Direction-finding intersection single-station passive positioning method and system

Abstract

The invention discloses a direction-finding intersection single-station passive positioning method and a direction-finding intersection single-station passive positioning system, relates to the technical field of passive positioning, and solves the problem that the positioning precision and the positioning stability are difficult to consider at the same time in the existing single-station passive positioning technology. On the basis of a sliding window mechanism, an expression of another intersection straight line is continuously and iteratively calculated, real-time changes of angle measurement values are dynamically adapted, in the data caching process, fluctuation values and abnormal points are removed in real time, data validity is ensured, positioning results at different moments are integrated, the geometric center of the cluster position is analyzed and calculated, and the clustering accuracy is improved. And outputting as an optimal positioning result.

Description

Technical Field

[0001] The present invention relates to the technical field of passive positioning, and more specifically, to a direction-finding intersection single-station passive positioning method and system. Background Art

[0002] Passive positioning technology has been widely used in various fields due to its advantages of passive reception, wide airspace coverage, long-distance detection, and low cost. According to the number of observation stations, passive positioning technology can be divided into single-station and multi-station positioning. The single-station system can be installed on moving platforms such as airplanes and vehicles because of its low cost, simple structure, and no data transmission synchronization problem, so it can provide better maneuverability.

[0003] Currently, single-station passive positioning technology mainly relies on two methods: direction-finding intersection and rate of change of phase difference method. Existing direction-finding intersection single-station positioning generally uses a direct intersection calculation method, which determines the target position by relying on the intersection of direction-finding lines at different times. This makes the method sensitive to angle measurement errors and requires a certain time accumulation to expand the angle difference between the two direction-finding lines, and there are limitations in positioning accuracy and stability. The latter calculates the rate of change of the phase difference at a certain moment to deduce the target position, and can provide better positioning accuracy when the single station moves along the tangent direction of the target, but this method is easily affected by phase measurement errors, resulting in large fluctuations in the calculation of the rate of change, and when the moving direction deviates from the tangent, the positioning accuracy will decrease significantly, so it is difficult to obtain a stable positioning result.

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

[0005] The purpose of this application is to provide a direction-finding intersection single-station passive positioning method and system, which solves the problem that the existing single-station passive positioning technology is difficult to take into account both positioning accuracy and positioning stability at the same time; by collecting a large amount of initial data, calculating a stable reference straight line, based on the sliding window mechanism, continuously iteratively calculating the expression of another intersection straight line, dynamically adapting to the real-time change of the angle measurement value, and in the process of data caching, real-time eliminating the fluctuation values and abnormal points to ensure the effectiveness of the data, integrating the positioning results at different times, analyzing and calculating the geometric center of the cluster position, and outputting it as the best positioning result.

[0006] The present application first provides a direction-finding and intersection single-station passive positioning method, including: measuring the phase differences 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 differences; 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, obtaining the direction-finding lines from the initial time based on the threshold window, removing the outlier direction-finding lines, and establishing a reference line based on the direction-finding lines after outlier removal; setting a sliding window, obtaining the direction-finding lines from the end time of the threshold window based on the sliding window and continuously iteratively updating, removing the outlier data from the iteratively updated data, and establishing a temporary line based on the direction-finding lines after outlier removal; continuously solving the target position coordinates based on the reference line and multiple temporary lines; caching the target position coordinates until a sufficient length is reached and then removing the outliers, and calculating the final target position coordinates based on the target position coordinates after outlier removal.

[0007] In a possible implementation manner, 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; includes: obtaining the GPS data of the single station at different times, converting the GPS data into the position coordinates in the northeast celestial right-angle coordinate system as the real-time position of the single station; 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 angle of the target.

[0008] In a possible implementation manner, setting a threshold window, obtaining the direction-finding lines from the initial time based on the threshold window, removing the outlier direction-finding lines, and establishing a reference line based on the direction-finding lines after outlier removal; includes: setting the threshold window according to the motion state of the single station and the density of the signals, where the threshold window has a window time threshold, a cache capacity threshold, and a distance threshold; obtaining multiple direction-finding lines from the initial time based on the threshold window to form a direction-finding line set; filtering out the interfering direction-finding lines in the direction-finding line set based on the outlier removal method; and substituting the direction-finding line set after outlier removal into the least squares method for fitting to obtain the reference line for intersection positioning.

[0009] In a possible implementation manner, setting a sliding window, obtaining the direction-finding lines from the end time of the threshold window based on the sliding window and continuously iteratively updating, removing the outlier data from the iteratively updated data, and establishing a temporary line based on the direction-finding lines after outlier removal; includes: caching multiple direction-finding lines from the end time of the threshold window based on the sliding window, substituting the multiple direction-finding lines into the least squares method for fitting to obtain the temporary line for intersection positioning; continuously updating the cached direction-finding lines based on the sliding window mechanism and removing the outliers, and continuously fitting the temporary line based on the direction-finding lines of the sliding window after outlier removal.

[0010] In a possible implementation, outlier rejection 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 within the neighborhood of point p and the Euclidean distance between the points; calculating the centroid of the neighborhood of point p based on the local densities of the points within the neighborhood of point p, the local density of point p, and the number of points within the neighborhood of point p; obtaining the cumulative fluctuation of the centroid of point p by weighted summation of the centroids of point p under different neighborhoods as the outlier factor of point p; sorting all data points in descending order according to the outlier factor, and identifying and removing the data points with outlier factors greater than the threshold as outliers.

[0011] The present application also provides a direction-finding intersection single-station passive positioning system, including: a data acquisition module for measuring and obtaining the phase differences of a long-baseline interferometer moving single station at different times, and calculating the azimuth angle of the target based on the phase differences; 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, obtaining direction-finding lines starting from the initial time based on the threshold window, rejecting outliers from the direction-finding lines, and establishing a reference line based on the direction-finding lines after outlier rejection; a temporary line establishment module for setting a sliding window, obtaining direction-finding lines starting from the end time of the threshold window based on the sliding window and continuously iterating and updating, rejecting outliers from the iteratively updated data, and establishing a temporary line based on the direction-finding lines after outlier rejection; 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 and then rejecting outliers, and calculating the final target position coordinates based on the target position coordinates after outlier rejection.

[0012] In a possible implementation, the direction-finding line calculation module specifically includes: a coordinate conversion module for obtaining the GPS data of the single station at different times, converting the GPS data into position coordinates in the northeast celestial right-angle coordinate system as the real-time position of the single station; and an equation construction module for 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 angle of the target.

[0013] In a possible implementation, the reference line establishment module specifically includes: a threshold window setting module for setting a threshold window according to the motion state of the single station and the density of signals, and the threshold window has a window time threshold, a cache capacity threshold, and a distance threshold; a threshold window cache module for obtaining multiple direction-finding lines starting from the initial time based on the threshold window to form a direction-finding line set; an interference filtering module for filtering out interference direction-finding lines in the direction-finding line set based on the outlier rejection method; and a reference line fitting module for substituting the direction-finding line set after outlier rejection into the least squares method for fitting to obtain the reference line for intersection positioning.

[0014] In a possible implementation manner, the temporary straight line establishment module specifically includes: a temporary straight line fitting module, configured to cache multiple direction lines starting from the end moment of the threshold window based on a sliding window, and bring the multiple direction lines into the least squares method for fitting to obtain a temporary straight line for intersection positioning; a temporary straight line update module, configured to continuously update the cached direction lines based on the sliding window mechanism and perform outlier rejection, and continuously fit the temporary straight line based on the direction lines of the sliding window after outlier rejection.

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

[0016] Compared with the prior art, the present application has the following beneficial effects: compared with the traditional phase difference change rate method, the direction finding and intersection single-station passive positioning method proposed by the present application realizes single-station passive positioning, avoids the difficult-to-accurately calculate phase difference change rate, and significantly reduces the influence of phase measurement fluctuations in a noise environment by using the sliding window iterative positioning and outlier rejection methods, thereby improving the stability of the system; compared with the Kalman filtering algorithm, the direction finding and intersection single-station passive positioning method proposed by the present application has better filtering stability based on the 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 rejection method proposed by the present application can effectively reduce noise interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not constitute a limitation to the embodiments of the present invention. In the drawings:

[0018] Figure 1 It is a schematic model diagram of a moving single-station receiving a target signal and passive positioning provided by an embodiment of the present application;

[0019] Figure 2 It is a flowchart of the direction finding and intersection single-station passive positioning method provided by an embodiment of the present application;

[0020] Figure 3 It is a schematic model diagram of the reference straight line establishment provided by an embodiment of the present application;

[0021] Figure 4 Schematic diagram of the model for iteratively establishing a temporary straight line using a sliding window provided by an embodiment of the present application;

[0022] Figure 5 Schematic diagram of the angle measurement results of Kalman filtering and this method;

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

[0024] Figure 7 Structural diagram of the direction-finding and intersection single-station passive positioning system provided by an embodiment of the present application. Detailed implementation manners

[0025] In the following, the term "including" or "may include" that can be used in various embodiments of the present application indicates the presence of the claimed functions, operations, or elements, and does not limit the addition of one or more functions, operations, or elements. Further, as used in various embodiments of the present application, the terms "including", "having" and their cognates are only intended to indicate specific features, numbers, steps, operations, elements, components, or combinations of the foregoing items, and should not be construed as precluding the existence or addition of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing items first.

[0026] The terms used in various embodiments of the present application are only for the purpose of describing specific embodiments and are not intended to limit the various embodiments of the present application. As used herein, the singular form is also intended to include the plural form 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 those of ordinary skill in the art to which the various embodiments of the present application belong. Terms (such as those defined in a commonly used dictionary) will be interpreted as having the same meaning as the contextual meaning in the relevant technical field and will not be interpreted as having an idealized meaning or being overly formal unless clearly defined in the various embodiments of the present application.

[0027] To make the objectives, technical solutions, and advantages of the present application clearer and more understandable, the present application will be further described in detail below in conjunction with embodiments and the accompanying drawings. The illustrative embodiments and descriptions of the present application are only used to explain the present application and do not serve as a limitation to the present application.

[0028] First, some technical terms involved in the present application are explained to facilitate those skilled in the art to fully understand the technical solutions of the present application.

[0029] Direction-finding and intersection passive positioning: Direction-finding and intersection passive positioning is a passive positioning method that determines the target position by measuring the direction angle of the target radiation source and using the intersection method. Passive positioning means that the reconnaissance equipment itself does not emit signals and only estimates the target position by passively receiving the electromagnetic wave signals radiated by the target. The core of the direction-finding and intersection method lies in measuring the direction of the target radiation source at multiple observation points (or the same observation point at different positions), and determining the target position through the intersection point of the direction lines.

[0030] Moving single-station positioning of fixed or slow radiation sources: Moving single-station positioning refers to the continuous observation of the target radiation source by a single observation station during movement, recording the coordinates of each observation point and information such as the direction of the target radiation source, so as to determine the target position. For the positioning of fixed or slow radiation sources, since the target itself does not move or moves slowly, the observation station can change the relative position relationship with the target through its own movement, so as to obtain sufficient information for positioning. The advantage of this method is that the measurement equipment is relatively simple and is not sensitive to the waveform and frequency agility of the signal.

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

[0032] Sliding iterative algorithm: The sliding iterative algorithm is an algorithm for optimization and estimation, usually used to process data in dynamic systems. In the field of positioning, the sliding iterative algorithm can improve the positioning accuracy by gradually updating and optimizing the estimated value. For example, in algorithms such as Kalman filtering, sliding iteration can adapt to the dynamic changes of the target by continuously adjusting parameters and state estimation.

[0033] Next, the application scenario of this application will be described. The single-station long-baseline interferometer can be moved by being carried on an automobile, ship, aircraft, etc., and its movement trajectory is a straight line, and the antenna direction of the long-baseline interferometer is oriented towards the target (radiation source). As Figure 1 shown, Figure 1 is a schematic model diagram of a moving single-station receiving target signals and passive positioning provided by an embodiment of this application. In the figure, the movement trajectory of the single station is from point A to point B, the distance between AB is d, and the azimuth angle between the single station and the radiation source is α.

[0034] Please refer to Figure 2 shown, Figure 2This is the flowchart of the direction-finding and intersection single-station passive positioning method provided by the embodiments of this application. The method includes: S1 Measuring the phase differences of the long-baseline interferometer moving single-station at different times, and calculating the azimuth angle of the target based on the phase differences; 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, obtaining the direction-finding lines starting from the initial time based on the threshold window, removing the outliers from the direction-finding lines, and establishing a reference straight line based on the direction-finding lines after outlier removal; S4 Setting a sliding window, obtaining the direction-finding lines starting from the end time of the threshold window based on the sliding window and continuously iterating and updating, removing the outliers from the iteratively updated data, and establishing a temporary straight line based on the direction-finding lines after outlier removal; S5 Continuously solving the target position coordinates based on the reference straight line and multiple temporary straight lines; S6 Caching the target position coordinates until a sufficient length is reached and then removing the outliers, and calculating the final target position coordinates based on the target position coordinates after outlier removal.

[0035] The improvement of this application lies in proposing a new direction-finding and intersection passive single-station positioning method and applying it to the passive positioning of long-baseline interferometers, improving the stability and robustness of the positioning system, which is superior to the traditional intersection positioning and phase difference change rate methods; specifically, based on sliding iterative positioning, by dynamically updating and optimizing historical data, ensuring the acquisition of real-time high-precision positioning performance; based on outlier removal, reducing the deviation of direction-finding values in complex environments, removing false positioning points, and improving the positioning accuracy.

[0036] Step S1, Azimuth Angle Measurement: Measuring the phase differences of the long-baseline interferometer moving single-station at different times, and calculating the azimuth angle of the target based on the phase differences. Specifically, measuring the phase differences of the interferometer And calculating the azimuth angle θ of the target through the following formula:

[0037]

[0038] Where, θ0 represents the angle between the single-station and the due 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 Solution: 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. In a possible implementation manner, step S2 includes: Obtaining the GPS data of the single-station at different times, converting the GPS data into the position coordinates in the east-north-up (ENU) rectangular coordinate system as the real-time position of the single-station; 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 angle of the target.

[0040] Specifically, first select the initial reference point as the origin of the northeast celestial rectangular coordinate system, that is, the X-axis points to the east and the Y-axis points to the north. Convert the GPS data of each moment of a single station into position coordinates in the northeast celestial rectangular coordinate system. Specifically as follows:

[0041] Define the longitude, latitude and altitude of the reference point P0 as (Lon0, Lat0, h0). Calculate:

[0042]

[0043] Calculate the radius of curvature R0 as:

[0044]

[0045] Among them, a = 6378.137 km, representing the radius of the earth; f o = 0.00669438, representing the flattening of the earth. Then 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 the single station P1. To obtain the ENU relative coordinates (x proj , y proj , z proj ) of P1 relative to P0, a projection transformation is required, that is, subtract the coordinates of P0 from the rectangular coordinates of P1, and then apply the rotation matrix to complete the projection conversion. Specifically 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] Convert (x proj , yproj ) As the real-time position of a single station. Finally, based on the real-time position (x proj , y proj ) of the single station and the azimuth angle θ of the target, the bearing line equation between the target and the single station at this moment is calculated as:

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

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

[0056] Step S3, reference line establishment: Set a threshold window, obtain bearing lines starting from the initial moment based on the threshold window, remove outliers from the bearing lines, and establish a reference line based on the bearing lines after outlier removal. In a possible implementation, step S3 includes: setting a threshold window according to the motion state of the single station and the density of signals, where the threshold window has a window time threshold, a cache capacity threshold, and a distance threshold; obtaining a set of bearing lines starting from the initial moment based on the threshold window; filtering out interfering bearing lines in the set of bearing lines based on an outlier removal method; and substituting the set of bearing lines after outlier removal into the least squares method for fitting to obtain the reference line for intersection positioning.

[0057] Specifically, please refer to Figure 3 as shown Figure 3 which is a schematic diagram of the model for establishing the reference line provided by the embodiment of the present application. Through the bearing line set accumulated by the single station in the initial period of time, it is integrated into a reference line through an outlier removal algorithm and the least squares method.

[0058] In the process of establishing the reference line, it is necessary to determine the threshold window according to the motion state of the single station and the density of signals. The limitations of the threshold window include: a window time threshold T, a cache capacity threshold N, and a distance threshold D max .

[0059] When new data points enter within the set window time threshold T, add this data to the cache array, and then detect whether the capacity of the array reaches the cache capacity threshold N. If the capacity is full, use the least squares method to find the best fitting line corresponding to this array, as follows:

[0060] For N lines, each line is expressed as y = k i x + b i , first collect the sampling points on these lines, expressed as (x ij , y ij ), where i represents each line and j represents the 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] Observation vector Y, which contains the y - coordinates of all data points.

[0064]

[0065] Use the least - squares method to solve for the slope K and intercept B of the best - fit line. The aim is to minimize the sum of the squares of the distances from all data points to the fit line, as follows:

[0066]

[0067] Obtain the solution:

[0068]

[0069] Subsequently, clear the array and cache this line in another container. Continuously loop through the above operations until the distance moved by a single station exceeds the distance threshold D max , or no new valid data has been received for a long time. Once the data caching stops, find the best - fit line for all the data in this container to obtain the reference line equation Y = Kx + B for intersection positioning.

[0070] In addition, outlier rejection work should be carried out before fitting the line each time to ensure the data quality and the accuracy of the reference line calculation.

[0071] Step S4, establishing a temporary line: Set a sliding window. Starting from the end time of the threshold window, obtain the bearing lines based on the sliding window and continuously iterate and update. Reject outliers from the iteratively updated data, and establish a temporary line based on the bearing lines after outlier rejection. In a possible implementation, step S4 includes: caching multiple bearing lines starting from the end time of the threshold window based on the sliding window, bringing the multiple bearing lines into the least - squares method for fitting to obtain the temporary line for intersection positioning; continuously updating the cached bearing lines based on the sliding - window mechanism and performing outlier rejection, and continuously fitting the temporary line based on the bearing lines of the sliding window after outlier rejection.

[0072] Specifically, please refer to Figure 4 as shown Figure 4 is a schematic model diagram of establishing a temporary line by sliding - window iteration provided by the embodiment of the present application. By accumulating the bearing lines obtained by a single station during the continuous movement process, integrating them into a temporary line, and using the sliding - window mechanism to ensure the real - time calculation of the temporary line. The following figure is a schematic model diagram of the present invention for implementing sliding - iteration to establish a temporary line. During the operation of the system, the temporary line will be continuously calculated and updated. The dots in the figure represent typical outlier lines.

[0073] After successfully establishing the reference line, start caching new data points to construct another line required for intersection positioning, which is referred to as the temporary line in this application. The specific implementation process is as follows:

[0074] a) Initialize caching and parameters: Set the maximum capacity of the cache array to m, denoted as L = {l1, l2…l m}, where each l i represents the line equation 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 incoming data points reaches the cache capacity m, use the least squares method to fit an optimal temporary line.

[0076] c) Sliding window mechanism and continuous update: Whenever the newly incoming data volume meets the sliding window size, perform the following operations: First, remove the earliest added n data points from the cache array and add the latest n data points to the cache. Subsequently, perform an outlier rejection step to ensure the validity and accuracy of the data. And based on the updated cache data, apply the least squares method again to refit the optimal temporary line, so that the temporary line iterates continuously as the single station moves and ensures that it always reflects the latest data distribution.

[0077] In a possible implementation manner, outlier rejection includes: For each data point p in the cache array, obtain the k-neighborhood of point p; Calculate the local density of point p based on the number of points within the neighborhood of point p and the Euclidean distance between points; Calculate the centroid of the neighborhood of point p based on the local densities of the points within the neighborhood of point p, the local density of point p, and the number of points within the neighborhood of point p; Calculate the cumulative fluctuation of the centroid of point p as the outlier factor by weighted summation of the centroids of point p under different neighborhoods; Sort all data points in descending order according to the outlier factor, and identify the data points with outlier factors greater than the threshold as outliers for rejection.

[0078] Specifically, during the process of fitting the reference line and the temporary line, outlier rejection 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) significantly deviates from the centroid of its neighborhood, then this point is very likely to be an outlier. Specifically as follows:

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

[0081] σ k (p) = {q | d(p, q) ≤ d(p, p k )}

[0082] d(p, q) represents the Euclidean distance between p and q, and p k represents the k objects that are the nearest neighbors of point p. Subsequently, the local reachability density ρ k (p) is calculated, which represents the reciprocal of the average of the sum of the distances between object p and all points within its k-neighborhood. As follows:

[0083]

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

[0085]

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

[0087] In order to stably represent the degree of outlier of data objects, this application obtains the cumulative fluctuation of the centroid, which is the outlier factor F(p, k), by performing a weighted sum of c k (p) under different neighborhoods. As follows:

[0088]

[0089] k represents the number of the nearest neighbors of object p, which is a preset value. Similarly, the higher the F(p, k), the greater the centroid fluctuation of p, and the more unstable its neighborhood structure is, so the higher the degree of outlier.

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

[0091]

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

[0093] Step S5, Calculation of target position coordinates: Continuously calculate the target position coordinates based on the reference line and multiple temporary lines. Specifically, during the iterative optimization process, continuously calculate the target coordinate position as ([y = k * x + b]) through the reference line y = Kx + B and the temporarily updated line y = kx + b. y tgt = k * x tgt + b).

[0094] Step S6, Caching and result output: Cache the target position coordinates until a sufficient length is reached, then perform outlier removal, and calculate the final target position coordinates based on the target position coordinates after outlier removal. Specifically, according to the steps in Step S5, cache the continuously calculated target positions. When the length of the position coordinate array meets the number of sliding windows, perform iterative update of the array, and at the same time perform outlier removal and averaging to continuously obtain the positioning result, thereby achieving the effect of real-time positioning.

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

[0096] Please refer to Figure 5 shown in Figure 5 the schematic diagram of the angle measurement results of the Kalman filter and this method. Figure 5 It is the schematic diagram of the optimized angle measurement results of the Kalman filter and the method of the present invention under the measured data with the distance between two elements of the long-baseline interferometer being 1.52 m, the target carrier frequency being 1.5 GHz, using a vehicle-mounted interferometer, and using Figure 1 the motion trajectory as the motion model. The black line segments in the figure represent the optimized angle measurement values. It can be seen that compared with the Kalman filter, the method of the present invention can more stably and smoothly reduce the angle measurement error.

[0097] Please refer to Figure 6 shown in Figure 6 the schematic diagram of the relative positioning error of the phase difference change rate and this method. Figure 6 It is the schematic diagram of the relative positioning error between the traditional phase difference change rate positioning method and the method of the present 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 through a certain period of accumulation and sliding window iterative optimization, and by integrating historical information and the latest data, the method of the present invention makes the positioning result gradually stable and maintains a certain accuracy; while the positioning result of the phase difference change rate algorithm fluctuates greatly. When the motion direction is the tangent direction to the target, the positioning is relatively accurate, and the error is large in other cases, and the anti-noise and stability are poor.

[0098] It can be understood that, compared with the traditional phase difference change rate method, the single-station passive positioning method based on direction finding and intersection proposed in this application realizes single-station passive positioning, avoids the phase difference change rate that is difficult to accurately calculate, and uses the sliding window iterative positioning and outlier rejection method to significantly reduce the influence of phase measurement fluctuations in a noisy environment, thereby improving the stability of the system; compared with the Kalman filtering algorithm, the single-station passive positioning method based on direction finding and intersection proposed in this application has better filtering stability based on sliding window iterative positioning, avoids the setting of empirical parameters, can make more efficient use of historical data, has a more obvious convergence effect, and higher positioning accuracy; the outlier rejection method proposed in this application can effectively reduce noise interference.

[0099] Please refer to Figure 7 as shown in Figure 7 the structure diagram of the single-station passive positioning system based on direction finding and intersection provided by an embodiment of this application. The system is used to implement the single-station passive positioning method based on direction finding and intersection as shown in Figure 2 The system includes: a data acquisition module, configured to measure the phase differences of the long-baseline interferometer moving single-station at different times, and calculate the azimuth angle of the target based on the phase differences; a direction finding line calculation module, configured 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 angle of the target; a reference line establishment module, configured to set a threshold window, obtain the direction finding lines starting from the initial time based on the threshold window, perform outlier rejection on the direction finding lines, and establish a reference line based on the direction finding lines after outlier rejection; a temporary line establishment module, configured to set a sliding window, obtain the direction finding lines starting from the end time of the threshold window based on the sliding window and continuously iterate and update, perform outlier rejection on the iteratively updated data, and establish a temporary line based on the direction finding lines after outlier rejection; a target position calculation module, configured to continuously calculate the target position coordinates based on the reference line and multiple temporary lines; a target positioning output module, configured to cache the target position coordinates until a sufficient length, perform outlier rejection, and calculate the final target position coordinates based on the target position coordinates after outlier rejection.

[0100] In a possible implementation manner, the direction finding line calculation module specifically includes: a coordinate conversion module, configured to obtain the GPS data of the single-station at different times, and convert the GPS data into the position coordinates in the northeast celestial rectangular coordinate system as the real-time position of the single-station; an equation construction module, configured 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 angle of the target.

[0101] In a possible implementation manner, the reference line establishment module specifically includes: a threshold window setting module for setting a threshold window according to the motion state of a single station and the density of signals. The threshold window has a window time threshold, a cache capacity threshold, and a distance threshold; a threshold window cache module for obtaining multiple bearing lines from the initial moment based on the threshold window to form a bearing line set; an interference filtering module for filtering out interfering bearing lines in the bearing line set based on an outlier rejection method; and a reference line fitting module for substituting the bearing line set after outlier rejection into the least squares method for fitting to obtain the reference line for intersection positioning.

[0102] In a possible implementation manner, the temporary line establishment module specifically includes: a temporary line fitting module for caching multiple bearing lines from the end moment of the threshold window based on a sliding window, and substituting the multiple bearing lines into the least squares method for fitting to obtain a temporary line for intersection positioning; and a temporary line update module for continuously updating the cached bearing lines based on a sliding window mechanism and performing outlier rejection, and continuously fitting the temporary line based on the bearing lines in the sliding window after outlier rejection.

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

[0104] It should be noted that the bearing intersection single-station passive positioning system provided by this application corresponds one-to-one with Figure 2 the bearing intersection single-station passive positioning method provided, and has corresponding technical effects, so it will not be elaborated here.

[0105] The above specific implementation manners further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific implementation manners of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A single-station passive positioning method for direction finding intersection, characterized in that: include: The phase difference of the long baseline interferometer mobile station 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 line between the target and the single station at different times is calculated; A threshold window is set, and a direction-finding line is obtained from an initial moment based on the threshold window, outliers are removed from the direction-finding line, and a reference straight line is established based on the direction-finding line after the outliers are removed; A sliding window is set, and a direction-finding line is obtained based on the sliding window from the end time of the threshold window and continuously updated iteratively, outliers are removed from the iteratively updated data, and a temporary straight line is established based on the direction-finding line after outliers are removed; Based on the reference straight line and multiple temporary straight lines, the target position coordinates are continuously calculated; The target position coordinates are cached until they are of sufficient length, and then outliers are removed. The final target position coordinates are calculated based on the target position coordinates after outliers are removed.

2. A single-station passive positioning method for direction finding intersection according to claim 1, characterized in that: Based on the real-time position of a single station and the azimuth of the target, the direction finding line between the target and the single station at different times is calculated; including: Obtain GPS data of a single station at different times, and convert the GPS data into position coordinates in the northeast celestial rectangular coordinate system as the real-time position of the single station; 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 at different times are constructed.

3. A single-station passive positioning method for direction finding intersection according to claim 1, characterized in that: Setting a threshold window, obtaining a direction-finding line from an initial moment based on the threshold window, removing outliers from the direction-finding line, and establishing a reference straight line based on the direction-finding line after the outliers have been removed; 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 cache capacity threshold and a distance threshold. Based on the threshold window, a plurality of direction finding lines are obtained from the initial moment to form a direction finding line set; Based on the outlier elimination method, the interference direction finding lines in the direction finding line set are filtered out; The set of direction finding lines after outliers are removed is put into the least squares fitting method to obtain the reference straight line for intersection positioning.

4. A single-station passive positioning method for direction finding intersection according to claim 1, characterized in that: A sliding window is set, and a direction-finding line is obtained based on the sliding window from the end time of the threshold window and continuously updated iteratively, outliers are removed from the iteratively updated data, and a temporary straight line is established based on the direction-finding line after outliers are removed; including: Based on the sliding window, multiple direction-finding lines are cached from the end time of the threshold window, and the multiple direction-finding lines are brought into the least square method fitting to obtain a temporary straight line for intersection positioning; Based on the sliding window mechanism, the cached direction-finding lines are continuously updated and outliers are removed. The temporary straight line is continuously fitted based on the sliding window direction-finding lines after outliers are removed.

5. The single-station passive positioning method for direction finding intersection according to claim 1, characterized in that: The outlier removal includes: For each data point p in the cache array, get the k-neighborhood of point p; Calculate the local density of point p based on the number of points in the area of ​​point p and the Euclidean distance between points; Calculate the centroid of the domain of point p based on the local density of each point in the domain of point p, the local density of point p, and the number of points in the domain of point p; Based on the weighted sum of the center of gravity of point p in different fields, the cumulative fluctuation of the center of gravity of point p is obtained as the outlier factor of point p; All data points are sorted in descending order according to the outlier factor, and the data points with outlier factors greater than the threshold are identified as outliers and removed.

6. A single-station passive positioning system for direction finding intersection, characterized in that: A system for implementing a direction finding intersection single-station passive positioning method as described in any one of claims 1 to 5, comprising: A data acquisition module is used to measure and obtain the phase difference of a long baseline interferometer mobile station at different times, and calculate the azimuth of the target based on the phase difference; A 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 the single station and the azimuth of the target; A reference straight line establishment module is used to set a threshold window, obtain a direction-finding line from an initial moment based on the threshold window, remove outliers from the direction-finding line, and establish a reference straight line based on the direction-finding line after the outliers are removed; A temporary straight line establishment module is used to set a sliding window, obtain a direction-finding line based on the sliding window from the end time of the threshold window and continuously iterate and update, remove outliers from the iteratively updated data, and establish a temporary straight line based on the direction-finding line after the outliers are removed; A target position calculation module is used to continuously calculate the target position coordinates based on the reference straight line and multiple temporary straight lines; The target positioning output module is used to cache the target position coordinates until they are of sufficient length to remove outliers, and calculate the final target position coordinates based on the target position coordinates after outliers are removed.

7. A single-station passive positioning system for direction finding intersection according to claim 6, characterized in that: The direction finding line calculation module specifically includes: The coordinate conversion module is used to obtain the GPS data of a single station at different times and convert the GPS data into position coordinates in the northeast celestial rectangular coordinate system as the real-time position of the single station; The equation construction module is used to construct the direction-finding line 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.

8. A single-station passive positioning system for direction finding intersection according to claim 6, characterized in that: The reference straight line establishment module specifically includes: A threshold window setting module is used to set a threshold window according to the motion state of a single station and the density of signals. The threshold window has a window time threshold, a cache capacity threshold and a distance threshold. A threshold window cache module is used to obtain a plurality of direction finding lines from an initial moment based on the threshold window to form a direction finding line set; An interference filtering module is used to filter out interference direction finding lines in the direction finding line set based on an outlier removal method; The reference straight line fitting module is used to bring the direction finding line set after outliers are removed into the least squares fitting to obtain the reference straight line for intersection positioning.

9. A single-station passive positioning system for direction finding intersection according to claim 6, characterized in that: The temporary straight line establishment module specifically includes: A temporary straight line fitting module is used to cache multiple direction finding lines starting from the end time of the threshold window based on the sliding window, and bring the multiple direction finding lines into the least square method fitting to obtain a temporary straight line for intersection positioning; The temporary straight line update module is used to continuously update the cached direction-finding line based on the sliding window mechanism and remove outliers, and continuously fit the temporary straight line based on the sliding window direction-finding line after outliers are removed.

10. The single-station passive positioning system for direction finding intersection according to claim 6, characterized in that: The outlier elimination in the reference straight line establishment module and the temporary straight line establishment module includes: For each data point p in the cache array, get the k-neighborhood of point p; Calculate the local density of point p based on the number of points in the area of ​​point p and the Euclidean distance between points; Calculate the centroid of the domain of point p based on the local density of each point in the domain of point p, the local density of point p, and the number of points in the domain of point p; Based on the weighted sum of the center of gravity of point p in different fields, the cumulative fluctuation of the center of gravity of point p is obtained as the outlier factor of point p; All data points are sorted in descending order according to the outlier factor, and the data points with outlier factors greater than the threshold are identified as outliers and removed.

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