Multi-source opportunity signal online screening optimization method and system based on density clustering

Abstract

The invention discloses a multi-source opportunity signal online screening optimization method and system based on density clustering, and belongs to the technical field of navigation positioning. According to the method, the pre-estimated positioning point set is generated by analyzing the types and characteristics of the opportunity signals, the known information of the signals is fully utilized, and the screening accuracy and efficiency are improved; density clustering is carried out on the pre-estimated positioning points to generate a cluster set, so that the authenticity and the abnormality of the signals can be distinguished; the abnormal opportunity signals are effectively identified and eliminated by using dual criteria of density clustering and support degree-contour coefficient; through a credible interval division mechanism in the step 3, screening a high-density cluster as a credible positioning interval, and eliminating interference of discrete abnormal points; the signals with the highest support degree are screened out one by one in turn and are clustered again, and the screened-out signal corresponding to the maximum contour coefficient is selected as the abnormal signal, so that the scientificity and accuracy of the screening process are ensured, and the accuracy and stability of positioning are improved.

Description

Technical Field

[0001] The present invention relates to the field of navigation and positioning technology, and in particular to a multi-source opportunity signal online screening optimization method and system based on density clustering. Background Art

[0002] As the current mainstream positioning and navigation technology, the global satellite positioning system has shown a high degree of maturity and accuracy in open outdoor areas. However, when faced with complex scenarios such as indoor environments, tunnels, densely populated areas, or when the system itself is damaged or fails, its positioning and navigation functions are often limited and cannot provide stable and reliable services. This limitation has prompted researchers to explore alternative or supplementary autonomous navigation solutions, among which navigation technology based on opportunity signals has emerged as a strong candidate for solving the above problems.

[0003] Navigation via Signals of Opportunity (NAVSOP) technology makes full use of the radio wave signals that are widely distributed in different frequency bands in the space domain as navigation resources. These opportunity signals are not only abundant in resources and diverse in user choices, but also provide a large amount of complementary information and have significant advantages such as high power and strong penetration. More importantly, NAVSOP technology does not need to rely on additional signal transmitters. Users can directly capture these signals from the environment for positioning, thereby reducing hardware costs and deployment difficulties.

[0004] In recent years, the NAVSOP research field has shown a booming trend. Domestic and foreign scholars have proposed a variety of innovative positioning methods around different types of SOP (Signals of Opportunity). For example, Wang Qin et al. achieved more accurate indoor positioning by improving the indoor TOA (Time of Arrival) ranging error model based on RSSI (Received Signal Strength Indicator) signals; Mauro Boccadoro et al. constructed a general framework for TDOA (Time Difference of Arrival) positioning under non-line-of-sight (NLOS) conditions, improving the positioning performance in complex environments; Heidi Steendam et al. developed a visible light AOA (Angle of Arrival) iterative positioning algorithm based on maximum likelihood estimation, providing new ideas for indoor light positioning; Hailiang Xiong proposed a hybrid positioning solution combining RSSI and arrival time information, further improving the reliability and accuracy of positioning.

[0005] However, despite the great application potential shown by the NAVSOP technology, it still faces an important challenge in practical applications: due to the interference of environmental noise, some received signals have static biases, which will directly affect the stability and accuracy of the navigation results. Unfortunately, the current research has not been able to effectively solve this problem, resulting in certain limitations in the positioning performance of the NAVSOP technology. Therefore, how to achieve online screening of multi-source opportunistic signals with unknown static biases and improve navigation accuracy has become a technical problem that needs to be overcome by those skilled in the art. Summary of the Invention

[0006] The purpose of the present invention is to provide an online screening and optimization method and system for multi-source opportunistic signals based on density clustering to overcome the problem in the prior art that it is unable to effectively cope with the static bias caused by environmental noise, thereby affecting the positioning accuracy.

[0007] The present invention solves the above technical problems through the following technical solutions: An online screening and optimization method for multi-source opportunistic signals based on density clustering includes the following steps: Step 1: According to the solvability of opportunistic signal navigation, randomly group the m opportunistic signals received by the aircraft. Based on the type of opportunistic signals, construct a ternary non-linear equation system for each group of opportunistic signals, and solve the ternary non-linear equation system through the Newton iteration method to generate a set of estimated positioning points P k , where the subscript k is the number of times of screening out abnormal opportunistic signals. At this time, k = 0; Step 2: Perform density clustering on the set of estimated positioning points P k to generate a set of clustering clusters J k ; Step 3: Calculate the density of each clustering cluster in the set of clustering clusters J k , and divide the clustering cluster with the highest density into a credible interval A k , and the remaining clustering clusters into an uncredible interval B k ; Step 4: Calculate the support degree of the opportunistic signal corresponding to each estimated positioning point in the uncredible interval B k . If the opportunistic signal with the highest support degree is unique, determine that the opportunistic signal is an abnormal opportunistic signal; otherwise, sequentially and alternately screen out each opportunistic signal with the highest support degree, re-cluster and calculate the silhouette coefficient, and select the opportunistic signal with the highest support degree corresponding to the maximum silhouette coefficient as the abnormal opportunistic signal; Step 5: Screen out the abnormal opportunistic signals, let k = k + 1, generate a set of estimated positioning points P k and a set of clustering clusters J k , and repeat Step 3 and Step 4 until the number of clustering clusters in the set of clustering clusters J k is unique; Step 6: Calculate the geometric center coordinates of the unique clustering cluster as the positioning result of the aircraft.

[0008] A further improvement of the present invention lies in that: Step 4 specifically is: Calculate the untrusted interval B k the support degree of the opportunity signal corresponding to each estimated positioning point in it, determine whether the opportunity signal with the highest support degree is unique. If the judgment result is yes, then this opportunity signal is an abnormal opportunity signal; if the judgment result is no, then sequentially and alternately screen out the opportunity signal with the highest support degree. After each round of re-density clustering of the remaining opportunity signals, calculate the silhouette coefficient, and select the round corresponding to the largest silhouette coefficient. The opportunity signal with the highest support degree screened out in this round is the abnormal opportunity signal; Step 5 specifically is: Screen out the abnormal opportunity signal, let k = k + 1, randomly group the remaining opportunity signals, and respectively construct a ternary non-linear equation system for each group of opportunity signals based on the type of opportunity signal, and solve the ternary non-linear equation system through the Newton iteration method to generate a set of estimated positioning points P k for the current set of estimated positioning points P k in all the estimated positioning points in it perform density clustering to obtain a set of clustering clusters J k and determine whether the number of clustering clusters in the set of clustering clusters J k is unique. If the judgment result is yes, then this clustering cluster is the unique clustering cluster; if the judgment result is no, then return to Step 3.

[0009] A further improvement of the present invention lies in that: in Step 5, if the judgment result is no, then the following steps are used for replacement: Calculate the density of each clustering cluster in the set of clustering clusters J k and divide the clustering cluster with the highest density into the trusted interval A k and the remaining clustering clusters into the untrusted interval B k ; Based on the trusted interval A k and the untrusted interval B k establish a function used to describe the landing positions of all the estimated positioning points in the current set of estimated positioning points P k and calculate the evaluation indexes and and ; Judge whether is greater than , if the judgment result is yes, then return to Step 4; if the judgment result is no, then restore the abnormal opportunity signal screened out this time, let k = k - 1, calculate the density of each clustering cluster in the set of clustering clusters J k and divide the clustering cluster with the second highest density into the trusted interval A k and the remaining clustering clusters into the untrusted interval Bk , and return to Step Four.

[0010] A further improvement of the present invention lies in that: in Step One, the specific method for randomly grouping the m opportunity signals received by the aircraft is as follows: each group of opportunity signals is 4, and there are a total of M groups of opportunity signals; where .

[0011] A further improvement of the present invention lies in that the function is specifically:

[0012] where is the j-th estimated positioning point in the set P of estimated positioning points k ; The evaluation index is specifically:

[0013] where , is the total number of estimated positioning points in the set P of estimated positioning points after the abnormal opportunity signals are screened out for the k th time.

[0014] A further improvement of the present invention lies in that: let the set of opportunity signals be N, , and the support degree is specifically:

[0015] where is the total number of clustering clusters in the untrusted interval B k ; is the th total number of remaining opportunity signals after the abnormal opportunity signals are screened out; h is the h-th clustering cluster in the untrusted interval B k ; is the judgment on the selection situation of the opportunity signal n i in the h-th cluster; n i is the i-th opportunity signal in the set N.

[0016] A further improvement of the present invention lies in that the types of opportunity signals include time of arrival, time difference of arrival, angle of arrival, received signal strength indication, and Doppler frequency shift difference.

[0017] A further improvement of the present invention lies in that the specific method for calculating the geometric center coordinates of the unique clustering cluster is:

[0018] where r is the total number of estimated positioning points in the unique clustering cluster, is the coordinate of the estimated positioning point in the only clustering cluster, and is the final positioning coordinate of the aircraft.

[0019] A further improvement of the present invention lies in: setting a clustering cluster set , and the density of the clustering cluster Specifically:

[0020] where u is the number of clustering clusters in the clustering cluster set J k ; J ki is the i-th clustering cluster in the clustering cluster set J k ; is any two points in the clustering cluster J ki .

[0021] The present invention also provides an online screening and optimization system for multi-source opportunistic signals based on density clustering, including the following modules: A preprocessing module, which is used to randomly group m opportunistic signals received by the aircraft according to the navigability based on opportunistic signals, construct a system of three-variable nonlinear equations for each group of opportunistic signals respectively based on the type of opportunistic signals, solve the system of three-variable nonlinear equations by the Newton iteration method, and generate a set of estimated positioning points P k , where the subscript k is the number of times of screening out abnormal opportunistic signals; A density clustering module, which is used to perform density clustering on the set of estimated positioning points P k to generate a set of clustering clusters J k ; An interval division module, which is used to calculate the density of each clustering cluster in the set of clustering clusters J k , divide the clustering cluster with the highest density into a credible interval A k , and divide the remaining clustering clusters into an uncredible interval B k ; An abnormal opportunistic signal recognition module: which is used to calculate the support degree of the opportunistic signal corresponding to each estimated positioning point in the uncredible interval B k . If the opportunistic signal with the highest support degree is unique, it is determined that the opportunistic signal is an abnormal opportunistic signal; otherwise, each opportunistic signal with the highest support degree is screened out one by one in turn, reclustered and the silhouette coefficient is calculated, and the opportunistic signal with the highest support degree corresponding to the maximum silhouette coefficient is selected as the abnormal opportunistic signal; An iteration module, which is used to screen out abnormal opportunistic signals, let k = k + 1, and generate a set of estimated positioning points P k and a set of clustering clusters J k , until the number of clustering clusters in the set of clustering clusters J k is unique; A positioning module, which is used to calculate the geometric center coordinates of the unique clustering cluster as the positioning result of the aircraft.

[0022] Compared with the prior art, the positive and progressive effects of the present invention are as follows: The online screening and optimization method for multi-source opportunistic signals based on density clustering provided by the present invention constructs an iterative screening model through Steps 1 to 6, thereby realizing the dynamic discrimination of the reliability of opportunistic signals, effectively overcoming the static deviation challenge faced by the NAVSOP technology in the prior art, and improving the stability and accuracy of the navigation result. Specifically: By analyzing the types and characteristics of opportunistic signals, constructing and solving a ternary nonlinear equation system to generate a set of predicted positioning points, making full use of the known information of the signals, and improving the accuracy and efficiency of screening; By performing density clustering on the predicted positioning points to generate a set of clustering clusters, which helps to distinguish the authenticity and abnormality of signals; Especially for signals with unknown static deviation, using the dual criteria of density clustering and support-degree silhouette coefficient to effectively identify and eliminate abnormal opportunistic signals; Through the credible interval partitioning mechanism in Step 3, screening the high-density clustering clusters as the credible positioning interval to eliminate the interference of discrete abnormal points; By sequentially and alternately screening out the signal with the highest support degree and re-clustering, and selecting the screened-out signal corresponding to the maximum silhouette coefficient as the abnormal signal, ensuring the scientificity and accuracy of the screening process and improving the accuracy and stability of positioning.

[0023] Furthermore, introducing a judgment mechanism for evaluation indicators can more accurately evaluate the quality of the current screening result. If the evaluation indicators indicate that the screening result is not ideal, then restore the abnormal opportunistic signals screened out this time and try to select the sub-optimal clustering cluster as the credible interval, which helps to avoid mis-screening important signals, improve the accuracy of the screening result, realize the dynamic adjustment and optimization of the screening process, and ensure that the screened signals are more reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings in the specification are used to provide a further understanding of the present invention, and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0025] Figure 1 It is a schematic flow chart of a method for online screening and optimization of multi-source opportunistic signals based on density clustering of the present invention without evaluation indicators; Figure 2 It is a logic block diagram of a method for online screening and optimization of multi-source opportunistic signals based on density clustering of the present invention including evaluation indicators; Figure 3 It is a schematic flow chart of a method for online screening and optimization of multi-source opportunistic signals based on density clustering of the present invention including evaluation indicators; Figure 4The figure of the comparative experiment results of the method of the present invention and the average value method when there is no static deviation; Figure 5 The figure of the comparative experiment results of the method of the present invention and the average value method when there is static deviation; Figure 6 The figure of the comparative experiment results of the method of the present invention and the average value method in the coordinate axis direction when there is static deviation; among them, figure (a) is the X-axis; figure (b) is the Y-axis; figure (c) is the Z-axis; Figure 7 The schematic diagram of different angles of the AOA information of the present invention; Figure 4 and Figure 5 In, the points of the blue line are the actual position coordinates; the points of the red line are the positioning point coordinates obtained by the method of the present invention; the points of the yellow line are the positioning point coordinates obtained by the average value method; Figure 6 In, the points of the blue dotted line are the values of the positioning point coordinates obtained by the method of the present invention on each coordinate axis; the points of the red dotted line are the values of the positioning point coordinates obtained by the average value method on each coordinate axis; the points of the black solid line are the values of the actual position coordinates on each coordinate axis. Specific embodiments

[0026] The following further elaborates on the present invention in detail in conjunction with the accompanying drawings and specific embodiments, which is an explanation rather than a limitation of the present invention.

[0027] See Figure 1 , a multi-source opportunistic signal online screening and optimization method based on density clustering, comprising the following steps: Step 1: According to the resolvability of opportunistic signal navigation, randomly group the m opportunistic signals received by the aircraft, and respectively construct a system of three nonlinear equations for each group of opportunistic signals based on the type of opportunistic signals, and solve the system of three nonlinear equations by the Newton iteration method to generate a set of estimated positioning points P k , where the subscript k is the number of times of screening out abnormal opportunistic signals. At this time, k = 0; Step 2: Perform density clustering on the set of estimated positioning points P k to generate a set of clustering clusters J k ;, , where u is the number of clustering clusters in the set of clustering clusters J k ; Step 3: Calculate the density of each clustering cluster in the set of clustering clusters J k , and classify the clustering cluster with the highest density as the credible interval A k , and classify the remaining clustering clusters as the non-credible interval B k ; Step 4: Calculate the non-credible interval B kFor each estimated positioning point, the support degree of the corresponding opportunity signal is calculated. If the opportunity signal with the highest support degree is unique, then this opportunity signal is determined as an abnormal opportunity signal; otherwise, each opportunity signal with the highest support degree is screened out one by one in turn, re-clustered, and the silhouette coefficient is calculated. The opportunity signal with the highest support degree that is screened out and corresponds to the maximum silhouette coefficient is selected as the abnormal opportunity signal; Step Five: Screen out the abnormal opportunity signals, let k = k + 1, and generate the set P of estimated positioning points k and the set J of clustering clusters k , and repeat Step Three and Step Four until the number of clustering clusters in the set J k is unique; Step Six: Calculate the geometric center coordinates of the unique clustering cluster as the positioning result of the aircraft.

[0028] Specifically, Step Four is as follows: Calculate the untrusted interval B k For each estimated positioning point, the support degree of the corresponding opportunity signal is calculated, and it is judged whether the opportunity signal with the highest support degree is unique. If the judgment result is yes, then this opportunity signal is an abnormal opportunity signal; if the judgment result is no, then the opportunity signal with the highest support degree is screened out one by one in turn. After re-density clustering the remaining opportunity signals in each round, the silhouette coefficient is calculated, and the round corresponding to the maximum silhouette coefficient is selected. The opportunity signal with the highest support degree screened out in this round is the abnormal opportunity signal; Step Five is specifically as follows: Screen out the abnormal opportunity signals, let k = k + 1, randomly group the remaining opportunity signals, and based on the type of opportunity signals, construct a system of three - variable non - linear equations for each group of opportunity signals, and solve the system of three - variable non - linear equations by the Newton iteration method to generate the set P of estimated positioning points k , for the current set P of estimated positioning points k all the estimated positioning points in it are density - clustered to obtain the set J of clustering clusters k , and it is judged whether the number of clustering clusters in the set J k is unique. If the judgment result is yes, then this clustering cluster is the unique clustering cluster; if the judgment result is no, then return to Step Three.

[0029] See Figure 2 and Figure 3 , specifically, in Step Five, if the judgment result is no, then the following steps are used for replacement: Calculate the density of each clustering cluster in the set J of clustering clusters, and divide the clustering cluster with the highest density into the trusted interval A k , and the remaining clustering clusters are divided into the untrusted interval B k ; k ; Based on the trusted interval A k and the untrusted interval B k , establish a function Used to describe the landing positions of all the estimated positioning points in the current estimated positioning point set P k Based on the function Calculate the evaluation index and ; Judge Whether it is greater than , if the judgment result is yes, return to step four; if the judgment result is no, restore the abnormal opportunity signal screened this time, let k = k - 1, calculate the density of each cluster in the cluster set J k , and divide the cluster with the second highest density into the credible interval A k , and divide the remaining clusters into the non-credible interval B k , and return to step four.

[0030] Specifically, in step one, the random grouping of the m opportunity signals received by the aircraft is specifically: each group of opportunity signals is 4, and there are a total of M groups of opportunity signals; among them, ; The signal set of the opportunity signals is N, .

[0031] For the solvability analysis of various opportunity signals, the number requirement of signals for the solvability of single-class opportunity signal positioning can be known. Based on the solvability results of single-class opportunity signals, the solvability conditions of multi-source opportunity signals can be obtained, which are specifically divided into the following three cases of solvable multi-source opportunity signal positioning: (1) Containing 2 groups of AOA signals; (2) Containing 1 group of AOA signals and 2 or more groups of other types of opportunity signals; (3) Not containing AOA signals, but containing 4 or more groups of other types of opportunity signals.

[0032] Since the AOA signal describes a spatial ray and other types of opportunity signals all describe spatial surfaces, 2 or more groups of non-AOA type opportunity signals determine a spatial curve. Combining with the spatial ray determined by the AOA signal, positioning and solving can be carried out, and thus the solvability situation (2) is obtained. Similarly, 2 or more groups of non-AOA type opportunity signals determine a spatial curve, and there will be 2 or more intersections with the spatial surface determined by the non-AOA type opportunity signal. It is still necessary to increase the non-AOA type opportunity signals for positioning and solving, and thus the solvability situation (3) is obtained.

[0033] Using the analysis of the solvable situation of multi-source opportunity signals, it can be obtained that at least 4 opportunity signals can perform a calculation of the estimated positioning result of the aircraft.

[0034] Specifically, the function Specifically is:

[0035] Among them, is the j-th estimated positioning point in the set P of estimated positioning points; k in. Evaluation index Specifically:

[0036] Among them, , is the total number of estimated positioning points in the set P of estimated positioning points after the abnormal opportunity signal is screened out for the k time.

[0037] Specifically, the support degree Specifically:

[0038] Among them, is the total number of clustering clusters in the untrusted interval B k ; is the total number of remaining opportunity signals after the abnormal opportunity signal is screened out for the k time; h is the h-th clustering cluster in the untrusted interval B is the judgment on the selection of the opportunity signal n i in the h-th cluster; n i is the i-th opportunity signal in the set N.

[0039] Specifically, the types of opportunity signals include arrival time, time difference of arrival, arrival angle, received signal strength indication, and Doppler frequency shift difference.

[0040] Specifically, calculating the geometric center coordinates of the unique clustering cluster is specifically:

[0041] Among them, r is the total number of estimated positioning points in the unique clustering cluster, is the coordinate of the estimated positioning point in the unique clustering cluster, is the final positioning coordinate of the aircraft.

[0042] Specifically, the density of the clustering cluster Specifically:

[0043] Among them, u is the number of clustering clusters in the clustering cluster set J k ; J ki is the clustering cluster set J k in the i-th clustering cluster; For any two points in the clustering cluster J ki among them.

[0044] Based on the same inventive concept, the present invention also provides a multi-source opportunistic signal online screening and optimization system based on density clustering, including the following modules: A preprocessing module, configured to randomly group m opportunistic signals received by the aircraft according to the navigability of the opportunistic signal, construct a system of ternary nonlinear equations for each group of opportunistic signals based on the type of the opportunistic signal, and solve the system of ternary nonlinear equations by the Newton iteration method to generate a set of estimated positioning points P k , where the subscript k is the number of times of screening abnormal opportunistic signals; A density clustering module, configured to perform density clustering on the set of estimated positioning points P k to generate a set of clustering clusters J k ; An interval partitioning module, configured to calculate the density of each clustering cluster in the set of clustering clusters J k , divide the clustering cluster with the highest density into a credible interval A k , and divide the remaining clustering clusters into an uncredible interval B k ; An abnormal opportunistic signal recognition module: configured to calculate the support degree of the opportunistic signal corresponding to each estimated positioning point in the uncredible interval B k , if the opportunistic signal with the highest support degree is unique, then determine that the opportunistic signal is an abnormal opportunistic signal; otherwise, sequentially and alternately screen out each opportunistic signal with the highest support degree, re-cluster and calculate the silhouette coefficient, and select the opportunistic signal with the highest support degree corresponding to the maximum silhouette coefficient as the abnormal opportunistic signal; An iteration module, configured to screen out abnormal opportunistic signals, let k = k + 1, and generate a set of estimated positioning points P k and a set of clustering clusters J k , until the number of clustering clusters in the set of clustering clusters J k is unique; A positioning module, configured to calculate the geometric center coordinates of the unique clustering cluster as the positioning result of the aircraft.

[0045] Embodiment 1 In order to test the applicability of the method of the present invention, an online screening simulation experiment of abnormal opportunistic signals was carried out for the physical opportunistic signal navigation experimental platform. The following are the specific steps of using this method: The parameters of the aircraft autonomous navigation system are modeled as: the initial position of the aircraft , the initial velocity , the position of the No. 1 transmitter , the position of the No. 2 transmitter , and the parameters of the opportunistic signal are , , , , , , , .

[0046] Step 1. According to the solvability of NAVSOP (Navigation via Signals of Opportunity), denote the sets of opportunity signals received by the aircraft as: , and randomly combine them in groups of 4 to obtain groups of SOP (Signals of Opportunity), and establish a ternary non-linear equation system between the measured values of each group of SOP information and the coordinates of the aircraft:

[0047] In the above formula, , , where:

[0048] represents the expression of the measured value of the th type of opportunity signal in this group, , .

[0049] There are six types of SOP in total, and the measured values and their expressions are as follows: The first type of SOP: RSSI information (Received Signal Strength Indicator), and its measured value has the following expression:

[0050] In the formula, is the position coordinate of the aircraft, is the position coordinate of the signal transmitter, is the nominal distance quantity, is the signal reception power when the distance between the aircraft and the transmitter is , is the channel attenuation coefficient.

[0051] The second type of SOP: TOA information (Time of Arrival), and its measured value has the following expression:

[0052] In the formula, is the signal speed.

[0053] The third type of SOP: TDOA information (Time Difference of Arrival), and its measured value The expression is:

[0054] In the formula, , are the position coordinates of the signal emission sources No. 1 and No. 2 respectively.

[0055] The fourth type of SOP: DFD information (Doppler Frequency Difference), and its measured value The expression is:

[0056] In the formula is the signal emission frequency, and are the relative speeds between the signal emission sources No. 1 and No. 2 and the aircraft respectively.

[0057] See Figure 7 , the fifth type of SOP: the first angle AOA information (Angle of Arrival), and its measured value The expression is:

[0058] Among them, is the relative azimuth angle between the emission source and the receiving source; is the position coordinate of the receiving source, is the signal source coordinate; The sixth type of SOP: the second angle AOA information (Angle of Arrival), and its measured value The expression is:

[0059] Among them, is the relative elevation angle between the emission source and the receiving source.

[0060] Use the Newton iteration method to solve each set of linear equations to obtain the set P of estimated positioning points of the opportunity signals k , the subscript k is the number of times of screening out abnormal opportunity signals. At this time, k = 0:

[0061] Step 2: Establish clustering conditions: For any point in the estimated positioning point set P k among them , define its neighborhood within a radius of as:

[0062] where represents the distance between point and ; is any point within the neighborhood.

[0063] Identify core points: Set the neighborhood radius and the density threshold . If the point satisfies the following equation:

[0064] then the point is a core point.

[0065] Form clustering clusters: Take any core point as the initial point , and denote the initial clustering cluster as . Let , and there is . For each point newly added to the clustering cluster , if is a core point, then let (that is, the points within are assigned to ), and repeat the above process until no point can be assigned to . Then, cluster the remaining points. Similarly, the clustering cluster can be obtained until all estimated positioning points are clustered.

[0066] Step 3: Based on the density of the clustering clusters, divide the confidence space A k and the untrusted interval B k ; Calculate the density of each clustering cluster, sort all clusters according to the density of the clustering clusters, and take the range covered by the clustering cluster with the highest density as the confidence interval A k , and there is

[0067] The remaining points form the untrusted interval .

[0068] Step 4: Establish the mapping from to ​ and function :

[0069]

[0070] where the set is the th estimated positioning point in the cluster of the

[0071] Set the set of estimated positioning points in the th cluster in the untrusted interval :

[0072] Establish the support degree of the opportunity signal n i in the untrusted interval, calculate the support degree of each estimated positioning point corresponding to the opportunity signal in the untrusted interval B , and judge whether the opportunity signal with the highest support degree is unique. If the judgment result is yes, then this opportunity signal is an abnormal opportunity signal; if the judgment result is no, then sequentially and alternately screen out the opportunity signal with the highest support degree. After re-density clustering the remaining opportunity signals in each round, calculate the silhouette coefficient, and select the round corresponding to the largest silhouette coefficient. The opportunity signal with the highest support degree screened out in this round is the abnormal opportunity signal. k

[0073]

[0074] Step 5. Screen out the abnormal opportunity signal, let k = k + 1, randomly group the remaining opportunity signals, and based on the type of opportunity signal, construct a system of ternary non-linear equations for each group of opportunity signals, and solve the system of ternary non-linear equations by the Newton iteration method to generate the set of estimated positioning points P k , perform density clustering on all the estimated positioning points in the current set of estimated positioning points P k to obtain the set of clustering clusters J k , judge whether the number of clustering clusters in the set of clustering clusters J k is unique. If the judgment result is yes, then this clustering cluster is the unique clustering cluster; if the judgment result is no, then return to Step 3.

[0075] Until the number of clustering clusters in the set of clustering clusters J k is unique, end the iteration.

[0075] Step 6. When the density clustering result is one cluster, at this time, calculate its geometric center according to the result of the unique clustering cluster as the final positioning coordinate of the aircraft.

[0076] To further study the applicability of the method of the present invention, considering the positioning of opportunistic signals under general conditions, the static deviation caused by measurement and other technical reasons, with the noise variance of the displacement process being 1, the noise variance of the velocity process being 0.01, and the measurement noise variance of the system equation being 1, a comparative simulation experiment between the method of the present invention and the average value method was carried out. Refer to Table 1, which shows the integrated square of the navigation error between the positioning results obtained by the method of the present invention and the average value method and the actual position under the above two conditions.

[0077] Table 1 Comparison Table of Integrated Square of Navigation Error

[0078] Among them: when there is no static deviation, the integrated square of the error of the average value method is 196.8651 ; when there is static deviation, the integrated square of the error is 620.9169 . When there is static deviation, the method of the present invention has higher control accuracy compared with the average value method: when there is no static deviation, the integrated square of the error is 47.3323 ; when there is static deviation, the integrated square of the error is 57.3303 .

[0079] Refer to Figure 4 、 Figure 5 and Figure 6 : The points on the yellow line fluctuate greatly because the average value method represented by the yellow line cannot accurately screen out abnormal signals, resulting in a large difference between the positioning result and the true value; when conducting the simulation experiment, the data was obtained at an interval of 0.01, resulting in the final trajectory not being a smooth curve. By comparing the large fluctuations of the yellow line close to the true value with the small fluctuations of the red line, the effectiveness of the red line using the algorithm of the present invention is proved; thus, it can be seen that the average value method will have a certain lag and amplitude deviation when tracking the actual positioning, and there are large fluctuations in the initial stage in the coordinate direction. The method of the present invention can better track the true value and provide a faster tracking control result.

[0080] This method establishes an online step-by-step screening model, makes full use of known information in a complex opportunistic signal navigation environment, differentiates the reliability of each received signal, processes signals with unknown static biases, reduces the impact of unknown static biases on navigation positioning, and improves the tracking actual positioning lag affected by static biases in traditional methods. According to the density clustering results, the concept of support degree is introduced, and the silhouette coefficient is combined to screen abnormal signals, thereby optimizing the screening process and positioning results. This quantitative evaluation method provides a scientific basis for further optimizing the screening and positioning processes, ensuring that the screened signals are more reliable and improving the accuracy and stability of positioning. At the same time, in the step-by-step screening model, evaluation indicators are used to measure the effectiveness of the screening operation, ensuring the scientific nature and accuracy of the screening process, effectively reducing the impact of external environmental interference on positioning, and enhancing the robustness and tracking positioning accuracy of opportunistic signal navigation technology. In complex environments where the global satellite positioning system is restricted, such as indoors, tunnels, densely populated areas, or in the event of system damage, failures and other unexpected situations, navigation based on opportunistic signals becomes a key technology. The present invention specifically screens and optimizes the static bias problem existing in opportunistic signals, and can provide reliable navigation positioning support for various devices, such as airplanes, etc. in these complex scenarios, demonstrating broad applicability and important practical value.

[0081] The above content is only to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. An online screening and optimization method for multi-source opportunistic signals based on density clustering, characterized in that It includes the following steps: Step 1: According to the solvability of the opportunity signal navigation, randomly group the m opportunity signals received by the aircraft. Based on the type of the opportunity signals, construct a system of three - variable nonlinear equations for each group of opportunity signals respectively, and solve the system of three - variable nonlinear equations by the Newton iteration method to generate a set of estimated positioning points P k , where the subscript k is the number of times of screening abnormal opportunity signals. At this time, k = 0; Step 2: Perform density clustering on the estimated positioning point set P k to generate a cluster set J k ; Step 3: Calculate the density of each cluster in the cluster set J k and classify the cluster with the highest density as the credible interval A k , and classify the remaining clusters as the non-credible interval B k ; Step 4. Calculate the untrusted interval B k Calculate the support degree of the opportunity signal corresponding to each estimated positioning point in k . If the opportunity signal with the highest support degree is unique, determine this opportunity signal as an abnormal opportunity signal; otherwise, sequentially and alternately screen out each opportunity signal with the highest support degree, recluster and calculate the silhouette coefficient, and select the opportunity signal with the highest support degree that is screened out corresponding to the maximum silhouette coefficient as the abnormal opportunity signal; Step 5: Screen out abnormal opportunity signals, let k = k + 1, and generate a set P of estimated positioning points k and a set J of clustering clusters k , and repeat Step 3 and Step 4 until the number of clustering clusters in the set J k is unique; Step 6: Calculate the geometric center coordinates of the unique clustering cluster as the positioning result of the aircraft.

2. The online screening and optimization method for multi-source opportunistic signals based on density clustering according to claim 1, characterized in that Step 4 specifically is: calculating the untrusted interval B k For each estimated positioning point in k , calculate the support degree of the corresponding opportunistic signal, and determine whether the opportunistic signal with the highest support degree is unique. If the judgment result is yes, then this opportunistic signal is an abnormal opportunistic signal; if the judgment result is no, then sequentially and alternately screen out the opportunistic signal with the highest support degree. After each round of re-density clustering of the remaining opportunistic signals, calculate the silhouette coefficient, and select the round corresponding to the largest silhouette coefficient. The opportunistic signal with the highest support degree screened out in this round is the abnormal opportunistic signal; Step 5 specifically includes: screening out abnormal opportunity signals, setting k = k + 1, randomly grouping the remaining opportunity signals, respectively constructing a system of three - variable nonlinear equations for each group of opportunity signals based on the type of opportunity signals, and solving the system of three - variable nonlinear equations through the Newton iteration method to generate a set of estimated positioning points P k , for the current set of estimated positioning points P k in all the estimated positioning points, perform density - based clustering to obtain a set of clustering clusters J k , determine whether the number of clustering clusters in the set of clustering clusters J k is unique. If the judgment result is yes, then this clustering cluster is the unique clustering cluster; If the judgment result is negative, return to Step 3.

3. The online screening and optimization method for multi-source opportunistic signals based on density clustering according to claim 2, characterized in that In Step 5, if the judgment result is negative, it is replaced by the following steps: Calculate the density of each cluster in the set of clusters J k and classify the cluster with the highest density as the credible interval A k and classify the remaining clusters as the non-credible interval B k ; Based on the credible interval A k and the non-credible interval B k , a function is established to describe the landing positions of all the estimated positioning points in the current set of estimated positioning points P k . Based on the function , the evaluation indices and are calculated; Judge whether it is greater than . If the judgment result is yes, return to step four; if the judgment result is no, restore the abnormal opportunity signal screened this time, let k = k - 1, and calculate the density of each cluster in the cluster set J k . Designate the cluster with the second highest density as the credible interval A k , and designate the remaining clusters as the non-credible interval B k , and return to step four.

4. A multi-source opportunistic signal online screening and optimization method based on density clustering according to claim 3, characterized in that In step 1, the specific operation of randomly grouping the m opportunity signals received by the aircraft is as follows: Each group of opportunity signals contains 4 signals, and there are a total of M groups of opportunity signals; among them, .

5. The online screening and optimization method for multi-source opportunistic signals based on density clustering according to claim 4, characterized in that Function Specifically: Among them, is the j-th estimated positioning point in the set P of estimated positioning points k ; Evaluation metrics Specifically: Among them, , is the total number of estimated positioning points in the set P k of estimated positioning points after the -th screening of abnormal opportunity signals.

6. The online screening and optimization method for multi-source opportunistic signals based on density clustering according to claim 1, wherein Let the set of opportunity signals be N, and the support is specifically as follows: Among them, is the total number of clustering clusters in the untrusted interval B k ; is the total number of remaining opportunity signals after the k h-th abnormal opportunity signal is screened out; h is the h-th clustering cluster in the untrusted interval B is the judgment on the selection situation of the opportunity signal n i in the h-th cluster; n i is the i-th opportunity signal in the set N.

7. A multi-source opportunistic signal online screening and optimization method based on density clustering according to claim 1, characterized in that The types of opportunity signals include time of arrival, time difference of arrival, angle of arrival, received signal strength indication, and Doppler frequency shift difference.

8. A multi-source opportunity signal online screening and optimization method based on density clustering according to claim 1, characterized in that Specifically, calculating the geometric center coordinates of the unique clustering cluster is as follows: where r is the total number of estimated positioning points in the unique clustering cluster, is the coordinate of the estimated positioning point in the unique clustering cluster, is the final positioning coordinate of the aircraft.

9. A multi-source opportunistic signal online screening and optimization method based on density clustering according to claim 1, characterized in that Set the clustering cluster set , the density of the clustering cluster Specifically: where u is the number of clusters in the cluster set J k ; J ki is the i-th cluster in the cluster set J k ; and J ki are any two points in the cluster J 10. A multi-source opportunistic signal online screening and optimization system based on density clustering, characterized in that, It includes the following modules: A preprocessing module, which is used to randomly group m opportunity signals received by an aircraft according to the navigability based on opportunity signals, construct a system of three - variable nonlinear equations for each group of opportunity signals respectively based on the type of opportunity signals, solve the system of three - variable nonlinear equations through the Newton iteration method, and generate a set P of estimated positioning points k , where the subscript k is the number of times of screening out abnormal opportunity signals; Density clustering module, used to perform density clustering on the estimated positioning point set P k to generate a clustering cluster set J k ; An interval division module, which is used to calculate the density of each cluster in the cluster set J k and divide the cluster with the highest density into the credible interval A k , and divide the remaining clusters into the non-credible interval B k ; Abnormal opportunity signal recognition module: used to calculate the untrusted interval B k For each estimated positioning point in, calculate the support degree of the corresponding opportunity signal. If the opportunity signal with the highest support degree is unique, determine this opportunity signal as the abnormal opportunity signal; otherwise, gradually and alternately screen out each opportunity signal with the highest support degree, re-cluster and calculate the silhouette coefficient, and select the opportunity signal with the highest support degree that is screened out corresponding to the maximum silhouette coefficient as the abnormal opportunity signal; An iterative module, which is used to screen out abnormal opportunity signals, make k = k + 1, and generate a set P of estimated positioning points k and a set J of clustering clusters k , until the number of clustering clusters in the set J k is unique; A positioning module, which is used to calculate the geometric center coordinates of the unique clustering cluster as the positioning result of the aircraft.

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