CN118011313A - Pulse direction-finding information sorting method based on Gaussian mixture model - Google Patents
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Abstract
Aiming at the problem that pulse direction finding information of a low orbit satellite is non-circular and non-normal, so that the traditional k-means clustering and other sorting methods are prone to losing pulses or mistaking, the invention discloses a pulse direction finding information sorting method based on a Gaussian mixture model. According to the method provided by the invention, the radiation source pulse sequences with non-circular and non-normal distribution of the incoming wave directions can be correctly distinguished, and the sorting effect of pulse signals is improved.
Description
Technical Field
The invention belongs to the electronic reconnaissance signal processing technology, and particularly relates to a pulse direction finding information sorting method based on a Gaussian mixture model.
Background
Pulse sorting refers to the pass frequencyPulse width/>And incoming wave direction/>Clustering the information to distinguish pulse sequences of different parameters of the radiation source. The arrival direction parameter is not affected by the change of the working parameter of the radar radiation source, and for most targets, the arrival direction of the target relative to the satellite cannot be changed rapidly in a short time, so that the arrival direction parameter is stable and is the most important parameter in pulse separation. However, under the high-density pulse scene, arrival angle parameters of the pulses of the radiation sources at similar positions are overlapped with each other, and are difficult to distinguish; the two-dimensional distribution parameters of the pulse arrival angle errors are not identical, but change along with the value of the arrival angle, and the errors in the azimuth direction and the pitching direction of the pulse are different, and the common clustering method needs to assume that the distribution of clusters is circular, so that the clustering result is split; the low orbit satellite moves at a relative target speed, the arrival angle of the same radiation source changes with time, errors are additionally introduced, and the distribution range of the pulse arrival angle is enlarged. How to distinguish radiation sources at different positions as far as possible by utilizing the error distribution characteristics of the angle of arrival parameters is an important problem to be solved in engineering practice.
Disclosure of Invention
The invention provides a pulse direction-finding information sorting method based on a Gaussian mixture model, aiming at the problem of pulse sorting based on direction-finding information in a single-satellite direction-finding system scene of a low-orbit satellite, which comprises the steps of firstly, locating and reversely pushing a reference moment pulse incoming wave direction through a single pulse to eliminate arrival angle drift, and then utilizingClustering and Gaussian mixture model/>And (3) performing pulse sorting by two-step clustering, and finally removing wrong sorting pulses in a clustering result by using a weighted iteration mode, thereby improving the accuracy of pulse sequence extraction.
The technical scheme for realizing the invention is as follows: a pulse direction-finding information sorting method based on Gaussian mixture model comprises the following steps:
step 1, calculating longitude, latitude and elevation of a target radiation source by utilizing DOA measurement values of incoming wave directions at pulse arrival time and combining DEM data, and reversely pushing DOA of the target radiation source at reference time according to satellite reconnaissance reference time position, so that DOA drift caused by movement of a low-orbit satellite relative to the radiation source is eliminated.
And step 2, performing DBSCAN clustering processing according to the antenna direction finding precision by using a threshold to obtain an initial clustering result, then checking the distribution size of the clusters, and performing Gaussian mixture model clustering processing on the clusters with larger distribution range to obtain a further clustering result, namely a pre-sorting result.
And step 3, calculating and sorting the variance of the DOA of the pulse sequence according to the pre-sorting result, carrying out hypothesis test, judging whether the clustering result has the gross error, and if the clustering result has the gross error, adopting a weight selecting iteration method to carry out the gross error rejection, thereby improving the pre-sorting accuracy.
Compared with the prior art, the invention has the advantages that:
(1) Combining digital elevation model by using satellite direction finding information The data locates the pulse and puts the pulse at the time/>Unifying and reversely pushing to the reference moment to eliminate/>, which is brought by the motion of the low-orbit satellite relative to the radiation sourceDrift, decrease the distribution range of the measured value, and ensure that the measured value accords with normal distribution.
(2) By means ofClustering the/>The clustering result is optimized to solve the single/>There may be multiple radiation sources within the cluster result.
(3) After the clustering sorting flow is finished, carrying out hypothesis testing on the positioning result of the pulse sequence to judge whether error sorting pulses exist, eliminating the error sorting pulses by using an error eliminating mode of weight selecting iteration, and improving the accuracy of pulse sequence extraction.
Drawings
FIG. 1 is a schematic view ofAnd (5) reversely pushing the flow chart.
FIG. 2 is a schematic view of/>A two-stage clustering flow chart.
Fig. 3 is a flowchart of coarse difference point elimination based on the weighted iteration method.
Fig. 4 is a flow chart of a pulse direction finding information sorting method based on a gaussian mixture model.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and examples.
The invention provides a pulse direction-finding information sorting method based on a Gaussian mixture model by combining FIG. 4Analysis of distribution characteristics, innovatively proposes the use of positioning results to extrapolate/>Eliminating the relative movementMethod of bleaching by binding/>And/>Process run/>Clustering, and introducing a weight selection iteration method to perform error sorting pulse rejection on sorting results. The invention significantly reduces the consumption ofThe problem of error sorting caused by non-circular distribution and non-Gaussian property of the measured value greatly improves the distinguishing capability of the algorithm on radiation sources at different positions and greatly improves the sorting accuracy.
The invention discloses a pulse direction-finding information sorting method based on a Gaussian mixture model, which comprises the following steps of:
Step 1, utilizing the positioning result to reversely push Elimination of relative motion induced/>Bleaching and changing:
calculating the position of the target radiation source using the pulse direction-finding azimuth and pitch angle measurements, and then based on Calculating the elevation of the target radiation source according to the data, and reversely pushing the/>, at the reference moment, of the target radiation source according to the satellite reference moment positionEliminating/>, caused by satellite motionAnd (5) bleaching.
The single star direction finding positioning model is as follows:
(1)，
In the method, in the process of the invention, For pulse arrival time,/>Target position in coordinate System/>；Representing an installation matrix of an attitude measurement system to a direction finding antenna coordinate system, wherein/>Representing the rotation angle around the X-axis,/>Representing the rotation angle around the Y-axis,/>Representing a rotation angle about the Z-axis; /(I)Indicating the arrival time of the pulse from/>A rotation matrix from the coordinate system to the satellite attitude measurement system coordinate system; /(I)For pulse incoming wave direction relative/>, under direction finding antenna coordinate systemThe direction angle of the axis,/>Relative/>, for the direction finding antenna coordinate system, the pulse wave direction is relatively movedThe direction angle of the axis. By/>And (5) carrying out data interpolation to obtain the target elevation, thereby obtaining the real position of the target. And calculating the position of each pulse positioning result relative to the satellite reference moment, and correcting the direction-finding offset error in the sorting period caused by the satellite relative motion, thereby ensuring that the measured value accords with normal distribution.
The specific implementation process of the reverse thrust flow is as follows:
Step 1.1, single pulse positioning: assuming the elevation of the radiation source is 0, calculating the position of the radiation source Position under the coordinate system. Let the pulse arrival time be/>，/>For/>Position of radiation source under time direction finding antenna coordinate system,/>For/>Position of the radiation source in the coordinate system (i.e. target position)/>Is thatThe instantaneous position of the satellite at time t in the coordinate system.
Recording deviceFor time t/>Conversion matrix from coordinate system to direction-finding antenna coordinate system
(2)，
And/>The conversion relation of (2) is:
(3)，
time pulse relative/> Axial direction tailpiece angle/>And/>Time pulse relative/>Angle of the direction chord of the shaftExpressed as:
(4)，
Due to the movement of the satellite(s), Will slowly change over time.
Assume that the range of the target to the satellite isLet vector/>：
(5)，
Decomposing the position vector of the radiation source under the coordinate system of the direction finding antenna into:
(6)，
Substitution equation Can be obtained with respect to/>Is a unitary quadratic equation of (a):
(7)，
solving the unitary quadratic equation to obtain two roots and selecting The smallest solution is the distance between the radiation source and the satellite.
The following equation is solved:
(8)，
obtaining the position of the radiation source In/>Respectively/>And the ellipsoid long half axis and the eccentricity are h, and the height of the radiation source is h.
Step 1.2 according toData iterative calculation target geodetic coordinates: position of the radiation source in WGS84 coordinate system/>And earth longitude and latitude height/>The conversion relation of (2) is shown in the formula (9):
(9)，
wherein B, L, H is latitude, longitude and altitude, and N is the radius of curvature of the local circle: R represents the earth's long half axis.
The iteration number is recorded as l, and the steps of iterative calculation of the elevation are as follows:
1) Recording the position of the radiation source obtained in the step 1.1 as Calculating the latitude and longitude of the radiation source according to the formula (9)。
2) Proceeding withElevation interpolation to obtain the elevation/>, of the radiation sourceRecord/>。
3) Order theWill/>Substituting (8) and recalculating the position/>, of the radiation sourceCalculating an iteration errorIf the error value is less than the threshold, the iteration is considered to be ended, otherwise, 2) is returned.
Step 1.3, according to the position of the satellite at the reference momentCalculating the position/>, of the radiation source under the coordinate system of the direction-finding antenna at the reference momentObtaining the residual chord angle/>, of the pulse direction at the reference moment、/>。
And step 1.4, processing all pulse direction finding results in the steps 1.1-1.3 to obtain the pulse direction cosine angle at the reference moment, wherein the pulse direction cosine angle at the reference moment is subjected to normal distribution.
Step 2, forPerforming two-stage clustering: firstly according to the antenna direction finding precision/>With a larger threshold (general choice/>) Go/>And (3) clustering to obtain an initial clustering result, checking the distribution of the clusters, and performing Gaussian mixture model clustering to obtain a pre-sorting result for the clusters with larger distribution range.
The specific implementation process is as follows:
Step 2.1, Clustering: /(I)Clustering is a density-based clustering method. The method considers the data set as a collection of several high density clusters separated by low density regions, and examines the connectivity between samples by sample density.
Input parameters of (a) include data samples/>Distance function between data samples/>Sample Density neighborhood radius/>And the minimum number of samples required to form a cluster/>. Let/>, let the total number of pulses be N p 、/>Respectively represent the reference moment pulse relative to/>Shaft sum/>The directional tailline angle of the axis defines the data sample point/>And/>The expression is:
(10)，
In the method, in the process of the invention, Is the pulse sequence number. Using mahalanobis distance as a function of distance between data samples/>The calculation expression is as follows:
(11)，
in the covariance matrix ，/>Is the standard deviation of X-axis direction,/>Is the standard deviation in the Y-axis direction,/>Is the covariance in the X-axis direction and the Y-axis direction.
For any arbitraryIt/>Set of pulse sample points contained within a neighborhood/>The method comprises the following steps:
(12)，
Definition of the definition For/>Number of pulse sample points,/>In order to form the minimum number of samples required for clustering,The method classifies the samples into 3 classes according to the conditions of the samples in the sample neighborhood:
1) Core sample: ；
2) Edge samples: but/> Includes a core sample;
3) Noise samples: And/> Core samples are not included.
For core sample pointsAnd another sample point/>If/>Is called/>Can be made byDirect density is reachable, description/>And/>Belonging to the same class. The density reachable relationship can be transferred unidirectionally, if present/>Wherein/>For the number of samples, satisfy/>，/>And (2) andAll satisfy/>Can be defined by/>The direct density is the term/>Can be defined by/>The indirect density is available. All by core samples/>The points with direct or indirect density are grouped into a cluster to obtain/>And (5) corresponding clustering.
The specific steps of (a) are as follows:
1) Selecting any one of the sample spaces Sample, search by/>Direct density reachable data samples。
2) If it isThen add a cluster/>And let/>Otherwise skip/>。
3) TraversingUnprocessed data samples/>If/>Let/>。
4) From the slaveRemoval from sample set/>If/>And returning to 1) continuing processing if unprocessed samples still remain in the set, and otherwise ending clustering.
Step 2.2,Clustering: counting the distribution range of DOA parameters in DBSCAN clustering results, and setting/>For the theoretical variance of the direction finding system, if the distribution range of the X-axis or Y-axis direction angles in the clustering result exceeds/>It is considered that a plurality of radiation sources may exist in the clustering result, and/>, the method is neededAnd (5) clustering.
The algorithm assumes that the samples of each cluster conform to a gaussian distribution, first randomizing the mean/>, of the clustersCovariance matrix/>And weight/>Subscript/>And expressing the sequence numbers of the radiation sources, respectively calculating the expectations of the samples belonging to each cluster, and continuously updating the clustering parameters to maximize expected values so as to realize the classification of the samples.
Assume thatClustering results/>Comprises/>Individual radiation sources and/>Pulse/>For pulse sequence number, set the/>, of each radiation sourceConform to the two-dimensional joint normal distribution/>：
(13)，
Calculating the expectations of each sample belonging to each cluster：
(14)，
Updating the weight of each cluster according to the expected valueMean/>Sum of variances/>：
(15)，
(16)，
(17)，
Wherein the method comprises the steps ofThe weight of each cluster can be calculated from the formulas (15) - (17) as DOA probability density function in the radiation sourceMean/>Sum of variances/>。
And recalculating the expectations of the samples belonging to each cluster and the weights, the mean values and the variances of each cluster until the parameters of the clusters are converged, and finally obtaining the distribution parameters of the DOA of the radiation source. Cannot be determined in actual operationThe value of (1) >, generally taken/>For 2 to 4 respectively/>And (5) processing, and selecting a result with the maximum expected value of the sample.
Step 2.3, recalculating the expectations of each pulse to each radiation sourceThe pulses are classified into the radiation source with the expected maximum, so that a pulse sequence corresponding to the radiation source, namely a pre-selection result, is obtained.
Step 3, eliminating the false sorting pulse: and carrying out single pulse positioning treatment on the pre-selected pulse sequence, counting the distribution range of the positioning result, and comparing with the system positioning precision. If the distribution range of the positioning result is too large, the pre-sorting pulse sequence is considered to contain pulses from other radiation sources, and the pulses are removed by adopting a weight selection iteration method, so that the de-staggered pulse sequence of the independent radiation source is obtained, and the sorting accuracy is improved.
If it isIf the measured value does not contain coarse differences, the observed value should follow normal distribution, and the variance should follow chi-square distribution. Taking the X-axis direction angle as an example, a statistic is constructed:
(18)，
In the middle of For finding the theoretical variance of the direction system,/>For radiation source/>Pulse number in (a), variable/>Subject to degrees of freedom/>Chi-square distribution/>，/>For radiation source/>Middle pulse X-axis direction angular variance.
Suppose 1:， /> Is free of other radiation source pulses,/> Is a mathematical expectation;
Suppose 2: ，/> contains other radiation source pulses, and selects significance level a for hypothesis testing if Then assume that 1 is not true. Calculating a variable/>, based on the X-axis direction angle and the Y-axis direction angle, respectivelyAnd variable/>If the assumption 1 is not satisfied, correction is required by a weighted iteration method.
The calculation process of the weighting iteration method is as follows:
step 3.1, let the weight function of each observation be 1, namely ；
Step 3.2, calculating the pulse positioning resultAverage/>And calculates the positioning error/>, of each pulse according to the average position，/>Is the pulse sequence number.
Step 3.3, calculating weight function according to the positioning error：
(19)，
Wherein the method comprises the steps ofAnd positioning errors for system theory.
Step 3.4, weighting the positioning result of each pulse, and recalculating the weighted average position of the radiation source;
And 3.5, updating the weight function again, and repeating the steps 3.2-3.4 until the weighted average position of the radiation source is not changed any more, and eliminating the pulse with the weight function of 0 to obtain a single radiation source pulse sequence.
The specific embodiments described herein are offered by way of example only to illustrate the spirit of the invention. Those skilled in the art may make various modifications or additions to the described embodiments or substitutions thereof without departing from the spirit of the invention or exceeding the scope of the invention as defined in the accompanying claims.
Claims (6)
1. A pulse direction-finding information sorting method based on a Gaussian mixture model is characterized by comprising the following steps:
Step 1, calculating longitude, latitude and elevation of a target radiation source by utilizing DOA measurement values of incoming wave directions at pulse arrival time and combining DEM data, and reversely pushing DOA of the target radiation source at reference time according to satellite reconnaissance reference time position, so that DOA drift caused by relative radiation source movement of a low-orbit satellite is eliminated;
Step2, performing DBSCAN clustering processing according to the antenna direction finding precision by using a threshold to obtain an initial clustering result, then checking the distribution size of the clusters, and performing Gaussian mixture model clustering processing on the clusters with larger distribution range to obtain a further clustering result, namely a pre-sorting result;
And step 3, calculating and sorting the variance of the DOA of the pulse sequence according to the pre-sorting result, carrying out hypothesis test, judging whether the clustering result has the gross error, and if the clustering result has the gross error, adopting a weight selecting iteration method to carry out the gross error rejection, thereby improving the pre-sorting accuracy.
2. The method for sorting pulse direction finding information based on Gaussian mixture model as claimed in claim 1, wherein in step 1, the latitude and longitude and elevation of the target radiation source are calculated by using DOA measurement value of incoming wave direction at pulse arrival time and combining with DEM data, and DOA of the target radiation source at reference time is reversely pushed according to satellite reconnaissance reference time position, thereby eliminating DOA drift caused by low orbit satellite relative radiation source movement, specifically comprising the following steps:
Step 1.1, assuming that the elevation under the WGS84 coordinate system of the radiation source is 0, solving the distance r between the target and the satellite according to the satellite position pulse DOA measured value at the moment of pulse arrival, and calculating the position of the radiation source under the WGS84 coordinate system;
step 1.2, interpolation is carried out on DEM data, the elevation H of the radiation source is calculated, the position and the elevation of the radiation source are continuously and iteratively calculated according to the distance r between the target and the satellite until the iteration result converges, and the accurate position and the elevation of the radiation source under the WGS84 coordinate system are obtained;
Step 1.3, calculating a scout reference moment pulse DOA according to the accurate position of the radiation source and the position of the scout reference moment satellite;
And step 1.4, processing the pulse direction finding results in the steps 1.1-1.3 to obtain the pulse direction residual chord angle at the reference moment, thereby eliminating DOA drift caused by satellite motion.
3. The pulse direction finding information sorting method based on the Gaussian mixture model as claimed in claim 2, wherein the method comprises the following steps: in step 2, performing DBSCAN clustering processing according to antenna direction-finding precision by using a threshold to obtain an initial clustering result, then checking the distribution of clusters, and performing Gaussian mixture model clustering processing on clusters with larger distribution range to obtain a further clustering result, wherein the method comprises the following steps of:
step 2.1, performing DBSCAN clustering treatment on the pulse DOA value to obtain DOA coarse clusters;
step 2.2, counting the distribution range of DOA parameters in the DBSCAN clustering result, setting For the theoretical variance of the direction finding system, if the distribution range of the X-axis or Y-axis direction angles in the clustering result exceeds/>A plurality of radiation sources possibly exist in the clustering result, and GMM clustering processing is needed; assuming that the number of the radiation sources in DOA coarse clustering is 2-4, respectively performing Gaussian mixture model clustering treatment, and selecting a clustering result with the expected maximum as an actual DOA probability density function of the radiation sources;
And 2.3, calculating the expectation that each pulse belongs to each radiation source again, and classifying the pulse into the radiation source with the expected maximum, so as to obtain a pulse sequence corresponding to the radiation source, namely a pre-selection result.
4. A method for sorting pulse direction finding information based on a gaussian mixture model according to claim 3, wherein: in step 2.1, the method for selecting the DBSCAN distance threshold comprises the following steps: if the direction-finding precision isSelect/>As a distance threshold.
5. The pulse direction finding information sorting method based on the Gaussian mixture model as claimed in claim 4, wherein the method comprises the following steps: in step 3, it is determined whether the clustering result has a rough difference, specifically as follows:
constructing statistics:
，
In the method, in the process of the invention, For finding the theoretical variance of the direction system,/>For radiation source/>Pulse number,/>For radiation source/>Middle pulse X-axis direction angular variance, variable/>Subject to degrees of freedom/>Chi-square distribution/>；
Suppose 1:，/> Is free of other radiation source pulses,/> Is a mathematical expectation;
Suppose 2: ，/> contains other radiation source pulses, and selects significance level alpha for hypothesis testing if Then assume that 1 is not true; calculating a variable/>, based on the X-axis direction angle and the Y-axis direction angle, respectivelyAnd variable/>If the hypothesis 1 is not satisfied, the hypothesis test process is performed, and if the hypothesis 1 is not satisfied, the false sort pulse is considered to exist.
6. The pulse direction finding information sorting method based on the Gaussian mixture model as claimed in claim 5, wherein the method comprises the following steps: in the step 3, if the coarse difference exists, adopting a weight selection iteration method to perform coarse difference rejection, wherein the method specifically comprises the following steps:
step 3.1, let the weight function of each observation be 1, namely ，/>For radiation source/>The number of pulses in (a);
Step 3.2, calculating the pulse positioning result Average/>And calculates the positioning error/>, of each pulse according to the average position，/>Is a pulse sequence number;
step 3.3, calculating weight function according to the positioning error ：
，
In the method, in the process of the invention,Positioning errors for system theory;
step 3.4, weighting the positioning result of each pulse, and recalculating the weighted average position of the radiation source;
and 3.5, updating the weight function again, and repeating the steps 3.2-3.4 until the weighted average position of the radiation source is not changed any more, and eliminating the pulse with the weight function of 0 to obtain a final clustering result.
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