Direction finding intersection single station passive location method and system

Abstract

The application discloses a direction-finding intersection single-station passive positioning method and system, relates to the technical field of passive positioning, and solves the problem that the existing single-station passive positioning technology is difficult to simultaneously consider positioning accuracy and positioning stability, and the technical scheme is as follows: a stable reference straight line is calculated through collection of a large amount of initial data, the expression of another intersection straight line is continuously iteratively calculated based on a sliding window mechanism, the real-time change of angle measurement values is dynamically adapted, and in the data buffering process, fluctuation values and abnormal points are removed in real time, the effectiveness of the data is ensured, the positioning results at different moments are integrated, the geometric center of the cluster position is analyzed and calculated as the best positioning result output.

Description

Technical Field

[0001] This invention relates to the field of passive positioning technology, and more specifically, to a direction finding and intersection single-station passive positioning method and system. Background Technology

[0002] Passive positioning technology, with its advantages of passive reception, wide airspace coverage, long-range detection, and low cost, is widely used in various fields. Based on the number of observation stations, passive positioning technology can be divided into single-station and multi-station positioning. Single-station systems, due to their lower cost, simpler structure, and lack of data transmission synchronization issues, can be installed on moving platforms such as aircraft and vehicles, thus providing better mobility.

[0003] Currently, single-station passive positioning technology mainly relies on two methods: direction finding intersection and the phase difference change rate method. Existing direction finding intersection single-station positioning generally uses a direct intersection calculation method, relying on the intersection of the direction finding lines at different times to determine the target position. This makes the method sensitive to angle measurement errors and requires a certain amount of time to accumulate and widen the angle difference between the two direction finding lines, resulting in limitations in positioning accuracy and stability. The latter method calculates the target position by measuring the phase difference change rate at a certain time. It can provide better positioning accuracy when the single station moves along the direction tangent to the target. However, this method is easily affected by phase measurement errors, leading to large fluctuations in the calculated change rate. Furthermore, when the direction of movement deviates from the tangent, the positioning accuracy decreases significantly, making it difficult to obtain stable positioning results.

[0004] Therefore, in order to achieve accurate positioning while meeting the requirements of system stability, this invention proposes a new passive single-station positioning method based on direction finding and intersection. Summary of the Invention

[0005] The purpose of this application is to provide a single-station passive positioning method and system for direction finding and intersection, which solves the problem that existing single-station passive positioning technologies cannot simultaneously achieve both positioning accuracy and positioning stability. By collecting a large amount of initial data, a stable reference line is calculated. Based on a sliding window mechanism, the expression of another intersection line is continuously calculated iteratively, dynamically adapting to real-time changes in angle measurements. During the data caching process, fluctuation values ​​and outliers are removed in real time to ensure data validity. The positioning results at different times are integrated, and the geometric center of the cluster location is analyzed and calculated as the optimal positioning result output.

[0006] This application first provides a passive single-station direction finding and rendezvous positioning method, comprising: measuring the phase difference of a long baseline interferometer moving single station at different times, and calculating the azimuth angle of the target based on the phase difference; calculating the direction finding lines between the target and the single station at different times based on the real-time position of the single station and the azimuth angle of the target; setting a threshold window, acquiring direction finding lines from the initial time based on the threshold window, removing outliers from the direction finding lines, and establishing a reference straight line based on the outlier-removed direction finding lines; setting a sliding window, acquiring direction finding lines from the end time of the threshold window based on the sliding window and continuously iterating and updating, removing outliers from the iteratively updated data, and establishing a temporary straight line based on the outlier-removed direction finding lines; continuously calculating the target position coordinates based on the reference straight line and multiple temporary straight lines; caching the target position coordinates until a sufficient length is reached, then removing outliers, and calculating the final target position coordinates based on the outlier-removed target position coordinates.

[0007] In one possible implementation, the direction finding lines between the target and the single station at different times are calculated based on the real-time position of a single station and the azimuth of the target; this includes: acquiring GPS data of the single station at different times, converting the GPS data into position coordinates in the Northeast-Eastern Celestial Rectangular Coordinate System as the real-time position of the single station; and constructing direction finding lines between the target and the single station at different times based on the real-time position of the single station and the azimuth of the target.

[0008] In one possible implementation, a threshold window is set, and direction finding lines are acquired from an initial time based on the threshold window. Outliers are removed from the direction finding lines, and a reference straight line is established based on the outlier-removed direction finding lines. This includes: setting a threshold window based on the motion state of a single station and the density of the signal; the threshold window has a window time threshold, a buffer capacity threshold, and a distance threshold; acquiring multiple direction finding lines from an initial time based on the threshold window to form a direction finding line set; filtering out interfering direction finding lines in the direction finding line set using an outlier removal method; and fitting the outlier-removed direction finding line set using the least squares method to obtain the reference straight line for intersection positioning.

[0009] In one possible implementation, a sliding window is set, and direction finding lines are acquired and iteratively updated starting from the end of the threshold window based on the sliding window. Outliers are removed from the iteratively updated data, and a temporary straight line is established based on the direction finding lines after outlier removal. This includes: caching multiple direction finding lines starting from the end of the threshold window based on the sliding window, fitting the multiple direction finding lines into the least squares method to obtain a temporary straight line for intersection positioning; continuously updating the cached direction finding lines based on the sliding window mechanism and removing outliers, and continuously fitting the temporary straight line based on the direction finding lines of the sliding window after outlier removal.

[0010] In one possible implementation, outlier removal includes: for each data point p in the cache array, obtaining the k-neighborhood of point p; calculating the local density of point p based on the number of points in the neighborhood and the Euclidean distance between the points; calculating the centroid of the neighborhood of point p based on the local density of each point in the neighborhood, the local density of point p, and the number of points in the neighborhood; obtaining the cumulative fluctuation of the centroid of point p by weighted summation based on the centroids of point p in different neighborhoods, which is used as the outlier factor of point p; sorting all data points in descending order according to the outlier factor, and identifying data points with outlier factors greater than a threshold as outliers for removal.

[0011] This application also provides a direction finding and rendezvous single-station passive positioning system, comprising: a data acquisition module for measuring the phase difference of a long baseline interferometer moving single station at different times and calculating the azimuth angle of the target based on the phase difference; a direction finding line calculation module for calculating the direction finding lines between the target and the single station at different times based on the real-time position of the single station and the azimuth angle of the target; a reference line establishment module for setting a threshold window, acquiring direction finding lines from the initial time based on the threshold window, removing outliers from the direction finding lines, and establishing a reference line based on the outlier-removed direction finding lines; a temporary line establishment module for setting a sliding window, acquiring direction finding lines from the end time of the threshold window based on the sliding window and continuously iterating and updating, removing outliers from the iteratively updated data, and establishing a temporary line based on the outlier-removed direction finding lines; a target position calculation module for continuously calculating the target position coordinates based on the reference line and multiple temporary lines; and a target positioning output module for caching the target position coordinates until a sufficient length is reached, removing outliers, and calculating the final target position coordinates based on the outlier-removed target position coordinates.

[0012] In one possible implementation, the direction finding line calculation module specifically includes: a coordinate transformation module, used to acquire GPS data of a single station at different times and convert the GPS data into position coordinates in the Northeast-Eastern Celestial Cartesian coordinate system as the real-time position of the single station; and an equation construction module, used to construct the direction finding lines between the target and the single station at different times based on the real-time position of the single station and the azimuth of the target.

[0013] In one possible implementation, the baseline establishment module specifically includes: a threshold window setting module, used to set a threshold window based on the motion state of a single station and the density of signals, wherein the threshold window has a window time threshold, a buffer capacity threshold, and a distance threshold; a threshold window buffering module, used to acquire multiple direction finding lines to form a direction finding line set based on the threshold window starting from the initial time; an interference filtering module, used to filter out interfering direction finding lines in the direction finding line set based on an outlier removal method; and a baseline fitting module, used to fit the direction finding line set after outlier removal into the least squares method to obtain the baseline line for intersection positioning.

[0014] In one possible implementation, the temporary straight line establishment module specifically includes: a temporary straight line fitting module, used to cache multiple direction finding lines based on a sliding window starting from the end time of the threshold window, and to fit the multiple direction finding lines into the least squares method to obtain a temporary straight line for intersection positioning; and a temporary straight line updating module, used to continuously update the cached direction finding lines based on the sliding window mechanism and remove outliers, and to continuously fit the temporary straight line based on the sliding window direction finding lines after outlier removal.

[0015] In one possible implementation, outlier removal in the baseline line establishment module and the temporary line establishment module includes: for each data point p in the cache array, obtaining the k-neighborhood of point p; calculating the local density of point p based on the number of points in the neighborhood and the Euclidean distance between the points; calculating the centroid of the neighborhood of point p based on the local density of each point in the neighborhood, the local density of point p, and the number of points in the neighborhood of point p; obtaining the cumulative fluctuation of the centroid of point p by weighted summation based on the centroids of point p in different neighborhoods, as the outlier factor of point p; sorting all data points in descending order according to the outlier factor, and identifying data points with outlier factors greater than a threshold as outliers for removal.

[0016] Compared with existing technologies, this application has the following advantages: Compared with the traditional phase difference change rate method, the direction finding and intersection single-station passive positioning method proposed in this application achieves single-station passive positioning, avoids the difficult-to-accurate calculation of the phase difference change rate, and significantly reduces the impact of phase measurement fluctuations in noisy environments by using sliding window iterative positioning and outlier removal methods, thereby improving the stability of the system; Compared with the Kalman filter algorithm, the direction finding and intersection single-station passive positioning method proposed in this application has better filtering stability based on sliding window iterative positioning, avoids the setting of empirical parameters, can utilize historical data more efficiently, has a more obvious convergence effect, and higher positioning accuracy; The outlier removal method proposed in this application can effectively reduce noise interference. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0018] Figure 1 A schematic diagram of a motion-based single-station receiving target signals and passive positioning model provided in an embodiment of this application;

[0019] Figure 2 A flowchart of the direction finding and intersection single-station passive positioning method provided in the embodiments of this application;

[0020] Figure 3 A schematic diagram of the model established for the reference line provided in the embodiments of this application;

[0021] Figure 4 A schematic diagram of a model for establishing temporary straight lines using sliding window iterations, as provided in an embodiment of this application;

[0022] Figure 5 This is a schematic diagram of the angle measurement results of Kalman filtering and this method;

[0023] Figure 6 This is a schematic diagram based on the phase difference change rate and the relative positioning error of this method;

[0024] Figure 7 This is a structural diagram of a single-station passive positioning system for direction finding and intersection provided in an embodiment of this application. Detailed Implementation

[0025] In the following, the terms “comprising” or “may include” as used in the various embodiments of this application indicate the presence of the claimed function, operation, or element, and do not limit the addition of one or more functions, operations, or elements. Furthermore, as used in the various embodiments of this application, the terms “comprising,” “having,” and their cognates are intended only to indicate a specific feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing, or the possibility of adding one or more combinations of the foregoing.

[0026] The terminology used in the various embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the various embodiments of this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of this application pertain. Terms (such as those defined in a generally used dictionary) are to be interpreted as having the same meaning as in the context of the relevant technical field and are not to be interpreted as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of this application.

[0027] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this application are only for explaining this application and are not intended to limit this application.

[0028] First, some of the technical terms involved in this application will be explained so that those skilled in the art can fully understand the technical solution of this application.

[0029] Direction-finding intersection passive positioning: Direction-finding intersection passive positioning is a passive positioning method that determines the target's position by measuring the azimuth angle of the target's radiation source and using intersection. Passive positioning means that the reconnaissance equipment itself does not emit signals, but only passively receives the electromagnetic wave signals radiated by the target to complete the target's position estimation. The core of the direction-finding intersection method is to use multiple observation points (or the same observation point at different locations) to measure the direction of the target's radiation source, and determine the target's position by the intersection of the direction lines.

[0030] Motion-based monostation positioning of fixed or slow-moving radiation sources: Motion-based monostation positioning refers to a single observation station continuously observing a target radiation source while in motion, recording the coordinates of each observation point and the direction of the target radiation source, thereby determining the target's location. For positioning fixed or slow-moving radiation sources, since the target itself is stationary or moves at a slow speed, the observation station can change its relative position to the target by moving itself, thus obtaining sufficient information for positioning. The advantage of this method is that the measurement equipment is relatively simple and it is not sensitive to changes in signal waveform and frequency.

[0031] Outlier removal: Outlier removal refers to identifying and removing data points that significantly deviate from the normal range during data processing. In positioning systems, outliers may be caused by measurement errors, interference, or abnormal environmental factors. Removing outliers can improve the accuracy and reliability of positioning algorithms and avoid the impact of abnormal data on the final results.

[0032] Sliding Iteration Algorithm: The sliding iteration algorithm is a type of algorithm used for optimization and estimation, typically applied to data in dynamic systems. In the field of positioning, iterative algorithms can improve positioning accuracy by progressively updating and optimizing estimates. For example, in algorithms such as Kalman filtering, sliding iteration adapts to dynamic changes in the target by continuously adjusting parameters and state estimates.

[0033] Next, the application scenarios of this application will be described. A single-station long-baseline interferometer can be moved by means of vehicles, ships, aircraft, etc., and its trajectory is a straight line, with the antenna of the long-baseline interferometer pointing towards the target (radiation source). For example... Figure 1 As shown, Figure 1 This is a schematic diagram of a moving single-station receiving target signals and passive positioning model provided in an embodiment of this application. In the diagram, the movement trajectory of the single station is from point A to point B, the distance between A and B is d, and the azimuth angle between the single station and the radiation source is α.

[0034] Please see Figure 2 As shown, Figure 2This is a flowchart of a single-station passive positioning method for direction finding and intersection provided in an embodiment of this application. The method includes: S1 Measuring the phase difference of a moving single station of a long baseline interferometer at different times, and calculating the azimuth angle of the target based on the phase difference; S2 Calculating the direction finding lines between the target and the single station at different times based on the real-time position of the single station and the azimuth angle of the target; S3 Setting a threshold window, acquiring direction finding lines from the initial time based on the threshold window, removing outliers from the direction finding lines, and establishing a reference straight line based on the outlier-removed direction finding lines; S4 Setting a sliding window, acquiring direction finding lines from the end time of the threshold window based on the sliding window and continuously iterating and updating, removing outliers from the iteratively updated data, and establishing a temporary straight line based on the outlier-removed direction finding lines; S5 Continuously calculating the target position coordinates based on the reference straight line and multiple temporary straight lines; S6 Cache the target position coordinates until a sufficient length is reached, then remove outliers, and calculate the final target position coordinates based on the outlier-removed target position coordinates.

[0035] The improvement of this application lies in proposing a novel direction-finding intersection passive single-station positioning method and applying it to long-baseline interferometer passive positioning, thereby improving the stability and robustness of the positioning system and outperforming traditional intersection positioning and phase difference rate of change methods. Specifically, based on sliding iterative positioning, historical data is dynamically updated and optimized to ensure real-time high-precision positioning performance; outlier removal reduces direction-finding value deviations in complex environments, eliminates false positioning points, and improves positioning accuracy.

[0036] Step S1, Azimuth Angle Measurement: The phase difference of the long-baseline interferometer at different times is measured, and the azimuth angle of the target is calculated based on the phase difference. Specifically, the phase difference of the interferometer is measured. The azimuth angle θ of the target is calculated using the following formula:

[0037]

[0038] Where θ0 represents the angle between a single station and the north direction of the y-axis, the y-axis points north, d is the distance between the two antennas, f is the carrier frequency of the target, and c is the speed of light.

[0039] Step S2, Direction Finding Line Calculation: Based on the real-time position of a single station and the azimuth of the target, calculate the direction finding lines between the target and the single station at different times. In one possible implementation, step S2 includes: acquiring GPS data of the single station at different times, converting the GPS data into position coordinates in the East-North-Up (ENU) rectangular coordinate system as the real-time position of the single station; and constructing the direction finding lines between the target and the single station at different times based on the real-time position of the single station and the azimuth of the target.

[0040] Specifically, an initial reference point is first selected as the origin of the Northeast-Eastern-Sky Rectangular Coordinate System, with the X-axis pointing east and the Y-axis pointing north. The GPS data for each station at each moment is then converted into position coordinates in the Northeast-Eastern-Sky Rectangular Coordinate System. The details are as follows:

[0041] Define the reference point P0 as (Lon0, Lat0, h0). Calculate:

[0042]

[0043] The radius of curvature R0 is calculated as follows:

[0044]

[0045] Where a is 6378.137 km, representing the Earth's radius; f o =0.00669438, representing the Earth's oblateness. Next, calculate the geocentric rectangular coordinates (x0, y0, z0) of P0.

[0046] x0=(R0+h0)*cosLat*cosLon

[0047] y0=(R0+h0)*cosLat*sinLon

[0048] z0=(R0*(1-f o )+h0)*sinLat

[0049] Similarly, calculate the geocentric coordinates (x1, y1, z1) of station P1. This is to obtain the ENU relative coordinates (x1, y1, z1) of P1 relative to P0. proj ,y proj ,z proj This requires a projection transformation, which involves subtracting the coordinates of P0 from the rectangular coordinates of P1, and then applying a rotation matrix to complete the projection transformation. Details are as follows:

[0050] x proj =-sinLon*(x1-x0)+cosLon*(y1-y0)

[0051] y proj =-sinLat*cosLon*(x1-x0)-sinLat*sinLon*(y1-y0)+cosLat*(z1-z0)

[0052] z proj =cosLat*cosLon*(x1-x0)+cosLat*sinLon*(y1-y0)+sinLat*(z1-z0)

[0053] (x) proj ,yproj The real-time location of a single station is used as the reference point. Finally, based on the real-time location (x) of the single station... proj ,y proj Given the target's azimuth angle θ, calculate the equations of the target and the direction finding line at this moment:

[0054] y = kx + b, k = cot(θ), b = y proj -k*x proj

[0055] Where k represents the slope of the direction finding line and b is the intercept. Each direction finding line represents the direction of observation of the target from a single station at a certain moment.

[0056] Step S3, Establishing the Baseline Line: A threshold window is set. Direction finding lines are acquired from the initial time based on the threshold window. Outliers are removed from the direction finding lines. A baseline line is established based on the outlier-removed direction finding lines. In one possible implementation, step S3 includes: setting a threshold window based on the motion state of a single station and the density of the signal; the threshold window has a window time threshold, a buffer capacity threshold, and a distance threshold; acquiring multiple direction finding lines from the initial time based on the threshold window to form a direction finding line set; filtering out interfering direction finding lines in the direction finding line set using an outlier removal method; and fitting the outlier-removed direction finding line set using the least squares method to obtain the baseline line for intersection positioning.

[0057] Specifically, please see Figure 3 As shown, Figure 3 This is a schematic diagram of the model for establishing a reference straight line provided in this application embodiment. The direction finding data accumulated over an initial period at a single station is integrated into a reference straight line using an outlier removal algorithm and the least squares method.

[0058] In establishing a baseline line, a threshold window needs to be determined based on the motion state of a single station and the density of the signal. The limitations of the threshold window include: window time threshold T, buffer capacity threshold N, and distance threshold D. max .

[0059] Within a set window time threshold T, when a new data point arrives, it is added to the cache array. Then, the array's capacity is checked to see if it has reached the cache capacity threshold N. If the capacity is full, the best-fit line corresponding to that array is found using the least squares method, as follows:

[0060] For N straight lines, each line is represented as y = k. i x+b i First, collect the sampling points on these lines, denoted as (x ij ,y ij ), where i represents each line and j represents a point on that line.

[0061] Construct matrix A, where each row corresponds to the x-coordinate of a data point and the constant 1.

[0062]

[0063] The observation vector Y contains the y-coordinates of all data.

[0064]

[0065] The slope K and intercept B of the best-fit line are found using the least squares method. The goal is to minimize the sum of squared distances from all data points to the fitted line, as follows:

[0066]

[0067] Solution obtained:

[0068]

[0069] Then, the array is cleared, and the line is cached in another container. This process is repeated until the distance traveled by a single station exceeds the distance threshold D. max If no new valid data is received for an extended period, the best-fit line is calculated for all data within the container once data caching stops, yielding the reference line equation for intersection positioning: Y = Kx + B.

[0070] In addition, outlier removal is performed before each iteration of the line fitting process to ensure data quality and the accuracy of the baseline line calculation.

[0071] Step S4, Temporary Straight Line Establishment: A sliding window is set up. Starting from the end of the threshold window, direction finding lines are acquired and continuously iterated and updated based on the sliding window. Outliers are removed from the iteratively updated data. A temporary straight line is established based on the outlier-removed direction finding lines. In one possible implementation, step S4 includes: caching multiple direction finding lines starting from the end of the threshold window based on the sliding window; fitting these multiple direction finding lines using the least squares method to obtain a temporary straight line for intersection positioning; continuously updating the cached direction finding lines based on the sliding window mechanism and removing outliers; and continuously fitting the temporary straight line based on the outlier-removed sliding window direction finding lines.

[0072] Specifically, please see Figure 4 As shown, Figure 4 This is a schematic diagram of a model for establishing a temporary straight line using a sliding window iterative method, as provided in this application embodiment. By accumulating the direction finding lines acquired at a single station during continuous motion, these lines are integrated into a temporary straight line, and a sliding window mechanism ensures the real-time calculation of the temporary straight line. The figure below is a schematic diagram of the sliding iterative model for establishing a temporary straight line according to this invention. During operation, the system continuously calculates and updates this temporary straight line. The dots in the figure represent typical outlier straight lines.

[0073] After successfully establishing the baseline line, new data points are cached to construct another line required for intersection positioning; this application refers to this as a temporary line. The specific implementation process is as follows:

[0074] a) Initialize the cache and parameters: Set the maximum capacity of the cache array to m, denoted as L = {l1, l2, ... l... m}, where each l i This represents the equation of the line corresponding to the data point. The sliding window size is set to n.

[0075] b) Data point acquisition and initial fitting: Within a limited time, when the number of newly acquired data points reaches the buffer capacity m, the least squares method is used to fit an optimal temporary straight line.

[0076] c) Sliding Window Mechanism and Continuous Updates: Whenever the amount of new data meets the sliding window size, the following operations are performed: First, the earliest n data points added are removed from the cache array, and the latest n data points are added to the cache. Then, an outlier removal step is performed to ensure the validity and accuracy of the data. Based on the updated cached data, the least squares method is applied again to refit the best temporary line, ensuring that the temporary line iterates continuously as the station moves, and always reflects the latest data distribution.

[0077] In one possible implementation, outlier removal includes: for each data point p in the cache array, obtaining the k-neighborhood of point p; calculating the local density of point p based on the number of points in the neighborhood and the Euclidean distance between the points; calculating the centroid of the neighborhood of point p based on the local density of each point in the neighborhood, the local density of point p, and the number of points in the neighborhood; obtaining the cumulative fluctuation of the centroid of point p by weighted summation based on the centroids of point p in different neighborhoods, which is used as the outlier factor of point p; sorting all data points in descending order according to the outlier factor, and identifying data points with outlier factors greater than a threshold as outliers for removal.

[0078] Specifically, during the fitting of the baseline and temporary lines, outlier removal needs to be performed on each cache array to ensure the accuracy and reliability of the data. Traditional density- and distance-based outlier detection algorithms have limitations in simultaneously identifying global and local outliers.

[0079] Therefore, this application introduces the concept of data centroid: if a data object (data point) deviates significantly from the centroid of its neighborhood, then that point is likely an outlier. Specifically:

[0080] For each data point p in the cache array, σ k (p) is a k-neighborhood of p, representing all neighborhoods of p that satisfy d(p,q)≤d(p,p)k The set of points q.

[0081] σ k (p)={q|d(p,q)≤d(p,p k )}

[0082] d(p,q) represents the Euclidean distance between p and q, where p k Let ρ represent the k nearest neighbors of point p. Then, calculate the local reachability density ρ of p. k (p) represents the reciprocal of the average of the distances between object p and all points in its k-neighborhood. As follows:

[0083]

[0084] Subsequently, σ is calculated. k The centroid c within (p) k (p), defined as follows.

[0085]

[0086] Where, ρ k (i) represents the local density of points within the neighborhood of point p, with centroid c k (p) represents the ratio of the average local density of all points within the neighborhood of point p to its own density. k The larger the value of (p), the higher the degree of outlier at point p.

[0087] In order to stably represent the outlier degree of data objects, this application addresses the outlier degree of c in different domains. k (p) Perform a weighted summation to obtain the cumulative fluctuation of the centroid, which is the outlier factor F(p,k). See below:

[0088]

[0089] k represents the number of nearest neighbors of object p, which is a preset value. Similarly, the higher F(p,k), the greater the fluctuation of p's center of gravity, and the more unstable its neighborhood structure becomes, thus the higher its degree of outlierness.

[0090] Finally, all data are sorted in descending order based on the calculated outlier factor, and data objects exceeding the threshold are identified as outliers and deleted. The threshold is defined as follows:

[0091]

[0092] That is, the threshold is set as the array mean plus three times the standard deviation.

[0093] Step S5: Target position coordinate calculation: Based on the baseline line and multiple temporary lines, the target position coordinates are continuously calculated. Specifically, during the iterative optimization process, the target position coordinates are continuously calculated using the baseline line y = Kx + B and the real-time updated temporary line y = kx + b. y tgt =k*x tgt +b).

[0094] Step S6, Caching and Result Output: After caching the target location coordinates to a sufficient length, outlier removal is performed. The final target location coordinates are then calculated based on the outlier-removed target location coordinates. Specifically, following the steps in S5, the continuously calculated target locations are cached. When the length of the location coordinate array meets the number of sliding windows, the array is iteratively updated, and outlier removal and mean averaging are performed simultaneously to continuously obtain positioning results, thereby achieving real-time positioning.

[0095] To verify the optimization effect of the direction finding and rendezvous single-station passive positioning method provided in this application compared with other methods, the angle measurement results of the method of the present invention are compared with those of the Kalman filter method, and the relative positioning error of the method of the present invention is compared with that of the phase difference rate of change method.

[0096] Please see Figure 5 As shown, Figure 5 This is a schematic diagram of the angle measurement results of Kalman filtering and this method. Figure 5 The long-baseline interferometer has an element spacing of 1.52m, a target carrier frequency of 1.5GHz, and uses a vehicle-mounted interferometer, in accordance with... Figure 1 The diagram illustrates the angle measurement optimization results using Kalman filtering and the method of this invention, with the motion trajectory as the measured data of the motion model. The black line segments in the diagram represent the optimized angle measurement values. It is evident that, compared to Kalman filtering, the method of this invention can reduce angle measurement errors more stably and smoothly.

[0097] Please see Figure 6 As shown, Figure 6 This is a schematic diagram based on the phase difference change rate and the relative positioning error of this method. Figure 6 This diagram illustrates the relative positioning errors of the traditional phase difference rate of change positioning method and the method of this invention under the same conditions. The relative distance error is expressed as the ratio of the positioning error to the target distance. It can be seen that the method of this invention, through a certain period of accumulation and iterative optimization via a sliding window, and by integrating historical information with the latest data, achieves a gradually stable positioning result while maintaining a certain level of accuracy. In contrast, the phase difference rate of change algorithm results in larger fluctuations in positioning. It is relatively accurate when the direction of movement is tangential to the target, but in other cases, the error is larger, and its noise resistance and stability are poor.

[0098] Understandably, compared to the traditional phase difference change rate method, the direction-finding intersection single-station passive positioning method proposed in this application achieves single-station passive positioning, avoids the difficult-to-accurate calculation of the phase difference change rate, and significantly reduces the impact of phase measurement fluctuations in noisy environments by utilizing sliding window iterative positioning and outlier removal methods, thereby improving system stability. Compared to the Kalman filter algorithm, the direction-finding intersection single-station passive positioning method proposed in this application, based on sliding window iterative positioning, has better filtering stability, avoids the setting of empirical parameters, can utilize historical data more efficiently, has a more obvious convergence effect, and higher positioning accuracy. The outlier removal method proposed in this application can effectively reduce noise interference.

[0099] Please see Figure 7 As shown, Figure 7 This is a structural diagram of a direction-finding and intersection single-station passive positioning system provided in an embodiment of this application. The system is used to achieve, for example... Figure 2 The direction finding and intersection single-station passive positioning method shown includes the following system: a data acquisition module, used to measure the phase difference of a long baseline interferometer moving single station at different times and calculate the azimuth of the target based on the phase difference; a direction finding line calculation module, used to calculate the direction finding lines between the target and the single station at different times based on the real-time position of the single station and the azimuth of the target; a reference line establishment module, used to set a threshold window, acquire direction finding lines from the initial time based on the threshold window, remove outliers from the direction finding lines, and establish a reference line based on the outlier-removed direction finding lines; a temporary line establishment module, used to set a sliding window, acquire direction finding lines from the end time of the threshold window based on the sliding window and continuously iterate and update, remove outliers from the iteratively updated data, and establish a temporary line based on the outlier-removed direction finding lines; a target position calculation module, used to continuously calculate the target position coordinates based on the reference line and multiple temporary lines; and a target positioning output module, used to cache the target position coordinates until a sufficient length is reached, remove outliers, and calculate the final target position coordinates based on the outlier-removed target position coordinates.

[0100] In one possible implementation, the direction finding line calculation module specifically includes: a coordinate transformation module, used to acquire GPS data of a single station at different times and convert the GPS data into position coordinates in the Northeast-Eastern Celestial Cartesian coordinate system as the real-time position of the single station; and an equation construction module, used to construct the direction finding lines between the target and the single station at different times based on the real-time position of the single station and the azimuth of the target.

[0101] In one possible implementation, the baseline establishment module specifically includes: a threshold window setting module, used to set a threshold window based on the motion state of a single station and the density of signals, wherein the threshold window has a window time threshold, a buffer capacity threshold, and a distance threshold; a threshold window buffering module, used to acquire multiple direction finding lines to form a direction finding line set based on the threshold window starting from the initial time; an interference filtering module, used to filter out interfering direction finding lines in the direction finding line set based on an outlier removal method; and a baseline fitting module, used to fit the direction finding line set after outlier removal into the least squares method to obtain the baseline line for intersection positioning.

[0102] In one possible implementation, the temporary straight line establishment module specifically includes: a temporary straight line fitting module, used to cache multiple direction finding lines based on a sliding window starting from the end time of the threshold window, and to fit the multiple direction finding lines into the least squares method to obtain a temporary straight line for intersection positioning; and a temporary straight line updating module, used to continuously update the cached direction finding lines based on the sliding window mechanism and remove outliers, and to continuously fit the temporary straight line based on the sliding window direction finding lines after outlier removal.

[0103] In one possible implementation, outlier removal in the baseline line establishment module and the temporary line establishment module includes: for each data point p in the cache array, obtaining the k-neighborhood of point p; calculating the local density of point p based on the number of points in the neighborhood and the Euclidean distance between the points; calculating the centroid of the neighborhood of point p based on the local density of each point in the neighborhood, the local density of point p, and the number of points in the neighborhood of point p; obtaining the cumulative fluctuation of the centroid of point p by weighted summation based on the centroids of point p in different neighborhoods, as the outlier factor of point p; sorting all data points in descending order according to the outlier factor, and identifying data points with outlier factors greater than a threshold as outliers for removal.

[0104] It should be noted that the direction-finding and rendezvous single-station passive positioning system provided in this application is similar to... Figure 2 The provided direction finding and intersection single-station passive positioning methods are all one-to-one and have corresponding technical effects, so they will not be elaborated further.

[0105] The above specific embodiments further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A single-station passive positioning method for direction finding and intersection, characterized in that, include: The phase difference of a single station moving with a long baseline interferometer at different times is measured, and the azimuth of the target is calculated based on the phase difference. Based on the real-time position of a single station and the azimuth of the target, the direction finding lines between the target and the single station are calculated at different times. Set a threshold window, acquire direction finding lines based on the threshold window starting from the initial time, remove outliers from the direction finding lines, and establish a reference straight line based on the direction finding lines after outlier removal. Set a sliding window, acquire direction finding lines from the end of the threshold window based on the sliding window and continuously iterate and update, remove outliers from the iteratively updated data, and establish a temporary straight line based on the direction finding lines after outlier removal; Based on the baseline and multiple temporary lines, the target position coordinates are continuously calculated; After caching the target location coordinates to a sufficient length, outlier removal is performed. The final target location coordinates are then calculated based on the outlier-removed target location coordinates. The outlier removal process includes: for each data point in the cache array... Acquisition Points k-domain; point-based The number of points in the neighborhood and the Euclidean distance between the points are used to calculate the points. Local density; based on points Local density of points within the domain, points Local density and points The number of points in the domain, and the calculation points. The focus of the domain; point-based The point is obtained by weighted summation of the centers of gravity in different fields. The cumulative fluctuation of the center of gravity, as a point The outlier factor is used to sort all data points in descending order based on the outlier factor, and data points with an outlier factor greater than the threshold are identified as outliers and removed.

2. The direction-finding intersection single-station passive positioning method according to claim 1, characterized in that, Based on the real-time position of a single station and the azimuth of the target, calculate the direction finding lines between the target and the single station at different times; including: Obtain GPS data for a single station at different times, and convert the GPS data into location coordinates in the Northeast-Southern Cartesian coordinate system as the real-time location of the single station; Based on the real-time position of a single station and the azimuth of the target, direction finding lines between the target and the single station are constructed at different times.

3. The direction-finding intersection single-station passive positioning method according to claim 1, characterized in that, A threshold window is set, and direction finding lines are acquired starting from the initial time based on the threshold window. Outlier values ​​are removed from the direction finding lines, and a baseline straight line is established based on the outlier-removed direction finding lines; including: The threshold window is set according to the motion state of a single station and the density of the signal. The threshold window has a window time threshold, a buffer capacity threshold, and a distance threshold. Multiple direction finding lines are acquired from the initial time based on a threshold window to form a set of direction finding lines; Interfering direction finding lines in the direction finding line set are filtered out based on outlier removal methods; The set of direction finding lines after removing outliers is fitted using the least squares method to obtain the reference straight line for intersection positioning.

4. The single-station passive positioning method for direction finding and intersection according to claim 1, characterized in that, A sliding window is set up, and direction finding lines are acquired and continuously iterated and updated starting from the end of the threshold window. Outliers are removed from the iteratively updated data, and a temporary straight line is established based on the outlier-removed direction finding lines; including: Based on the sliding window, multiple direction finding lines are cached starting from the end of the threshold window. The multiple direction finding lines are then fitted using the least squares method to obtain a temporary straight line for intersection positioning. The cached direction finder lines are continuously updated based on the sliding window mechanism, and outliers are removed. The temporary straight line is then continuously fitted based on the sliding window direction finder lines after outlier removal.

5. A direction-finding and intersection single-station passive positioning system, characterized in that, For implementing a single-station passive positioning method for direction finding and intersection as described in any one of claims 1-4, the system includes: The data acquisition module is used to measure the phase difference of a single station of a long baseline interferometer at different times, and to calculate the azimuth angle of the target based on the phase difference; The direction finding line calculation module is used to calculate the direction finding line between the target and the single station at different times based on the real-time position of a single station and the azimuth angle of the target. The baseline line establishment module is used to set a threshold window, acquire direction finding lines from the initial time based on the threshold window, remove outliers from the direction finding lines, and establish a baseline line based on the outlier-removed direction finding lines. The temporary straight line establishment module is used to set a sliding window, acquire direction finding lines based on the sliding window starting from the end of the threshold window and continuously iterate and update them, remove outliers from the iteratively updated data, and establish temporary straight lines based on the direction finding lines after outlier removal. The target position calculation module is used to continuously calculate the target position coordinates based on the baseline line and multiple temporary lines; The target localization output module is used to cache the target position coordinates until a sufficient length is reached, then remove outliers, and calculate the final target position coordinates based on the target position coordinates after outlier removal.

6. A direction-finding, intersection, single-station passive positioning system according to claim 5, characterized in that, The direction finding line calculation module specifically includes: The coordinate transformation module is used to acquire GPS data of a single station at different times and convert the GPS data into position coordinates in the Northeast-Southern Cartesian coordinate system as the real-time position of the single station. The equation construction module is used to construct the direction finding lines between the target and the single station at different times, based on the real-time position of a single station and the azimuth of the target.

7. A direction-finding and intersection single-station passive positioning system according to claim 6, characterized in that, The baseline line establishment module specifically includes: The threshold window setting module is used to set the threshold window according to the motion state of a single station and the density of the signal. The threshold window has a window time threshold, a buffer capacity threshold, and a distance threshold. The threshold window caching module is used to acquire multiple direction finding lines to form a direction finding line set based on the threshold window starting from the initial time. The interference filtering module is used to filter out interfering direction finding lines in the direction finding line set based on the outlier removal method. The baseline fitting module is used to fit the set of direction finding lines after outlier removal into the least squares method to obtain the baseline line for intersection positioning.

8. A direction-finding and intersection single-station passive positioning system according to claim 7, characterized in that, The temporary straight line establishment module specifically includes: The temporary straight line fitting module is used to cache multiple direction finding lines based on the sliding window starting from the end of the threshold window, and then use the least squares method to fit the multiple direction finding lines to obtain a temporary straight line for intersection positioning. The temporary straight line update module is used to continuously update the cached direction finding lines based on the sliding window mechanism and remove outliers. The temporary straight line is then continuously fitted based on the sliding window direction finding lines after outlier removal.

9. A direction-finding, intersection, single-station passive positioning system according to claim 8, characterized in that, Outlier removal in the baseline line establishment module and the temporary line establishment module includes: For each data point in the cache array Acquisition Points k-domain; Based on points The number of points in the neighborhood and the Euclidean distance between the points are used to calculate the points. Local density; Based on points Local density of points within the domain, points Local density and points The number of points in the domain, and the calculation points. The focus of the field; Based on points The point is obtained by weighted summation of the centers of gravity in different fields. The cumulative fluctuation of the center of gravity, as a point Outlier factor; All data points are sorted in descending order based on outlier factor, and data points with outlier factors greater than a threshold are identified as outliers and removed.

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