSI values ​​are filtered and smoothed to eliminate instantaneous fluctuations; and the angle measurement values ​​are periodically processed to ensure they are within the effective range, filtering out obvious outliers and identifying and marking unreliable measurements. This forms a set of user-measured characteristics: a delay vector. Signal strength vector , arrival angle vector For base stations that are not measured or have a low signal-to-noise ratio, their corresponding components can be set to invalid values ​​and ignored or assigned lower weights in subsequent processing.

[0019] Step 108: Calculate the joint distance between the measured multidimensional feature values ​​and the multidimensional feature values ​​of each grid in the multi-feature grid database, and determine the grid with the smallest joint distance as the initial matching grid.

[0020] Because different features have different dimensions and numerical ranges (e.g., latency is in nanoseconds, RSSI is in dBm, and angle is in radians), normalization is required to ensure comparability in distance calculations. Z-score normalization or min-max normalization can be used to ensure that the numerical range is within [0,1]. The similarity between the user's measured feature vector and the feature vectors of all grids in the offline database is calculated, using a weighted multi-feature joint distance as the matching metric. All grids in the database are traversed (or quickly filtered using spatial indexing), and the joint distance of each grid is calculated. The grid with the smallest joint distance is selected as the initial matching grid, denoted as grid . Its center point is This step allows for rapid narrowing of the search area, locking the user's location within a grid-sized neighborhood.

[0021] Step 110: Using the initial matching grid as the center, select multiple adjacent grids around the initial matching grid to form a local neighborhood.

[0022] With initial matching grid Centered on a given area, a local neighborhood is formed by selecting adjacent grid cells. A typical selection method is a 3×3 neighborhood. The local area consists of either a 9-grid region (including the base stations above, below, left, right, and four corners) or a 5×5 neighborhood (25 grids in total; if the base stations are densely distributed or the environment is complex, the number of grids can be increased to 25 to increase the number of fitted samples). The specific size can be adjusted according to the base station density and environmental complexity. Let the set of grid center points in this local area be... ( (to ensure that the fit has a solution).

[0023] Step 112: Using the coordinates of each grid center point in the local neighborhood and the corresponding multidimensional feature values, construct a polynomial fitting model between the multidimensional features and the position coordinates.

[0024] Within a small local area, each feature (time delay, RSSI, AOA, etc.) is considered to be related to the location coordinates. There exists a continuous and smooth functional relationship, which can be approximated using a bivariate polynomial. For each base station For each feature, an independent fitting model is established. The polynomial order can be adaptively selected based on the number of neighborhood grid cells: if Use quadratic fitting; if Linear fitting (retaining only the constant and first-order terms) is used to prevent overfitting. For 3D positioning scenarios, this can be expanded to a ternary quadratic polynomial. For each base station... Each feature, utilizing the local area Known grid points Based on the corresponding eigenvalues, establish the coefficients for solving the least squares problem. Taking time delay features as an example, construct the matrix: ; By solving the normal equation Obtain the coefficient vector To enhance numerical stability, QR decomposition or singular value decomposition (SVD) can be used to solve the problem.

[0025] Step 114: Substitute the measured multidimensional feature values ​​into the multinomial fitting model to construct a multi-feature joint objective function, and optimize the objective function to obtain the estimated position coordinates of the terminal to be located.

[0026] After obtaining the fitting polynomial for each feature of each base station, the user location... The fitted values ​​of each feature should be as consistent as possible with the measured values. Construct a joint objective function for multiple features, which is about... The multivariate function typically exhibits unimodal characteristics within small local regions. The solution can be obtained through numerical optimization or mesh refinement search. The solution will then... As the user's final estimated location output, the location is a continuous coordinate system with sub-grid accuracy and incorporates multiple feature information.

[0027] The aforementioned wireless terminal positioning method based on multi-feature polynomial fitting achieves low-complexity real-time positioning by calculating only the joint distance between measured features and finite grid center point features in the coarse positioning stage and constructing a polynomial fitting model only in the local neighborhood in the fine positioning stage. This avoids the high computational overhead of global fine search. Simultaneously, the polynomial fitting model constructs a continuous functional relationship between features and position. Through local nonlinear fitting, a continuous multi-feature spatial surface is constructed within the initial matching grid, which can accurately characterize the spatial changes of each feature, thereby obtaining a more refined positioning result than the grid size. This breaks through the grid resolution limitation and eliminates the "step effect" of traditional grid methods, thus achieving both high accuracy and high efficiency. Secondly, the system deeply integrates three complementary physical features: propagation delay, signal strength, and angle of arrival. In the coarse matching stage, similarity is comprehensively evaluated through a weighted multi-feature joint distance. In the fine localization stage, the fitting error of all features is simultaneously optimized through a multi-feature joint objective function. This allows the system to automatically balance the contribution of each feature. Even if one feature is severely distorted in complex environments, other features can still provide effective constraints, significantly enhancing its resistance to interference such as multipath interference, occlusion, and NLOS. Furthermore, the system incorporates information from multiple neighboring grids for joint fitting, effectively reducing the impact of database construction errors or measurement noise from a single base station through least-squares smoothing. In addition, the multi-feature grid database generated offline in this application can be used long-term, requiring only table lookups and simple matrix operations in the online stage, making it suitable for embedded or cloud deployment. Feature weights and base station weights can be dynamically adjusted according to the environment, and grid size and fitting order can be adaptively selected based on regional characteristics. It supports expansion to 3D localization and has good engineering feasibility and scene adaptability.

[0028] In one embodiment, the joint distance calculation is performed between the measured multidimensional feature values ​​and the multidimensional feature values ​​of each grid stored in the multi-feature grid database, including: Read the propagation delay feature vector, signal strength feature vector, and angle of arrival feature vector of each grid from the multi-feature grid database, and calculate the time delay feature distance between the measured propagation delay feature vector and the propagation delay feature vector of the grid in the database, the signal strength feature distance between the measured signal strength feature vector and the signal strength feature vector of the grid in the database, and the angle of arrival feature distance between the measured angle of arrival feature vector and the angle of arrival feature vector of the grid in the database, respectively. The joint distance is obtained by weighting and summing the time delay characteristic distance, signal strength characteristic distance, and angle of arrival characteristic distance.

[0029] Specifically, this embodiment calculates the weighted distances of the three features separately and then performs a weighted summation. This fully utilizes the complementarity of different features in the environment. The time delay has high accuracy in line-of-sight environments, RSSI provides additional constraints in NLOS environments, and AOA provides directional information. By jointly weighting the distances of multiple features, the system can automatically balance the contributions of each feature, significantly enhancing its resistance to interference from multipath, occlusion, and NLOS, and improving the accuracy of coarse matching.

[0030] In one embodiment, the time delay feature distance is: ; in, Indicates the base station index. , Indicates base station Delay weighting, This represents the normalized measured time delay value. This represents the normalized grid delay value read from the multi-feature grid database.

[0031] Specifically, this embodiment provides a specific formula for calculating the time delay feature distance, using a weighted Euclidean distance to measure the similarity between the measured time delay vector and the grid time delay vector. Base station-level weights can be dynamically set based on real-time signal quality (such as RSRP and signal-to-noise ratio) to reflect the reliability of each base station's measurements, thereby improving the accuracy of distance measurement.

[0032] In one embodiment, the signal strength characteristic distance is: ; in, Indicates base station Signal strength weights, This represents the normalized measured signal strength value. This represents the normalized grid signal strength value read from a multi-feature grid database.

[0033] In one embodiment, the distance to the angular feature is: ; in, , Indicates base station The angle of arrival weight, Indicates the terminal relative to the base station The measured angle of arrival value after normalization. This represents a mesh read from a multi-feature mesh database. Relative to base station The angle of arrival feature is the normalized mesh angle of arrival value.

[0034] In one embodiment, the time delay feature distance, signal strength feature distance, and angle of arrival feature distance are weighted and summed to obtain the joint distance, including: The joint distance is obtained by weighting and summing the time delay feature distance, signal strength feature distance, and angle of arrival feature distance. ; in, For feature weights, For time delay feature distance, For signal strength characteristic distance, For the angular feature distance, Distance to other optional features.

[0035] Specifically, feature weights can be dynamically adjusted based on prior environmental information, and base station-level weights can be dynamically set based on real-time signal quality. Through multi-feature weighted fusion, the system can adapt to different environments, improving the robustness and accuracy of coarse matching. Other optional features include statistics of channel state information (CSI) (delay spread, angle spread, channel correlation, etc.), round-trip time (RTT), and reference signal reception quality (RSRQ).

[0036] In one embodiment, a multinomial fitting model is established for each feature of each base station, including a delay feature fitting model, an RSSI feature fitting model, and an AOA feature fitting model. The time delay feature fitting model is as follows: ; in, Indicates position Location relative to base station The propagation delay fitting value, , , , , , The coefficients are polynomials, obtained by least-squares solution using the coordinates of the center points of each grid in the local neighborhood dataset and their corresponding propagation delay eigenvalues. The RSSI feature fitting model is ; in, Indicates position Location relative to base station The fitted value of the signal strength. , , , , , The coefficients are polynomials, obtained by least-squares calculation using the coordinates of the center points of each grid in the local neighborhood dataset and their corresponding signal strength features. The AOA feature fitting model is ; in, Indicates position Location relative to base station The angle of arrival fitted value, , , , , , The coefficients are polynomials, obtained by least-squares calculation using the coordinates of the center points of each grid in the local neighborhood dataset and their corresponding angle-of-arrival eigenvalues.

[0037] Specifically, this embodiment uses a bivariate quadratic polynomial to locally fit each feature. Within a small local area, there exists a continuous and smooth functional relationship between the feature and its position coordinates, which the bivariate quadratic polynomial can approximate well. By solving the polynomial coefficients using least squares, a mapping model between the feature and its position is constructed. For 3D localization scenarios, this can be extended to a ternary quadratic polynomial. This modeling method can accurately characterize the nonlinear changes of each feature in space, laying the foundation for subsequent precise localization.

[0038] In one embodiment, the joint objective function for multiple features is: ; in, , , These represent the measured propagation delay, measured signal strength, and measured angle of arrival, respectively. The feature-level weights represent the time delay characteristics. Indicates base station Delay measurement weights, This indicates the total number of base stations participating in the positioning process. The feature-level weights represent the signal strength characteristics. Indicates base station Signal strength measurement weights The feature level weights represent the angle of arrival features. Indicates base station The weight of the angle of arrival measurement.

[0039] Specifically, this embodiment constructs a multi-feature joint objective function, and the optimal user location is solved by minimizing this objective function. This objective function consists of three weighted sums of squares: the delay term calculates the square of the difference between the fitted and measured delay values ​​of all base stations, sums them according to the base station weights, and then multiplies by the delay feature weights; the signal strength term and the angle of arrival term are calculated similarly. By minimizing this objective function, the user location that achieves the optimal fit of all features can be found. The objective function typically exhibits a unimodal characteristic within a small local region, and can be solved using the Gauss-Newton method or by mesh refinement search.

[0040] In one embodiment, constructing the polynomial fitting model further includes: The polynomial order is adaptively selected based on the number of grids in the local neighborhood dataset. If the number of grids in the local neighborhood dataset A quadratic fitting is used; if Linear fitting was used.

[0041] Specifically, in this embodiment, the polynomial order is adaptively selected based on the number of neighboring grid cells to prevent overfitting. When the number of neighboring grid cells is large ( Using quadratic fitting can more accurately characterize the spatial variations of features; when the number of neighborhood grids is small ( Linear fitting (keeping only constant and linear terms) is used to ensure the stability and generalization ability of the fit.

[0042] In one embodiment, a local neighborhood is formed by selecting multiple adjacent grids around the initial matching grid as the center, including: Centered on the initial matching grid, extract the surrounding features of the initial matching grid from the multi-feature grid database. Neighborhood or The coordinates of the center points of all grids within the neighborhood and their corresponding multidimensional feature values ​​constitute the local neighborhood.

[0043] Specifically, this embodiment provides a specific method for selecting local neighborhoods. Using an initial matching grid... Centered on a given location, a local neighborhood region is formed by selecting adjacent grid cells. A typical selection method is... Neighborhood ( (including the top, bottom, left, right, and four corner grids, totaling 9 grids) or The neighborhood (25 grids in total) can be expanded to 25 grids if the base stations are densely distributed or the environment is complex. The specific size can be adjusted according to the base station density and environmental complexity. Figure 3 The diagram illustrates the grid division method for the target region and the selection of local neighborhoods. Using a square grid as an example, the diagram shows the global grid layout and highlights the initial matching grid. The positional relationship between the grid and its surrounding 3×3 neighborhood grid is used to intuitively understand the spatial concept of "coarse positioning to lock the range and fine positioning to utilize the neighborhood".

[0044] In a specific embodiment, assume that there are 8 5G macro base stations deployed in the central area of ​​a city, and the coordinates of the base stations are known (unit: meters). The target positioning area is a rectangular area of ​​2km × 2km, including complex environments such as high-rise buildings, streets, and canyons, where the NLOS phenomenon is common. If the grid side length is set to 50 meters, then the number of grids is 40 × 40 = 1600.

[0045] Offline phase: Construction of a multi-feature fingerprint database: Calculate the following characteristics from each grid center point to the 8 base stations: a) Time Delay Feature (TOA): Based on geometric distance divided by the speed of light ( Calculated in m / s, unit: nanosecond.

[0046] b) Signal strength characteristics (RSSI): Calculated using the Cost-231 Hata propagation model combined with urban environmental correction factors, and random noise was added to simulate measured fluctuations. Unit: dBm.

[0047] c) Angle of Arrival (AOA): The azimuth angle is calculated based on geometric relationships and normalized to... , Unit: radians.

[0048] A 1600×(8×3) multi-feature database was constructed, with each record containing the grid center coordinates, latency of 8 base stations, RSSI, and AOA values. Z-score normalization was performed on each feature, and the normalization parameters (mean and standard deviation) were saved.

[0049] User Measurement: A user device initiates a location request in a street canyon, measuring the TOA, RSSI, and AOA values ​​of 6 base stations with relatively good signal strength (the other 2 base stations had weak signals, so their weights were reset to zero). After correction, the measured feature vector (original value) is obtained: a) Delay vector (ns): ; b) RSSI vector (dBm): ; c) AOA vector (radians):

[0050] Assuming the signal quality of these six base stations is comparable, each base station is assigned a weight of 1. Based on prior environmental information (urban canyon, high NLOS), feature weights are set accordingly. .

[0051] Feature normalization: Using the mean and standard deviation of offline database statistics, the measured features and database features are normalized to obtain the normalized feature vector. and database .

[0052] Coarse localization using multi-feature joint mesh matching: calculation Weighted joint distance with the normalized feature vectors of all 1600 grids in the database By traversing the grid, the grid with the smallest joint distance is found, whose center point coordinates are (350, 450) (in meters). This grid is denoted as [Grid Name]. .

[0053] Local polynomial fitting for precise localization: taking It includes 8 adjacent grids (3×3 neighborhoods), for a total of 9 grids.

[0054] For each base station For each feature, a bivariate quadratic polynomial fitting model was established, and the coefficients were solved. A joint objective function was constructed, and a mesh refinement search (step size 1 meter) was used to obtain the optimal position (351.6, 449.3). Compared with the true position (351.2, 449.8), the error was 0.7 meters.

[0055] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but may be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0056] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0057] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. 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 modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A wireless terminal positioning method based on multi-feature polynomial fitting, characterized in that, The method includes an offline database construction phase and an online location phase; The offline database construction phase includes: The target geographic area is divided into multiple grids, and the center point coordinates of each grid are determined. For each grid center point, obtain its own multi-dimensional feature value relative to each base station. The multi-dimensional feature value includes propagation delay feature value, signal strength feature value and angle of arrival feature value. Store the coordinates of all grid center points and their corresponding multi-dimensional feature values ​​as a multi-feature grid database. The online positioning phase includes: The measured multidimensional feature values ​​of the terminal to be located relative to each base station are collected. The measured multidimensional feature values ​​include measured propagation delay feature values, measured signal strength feature values, and measured angle of arrival feature values. Calculate the joint distance between the measured multidimensional feature values ​​and the multidimensional feature values ​​of each grid in the multi-feature grid database, and determine the grid with the smallest joint distance as the initial matching grid; Centered on the initial matching grid, multiple adjacent grids around the initial matching grid are selected to form a local neighborhood; Using the coordinates of each grid center point in the local neighborhood and the corresponding multidimensional feature values, a multinomial fitting model between the multidimensional features and the position coordinates is constructed. The measured multidimensional feature values ​​are substituted into the polynomial fitting model to construct a multi-feature joint objective function, and the objective function is optimized to obtain the estimated position coordinates of the terminal to be located.

2. The method according to claim 1, characterized in that, The joint distance calculation is performed between the measured multidimensional feature values ​​and the multidimensional feature values ​​of each grid stored in the multi-feature grid database, including: Read the propagation delay feature vector, signal strength feature vector, and angle of arrival feature vector of each grid from the multi-feature grid database, and calculate the time delay feature distance between the measured propagation delay feature vector and the propagation delay feature vector of the grid in the database, the signal strength feature distance between the measured signal strength feature vector and the signal strength feature vector of the grid in the database, and the angle of arrival feature distance between the measured angle of arrival feature vector and the angle of arrival feature vector of the grid in the database, respectively. The joint distance is obtained by weighted summation of the time delay feature distance, signal strength feature distance, and angle of arrival feature distance.

3. The method according to claim 2, characterized in that, The time delay feature distance is: ； in, Indicates the base station index. , Indicates base station Delay weighting, This represents the normalized measured time delay value. This represents the normalized grid delay value read from the multi-feature grid database.

4. The method according to claim 2, characterized in that, The signal strength characteristic distance is: ； in, Indicates base station Signal strength weights, This represents the normalized measured signal strength value. This represents the normalized grid signal strength value read from the multi-feature grid database.

5. The method according to claim 2, characterized in that, The arrival angle feature distance is: ； in, , Indicates base station The angle of arrival weight, Indicates the terminal relative to the base station The measured angle of arrival value after normalization. This represents the mesh read from a multi-feature mesh database. Relative to base station The angle of arrival feature is the normalized mesh angle of arrival value.

6. The method according to claim 2, characterized in that, The joint distance is obtained by weighted summation of the time delay feature distance, signal strength feature distance, and angle of arrival feature distance, including: The joint distance is obtained by weighted summing of the time delay feature distance, signal strength feature distance, and angle of arrival feature distance: ； in, For feature weights, For time delay feature distance, For signal strength characteristic distance, For the angular feature distance, Distance to other optional features.

7. The method according to claim 1, characterized in that, The polynomial fitting model is established for each feature of each base station, including a delay feature fitting model, an RSSI feature fitting model, and an AOA feature fitting model. The time delay feature fitting model is as follows: ； in, Indicates position Location relative to base station The propagation delay fitting value, , , , , , The coefficients are polynomials, obtained by least-squares solution using the coordinates of the center points of each grid in the local neighborhood dataset and their corresponding propagation delay eigenvalues. The RSSI feature fitting model is as follows: ； in, Indicates position Location relative to base station The fitted value of the signal strength. , , , , , The coefficients are polynomials, obtained by least-squares solution using the coordinates of the center points of each grid in the local neighborhood dataset and their corresponding signal strength feature values. The AOA feature fitting model is as follows: ； in, Indicates position Location relative to base station The angle of arrival fitted value, , , , , , The coefficients are polynomials, obtained by least-squares calculation using the coordinates of the center points of each grid in the local neighborhood dataset and their corresponding angle-of-arrival eigenvalues.

8. The method according to claim 1, characterized in that, The joint objective function for the multiple features is: ; in, , , These represent the measured propagation delay, measured signal strength, and measured angle of arrival, respectively. The feature-level weights represent the time delay characteristics. Indicates base station Delay measurement weights, This indicates the total number of base stations participating in the positioning process. The feature-level weights represent the signal strength characteristics. Indicates base station Signal strength measurement weights The feature level weights represent the angle of arrival features. Indicates base station The weight of the angle of arrival measurement.

9. The method according to claim 7, characterized in that, When constructing the polynomial fitting model, the following is also included: The polynomial order is adaptively selected based on the number of grids in the local neighborhood dataset. If the number of grids in the local neighborhood dataset A quadratic fitting is used; if Linear fitting was used.

10. The method according to claim 1, characterized in that, Centered on the initial matching grid, a local neighborhood is formed by selecting multiple adjacent grids around the initial matching grid, including: Centered on the initial matching grid, extract the surrounding features of the initial matching grid from the multi-feature grid database. Neighborhood or The coordinates of the center points of all grids within the neighborhood and their corresponding multidimensional feature values ​​constitute the local neighborhood.

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