Low-delay high-precision single-satellite passive positioning method and system

Abstract

The invention discloses a low-delay high-precision single-satellite passive positioning method, which mainly solves the problems of large positioning error, long positioning time and more satellite positioning resources in the prior art. According to the implementation scheme, the method comprises the steps that a satellite monitoring signal frequency Doppler frequency equation set is constructed, a monitoring area is divided into grids with equal longitude and latitude, the residual sum of squares of the grids is calculated to obtain a candidate position set, 2-clustering is carried out, and first elements of two position point sets are obtained; repeating the steps every time the time window slides for one monitoring time unit, and updating the two position point sets; calculating the dispersion of the two types of position point sets, distinguishing real point sets, calculating the average latitude and longitude of the real point sets, and determining the position of a target signal source; and sliding the time window to continuously update the positioning result until the satellite cannot detect the target signal source, and outputting a final positioning result. The method can reduce the positioning error, shorten the positioning time, improve the positioning speed of the target radiation source, and can be used for determining the position of the ground electromagnetic signal radiation source on the satellite.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic spectrum monitoring, and particularly relates to a method and system for locating electromagnetic signal sources from a single satellite, which can be used to determine the location of electromagnetic signal radiation sources on the ground from a satellite. Background Technology

[0002] In recent years, with the rapid development of electronic information technology, electromagnetic signal positioning has been widely used in both military and civilian fields. Electromagnetic signal positioning technology is divided into passive and active positioning based on the signal source. Passive positioning technology, due to its lack of active signal transmission, has advantages such as low cost and strong concealment, and is widely used in frequency management, military applications, and other fields. With the continuous development and improvement of space technology, passive positioning technology has gradually expanded from the ground to the air. Satellites, as a carrier for the current deployment of passive positioning technology, not only fully leverage the advantages of passive positioning and greatly expand its application areas compared to ground-based passive positioning technology, but also have a larger reconnaissance range and stronger concealment. Especially with the development of microsatellites, satellite passive positioning has gradually become one of the most effective and popular passive positioning methods. However, satellite passive technology suffers from limitations in payload and energy. With the continuous development of frequency measurement technology, single-satellite passive positioning technology based on Doppler information uses the Doppler effect generated by the relative motion between the signal source and the satellite to calculate the target signal location, providing reliable technical support for solving the above problems.

[0003] In his paper "Research on Key Technologies of Passive Positioning for Low-Earth Orbit Satellites," Zhu Chongru proposed a positioning ambiguity resolution method based on nadir point trajectory. This method approximates the nadir point trajectory as a linear function, selecting the latitude and longitude coordinates corresponding to a peak on each side of the trajectory during a single positioning time period as the positioning result. Then, using a time-division revisit method, the N times of satellite transit are divided into K time periods. Based on the divergent nature of the spurious point coordinates in the positioning results of the K time periods, the set of spurious point coordinates is eliminated, leaving the set of true coordinates. The average of the true coordinates is then used as the final positioning result. This technical solution uses a nadir point trajectory functionization algorithm and a time-division revisit algorithm for passive positioning. Due to the approximately symmetrical nature of the Doppler effect on both sides of the nadir trajectory, when the nadir point is close to the radiation source, the true positioning point and the false positioning point will be located on the same side of the approximately linear function of the nadir trajectory. Therefore, the peak values ​​selected from both sides of the nadir trajectory will have a significant impact on the positioning error. At the same time, since this method uses time-division revisit, it prolongs the time required to locate the target radiation source.

[0004] Patent document CN112114341A discloses a "Low-Earth Orbit Satellite Cooperative Frequency Measurement Passive Positioning Method," which uses Gauss-Newton iteration to calculate the coordinates of a ground radiation source. It employs weighted calculations based on the coordinate measurements of the target radiation source from multiple low-Earth orbit satellites to determine the final coordinate values. However, the initial value selection in the Gauss-Newton iteration algorithm is sensitive and prone to getting trapped in local optima, requiring iterative calculations and thus resulting in high computational complexity. Furthermore, the use of multiple satellites to calculate the position of the target radiation source makes implementation difficult. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing satellite passive positioning technologies by proposing a low-latency, high-precision single-satellite passive positioning method and system. This aims to reduce positioning errors in scenarios where the radiation source is close to the satellite's ground trajectory, shorten the time required to locate the target radiation source, and reduce the number of positioning satellites required.

[0006] The technical solutions for achieving the objectives of this invention include:

[0007] Technical Solution 1: A low-latency, high-precision single-satellite passive positioning method, characterized by comprising:

[0008] A set of Doppler frequency equations is constructed for the satellite monitoring signal frequency within a single time window, and the monitoring area of ​​the satellite within that time window is divided into a grid of equal latitude and longitude.

[0009] The residual sum of squares of the Doppler frequency equations is calculated to obtain the candidate location set. The candidate location set within a single time window is then 2-clustered using a clustering algorithm to obtain the first element of the two location point sets, thus achieving accurate separation of false points from true points.

[0010] Based on the characteristic that the set of real location points aggregates while the set of false location points gradually diverges as the satellite approaches the radiation source, a sliding window algorithm is adopted. The above steps are repeated every time the time window slides by one monitoring time unit to update the two sets of location points and calculate the dispersion of the two types of location point sets.

[0011] By distinguishing the set of false points based on the dispersion of the two types of location point sets, the true location point of the radiation source can be determined and output early, thus completing the target positioning. Furthermore, the positioning accuracy can be continuously improved by sliding the time window.

[0012] Technical Solution 2: A low-latency, high-precision single-satellite passive positioning system, characterized in that it includes:

[0013] The grid division module is used to divide the monitoring area into grids within a single time window and convert the latitude and longitude coordinates of the grid center point into three-dimensional coordinates of the Earth's core and solid surface.

[0014] The candidate location calculation module is used to calculate the residual sum of squares for each grid center point and select the m grid centers with the smallest residual sum of squares as the candidate location set.

[0015] The clustering module is used to perform 2-clustering on the candidate location set;

[0016] The discreteness calculation module is used to calculate the discreteness of two sets of points at different locations.

[0017] The positioning result output module is used to compare the dispersion of two different sets of location points, determine the set of location points that meet the judgment conditions of false point sets, calculate the average latitude and longitude of the real point set as the positioning result output, and continuously output the updated positioning result according to the sliding time window.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] Firstly, this invention uses a clustering algorithm to perform 2-clustering on the candidate location set within a single time window, determining two possible location results from the candidate location set, thus achieving accurate separation between real and false location points. In scenarios where the radiation source is close to the trajectory of the satellite's nadir point, this invention reduces the positioning error compared to traditional single-satellite positioning algorithms.

[0020] Secondly, this invention uses a sliding time window for dynamic observation and continuously calculates the degree of dispersion of two sets of positioning points. When the differentiation condition is met, the false point set and the real point set are determined, thus realizing the early determination of the real location points and reducing the positioning time.

[0021] Third, this invention uses a single satellite to locate the target radiation source. Compared with existing satellite positioning algorithms, it does not require multiple satellites to simultaneously view the target radiation source or for data communication between satellites, thus reducing the demand for satellite positioning resources. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention;

[0023] Figure 2 This is a functional block diagram of the system of the present invention;

[0024] Figure 3 This is a comparison chart of the positioning errors of the present invention and Zhu Chongru's nadir point trajectory functionization algorithm;

[0025] Figure 4 This is a two-dimensional representation of the latitude and longitude of the two types of location points in this invention;

[0026] Figure 5 This is a graph showing the trend of the positioning error of the present invention as the time window slides. Detailed Implementation

[0027] The embodiments and effects of the present invention will be further described in detail below with reference to the accompanying drawings.

[0028] This example uses a single satellite to locate ground-based radiation sources.

[0029] Reference Figure 1 The implementation steps for the instance include the following:

[0030] Step 1: Establish the Doppler frequency equations.

[0031] A single satellite continuously detects signals at time intervals τ, starting to detect the target signal at time t1, and continuously records the frequency f of the signal. i , until no target signal can be detected;

[0032] Based on the satellite position, velocity, and estimated transmission frequency f0 of the signal at all detection times within the time window (t1, t1+nτ), the following Doppler frequency equations are constructed:

[0033]

[0034] Among them, f i Let fi be the satellite measurement frequency value at time i within this time window, f0 be the estimated transmission frequency of the signal, and (x,y,z) be the three-dimensional coordinates of the radiation source. i ,y i ,z i Let (v) be the three-dimensional coordinates of the satellite at time i, and (v) be the coordinates of the satellite at time xi ,v yi ,v zi Let be the three-dimensional velocity vector of the satellite at time i, where c is the speed of light, and r is the velocity vector of the satellite at time i. i Let be the straight-line distance between the satellite and the radiation source at time i, where i = 1, 2, ..., n+1, and n+1 is the number of detection times of the frequency within this time window.

[0035] Step 2: Grid generation.

[0036] The satellite's monitoring range within this time window is too large, so the monitoring area needs to be divided into grids to determine the optimal location of the target radiation source. The fineness of the grid division will greatly affect the positioning error of this algorithm.

[0037] 2.1) The satellite will be launched within the time window (t) b ,t b The monitoring area D covered by +nτ) is divided into H×L grids at equal intervals according to latitude and longitude, where the center point C of the k-th grid is... k The latitude and longitude coordinates are (λ k , ), k = 1, 2, ..., H × L;

[0038] 2.2) Set the latitude and longitude coordinates (λ) of each grid center point. k , Convert to Earth-centered Earth-fixed coordinates (x) k ,y k ,z k ):

[0039]

[0040] Where e is the first eccentricity of the Earth. Let λ be the latitude of the center point of the grid. k The longitude of the center point of this grid. denoted as y, the length from the center point of the grid along the normal to the y-axis of the meridian plane in the rectangular coordinate system, where a is the length of the Earth's semi-major axis.

[0041] Step 3: Calculate the set of candidate locations for the current positioning window.

[0042] Due to the symmetry of the Doppler effect, there are false points in the current positioning window that are symmetrical to the target radiation source position with respect to the satellite's nadir trajectory. Therefore, it is necessary to first select a certain number of grids as the set of candidate positions that are most likely to be the true points.

[0043] 3.1) Using the center point of each grid as the location of the radiation source, calculate the sum of squared residuals:

[0044]

[0045] Among them, RSS k This represents the sum of squared residuals at the k-th grid center point;

[0046] 3.2) Select the grid center point with the smallest sum of squared residuals among the first m. As a set of candidate locations.

[0047] Step 4: Perform 2-clustering on the candidate location set using a clustering algorithm.

[0048] Existing clustering algorithms include K-means clustering, density-based DBSCAN, and reinforcement learning clustering. Since K-means clustering has extremely low computational complexity and is simple to implement, and allows specifying the number of clusters, this embodiment uses K-means clustering to perform 2-clustering on the candidate location set to determine the unique true and false points symmetrical about the nadir trajectory. Its specific implementation includes the following:

[0049] 4.1) Take the m elements in the candidate location set as the clustered dataset, and pre-specify the number of clusters as 2;

[0050] 4.2) Randomly select two data points as the initial cluster centers;

[0051] 4.3) Cluster Assignment: For each sample in the dataset, calculate its distance to the two cluster centers, and assign each sample to the cluster corresponding to the nearest cluster center;

[0052] 4.4) Update cluster center: For each divided cluster, calculate the average value of all data points in the cluster and use this average value as the new cluster center;

[0053] 4.5) Repeat steps 4.3) to 4.4) until the cluster centers no longer change significantly, and obtain the clustering results;

[0054] 4.6) The grid center point with the smallest sum of squared residuals within each cluster is taken as the possible location result within the time window, which is the undifferentiated real point and false point, and is taken as the first element of the two sets of observation location points.

[0055] Step 5: Update the two location point sets.

[0056] 5.1) Sliding time window: Repeat steps one through four every τ time units to obtain two possible positioning results. Calculate the distances d1 and d2 from each of the points to the center of any set of points:

[0057]

[0058] in, The average latitude and longitude center of this set of locations;

[0059] 5.2) Compare the distances d1 and d2 from the two possible positioning results to the center of either location point set, and update the location point set accordingly:

[0060] If d1 < d2, then Assign it to this set of location points Assign it to another set of location points;

[0061] If d1 > d2, then Assign it to this set of location points Assign it to another set of location points;

[0062] 5.3) Determine whether to distinguish between the set of false points and the set of true points:

[0063] If there is no distinction, proceed to step six;

[0064] If the distinction has been made, proceed to step seven.

[0065] Step six: Calculate the degree of dispersion and distinguish between the two types of location point sets.

[0066] 6.1) Calculate the distance d from the i-th location result in the first type of location point set to the centroid of the set. 1i :

[0067]

[0068] Among them, (x 1i ,y 1i ,z 1i Let be the geocentric and geofixed coordinates of the i-th location result in the first set. The coordinates of the centroid in the first type of set;

[0069] 6.2) Calculate the distance d from the i-th location result in the second type of location point set to the centroid of the set. 2i :

[0070]

[0071] Among them, (x 2i ,y 2i ,z 2i Let be the geocentric and geofixed coordinates of the i-th location result in the second set. The coordinates of the centroid in the second type of set;

[0072] 6.3) Calculate the discreteness of the two types of location point sets.

[0073]

[0074] Where q is the number of time windows;

[0075] 6.4) Distinguishing between true and false attributes for two types of location point sets:

[0076] if And if it has already been p-1 times consecutively Then, the first set of location points is determined to be the set of false points, and the second set of location points is determined to be the set of real points. Proceed to step seven; if there have been no consecutive p-1 times before... If the two sets of location points cannot be distinguished, return to step one, where p is the manually set threshold for the number of judgments;

[0077] if And if it has already been p-1 times consecutively Then, the first set of location points is determined to be the set of real points, and the second set of location points is determined to be the set of spurious points. Proceed to step seven; if there have been no consecutive p-1 times before... If the two sets of location points cannot be distinguished, return to step one;

[0078] if If the two sets of location points cannot be distinguished, return to step one.

[0079] Step 7: Output the location results.

[0080] 7.1) Calculate the average latitude and longitude based on the confirmed set of real points. As the location of the target signal source, output the positioning result for this round;

[0081] 7.2) After sliding the time window for τ units, return to step one and calculate the positioning results for the next round;

[0082] 7.3) Repeat step 7.2) until the satellite can no longer detect the target signal source, and output the final positioning result.

[0083] Example 2: Low-latency, high-precision single-satellite passive positioning system.

[0084] Reference Figure 2 This example includes a mesh generation module 1, a candidate location calculation module 2, a clustering module 3, a dispersion calculation module 4, and a location result output module 5. Its working principle is as follows:

[0085] The grid division module 1 divides the monitoring area within a single time window into grids and converts the latitude and longitude coordinates of the grid center points into geocentric and geofixed three-dimensional coordinates. The candidate location calculation module 2 calculates the residual sum of squares for each grid center point and selects the grid center with the smallest residual sum of squares as the candidate location set, which is then input to the clustering module 3. The clustering module 3 performs 2-clustering on the candidate location set and updates the two types of location point sets, which are then input to the dispersion calculation module 4. The dispersion calculation module 4 calculates the dispersion of the two types of location point sets and compares them: if the true point set and the false point set can be distinguished, the result is output to the positioning result module 5; if the true point set and the false point set cannot be distinguished, the result is returned to the grid division module 1. The positioning result output module 5 calculates the average latitude and longitude of the true point set as the positioning result for this round, slides the time window, and returns to the grid division module 1 until the satellite can no longer detect the target signal source, at which point the final positioning result is output.

[0086] The effects of this invention will be further illustrated below with simulation experiments:

[0087] 1. Simulation parameter settings:

[0088] The simulation experiment software platform is as follows: the experimental computer operating system is Windows 10 (64-bit), the memory is 32GB, and the processor configuration is: Intel(R) Core(TM) i7-10870H CPU@2.20GHz 2.21GHz. It is implemented using STK software in conjunction with MATLAB. The STK version is 11.6 and the MATLAB version is 2024b.

[0089] The parameter settings for the signal source, communication environment, and satellite in STK are shown in Table 1:

[0090] Table 1 Signal Source, Communication Environment, and Satellite Parameter Settings

[0091] parameter Value Earth Model WGS-84 Rain attenuation model ITU-R_P618-8 Ionospheric scintillation model ITU-R_P618-12 Atmospheric loss model ITU-R_P676-9 ground temperature 293.15K Ground signal source transmission frequency 1.3GHz signal power 20dBW Signal modulation type BPSK signal bandwidth 10MHz Antenna type Non-directional Gaussian antenna Antenna gain 15.6dB Tropospheric refractive index 4 / 3 satellite model Ningxia No. 1 Satellite observation angle 60° Monitoring time interval 1s Actual location of the signal source (34.9363N, 109.966E)

[0092] 2. Simulation Content and Results

[0093] Simulation 1: Under the above environmental configuration and parameter settings, the target signal source was located using both the present invention and the existing Zhu Chongru's nadir point trajectory function algorithm. The positioning error for each time window was calculated, and the results are as follows: Figure 3 As shown. From Figure 3 It can be seen that during the time the satellite passes over the signal, the positioning error of this invention is significantly better than that of Zhu Chongru's positioning algorithm.

[0094] Simulation 2: Under the above environmental configuration and parameter settings, the present invention is used to locate the target signal source, and the latitude and longitude of the two types of location points are calculated. The results are as follows: Figure 4 As shown. Among them Figure 4 (a) represents the two-dimensional latitude and longitude of the real point set. Figure 4 (b) is the two-dimensional latitude and longitude of the set of spurious points.

[0095] from Figure 4 As can be seen, the discrepancies between the real point set and the false point set are quite large. This invention can better distinguish between the real point set and the false point set and determine the location of the target radiation source.

[0096] Simulation 3: Under the above environmental configuration and parameter settings, the present invention is used to locate the target signal source, and the positioning error in each round is calculated. The results are as follows: Figure 5 As shown, it can be seen that by sliding the time window, the positioning error of the present invention gradually decreases, and the final positioning error is within 200m.

[0097] The simulation results above show that the present invention can effectively solve the problem of large positioning error in existing methods when the radiation source is close to the trajectory of the satellite, and can significantly reduce the positioning time. By sliding the time window, the positioning accuracy can be improved.

[0098] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the protection scope of the claims of the present invention.

[0099] It should be noted that the step numbers in the specification and claims of this invention are only for the purpose of clearly describing the embodiments of this invention and facilitating understanding, and their order is not limited.

Claims

1. A low-latency high-precision single-satellite passive positioning method, characterized in that, The method comprises the following steps: A Doppler frequency equation set is constructed according to the satellite monitoring signal frequency in a single time window, and the monitoring area of the satellite in the time window is divided into an equal latitude-longitude grid; Residual sum of squares of the Doppler frequency equation set of each grid is calculated to obtain a candidate position set, and 2-clustering is performed on the candidate position set in the single time window by using a clustering algorithm to obtain the first elements of two position point sets, and accurate separation of false points and real points is realized; According to the characteristics that the real positioning point set gradually converges and the false positioning point set gradually diverges in the process that the satellite gradually approaches the radiation source, a sliding time window algorithm is adopted, the above steps are repeatedly executed, and the two position point sets are updated and the dispersion degrees of the two types of position point sets are calculated when the time window slides by one monitoring time unit; The false point set is distinguished according to the dispersion degrees of the two types of position point sets, early determination and output of the real position point of the radiation source are realized, target positioning is completed, and the positioning accuracy is continuously improved according to the sliding of the time window.

2. The method of claim 1, wherein, The Doppler frequency equation set is constructed according to the satellite monitoring signal frequency in a single time window, and the monitoring area of the satellite in the time window is divided into an equal latitude-longitude grid; The single satellite continuously performs signal detection with a time interval τ, starts to monitor the target signal at time t1, and continuously records the frequency f of the signal until the target signal is not detected i . A Doppler frequency equation set is constructed according to the satellite position, speed and estimated signal transmission frequency f0 of all detection time points in the time window (t1, t1+nτ): where f i is the satellite measurement frequency value at time i in the time window, f0is the estimated transmission frequency of the signal, (x, y, z) is the three-dimensional coordinates of the radiation source, (x i ,y i ,z i ) is the three-dimensional coordinates of the satellite at time i, (v xi ,v yi ,v zi ) is the speed three-dimensional vector of the satellite at time i, c is the speed of light, r i is the straight-line distance between the satellite and the radiation source at time i, where i = 1, 2,... n + 1, and n + 1 is the number of detection times of the frequency in the time window.

3. The method of claim 1, wherein, The monitoring area of the satellite in the time window is divided into an equal latitude-longitude grid, and the latitude and longitude coordinates of the grid center points are converted into geocentric and terrestrial three-dimensional coordinates; The monitoring area D covered by the satellite in the time window (t1, t1+nτ) is divided into HxL grids with equal intervals of longitude and latitude, wherein the longitude and latitude coordinates of the center point C of the kth grid are k wherein k = 1, 2,..., HxL;​ Convert the longitude and latitude coordinates of each grid center point to geocentric geodetic coordinates (x k ,y k ,z k ): where e is the first eccentricity of the earth, is the latitude of the center of the grid, λ k is the longitude of the center of the grid, is the length of the grid center point along the normal to the y-axis of the rectangular coordinate system in the meridian plane, and a is the length of the semi-major axis of the earth.

4. The method of claim 1, wherein, The residual sum of squares of each grid center point is calculated, and m grid center points with the smallest residual sum of squares are selected as the candidate position set; 2-clustering is performed on the candidate position set by using a clustering algorithm, and the first elements of two position point sets are obtained; where RSS k the residual sum of squares representing the kth grid center point; Select the grid center point with the smallest residual sum of squares of the first m as a candidate position set.

5. The method of claim 1, wherein, m elements in the candidate position set are taken as a clustering data set, and the clustering algorithm is used to cluster the m elements into two clusters; The grid center point with the smallest residual sum of squares in each cluster is taken as a possible positioning result in the time window, and is taken as the first element of the two types of position point sets to be observed. The two position point sets are updated, and the dispersion degrees of the two types of position point sets are calculated; 6. The method of claim 1, wherein, 6b) The distances d1 and d2 of the two possible positioning results to the center of any one of the position point sets are compared, and the position point sets are updated; 6a) sliding time window, two possible positioning results are obtained for each time window of τ time units Calculate the distance d1, d2 to the center of any set of position points, respectively wherein, is the average longitude and latitude center of the set of location points; The false point set is distinguished according to the dispersion degrees of the two types of position point sets, early determination and output of the real position point of the radiation source are realized, target positioning is completed, and the positioning accuracy is continuously improved according to the sliding of the time window. If d1 < d2, then the location point set is divided into the location point set is divided into another location point set. If d1 > d2, then the location point set is divided into the location point set is divided into another location point set. 6c) calculating the dispersion of the two sets of position points wherein, is the distance from the i-th positioning result in the first set of position points to the centroid of the set, (x 1i ,y 1i ,z 1i ) is the geodetic coordinate of the i-th positioning result in the first set, is the coordinate of the centroid of the first set, and q is the number of time windows. is the distance of the i-th position result in the second set of position points to the centroid of the set, (x 2i ,y 2i ,z 2i ) is the geodetic coordinate of the i-th position result in the second set, is the coordinate of the centroid of the second set.

7. The method of claim 1, wherein, The positioning result of the new time window is continuously added to the real point set by sliding the time window; The method comprises the following steps: Computing average longitude and latitude of positioning results in a set of real points Coordinates of the target signal source are output as the position of the target signal source.

8. The method of claim 1, wherein, A grid division module is configured to divide the monitoring area in a single time window into a grid, and convert the latitude and longitude coordinates of the grid center points into geocentric and terrestrial three-dimensional coordinates; A candidate position calculation module is configured to calculate the residual sum of squares of each grid center point, and select m grid center points with the smallest residual sum of squares as a candidate position set; recomputing the average longitude and latitude in the set of fix points As the updated target signal source position, the position of the target signal source gradually approaches the real position of the radiation source, and the positioning accuracy is improved.

9. The method of claim 7, wherein, calculating the average longitude and latitude of the positioning result in the set of real points The formula is as follows: wherein, is the positioning result in the real point set under the i-th time window.

10. A low-latency high-precision single-satellite passive positioning system, characterized in that, A clustering module is configured to perform 2-clustering on the candidate position set. ​ ​ ​ The dispersion calculation module is configured to calculate the dispersion of the two different position point sets; The positioning result output module is configured to compare the dispersion of the two different position point sets, determine the position point set satisfying the false point set judgment condition, calculate the average longitude and latitude of the true point set as the positioning result output, and continuously output the updated positioning result according to the time window sliding.

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