A wi-fi precise time measurement double-terminal cooperative positioning method based on error correction and fingerprint matching constraint

Abstract

The application discloses a Wi-Fi precise time measurement double-terminal cooperative positioning method based on error correction and fingerprint matching constraint, which comprises the following steps: in an offline stage, a basic fingerprint database containing position information and angle information is constructed; in a single-point positioning stage, systematic error correction is performed on Wi-Fi precise time measurement original ranging values collected by double terminals to obtain initial positioning results; in a time matching stage, observation epochs of the double terminals are matched based on coordinated universal time to obtain synchronized observation data; in a fingerprint matching stage, double fingerprint matching is performed based on the initial positioning results and the fingerprint database to estimate real-time distances between the double terminals; in a cooperative positioning stage, the real-time distances are taken as geometric constraints, combined observation equations are constructed with the corrected ranging values, and the double-terminal final cooperative positioning results are solved. Through error correction, the single-point positioning precision is improved, distance constraints between the terminals are constructed by using angle fingerprint matching, and high-precision, low-cost and low-power indoor cooperative positioning is realized.

Description

Technical Field

[0001] This invention belongs to the field of indoor positioning technology, specifically relating to a dual-terminal collaborative positioning method based on error correction and fingerprint matching constraints using precise time measurement via Wi-Fi. Background Technology

[0002] With the rapid development of the Internet of Things (IoT), numerous scenarios, such as indoor navigation in large shopping malls, refined equipment management in smart factories, and positioning of medical equipment and patient monitoring, are continuously increasing their demands for the accuracy and reliability of indoor location information. However, global navigation satellite system (GNSS) signals are easily blocked, reflected, and refracted by buildings in indoor environments, making stable positioning impossible and failing to meet the usage requirements of various indoor scenarios. Therefore, the research and application of high-precision indoor positioning technology has become a key focus of the industry.

[0003] To fill the gap in indoor positioning capabilities of global navigation satellite systems, researchers both domestically and internationally have conducted extensive research on various indoor positioning technologies. The mainstream technologies can be categorized into five main types: wireless signal positioning, geomagnetic positioning, physical quantity sensing positioning, visual positioning, and multi-technology fusion positioning. Among these, Wi-Fi precise time measurement positioning technology based on the IEEE 802.11mc protocol, and the multi-terminal collaborative positioning scheme derived from it, can effectively improve the low positioning accuracy caused by traditional Wi-Fi signal strength reception. It possesses core advantages such as requiring no dedicated equipment, strong adaptability, and low deployment costs.

[0004] While existing research on precise time measurement via Wi-Fi has yielded some results, it cannot overcome the performance limitations of a single terminal. Currently, there are two main technical approaches: differential positioning and cooperative positioning. Differential positioning traditionally eliminates common errors such as environmental and clock errors by deploying reference terminals or access points, but its implementation relies on a high density of reference nodes. Cooperative positioning improves positioning results through relative observation or information exchange between multiple terminals, and has been validated in fields such as drones and robot swarms. However, existing cooperative solutions rely on dedicated ranging capabilities such as ultra-wideband and Bluetooth round-trip time to achieve relative transfer measurement, resulting in extremely low support on ordinary smartphones and making it difficult to establish low-cost, usable relative position constraints between terminals.

[0005] Meanwhile, the applicant previously proposed a high-precision indoor and outdoor positioning scheme based on Wi-Fi precise time measurement distance estimation. This prior scheme significantly improved the independent positioning accuracy and reliability of a single terminal by systematically modeling and correcting the distance measurement error of precise time measurement. However, this prior scheme only addresses independent positioning of a single terminal and does not involve information fusion, relative constraints, and cooperative positioning mechanisms between multiple terminals. In complex indoor environments such as occlusion, weak signals, and observation geometric differences, the observation performance of a single terminal is still insufficient, and the positioning results still suffer from fluctuations and limitations.

[0006] In summary, the existing technology has the following problems:

[0007] First, Wi-Fi's accurate time measurement and ranging are easily affected by complex indoor environments and differences in terminal hardware, and the error mechanism is unclear and difficult to be effectively corrected.

[0008] Second, the positioning performance of a single terminal drops sharply under adverse observation conditions such as obstruction and weak signal.

[0009] Third, multi-technology fusion positioning solutions cannot simultaneously meet the comprehensive requirements of accuracy, cost, and power consumption;

[0010] Fourth, traditional differential positioning solutions have high deployment costs and weak dynamic adaptability to the environment;

[0011] Fifth, the Wi-Fi precise time measurement system lacks a feasible multi-terminal collaborative positioning method, thus failing to fully realize its positioning potential. Summary of the Invention

[0012] This invention addresses the challenges of modeling and correcting ranging errors in Wi-Fi precise time measurement caused by complex indoor environments and differences in terminal hardware, resulting in limited positioning accuracy and stability. It proposes a dual-terminal collaborative positioning method based on error correction and fingerprint matching constraints using Wi-Fi precise time measurement. This method fully utilizes existing Wi-Fi precise time measurement infrastructure and the native precise time measurement capabilities of smartphones to achieve high-precision, low-cost, low-power, and robust indoor collaborative positioning without requiring additional dedicated equipment or external sensors. This improves positioning accuracy, availability, and environmental adaptability to meet various indoor high-precision positioning needs.

[0013] To achieve the above objectives, the present invention adopts the following technical solution:

[0014] A dual-terminal cooperative positioning method based on error correction and fingerprint matching constraints using precise time measurement via Wi-Fi includes the following steps:

[0015] Step 1: Offline stage, construct a fingerprint database in the target area. The fingerprint database contains the position information of each reference point and the corresponding angle information. The angle information is calculated based on the geometric relationship between the reference point and each access point.

[0016] Step 2: In the single-point positioning stage, the original ranging values ​​of Wi-Fi precise time measurement collected by the first terminal and the second terminal are corrected for errors, and single-point positioning is performed based on the corrected ranging values ​​to obtain the initial positioning results of the first terminal and the second terminal.

[0017] Step 3: Time matching stage. Based on the Coordinated Universal Time recorded when the first terminal and the second terminal perform precise time measurement and ranging, the observation epochs of the two terminals are matched to obtain synchronized observation data.

[0018] Step 4: Fingerprint matching stage. Based on the initial positioning results of the first terminal and the second terminal, dual fingerprint matching is performed in combination with the fingerprint database to estimate the real-time distance between the first terminal and the second terminal.

[0019] Step 5: In the collaborative positioning stage, the real-time distance is used as a geometric constraint to construct a joint observation equation with the error-corrected accurate time measurement distance value in the synchronized observation data. By solving the joint observation equation, the final collaborative positioning result of the first terminal and the second terminal is obtained.

[0020] In some embodiments, step 1 of constructing the fingerprint database specifically includes: dividing the target area into grids, calculating the precise coordinates of each grid point and its azimuth and incident angle with each access point, and forming a basic fingerprint database containing location information and angle information.

[0021] In some embodiments, step 2, which corrects the error in the original ranging value of the Wi-Fi accurate time measurement, specifically includes:

[0022] Calibrate systematic delay deviations caused by differences in terminal and access point hardware;

[0023] Correcting physical deviations caused by geometric distances based on polynomial models;

[0024] Multipath propagation bias is solved and eliminated through regression model;

[0025] Signal quality is identified through a classification model, and a stochastic model for single-point localization is optimized.

[0026] In some embodiments, in step 3, the principle of observation epoch matching is: epochs in the first terminal and the second terminal whose absolute value of the difference in observation time is less than a preset threshold are matched as a group.

[0027] In some embodiments, step 4, the dual fingerprint matching specifically includes:

[0028] Coarse matching: Calculate the angle information based on the initial positioning result of the first terminal or the second terminal, and perform a dual comparison of similarity and distance with the angle information in the fingerprint database to filter out candidate matching points;

[0029] Fine matching: Within the fine-grained grid around the candidate matching point, a fine fingerprint database containing angle information and true distance is constructed, and a secondary matching is performed based on the fine fingerprint databases of the first terminal and the second terminal respectively to obtain multiple distance estimates.

[0030] In some embodiments, the fine matching further includes: calculating the angular similarity and angular distance between the first terminal and the second terminal based on their angular information at the current moment, comparing the differences with the data in the fine fingerprint database, and selecting the matching result with the smallest difference as the distance estimate for the current fine matching.

[0031] In some embodiments, step 4 further includes result fusion: performing cluster analysis on all distance estimates obtained from fine matching, selecting the cluster with the highest consistency, and using the mean of the distance estimates within that cluster as the real-time distance between the first terminal and the second terminal.

[0032] In some embodiments, in step 5, the function model of the joint observation equation is constructed based on the error-corrected accurate time measurement distance values ​​of the first terminal and the second terminal and the real-time distance. Its stochastic model is iteratively updated using the variance component estimation method to optimize the weights of each observation.

[0033] In some embodiments, the method further includes an iterative optimization step: based on the cooperative localization result obtained in step 5, steps 4 and 5 are repeated to update the real-time distance and perform cooperative localization again until a preset iteration termination condition is met.

[0034] In some embodiments, the method can be extended to collaborative positioning scenarios involving multiple terminals, by establishing real-time distance constraints as described in claim 1 between multiple pairs of terminals to form multiple geometric constraints for joint solution.

[0035] The beneficial effects that the Wi-Fi precise time measurement dual-terminal cooperative positioning method disclosed in this application, based on error correction and fingerprint matching constraints, may bring include, but are not limited to:

[0036] I. Significantly improves positioning accuracy

[0037] This invention effectively eliminates the impact of various error sources, such as hardware deviation, geometric deviation, and multipath interference, on accurate time measurement and ranging through systematic error correction, providing high-quality observation data for positioning. Based on this, the dual-terminal distance constraint constructed through fingerprint matching further enhances observation redundancy, achieving information complementarity and error cancellation. Static experimental data shows that the distance estimation accuracy between the two terminals reaches 0.53 meters, an improvement of 75.23% compared to the 2.14 meters estimated based on the original observations; the overall cooperative positioning accuracy of the two terminals is 0.64 meters and 0.87 meters, respectively, an improvement of 13.51% and 16.35% compared to the 0.74 meters and 1.04 meters of single-point positioning. Dynamic experimental results show that when the distance is fixed, the positioning error of the two terminals decreases from 0.52 meters and 1.01 meters in single-point positioning to 0.39 meters and 0.95 meters; when the distance changes, it decreases from 1.68 meters and 0.53 meters to 1.59 meters and 0.46 meters.

[0038] II. Enhancing positioning robustness and environmental adaptability

[0039] This invention constructs a dual-terminal distance constraint through a fingerprint matching mechanism, achieving deep fusion of observation information from both terminals. This effectively alleviates the problem of a single terminal's positioning performance drastically declining in complex indoor environments such as occlusion, weak signals, and observation geometric differences. Experimental results show that this invention can achieve planar positioning accuracies of 0.60 meters and 0.77 meters in weak interference environments, and 0.68 meters and 0.98 meters in complex interference environments, demonstrating good environmental adaptability. Furthermore, dynamic experimental results show that the estimated trajectory of this invention is the smoothest, with the highest degree of agreement with the reference trajectory, low positioning dispersion, and no obvious outliers, proving the stability and robustness of this invention in dynamic scenarios.

[0040] III. Achieving Low-Cost, High-Precision Positioning

[0041] This invention fully leverages existing Wi-Fi precise time measurement infrastructure and the native precise time measurement capabilities of smartphones, eliminating the need for additional dedicated equipment (such as ultra-wideband base stations) or external sensors (such as inertial measurement units). It achieves high-precision collaborative positioning solely through algorithmic innovation. Compared to traditional differential positioning schemes that require the deployment of high-density reference nodes, this invention requires no additional hardware investment, resulting in extremely low deployment costs. Furthermore, the fingerprint database of this invention is constructed based on mesh partitioning and geometric calculations, eliminating the need for manual collection of large amounts of fingerprint data, further reducing implementation costs.

[0042] IV. Overcoming the Bottleneck of Cooperative Positioning in Wi-Fi Precise Time Measurement System

[0043] Existing Wi-Fi precise time measurement positioning schemes lack relative position constraints and information sharing mechanisms between terminals, failing to fully realize the potential of multi-terminal collaborative positioning. This invention innovatively proposes a terminal distance estimation method based on angular fingerprint matching, achieving stable and reliable relative position constraints between terminals without relying on dedicated ranging capabilities such as ultra-wideband or Bluetooth. This breakthrough enables ordinary smartphones to achieve collaborative positioning within the Wi-Fi precise time measurement framework, providing a feasible technical path for large-scale indoor positioning applications.

[0044] V. Excellent scalability and compatibility

[0045] This invention uses dual terminals as the basic unit and can be easily extended to multi-terminal collaborative positioning scenarios. By establishing distance constraints between multiple pairs of terminals, multiple geometric constraints are formed for joint solution, further improving positioning accuracy and reliability. Furthermore, this invention is fully compatible with existing Wi-Fi precise time measurement standards and can be directly deployed on smartphones and access point devices supporting the IEEE 802.11mc protocol without any hardware modifications, demonstrating promising application prospects and commercial value.

[0046] In summary, this invention achieves high-precision, low-cost, low-power, and highly robust indoor collaborative positioning by organically combining error correction, time matching, fingerprint matching, and collaborative positioning. It effectively solves a series of technical problems in existing technologies, such as the difficulty in correcting ranging errors in Wi-Fi precise time measurement, the limited positioning performance of single terminals, the high cost and power consumption of multi-technology fusion solutions, the high deployment cost of differential positioning, and the lack of collaborative positioning mechanisms in Wi-Fi precise time measurement systems. This provides an innovative solution for high-precision indoor positioning. Attached Figure Description

[0047] Figure 1 This is a flowchart of a dual-terminal collaborative positioning method for precise time measurement based on error correction and fingerprint matching constraints according to this application. Detailed Implementation

[0048] Various exemplary embodiments, features, and aspects of this application will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0049] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, an indirect connection through an intermediate medium, or the internal communication between two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0050] See Figure 1 As shown, a dual-terminal cooperative positioning method based on error correction and fingerprint matching constraints using precise time measurement via Wi-Fi includes the following steps:

[0051] Step 1, Offline Stage: Fingerprint Database Construction

[0052] The target area is divided into grids, the precise coordinates of each grid point are calculated, and the azimuth and incident angles between each grid point and each access point are calculated. The location information of each grid point, along with its corresponding azimuth and incident angles, constitutes a fingerprint sample. The collection of all samples forms the basic fingerprint database.

[0053] The fingerprint database constructed in this way is calculated based on geometric relationships, eliminating the need for manual collection of large amounts of fingerprint data, reducing construction costs, and exhibiting strong environmental adaptability.

[0054] For example:

[0055] Divide the scene into a grid and count the... Precise coordinates of each point

[0056] and AP prior coordinates The azimuth and the angle of incidence are and Ultimately based on A basic fingerprint database is formed from individual sample collection points:

[0057]

[0058] The second step, the single-point positioning stage: error correction and single-point positioning.

[0059] Error corrections were performed on the raw ranging values ​​of Wi-Fi precise time measurement collected by the first terminal and the second terminal, respectively.

[0060] In Wi-Fi precise time measurement and ranging, the terminal and access point exchange multiple precise time measurement frames continuously within a burst period, and the distance estimate is obtained by processing the round-trip time. However, in real-world applications, due to limitations in hardware and software conditions and the influence of complex environments, the measured values ​​contain various error components, including systematic delay deviations caused by hardware differences, physical deviations caused by geometric distances, multipath propagation deviations, and measurement noise.

[0061] To solve the above problems, the present invention employs the following error correction steps:

[0062] First, the hardware deviations of different access points and specific terminals are determined by large sample data, and then the hardware deviations between terminals are further determined, thereby calibrating the systematic delay deviations caused by hardware differences.

[0063] Secondly, based on the corrected distance measurement value and the established polynomial model, the physical deviation caused by geometric distance is calculated and corrected.

[0064] Then, feature engineering is constructed based on the corrected ranging values, and the trained regression model is input to solve for and correct multipath interference.

[0065] Finally, feature engineering is reconstructed based on the third corrected ranging values, input into the trained classification model to identify signal quality, optimize the random model, and perform weighted least squares localization for a single terminal to obtain the initial localization results for the first and second terminals.

[0066] For example:

[0067] FTM error correction and single-point positioning;

[0068] Theoretically, the functional expression for FTM distance estimation is as follows:

[0069]

[0070] During each burst period, AP and STA will continuously exchange... One FTM frame, Represents the speed of light. This is the theoretical value for the round-trip time. and The AP captures the time of transmission measurement frames and the arrival time of acknowledgment frames (ACKs). and Capture the arrival time of the measurement frame and the response time for sending the ACK for the STA; Mean of repeated measures This is the distance estimate output by the FTM protocol.

[0071] However, in real-world applications, due to limitations in hardware and software conditions and the influence of complex environments, this measurement process often faces numerous challenges, which can adversely affect application performance. ,

[0072] Subscripts and superscripts and They represent AP and STA respectively. and This represents the actual measured distance and the theoretical distance between AP and STA. These are the actual observed round-trip times. Initial deviations for different APs and STAs and The sum of, and ,in For different APs and a certain fixed STA, i.e. The initial deviation between them Compared to other STAs The difference of the initial deviation, These are the distance, non-line-of-sight, and multipath propagation biases, respectively. Noise for distance measurement.

[0073] To effectively address these issues, a comprehensive improvement approach combining hardware optimization, algorithm enhancement, and environmental adaptation is needed to improve the system's ranging accuracy and robustness. First, with the environment and configuration parameters fixed, the initial hardware deviations between different access points (APs) and a specific STA are determined based on large sample data. Further determine the hardware deviation between STAs as This allows for the calibration of systematic delay biases caused by hardware differences.

[0074] Secondly, based on the corrected distance measurement value The established polynomial model solves for the physical deviations caused by geometric distance. And make corrections; based on the corrected distance measurement values Feature engineering is performed, and the trained regression model is input to solve for multipath interference. And make corrections; based on the corrected distance measurement values Feature engineering is reconstructed, input into the trained classification model to identify signal quality, the random model is optimized, and weighted least squares (WLS) localization is performed on a single terminal.

[0075] The third step is the time matching stage: epoch matching between terminals.

[0076] In collaborative positioning scenarios, different terminals observe the same access point asynchronously, which significantly impacts collaborative positioning in dynamic scenarios, especially when terminals move rapidly or the environment changes drastically. Therefore, the primary challenge for collaborative positioning is addressing the time synchronization issue between terminals.

[0077] Terminals typically use the mobile phone's built-in Network Time Protocol (NTP) service to calibrate their clocks, achieving millisecond-level accuracy. When performing precise time measurement and ranging, their Coordinated Universal Time (UTC) can be simultaneously recorded as a reference for epoch matching. To address the asynchronous observations of the first and second terminals, the single-epoch observation times of both terminals are read, and epoch matching is performed based on the principle that the absolute value of the difference between their observation times is less than a preset threshold, resulting in synchronized observation data. If matching is successful, subsequent collaborative positioning is performed; otherwise, single-point positioning is used. This method keeps asynchronous errors within an acceptable range, providing a synchronization basis for multi-terminal collaborative positioning.

[0078] For example:

[0079] In collaborative positioning scenarios, different terminals observe the same access point (AP) asynchronously, which significantly impacts collaborative positioning in dynamic scenarios, especially when terminals move rapidly or the environment changes drastically. Therefore, the primary challenge for collaborative positioning is time synchronization between terminals. STAs typically utilize the mobile phone's built-in Network Time Protocol (NTP) service to calibrate the clock and control clock errors, achieving millisecond-level accuracy. During FTM ranging, Coordinated Universal Time (UTC) can be simultaneously recorded as a reference for epoch matching. Therefore, to address the asynchronous issue, for necessary... The first STA, this article reads other first... Single-epoch observation time of each STA Then, according to The principle of epoch matching is used, where This represents the empirical threshold used in this paper. If a match is successful, subsequent collaborative positioning is performed; otherwise, single-point positioning is used. This method keeps asynchronous errors within an acceptable range, providing a synchronization basis for multi-terminal collaborative positioning.

[0080] Step 4, fingerprint matching stage: real-time distance estimation

[0081] This stage includes three sub-steps: coarse matching, fine matching, and result fusion.

[0082] In the coarse matching, the angle vector of the first or second terminal is calculated based on its initial positioning result, and then compared with the azimuth and incident angle in the fingerprint database using both comprehensive similarity and Euclidean distance. Several candidate matching points are selected according to descending similarity and ascending Euclidean distance, respectively. After removing matches with abnormal positions, the intersection of these points is determined from both directional and distance perspectives as the result of the coarse matching.

[0083] In fine-grained matching, a fine-grained grid is created within a fixed range, centered on the coarse-matched points. After eliminating duplicates, a fine-grained fingerprint database for each terminal is obtained. The sample points in the fine-grained fingerprint database are traversed, and the azimuth cosine similarity, incident angle cosine similarity, azimuth Euclidean distance, and incident angle Euclidean distance between corresponding sample points of two terminals are calculated. Simultaneously, the physical distance between the sample points is calculated, thus constructing a fine-grained fingerprint database containing the actual distances online. Then, based on the initial positioning results of both terminals, the azimuth cosine similarity, incident angle cosine similarity, azimuth Euclidean distance, and incident angle Euclidean distance between them are calculated and compared with the data in the fine-grained fingerprint database. Several optimal matches are selected in ascending order of difference, and the match with the smallest difference is taken as the distance estimate for each fine-grained match.

[0084] In the result fusion, density-based noisy spatial clustering analysis is performed on all distance estimates obtained from fine matching. The neighborhood radius and the minimum number of points required to form the core point are empirically set, and the cluster with the highest consistency is selected. The mean of the distance estimates within this cluster is used as the real-time distance between the first and second terminals. Since the single-point positioning accuracy of the two terminals may differ, a fine matching is performed for each terminal, and the distance estimate corresponding to the terminal with the better consistency index is selected as the final real-time distance.

[0085] For example:

[0086] Coarse match;

[0087] After the terminal is synchronized, according to Single point positioning results Angle vector and Statistics and fingerprint database Overall similarity European distance ,Right now

[0088]

[0089] According to descending order and Filter by ascending order After eliminating candidate matches and removing those with abnormal positions, the intersection of these matches is determined based on both directionality and distance, resulting in a coarse match. .

[0090] Precise matching;

[0091] For any In terms of, in Fine-grained meshing is performed within a fixed area centered on the point. Finally, based on the coarsely matched points, duplicates are eliminated to obtain the final result. Fine fingerprint database For any traverse the synchronization terminals of And calculate the cosine similarity and Euclidean distance respectively:

[0092]

[0093] Calculate the physical distance between every two sample points. This allows for the online construction of a detailed fingerprint database containing real-world distances.

[0094]

[0095] Simultaneously, calculations are performed based on the current positioning results of the two terminals. , and , Statistical estimates and The differences in, namely and Filter by the intersection in ascending order. Find the optimal match. and , This serves as the estimation result for each fine match.

[0096] Results fusion;

[0097] For all Each precise matching estimate is clustered using the density-based noisy spatial clustering (DBSCAN) method. Empirical settings are made for the neighborhood radius and the minimum number of points required to form a core point. The similarity within each cluster and the mean of the estimated values ​​are then used as the basis for the clustering. and As The accurate estimation results. Because the single-point positioning accuracy varies among terminals, a fine-matching process needs to be performed for each terminal to select... The estimated value corresponding to the smaller terminal As a real-time distance estimation between two terminals .

[0098] Step 5, Cooperative Localization Phase: Joint Solution

[0099] This phase includes single-stage cooperative localization and multiple-stage cooperative localization.

[0100] In a single collaborative localization operation, real-time distance is used as a geometric constraint, and together with the error-corrected, precise time-measured distance values ​​from the synchronized observation data, a joint observation equation is constructed. The functional model of the joint observation equation includes the error-corrected distance values ​​from the first and second terminals, as well as the real-time distance. Its stochastic model is iteratively updated using the Helmert variance component estimation method to optimize the weights of each observation. The joint observation equation is solved using weighted least squares estimation to obtain the final collaborative localization result for the first and second terminals. In actual processing, since some covariance matrices are unknown, a consistency index obtained from fingerprint matching is used as the variance of the distance estimate, and the covariance matrices of different terminals and distance estimates are iteratively updated using Helmert variance component estimation. Because there is significant redundancy in the combined localization observations at this point, abnormal observations can be directly removed through quality control measures. The above steps are iterated until the absolute value of the coordinate correction is less than a preset threshold or the number of iterations exceeds a preset threshold.

[0101] For example, specifically: the function model is defined as ,in , This is the residual observation vector after various error corrections. for initial coordinates With the Geometric distance between APs.

[0102]

[0103] in and These are the position error coefficient matrices, for The three-dimensional coordinate corrections, the stochastic model satisfies:

[0104]

[0105] here , The variance of the error in the distance estimate given empirically. .

[0106] Construct the following objective function:

[0107]

[0108] in Assuming unit weighted variance, the final WLS estimate is: In actual processing, and Unknown, to avoid introducing more errors, we adopt The covariance matrix of different terminals and distance estimates is iteratively updated using Helmert variance component estimation. Since there is a lot of redundancy in the combined positioning observations at this time, abnormal observations can be directly removed through quality control measures. The above steps are iterated until the absolute value of the correction is less than the threshold or the number of iterations is greater than the threshold.

[0109] In multiple collaborative localization processes, since the fingerprint matching accuracy is related to the localization accuracy, the fingerprint matching stage can be re-executed based on the results of each collaborative localization process to obtain a more accurate real-time distance constraint. This process can be repeated multiple times until the preset iteration termination condition is met, thus achieving the final collaborative localization.

[0110] Furthermore, the method of the present invention uses dual terminals as the basic unit and can be extended to multi-terminal scenarios. By establishing real-time distance constraints between multiple pairs of terminals, multiple geometric constraints are formed for joint solution.

[0111] Those skilled in the art should understand that various modifications can be made to the above technical solutions without departing from the principles of the present invention, for example:

[0112] Time matching can introduce a more precise clock source based on actual conditions to achieve higher matching performance;

[0113] The current fingerprint database and matching model are constructed based on information such as angle vectors calculated from the localization results. They can be replaced with other information, but the single mapping characteristic must be guaranteed. The typical DBSCAN clustering method is used when fusing the results, and it can be changed to other models.

[0114] The variance covariance matrix of the cooperative localization model is iteratively adjusted based on the initial localization results and Helmert variance component estimation. It can be set to a fixed value or dynamically adjusted by changing to other estimation models according to the actual accuracy.

[0115] This embodiment uses an underground parking lot as an experimental scenario to verify the dual-terminal collaborative positioning method for Wi-Fi accurate time measurement based on error correction and fingerprint matching constraints proposed in this invention.

[0116] I. Experimental Environment and Equipment Configuration

[0117] The experimental scenario selected in this embodiment is an underground parking lot, which has typical characteristics of a complex indoor environment, including interference factors such as multipath reflection, signal obstruction, and non-line-of-sight propagation, effectively verifying the performance of the method of this invention. A total of 18 Wi-Fi base stations were deployed in the experimental area, with an interval of approximately 10 meters between each base station. The coordinates of the base stations were pre-calibrated using high-precision measuring instruments.

[0118] The terminal devices used were two smartphones, a Google Pixel 6 and a Google Pixel 6 Pro. Both phones support the IEEE 802.11mc protocol and have native Wi-Fi accurate time measurement and ranging capabilities. During the experiment, the sampling frequency of both phones was set to 5 Hz, that is, 5 ranging data points were collected per second, and the communication protocol adopted the IEEE 802.11ax standard.

[0119] II. Offline fingerprint database construction

[0120] Before the experiment began, an offline fingerprint database was constructed within the target area. Based on the actual area of ​​the experimental site, the X-axis coordinate range was set to 5260 meters to 5308 meters, the Y-axis coordinate range to 2963 meters to 3012 meters, and the Z-axis coordinate range to -1.25 meters to 0.75 meters. Within this spatial range, a grid was created with an initial interval of 2 meters between the X and Y axes and 0.1 meters between the Z axes, forming multiple grid points.

[0121] For each grid point, its precise coordinates are first determined. Then, based on the prior coordinates of each access point, the azimuth and incident angle between the grid point and each access point are calculated. The location information of each grid point, along with its corresponding azimuth and incident angle, constitutes a fingerprint sample. The collection of fingerprint samples from all grid points forms the basic fingerprint database. This fingerprint database is used as a matching benchmark in the subsequent online positioning phase.

[0122] III. Single-point positioning and error correction

[0123] After the experiment began, two smartphones collected raw distance measurements using precise time measurement (RTM) over Wi-Fi. During the data collection process, multiple RTM frames were continuously exchanged between the terminal and the access point within each burst period. The distance estimate was obtained by processing the round-trip time. However, the raw distance measurements contained various error components, including systematic delay bias caused by hardware differences, physical bias caused by geometric distance, multipath propagation bias, and measurement noise.

[0124] This embodiment uses the following steps to correct the error in the original ranging value:

[0125] First, the hardware deviation between different access points and the first mobile phone is determined by large sample data, and then the hardware deviation difference between the second mobile phone and the first mobile phone is determined, thereby calibrating the systematic delay deviation caused by hardware differences.

[0126] Secondly, based on the distance measurement value after the first correction and the pre-established polynomial model, the physical deviation caused by the geometric distance is calculated and a second correction is performed.

[0127] Then, feature engineering is constructed based on the second corrected ranging values, and the trained regression model is input to solve multipath interference and perform a third correction.

[0128] Finally, based on the distance measurement values ​​after the third correction, the feature engineering is reconstructed, input into the trained classification model to identify signal quality, optimize the random model, and perform weighted least squares localization for a single terminal to obtain the initial localization results for the first and second mobile phones.

[0129] IV. Time Matching

[0130] Because the observations of the same access point by the two mobile phones are asynchronous, especially in dynamic moving scenarios, time asynchrony can introduce significant positioning errors. Therefore, in this embodiment, when performing precise time measurement and ranging, both mobile phones simultaneously record their respective Coordinated Universal Time (UTC) as the reference for inter-epoch matching.

[0131] During the experiment, the single-epoch observation times of the first and second mobile phones were read, and epoch matching was performed according to the principle that the absolute value of the difference between the two observation times was less than 500 milliseconds. For time points that met this condition, their observation data were matched into a set of synchronized data for subsequent cooperative positioning; for epochs that did not meet the condition, cooperative positioning was abandoned and single-point positioning was switched to processing.

[0132] V. Fingerprint matching and real-time distance estimation

[0133] After time matching is completed, the fingerprint matching stage begins, which includes three sub-steps: coarse matching, fine matching, and result fusion.

[0134] In the coarse matching, the angle vector of the first mobile phone is calculated based on its initial positioning result, and then compared with the azimuth and incident angle in the basic fingerprint database using both comprehensive similarity and Euclidean distance. Specifically, nine candidate matching points are selected in descending order of similarity and ascending order of Euclidean distance. After removing matches with abnormal positions, the intersection of these points is determined from both directional and distance perspectives as the result of the coarse matching.

[0135] In the fine matching process, a fine-grained grid is created within a 2-meter radius in both the X and Y directions, centered on the coarse matching points, with a grid interval of 0.5 meters. The Z direction remains unsubdivided. After eliminating duplicates, a fine fingerprint database for the first mobile phone is obtained. The sample points in the fine fingerprint database are traversed, and the azimuth cosine similarity, incident angle cosine similarity, azimuth Euclidean distance, and incident angle Euclidean distance are calculated between corresponding sample points of the first and second mobile phones. Simultaneously, the physical distances between sample points are calculated, thus constructing an online fine fingerprint database containing real-world distances.

[0136] Then, based on the initial positioning results of the two terminals, the azimuth cosine similarity, incident angle cosine similarity, azimuth Euclidean distance, and incident angle Euclidean distance between them are calculated and compared with the data in the fine fingerprint database. Several optimal matches are selected in ascending order of difference, and the match with the smallest difference is taken as the distance estimate for each fine match.

[0137] In the result fusion, density-based noisy spatial clustering analysis was performed on all distance estimates obtained from fine matching, with a neighborhood radius of 0.25 meters and a minimum number of points required to form a core point of 2. If no effective cluster was formed, the neighborhood radius was doubled and clustering continued. The cluster with the highest consistency was selected, and the mean of the distance estimates within that cluster was used as the real-time distance between the first and second mobile phones. Since the single-point positioning accuracy of the two mobile phones may differ, a fine matching was performed on each mobile phone, and the distance estimate corresponding to the mobile phone with better consistency was selected as the final real-time distance.

[0138] VI. Collaborative Positioning

[0139] After obtaining the real-time distance between the two terminals, the collaborative positioning phase begins. This embodiment first performs a single collaborative positioning operation: using the real-time distance as a geometric constraint, it is combined with the error-corrected, precise time-measured distance values ​​from the synchronized observation data to construct a joint observation equation. The functional model of the joint observation equation includes the error-corrected distance values ​​from both the first and second mobile phones, as well as the real-time distance. Its stochastic model is iteratively updated using the Helmert variance component estimation method to optimize the weights of each observation.

[0140] In actual processing, since some covariance matrices are unknown, the consistency index obtained from fingerprint matching is used as the variance of the distance estimate, and Helmholtz variance component estimation is used to iteratively update the covariance matrices of different terminals and distance estimates. Because there is significant redundancy in the combined positioning observations at this point, abnormal observations can be directly eliminated through quality control measures. The above steps are iterated until the absolute value of the coordinate correction is less than a preset threshold or the number of iterations exceeds a preset threshold, thus obtaining the final collaborative positioning result of the first and second mobile phones.

[0141] To further improve positioning accuracy, this embodiment also performs multiple collaborative positioning operations: based on the results of a single collaborative positioning operation, the fingerprint matching stage is re-executed to obtain a more accurate real-time distance constraint, and collaborative positioning is performed again. This process is repeated multiple times until convergence is achieved, thus realizing the final collaborative positioning.

[0142] VII. Experimental Results

[0143] The experiment was conducted using the method described above, and the results are as follows:

[0144] Static positioning experiments showed that the overall collaborative positioning accuracy of the two mobile phones was 0.64 meters and 0.87 meters, respectively. Compared with the single-point positioning accuracy of 0.74 meters and 1.04 meters, the collaborative positioning accuracy improved by 13.51% and 16.35%, respectively. In a weak interference environment, collaborative positioning can achieve planar positioning accuracy of 0.60 meters and 0.77 meters; in a complex interference environment, it can achieve planar positioning accuracy of 0.68 meters and 0.98 meters.

[0145] The dynamic positioning experiment covered typical indoor scenarios. The precise coordinates of the starting point, waypoints, and ending point were determined using a total station. A reference trajectory was generated using spline interpolation. The positioning error was measured using the closest distance between the positioning result and the interpolated points of the reference trajectory. Dynamic positioning performance was evaluated. With a fixed distance, the dynamic positioning errors of the two mobile phones decreased from 0.52 meters and 1.01 meters for single-point positioning to 0.39 meters and 0.95 meters. With varying distances, the dynamic positioning errors decreased from 1.68 meters and 0.53 meters for single-point positioning to 1.59 meters and 0.46 meters. Experimental results show that the estimated trajectory of this invention is the smoothest, has the highest degree of agreement with the reference trajectory, and exhibits low positioning dispersion with no obvious outliers.

[0146] VIII. Summary of Implementation Examples

[0147] This embodiment uses an underground parking lot as the experimental scenario. By deploying 18 Wi-Fi base stations and two smartphones, it fully verifies the feasibility and effectiveness of the proposed dual-terminal collaborative positioning method based on error correction and fingerprint matching constraints using Wi-Fi precise time measurement. Experimental results show that this invention can significantly improve the collaborative positioning accuracy and stability of dual terminals using Wi-Fi precise time measurement, achieving good positioning results in both static and dynamic scenarios. Furthermore, it requires no additional dedicated hardware support, demonstrating good practical value and promising prospects for widespread application.

[0148] The above embodiments illustrate in detail the specific implementation of the technical solution of the present invention, the logical and connection relationships of each component, and the complete working process. Those skilled in the art will understand that various changes and modifications can be made to the above embodiments without departing from the principles and spirit of the present invention, and all such changes and modifications should fall within the protection scope of the appended claims.

Claims

1. A dual-terminal collaborative positioning method based on error correction and fingerprint matching constraints using precise time measurement in Wi-Fi, characterized in that, Includes the following steps: Step 1: Offline stage, a fingerprint database is constructed in the target area. The fingerprint database contains the position information of each reference point and the corresponding angle information. The angle information is calculated based on the geometric relationship between the reference point and each access point. Step 2: In the single-point positioning stage, the original ranging values ​​of Wi-Fi precise time measurement collected by the first terminal and the second terminal are corrected for errors, and single-point positioning is performed based on the corrected ranging values ​​to obtain the initial positioning results of the first terminal and the second terminal. Step 3: Time matching stage. Based on the Coordinated Universal Time recorded when the first terminal and the second terminal perform precise time measurement and ranging, the observation epochs of the two terminals are matched to obtain synchronized observation data. Step 4: Fingerprint matching stage. Based on the initial positioning results of the first terminal and the second terminal, dual fingerprint matching is performed in combination with the fingerprint database to estimate the real-time distance between the first terminal and the second terminal. Step 5: In the collaborative positioning stage, the real-time distance is used as a geometric constraint to construct a joint observation equation with the error-corrected accurate time measurement distance value in the synchronized observation data. By solving the joint observation equation, the final collaborative positioning result of the first terminal and the second terminal is obtained.

2. The method according to claim 1, characterized in that, Step 1, which involves building a fingerprint database, specifically includes: dividing the target area into grids, calculating the precise coordinates of each grid point and its azimuth and incident angles with each access point, and forming a basic fingerprint database containing location and angle information.

3. The method according to claim 1, characterized in that, Step 2 involves error correction of the original ranging value for Wi-Fi accurate time measurement, specifically including: Calibrate systematic delay deviations caused by differences in terminal and access point hardware; Correcting physical deviations caused by geometric distances based on polynomial models; Multipath propagation bias is solved and eliminated through regression model; Signal quality is identified through a classification model, and a stochastic model for single-point localization is optimized.

4. The method according to claim 1, characterized in that, In step 3, the principle of observation epoch matching is: epochs in the first terminal and the second terminal whose absolute value of the difference between observation times is less than a preset threshold are matched as a group.

5. The method according to claim 1, characterized in that, Step 4, the dual fingerprint matching specifically includes: Coarse matching: Calculate the angle information based on the initial positioning result of the first terminal or the second terminal, and perform a dual comparison of similarity and distance with the angle information in the fingerprint database to filter out candidate matching points; Fine matching: Within the fine-grained grid around the candidate matching point, a fine fingerprint database containing angle information and true distance is constructed, and a secondary matching is performed based on the fine fingerprint databases of the first terminal and the second terminal respectively to obtain multiple distance estimates.

6. The method according to claim 5, characterized in that, The fine matching further includes: calculating the angular similarity and angular distance between the first terminal and the second terminal based on their angular information at the current moment, comparing the differences with the data in the fine fingerprint database, and selecting the matching result with the smallest difference as the distance estimate for the current fine matching.

7. The method according to claim 5, characterized in that, Step 4 also includes result fusion: perform cluster analysis on all distance estimates obtained from fine matching, select the cluster with the highest consistency, and use the mean of the distance estimates within the cluster as the real-time distance between the first terminal and the second terminal.

8. The method according to claim 1, characterized in that, In step 5, the function model of the joint observation equation is constructed based on the error-corrected accurate time measurement distance values ​​of the first terminal and the second terminal and the real-time distance. Its stochastic model is iteratively updated using the variance component estimation method to optimize the weight of each observation.

9. The method according to claim 1, characterized in that, The method further includes an iterative optimization step: based on the cooperative localization result obtained in step 5, steps 4 and 5 are repeated to update the real-time distance and perform cooperative localization again until the preset iteration termination condition is met.

10. The method according to claim 1, characterized in that, The method can be extended to collaborative positioning scenarios involving multiple terminals. By establishing real-time distance constraints as described in claim 1 between multiple pairs of terminals, multiple geometric constraints are formed for joint solution.

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