A mobile tracking and positioning method based on bluetooth signals

By using a single mobile base station combined with Bluetooth signals and Kalman filtering in outdoor environments, the problem of high accuracy and low cost in outdoor mobile positioning has been solved, and high-precision real-time positioning in complex interference environments has been achieved.

CN115696206BActive Publication Date: 2026-07-31FUDAN UNIVERSITY
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
FUDAN UNIVERSITY
Filing Date
2022-10-18
Publication Date
2026-07-31

AI Technical Summary

Technical Problem

Existing outdoor mobile positioning technologies struggle to balance cost and accuracy. Traditional methods suffer from large positioning errors and high costs in outdoor environments, especially in complex and interference-prone environments where high-precision real-time positioning is difficult to achieve.

Method used

A GPS/BeiDou locator is installed on a single mobile base station. The method combines Bluetooth signal multi-signal classification and unscented Kalman filtering. The direction finding method is selected according to the interference environment. The range finding and positioning are performed by RSSI value method. The direction finding and positioning are further performed by combining forward and backward spatial smoothing or expanding noise subspace method. The position estimation is corrected by unscented Kalman filtering.

Benefits of technology

It achieves low-cost, high-precision real-time positioning in outdoor mobile environments, reduces positioning errors, has anti-interference capabilities, good stability, and low power consumption.

✦ Generated by Eureka AI based on patent content.

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Abstract

This invention discloses a mobile tracking and positioning method based on Bluetooth signals. It uses a single mobile base station equipped with a GPS / BeiDou locator to locate multiple points to be positioned. The specific steps include: determining the interference environment of the scene based on a multi-signal classification method; selecting a direction-finding positioning method based on the interference environment to obtain the orientation of the moving point relative to the mobile base station; further combining RSSI values ​​for ranging positioning to obtain the measured position of the moving point to be positioned; and then combining the measured value of the point to be positioned at the current moment with the state value of the point to be positioned at the past moment using an unscented Kalman filter for mobile tracking and positioning. This mobile tracking and positioning method significantly reduces costs by only installing GPS / BeiDou locators on a few mobile base stations; it employs appropriate positioning methods for different types of interference, and uses an unscented Kalman filter to correct the observed values ​​to obtain the optimal estimate of the real-time position, ensuring the accuracy of the positioning service even in unknown outdoor scenarios.
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Description

Technical Field

[0001] This invention relates to the field of Bluetooth positioning technology, and more specifically to a mobile tracking and positioning method based on Bluetooth signals. Background Technology

[0002] In recent years, with the increasing demand for location information in the field of vehicle networking, improving positioning accuracy in outdoor mobile environments has become a key challenge.

[0003] Bluetooth Low Energy (BLE) based positioning technology has advantages such as low power consumption and high security. It also enters a sleep state when not in use, further improving product lifespan. These advantages have enabled the technology to develop rapidly in the overseas positioning service market and occupy an irreplaceable market position.

[0004] The existing target location positioning mainly adopts the following methods and schemes: The first type of method directly obtains the target's location information by installing a GPS / BeiDou locator on the target. Although the GPS / BeiDou positioning system can provide relatively accurate positioning technology with low positioning error, the power consumption of the chip and peripheral circuits is too high when communicating with the base station to provide positioning services. Due to power limitations, GPS / BeiDou devices are not suitable for providing long-term location positioning services, and the cost would be too high if a GPS / BeiDou locator were installed on each positioning target.

[0005] The second category of methods indirectly obtains target-related location information through measurement systems using known node positions and relative position information. Based on whether it is range-based, it can be divided into range-free positioning technology and range-based positioning technology. Range-free positioning technology mainly employs location fingerprinting methods. It constructs a fingerprint database by collecting one or more signal characteristics at a known location, such as signal strength and the number of connected devices. Pattern recognition is then used to pair the detected signals with the database. However, this method is mainly applicable to indoor positioning and requires prior signal acquisition to establish the database, making it unsuitable for real-time outdoor mobile positioning. Range-based positioning technology achieves positioning and tracking through the relative distance and direction between nodes. Methods include Time of Arrival (TOA), Time Difference of Arrival (TDOA), Angle of Arrival (AOA), and RSSI value-based positioning. However, due to the complexity of the outdoor environment and interference from propagation noise and channel delay, it is difficult to obtain ideal positioning results.

[0006] In positioning systems, the most important technology is the target location positioning method. However, traditional positioning methods all have their own shortcomings and cannot balance the cost and accuracy of real-time outdoor mobile positioning. Summary of the Invention

[0007] To address the aforementioned issues, this invention provides a mobile tracking and positioning method. This method can automatically select the appropriate positioning method based on different scenarios, and only requires a mobile base station equipped with a GPS / BeiDou locator to complete the positioning. This ensures the accuracy of positioning services in outdoor mobile scenarios while reducing costs.

[0008] This invention determines the interference environment of a scene based on a multiple signal classification method, selects a direction-finding positioning method based on the interference environment to obtain the orientation of the moving point relative to the mobile base station, and further combines RSSI values ​​for ranging positioning to obtain the measured position of the moving point to be located. Then, it uses an unscented Kalman filter method to perform motion tracking and positioning, combining the measured value of the point to be located at the current time with the state value of the point to be located at the past time. The specific technical solution provided by this invention is as follows.

[0009] A mobile tracking and positioning method based on Bluetooth signals, which uses a single mobile base station equipped with GPS / BeiDou positioning The device locates multiple moving points to be located, including the following steps: (1) Ranging and positioning based on RSSI value method for distance measurement between the mobile point to be located and the mobile base station. (2) Determine whether there is coherent signal interference in the signal of the currently received moving point to be located based on the multiple signal classification method; (3) If the received signal is subject to coherent signal interference, the forward and backward spatial smoothing method is selected to locate the position of the moving point to be located relative to the mobile base station. If the received signal is not subject to coherent signal interference, the extended noise subspace method is selected to locate the position of the moving point to be located relative to the mobile base station. (4) Combine the distance between the mobile point to be located and the mobile base station obtained in step (1) and the orientation of the mobile point to be located relative to the mobile base station obtained in step (3) to obtain the current measurement position observation value of the mobile point to be located. (5) Combining the past state of the moving point to be located and the current position of the moving point to be located, the Kalman filter gain is calculated by the unscented Kalman filter method, and the current position observation value of the moving point to be located is corrected to obtain the optimal estimate of the real-time position in order to achieve real-time movement tracking.

[0010] In this invention, step (2) of the multiple signal classification method is as follows: Step S201: Collect the Bluetooth signal of the moving point to be located once; Step S202: Calculate the array covariance matrix of the received Bluetooth signal based on the collected Bluetooth signal. Step S203: Obtain the signal spatial spectrum function by eigenvalue decomposition of the array covariance matrix of the received Bluetooth signal; Step S204: The results of the multiple signal classification method are obtained by frequently searching the spectral peaks of the signal spatial spectral function to determine whether there is any coherent signal interference.

[0011] In this invention, the forward and backward spatial smoothing method in step (3) is as follows: Step S301: Divide the uniform receiving array into multiple subarrays that have the same array manifold matrix; Step S302: Perform weighted averaging on the covariance matrix of the received signals of each subarray. Step S303: The signal spatial spectrum function is obtained by eigenvalue decomposition of the covariance matrix of the signal array after weighted averaging. Step S304: The orientation of the moving point to be located relative to the mobile base station under coherent signal interference is obtained by frequently searching the spectral peaks of the signal spatial spectrum function.

[0012] In this invention, the method for expanding the noise subspace in step (3) is as follows: Step S401: Perform eigenvalue decomposition on the covariance matrix of the signal array, dividing it into a noise subspace and a signal subspace based on eigenvalues; Step S402: Find the strong signal subspace based on the results of the multiple signal classification method; Step S403: Incorporate the strong signal subspace into the noise subspace to construct an extended noise subspace; Step S404: Spatial spectrum estimation is performed using the extended noise subspace to determine the orientation of the mobile point to be located relative to the mobile base station under coherent signal interference.

[0013] In this invention, in step (5), the Kalman filter gain is calculated using the unscented Kalman filter method, and the optimal estimate of the real-time position is obtained by correcting the current position observation value of the moving point to be located, so as to achieve real-time motion tracking. The method is as follows: Step S601: Predict the state of the target point at the next moment based on the process model and the past states of the target point. Based on the state and covariance matrix of the moving point to be located in the past, a proportionally modified symmetric sampling strategy is used to generate sigma points and their corresponding weights in the past. The sigma points in the past are projected forward by the process model to obtain the one-step sigma prediction point in the current time. The mean and covariance of the one-step sigma prediction point in the current time are calculated based on the unscented transformation. Step S602: Map the predicted measurement value of the target point at the current moment to the observation model and the predicted state of the target point. Based on the mean and covariance of the one-step sigma prediction point at the current time, a new sigma point and its corresponding weight are generated by proportionally correcting the symmetric sampling strategy. The new sigma point is mapped to the two-step sigma prediction point at the current time through the observation model. The mean and covariance of the two-step sigma prediction point are calculated based on the unscented transformation. Step S603: Obtain the Kalman gain using the predicted and actual measurements of the point to be located, generate the optimal estimate of the moving point at the current moment, and return the positioning result. Update the state of the moving point at past moments. Calculate the residuals and Kalman gain based on the mean and covariance of the two-step sigma prediction points and the position measurement of the moving point to be located at the current time; generate the optimal position estimate of the moving point to be located at the current time using the residuals and Kalman gain; update the optimal position estimate and covariance matrix of the moving point to be located, and return the optimal position estimate of the moving point to be located at the current time.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention provides a Bluetooth-based mobile tracking and positioning method. The receiving end of the mobile base station receives the Bluetooth signal transmitted by the mobile point to be located and combines it with the GPS / BeiDou locator of the base station to observe the mobile point in real time. It utilizes the advantages of Bluetooth technology itself, which has the characteristics of low cost, low power consumption, strong anti-interference ability, and good stability. Appropriate positioning methods are adopted for different interference scenarios. The observation value of the mobile point to be located obtained by real-time positioning is corrected by unscented Kalman filtering based on past state values ​​to obtain the optimal estimate of the real-time position. During the running time, continuous positioning and tracking are performed according to the requirements of mobile tracking and positioning, which ensures the accuracy of the positioning service and reduces positioning error. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a mobile tracking and positioning method according to the present invention.

[0016] Figure 2 This is a schematic diagram of the first process of a mobile tracking and positioning method according to the present invention.

[0017] Figure 3 This is a schematic diagram of the second process of a mobile tracking and positioning method according to the present invention.

[0018] Figure 4 This is a schematic diagram of the third process of a mobile tracking and positioning method according to the present invention.

[0019] Figure 5 This is a schematic diagram of the fourth process of a mobile tracking and positioning method according to the present invention.

[0020] Figure 6This is a schematic diagram of the fifth step of a mobile tracking and positioning method according to the present invention.

[0021] Figure 7 This is a schematic diagram of the sixth process of a mobile tracking and positioning method according to the present invention.

[0022] Figure 8 This is a schematic diagram of the seventh process of a mobile tracking and positioning method according to the present invention.

[0023] Figure 9 This is a schematic diagram of the eighth process of a mobile tracking and positioning method according to the present invention.

[0024] Figure 10 This is a schematic diagram of the ninth process of a mobile tracking and positioning method according to the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0026] This invention provides a mobile tracking and positioning method based on Bluetooth signals, which uses a single mobile base station. GPS / BeiDou locators can locate multiple points to be located. At the same time, they can automatically select different direction finding and positioning methods according to different signal interference scenarios, and predict and track based on past status. This not only meets the positioning needs under different signal interference scenarios, but also overcomes the shortcomings of different positioning methods and reduces costs.

[0027] Specifically, the present invention provides a mobile tracking and positioning method based on Bluetooth signals. It determines whether the current scene is a scene with coherent signal interference or a scene without coherent signal interference but with possible strong signal interference, automatically selects the appropriate direction finding method for direction finding, and combines RSSI ranging method to obtain the measured position of the point to be located at the current moment. Based on past states, it uses unscented Kalman filtering method to predict and track the actual position of the point to be located at the current moment.

[0028] The direction finding method for the coherent signal interference scenario uses a forward and backward spatial smoothing method for direction finding.

[0029] The direction finding method for scenarios without coherent signal interference but potentially with strong signal interference is to perform direction finding by extending the noise subspace method.

[0030] like Figure 1As shown, the system determines the possible signal interference in the current scene. If the multiple signal classification method fails to obtain a result, it determines that there is coherent signal interference and adopts the forward and backward spatial smoothing method. It combines RSSI ranging method and unscented Kalman filtering method to perform motion tracking and positioning of the measured signal to obtain the positioning result.

[0031] If the multiple signal classification method can obtain results, then the method of extended noise subspace is used to determine that there is no coherent signal interference but there may be strong signal interference. Combined with RSSI ranging and unscented Kalman filtering, the measured signal is used to perform motion tracking and positioning to obtain the positioning result.

[0032] If as Figures 2 to 9 As shown, automatically selecting different measurement methods and performing motion tracking prediction based on the current scene includes: Step S101 uses the RSSI value method for distance measurement and positioning; Step S102: Determine whether there is coherent signal interference in the currently received signal based on the multiple signal classification method; the specific method is as follows: Step S201: Collect the Bluetooth signal of the moving point to be located once; Step S202: Calculate the array covariance matrix of the received Bluetooth signal based on the collected Bluetooth signal. Step S203: Obtain the signal spatial spectrum function by eigenvalue decomposition of the array covariance matrix of the received Bluetooth signal; Step S204: The results of the multiple signal classification method are obtained by frequently searching the spectral peaks of the signal spatial spectral function to determine whether there is any coherent signal interference. Step S103: If the received signal has coherent signal interference, select the forward and backward spatial smoothing method for direction finding and positioning; the forward and backward spatial smoothing method specifically includes: Step S301: Divide the uniform receiving array into multiple subarrays that have the same array manifold matrix; Step S302: Perform weighted averaging on the covariance matrix of the received signals of each subarray. Step S303: The signal spatial spectrum function is obtained by eigenvalue decomposition of the covariance matrix of the signal array after weighted averaging. Step S304: The relative orientation of the moving point to be located relative to the mobile base station under coherent signal interference is obtained by frequently searching the spectral peaks of the signal spatial spectrum function, and the measured position of the moving point to be located is obtained by combining the RSSI value method for ranging and positioning. Step S104: If the received signal has no coherent signal interference, select the extended noise subspace method for direction finding and positioning; specifically including: Step S401: Perform eigenvalue decomposition on the covariance matrix of the signal array, dividing it into noise subspace and signal subspace according to eigenvalues.

[0033] Step S402: Find the strong signal subspace based on the results of the multiple signal classification method.

[0034] Step S403: Incorporate the strong signal subspace into the noise subspace to construct an extended noise subspace; Step S404: Spatial spectrum estimation is performed using the extended noise subspace to obtain the relative orientation of the mobile point to be located relative to the mobile base station under coherent signal interference. The measured position of the mobile point to be located is obtained by combining the RSSI value method for ranging and positioning.

[0035] Step S105 combines the past state of the moving point to be located with the current position of the moving point to be located, and performs motion tracking using an unscented Kalman filter method. This includes: Step S501: Send the measured location of the moving point to be located to the positioning server; Step S502: Send a location request to the location server; Step S503: The positioning server calculates the current position of the target mobile point based on the past status of the target mobile point in the database using the unscented Kalman filter method, and updates the past status of the target mobile point in the database; the specific method is as follows: Step S601: Predict the state of the point to be located at the next moment based on the process model and the state of the point to be located at the past moment. This includes: Step S701: Generate the sigma points and their corresponding weights at past moments using a proportionally corrected symmetric sampling strategy based on the state and covariance matrix of the point to be located at the past moment; Step S702: Project the sigma points at past moments forward using the process model to obtain the one-step sigma prediction point at the current moment; Step S703: Calculate the mean and covariance of the one-step sigma prediction point at the current moment based on the unscented transformation.

[0036] Step S602: Map the predicted measurement value of the target point at the current time according to the observation model and the predicted state of the target point. This includes: Step S801: Generate a new sigma point and its corresponding weight at the current time based on the mean and covariance of the one-step sigma prediction point at the current time using a proportionally corrected symmetric sampling strategy; Step S802: Map the new sigma point to the two-step sigma prediction point at the current time through the observation model; Step S803: Calculate the mean and covariance of the two-step sigma prediction point based on the unscented transformation.

[0037] Step S603: Obtain the Kalman gain from the predicted and actual measurements of the point to be located, generate the optimal estimate of the moving point at the current moment, and return the positioning result. Update the past position of the moving point in the database. This includes: Step S901: Calculate the residual and Kalman gain based on the mean and covariance of the two-step sigma prediction points and the position measurement of the moving point at the current moment; Step S902: Generate the optimal position estimate of the moving point at the current moment using the residual and Kalman gain; Step S903: Update the optimal position estimate and covariance matrix of the moving point in the positioning server, and return the optimal position estimate of the moving point at the current moment.

[0038] Step S504: The positioning server returns the location of the moving point to be located.

[0039] The steps S103 and S104 mentioned above do not have a necessary order; they are triggered based on different conditions.

[0040] In this invention, the positions of the mobile point to be located and the mobile base station are changed according to the motion model. Steps S101, S102, S103, and S104 are repeated to obtain the measurement value of the mobile point to be located and the position of the mobile base station, and the position of the mobile point to be located is obtained again. The re-obtained position of the mobile point to be located is input into the positioning server, combined with the past status of the mobile point to be located in the database, and step S105 is repeated until a preset test time or a preset number of tests is reached, at which point the positioning is terminated.

[0041] The specific implementation steps are explained below with reference to the embodiments: (1) Deploy mobile base station A1 and mobile points B1 and B2 to be located according to the positioning scenario. The initial distances between the mobile base station and the mobile base station are 50m and 100m respectively. Different interferences are added according to the scenario requirements. The mobile base station and the mobile points to be located move according to the given process model.

[0042] (2) The deployed mobile base station collects Bluetooth signals for each mobile point to be located at the current time. The base station obtains the measurement information of the mobile point to be located by receiving signals via Bluetooth through ranging and direction finding positioning methods. The measurement information is arranged according to vector... Send in the format, where, This indicates the number of samples collected at the mobile base station. The relative orientation measurement information of the movement to be located. The data collected at the mobile base station The relative distance measurement information of the movement to be located The number of detected points to be located is stored in a file on the base station according to the identification of the mobile point number.

[0043] Direction finding and localization methods are categorized into those targeting coherent signal interference and those targeting high-noise signal interference, depending on the specific scenario. The presence of coherent signal interference within the scenario is determined using a multi-signal classification method. When coherent signal interference exists in the scenario, a forward and backward spatial smoothing method is employed for direction finding and localization. When there is no coherent signal interference in the scenario but weak signals may exist, an extended noise subspace is used.

[0044] (3) After all the measurement information obtained by the mobile base station at the current moment has been collected, all the files constitute the measurement information required for positioning. All the measurement information collected by the mobile base station at the current moment is used as the input of the positioning server. The measurement information of the same mobile point tag to be located is grouped into a set of location information of the mobile point to be located. The positioning server calculates the optimal location estimate and mobile point status of the current positioning mobile point by combining the current location information of the mobile point to be located with the optimal location estimate and mobile point status of the mobile point to be located at the past moment through the unscented Kalman filter algorithm. The above steps are repeated to obtain the optimal location estimate and mobile point status of all mobile points to be located at the current moment.

[0045] (4) Transmit the best estimated position and status of all the mobile points to be located at the current time to the database, update the best estimated position and status of the mobile points to be located at the past time, and end the current time positioning.

[0046] (5) Based on the process model, move the mobile point to be located and the base station, repeat steps (2), (3) and (4) to track the movement of the mobile point to be located until the preset test time or the preset number of tests is reached, and then terminate the positioning.

[0047] It should be understood that the specific embodiments described above are merely illustrative or explanatory of the principles of the invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the invention should be included within the protection scope of the invention. Furthermore, the appended claims are intended to cover all variations and modifications falling within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. A method for tracking and locating a mobile object based on Bluetooth signals, characterized in that, The receiving end of the mobile base station receives the Bluetooth signal transmitted by the mobile point to be located, and locates multiple mobile points by installing a GPS / BeiDou locator on a single mobile base station, including the following steps: (1) Ranging and positioning are performed based on the RSSI value method to measure the distance between the mobile point to be located and the mobile base station; (2) Determine whether there is coherent signal interference in the Bluetooth signal of the currently received mobile point to be located based on the multiple signal classification method; (3) If the received Bluetooth signal of the mobile point to be located has coherent signal interference, the forward and backward spatial smoothing method is selected to locate the direction of the mobile point to be located relative to the mobile base station. If the received signal has no coherent signal interference, the extended noise subspace method is selected to locate the direction of the mobile point to be located relative to the mobile base station. (4) Combine the distance between the mobile point to be located and the mobile base station obtained in step (1) and the orientation of the mobile point to be located relative to the mobile base station obtained in step (3) to obtain the current position observation value of the mobile point to be located. (5) Combining the past state of the target point and the current position observation of the target point, the Kalman filter gain is calculated using the unscented Kalman filter method. The current position observation of the target point is then corrected to obtain the optimal estimate of the real-time position, thereby achieving real-time motion tracking; where: In step (2), the multiple signal classification method is as follows: Step S201: Collect the Bluetooth signal of the moving point to be located once; Step S202: Calculate the array covariance matrix of the received Bluetooth signal based on the collected Bluetooth signal. Step S203: Obtain the signal spatial spectrum function by eigenvalue decomposition of the array covariance matrix of the received Bluetooth signal; Step S204: The results of the multiple signal classification method are obtained by frequently searching the spectral peaks of the signal spatial spectral function to determine whether there is any coherent signal interference. In step (3), the forward and backward spatial smoothing method is as follows: Step S301: Divide the uniform receiving array into multiple subarrays that have the same array manifold matrix; Step S302: Perform weighted averaging on the covariance matrix of the received signals of each subarray. Step S303: The signal spatial spectrum function is obtained by eigenvalue decomposition of the covariance matrix of the signal array after weighted averaging. Step S304: The orientation of the moving point to be located relative to the mobile base station under coherent signal interference is obtained by frequently searching the spectral peaks of the signal spatial spectrum function. In step (3), the method for expanding the noise subspace is as follows: Step S401: Perform eigenvalue decomposition on the covariance matrix of the signal array, dividing it into a noise subspace and a signal subspace based on eigenvalues. between; Step S402: Find the strong signal subspace based on the results of the multiple signal classification method; Step S403: Incorporate the strong signal subspace into the noise subspace to construct an extended noise subspace; Step S404: Spatial spectrum estimation is performed using the extended noise subspace to determine the orientation of the mobile point to be located relative to the mobile base station under coherent signal interference.

2. The mobile tracking and positioning method based on Bluetooth signals according to claim 1, characterized in that, In step (5), the Kalman filter gain is calculated using the unscented Kalman filter method, and the current position observation value of the moving point to be located is corrected to obtain the optimal estimate of the real-time position in order to achieve real-time motion tracking. The method is as follows: Step S601: Predict the state of the moving point to be located at the next moment based on the process model and the state of the point to be located at the past moment. Based on the state and covariance matrix of the moving point to be located in the past, a proportionally modified symmetric sampling strategy is used to generate the sigma points and their corresponding weights in the past. The process model is used to project the sigma points from past time steps forward to obtain the one-step sigma prediction point at the current time step; the mean and covariance of the one-step sigma prediction point at the current time step step are calculated based on the unscented transformation. Step S602: Map the current position observation value of the moving point to be located to the observation model and the predicted state of the point to be located. Based on the mean and covariance of the one-step sigma prediction point at the current time, a new sigma point and its corresponding weight are generated by proportionally correcting the symmetric sampling strategy. The new sigma point is mapped to the two-step sigma prediction point at the current time through the observation model. The mean and covariance of the two-step sigma prediction point are calculated based on the unscented transformation. Step S603: Obtain the Kalman gain by using the current position observation value and actual measurement value of the moving point to be located, generate the optimal estimate value of the moving point to be located at the current time and return the positioning result, and update the state of the moving point to be located at the past time. The residuals and Kalman gain are calculated based on the mean and covariance of the two-step sigma prediction points and the observed position of the moving point to be located at the current time. The optimal estimated position of the moving point to be located at the current time is generated by the residuals and Kalman gain. Update the optimal position estimate and covariance matrix of the point to be located, and return the optimal position estimate of the point to be located at the current time.