A signal sorting error detection method based on multi-dimensional scaling transformation

Abstract

The application discloses a signal sorting error detection method based on multi-dimensional scaling transformation. The method first adopts a rectangular window to cut off an angle of arrival sequence to be detected once; second, different size rectangular windows are adopted to cut off the cut-off sequence twice, a scale space is constructed to locate potential error fragments; third, stretching and shrinking transformation is carried out on each cut-off fragment, and the angle of arrival difference between multiple radiation sources in the fragment is enlarged; fourth, based on singular value decomposition of a covariance matrix, each fragment is rotated along a main direction, and the angle of arrival difference is converted into an intercept difference; fifth, hierarchical clustering is carried out on the rotated fragment, a minimum distance between adjacent classes and a contour coefficient are adopted to form a double decision basis, all fragments in the scale space are traversed, and when any fragment meets any basis, sorting error is determined. The method effectively solves the problem that when multiple signal parameters are close to each other, the radiation sources move in the form of relatively small angle of arrival difference with respect to an observation point, and signal sorting error is easily caused.

Description

Technical Field

[0001] This invention belongs to the field of signal sorting, and specifically relates to a signal sorting error detection method based on multidimensional scale transformation. Background Technology

[0002] Signal sorting is a core technology for accurately separating and identifying each independent radiation source in a complex, dense, and intertwined electromagnetic signal environment. In modern electronic information systems, the electromagnetic environment exhibits unprecedented complexity. Various radar, communication, identification, and jamming signals highly overlap in the time, frequency, spatial, and energy domains, forming densely interwoven signal flows. Accurately extracting the independent pulse sequence of each radiation source from such a complex signal background directly affects the accuracy of subsequent signal analysis and situational awareness, as well as the efficiency of the information processing system. The success or failure of signal sorting often determines whether valuable feature information can be extracted from massive amounts of data, thereby identifying high-value targets and guiding subsequent electronic countermeasures or spectrum management operations.

[0003] From a theoretical perspective, because the spatial position of the same radiation source remains relatively stable or changes continuously over a short period, all signals radiated by it also exhibit stable changes in their azimuth angle of arrival (AOA). This physical constraint makes AOA a robust and difficult-to-forge classification feature. Compared to parameters such as carrier frequency, pulse width, and repetition rate, AOA is directly related to the spatial geometric position of the radiation source and is not easily affected by changes in the radiation source's operating mode or modulation method, exhibiting strong geometric invariance. Therefore, in environments with multiple radiation sources and overlapping parameters, AOA is often used to distinguish radiation sources of the same type and similar parameters but located in different spatial positions, becoming an important spatial characteristic parameter for signal sorting.

[0004] However, when multiple radiation sources with similar parameters have small differences in their direction of arrival (AOA) relative to the observation and receiving system, the reliability of signal sorting faces a severe challenge. This situation is common in scenarios such as close formation flying, collaborative operation formations, or formation navigation of similar platforms. Because the radiated signals from each platform highly overlap in the time and frequency domains, and the azimuth differences are less than the system's angle measurement error or the sorting algorithm's tolerance threshold, pulse interleaving and misclassification errors can easily occur, misclassifying multiple radiation sources as a single source, or splitting a single radiation source into multiple false sources. Such sorting errors directly lead to cognitive biases at the information processing level, potentially causing high-threat radiation source carrier platforms to be missed, and in severe cases, obscuring the true existence of critical targets and interfering with the accuracy of command and decision-making systems.

[0005] The causes of signal sorting errors are multifaceted. First, direction-finding systems inherently have accuracy limitations; when the angular difference between radiation sources is less than the system's angular measurement error, the azimuth angle loses its effective distinguishing ability. Second, the processing granularity and time window selection of the sorting algorithm also affect the stability of the azimuth angle judgment; overly precise or coarse parameter settings can both lead to misclassification. Furthermore, channel environment factors such as multipath effects and abnormal electromagnetic wave propagation can introduce azimuth measurement deviations, further blurring the spatial boundaries between radiation sources. In complex electromagnetic interference environments, interference signals and real signals superimpose, further exacerbating the technical difficulty of the sorting process.

[0006] Existing literature, whether using hierarchical clustering sorting methods based on pulse descriptors or main sorting methods based on PRI transform, aims to improve the sorting algorithm itself to increase sorting accuracy. However, existing technologies lack a reliable post-processing verification mechanism to address the question of whether the sorted results are reliable. Therefore, effective detection of signal sorting errors is particularly urgent. An error detection mechanism should be integrated throughout the entire sorting process, capable of identifying abnormal states in real time during sorting and also possessing post-processing analysis capabilities to retrospectively verify suspicious signal segments. Summary of the Invention

[0007] To address the technical problem mentioned in the background art that "when multiple radiation sources with similar signal parameters move in a manner with relatively small differences in the direction of arrival angle relative to the observation point, it is easy to cause errors in signal sorting," this invention aims to design a method for detecting sorting errors based on the direction of arrival, and proposes a signal sorting error detection method based on multidimensional scale transformation.

[0008] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0009] A signal sorting error detection method based on multidimensional scaling transformation, characterized in that it is used to detect the first error among multiple sorted radiation sources. The method for self-checking errors in the angle of arrival sequence of several radiation sources includes the following steps:

[0010] Step 1: Truncate using a rectangular window. The sorted first sequence of angles of arrival of radiation sources After truncating once, the truncated sequence is obtained, represented as:

[0011]

[0012] Step 2: Scale transformation, using... Layers, rectangular windows of different sizes on each layer and The truncated sequence is further truncated to obtain a scale space composed of multiple pairs of truncated segments, wherein Indicates the layer number of the second truncation, Indicates the first The segment number within the rectangular window is represented as follows:

[0013]

[0014] Step 3: Scaling transformation. For each quadratic truncated segment in the scale space, scale it by a scaling factor. The time axis and amplitude axis are scaled as a whole, with the time axis being placed at equal intervals according to the original segment length and then multiplied by . After normalizing the arrival angle values ​​of the amplitude axis, it is mapped to... Interval and multiply by the whole This is done to amplify the difference in the angle of arrival between multiple radiation sources within each truncated segment, resulting in a two-dimensional point set after scaling transformation.

[0015] Step 4: Rotate in the principal direction and calculate the covariance matrix for each two-dimensional point set after the scaling transformation. and Then, singular value decomposition is performed, and each two-dimensional point set is rotated along the principal direction determined by the right singular vector matrix V to obtain the rotated fragment. and This is to convert the difference in the angle of arrival between radiation sources into a difference in the intercept of the rotated space;

[0016] Step 5: Sorting error detection. For each rotated segment, check its second dimension component. , Hierarchical clustering is performed on the top layer, assuming that a single fragment is clustered into... Class, and calculate the minimum distance between adjacent classes. and contour coefficient ; Traverse all secondary truncation segments generated in step two within the scale space, as long as any segment satisfies criterion 1: Or, based on judgment 2: Then determine the first The sorting results for the radiation sources contained errors; among them , , and These are preset threshold values. The length of a single segment; the minimum distance between adjacent classes. For the first The minimum value of the class and the first The difference between the maximum values ​​of the -1 class, the silhouette coefficient Defined as:

[0017]

[0018] in For point The average distance to other points of the same type For point The minimum average distance to all points of other classes.

[0019] Furthermore, the rectangular window function in step one... Defined as:

[0020]

[0021] in This indicates the initial time of the intercept. Indicates the length of the rectangular window.

[0022] Furthermore, the two sets of quadratic truncated rectangular window functions in step two are defined as follows:

[0023]

[0024]

[0025] By taking different values ​​at each level The values ​​constitute the segmentation of the original truncated sequence across multiple time scales.

[0026] Furthermore, the scaling transformation in step three is implemented according to the following formula:

[0027]

[0028]

[0029] in This is the scaling factor, applied to both the time axis and the amplitude axis. This is the upper limit of the amplitude mapping.

[0030] Furthermore, in step four, the covariance matrix of each two-dimensional point set is constructed using the following formula, and singular value decomposition is performed:

[0031]

[0032]

[0033]

[0034]

[0035] Rotating the segment along the main direction is represented as:

[0036]

[0037]

[0038] Furthermore, the hierarchical clustering in step five is a bottom-up agglomerative hierarchical clustering; individual segments are clustered as A class, represented as:

[0039]

[0040]

[0041] Furthermore, the specific form of the minimum distance between adjacent classes in step five is as follows:

[0042]

[0043] During the traversal decision, if there exists any quadratic truncation segment such that... or If true, then determine the first [number]th ... The sorting result of the first radiation source is incorrect; conversely, if all segments in the scale space do not meet the above two criteria, then the first radiation source is determined to be incorrect. The results of the radiation source sorting were correct.

[0044] Furthermore, the threshold The range of values ​​is The threshold The range of values ​​is The amplitude mapping upper limit value The range of values ​​is The number of secondary cut-off layers The range of values ​​is .

[0045] Furthermore, independent error detection is performed on each of the multiple radiation sources, that is, steps one to five are performed sequentially for the angle of arrival sequence of each sorted radiation source.

[0046] Compared with the prior art, the beneficial effects of this invention are reflected in the following aspects:

[0047] First, this invention does not directly improve the sorting algorithm itself, but performs post-sorting self-verification on the sorted results, which has good versatility and can be used with any sorting algorithm based on features such as DOA, RF, PW, PRI, etc. without changing the original sorting process.

[0048] Second, by introducing a scale space constructed with rectangular windows of different sizes, erroneous segments can be effectively identified at an appropriate time scale, avoiding false alarms and missed alarms under a single window length.

[0049] Third, the two-stage geometric preprocessing of scaling transformation and principal direction rotation based on SVD significantly amplifies the differences between multiple radiation sources that were originally close to each other in the angle of arrival space into intercept differences in the rotated space, which significantly improves the distinguishability of subsequent clustering decisions.

[0050] Fourth, it adopts a dual decision criterion consisting of the minimum distance between adjacent classes and the silhouette coefficient, which has both sensitivity to the "separability" and "cohesion" of clustering, strong robustness and low probability of false alarms.

[0051] Fifth, the present invention has the characteristics of high detection sensitivity and strong robustness, and is especially suitable for high-challenge scenarios with small differences in arrival azimuth angle, such as dense formation flight, collaborative operation formation, or formation navigation of the same type of platform. Attached Figure Description

[0052] Figure 1 This is a schematic diagram illustrating the algorithm principle of the signal sorting error detection method based on multidimensional scale transformation provided in an embodiment of the present invention. Detailed Implementation

[0053] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0054] This embodiment provides a signal sorting error detection method based on multi-dimensional scaling transformation, such as... Figure 1 As shown, it is used to sort out the first of the multiple radiation sources that have been selected. The arrival angle sequence of each radiation source is used for error self-checking, specifically including steps one through five.

[0055] Step 1: Truncate.

[0056] The sorted first A sequence of radiation source angles of arrival A truncation is performed to obtain the sequence segment to be detected, as shown in the following formula:

[0057]

[0058] in Indicates the sorted first One radiation source, Indicates the sorted first A sequence of angles of arrival for each radiation source. It is a rectangular window function, as shown in the following formula:

[0059]

[0060] in This indicates the initial time of the intercept. This indicates the length of the rectangular window. The purpose of truncation is to extract a segment from the sorted angle of arrival sequence for subsequent verification. The length of the rectangular window... The choice depends on the observation duration and the system sampling rate.

[0061] Step 2: Scale transformation.

[0062] The truncated sequence is further truncated to construct a scale space, as shown in the following equation:

[0063]

[0064] in and It is a rectangular window function, as shown in the following formula:

[0065]

[0066]

[0067] in Indicates the layer number of the second truncation. Indicates the first The segment number within each rectangular window. This is achieved by taking different numbers within each layer. Values ​​(e.g.) =2, 3, 4,…), constituting a segmentation of the original truncated sequence across multiple time scales; within each layer Take 1 to This corresponds to different dividing point positions. This forms a system consisting of multiple pairs of... , The scale space composed of sub-segments contains both coarse-scale two-segments and fine-scale multi-segments; the time window in which the error occurs is related to a certain pair of... If the segments are close in position, the sub-segments at the corresponding level will exhibit the strongest separability, which is convenient for subsequent clustering decisions.

[0068] Step 3: Scale transformation.

[0069] The truncated angle of arrival sequence is scaled to amplify the differences in angle of arrival between multiple radiation sources that may exist within each truncated segment, as shown in the following equation:

[0070]

[0071]

[0072] in This is a scaling factor that applies to both the time axis and the amplitude axis, resulting in overall scaling. This is the upper limit of the amplitude mapping. The scaling transform resets the sampling points on the time axis at equal intervals according to the original segment length, and normalizes the angle of arrival value on the amplitude axis. After the interval, multiply the whole by the scaling factor. In this embodiment The preferred value is 1, in which case both the time axis and amplitude axis are preserved at their original scale; when it is necessary to scale the entire segment proportionally, a value of 1 can be used. >1, synchronizing the expansion of the time axis and amplitude axis. The geometric significance of this step is that the azimuth differences of multiple radiation sources in the original angle of arrival sequence may be within the measurement error range, resulting in noise overwhelming the signal during direct clustering; after the scaling transformation, the azimuth differences are linearly mapped to... Within the amplitude range, it is thus fully amplified for subsequent clustering distinction.

[0073] Step 4: Rotate in the main direction.

[0074] For a single truncated segment Its covariance matrix is ​​expressed as:

[0075]

[0076] For a single truncated segment Its covariance matrix is ​​expressed as:

[0077]

[0078] in This represents the mean function. Singular value decomposition of the covariance matrix yields:

[0079]

[0080]

[0081] The column vectors of the V matrix obtained from singular value decomposition are the principal directions of the point set. Rotating the segment along the principal direction is represented as:

[0082]

[0083]

[0084] in and This represents the rotated segment. The geometric meaning of rotation in the principal direction is as follows: if the angles of arrival of two radiation sources in a segment change approximately linearly with time, then before rotation, they form two approximately parallel oblique lines on the (x, y) plane; after rotation along the principal direction, these two oblique lines become two approximately horizontal parallel straight lines, and their second-dimensional components... (or The difference in arrival angle is the intercept difference between the two radiation sources, thus stabilizing the temporal difference in arrival angle into a static intercept difference that can be clustered for analysis.

[0085] Step 5: Sorting error detection.

[0086] After rotation and Hierarchical cluster analysis was performed on the fragments respectively, assuming that a single fragment was clustered into 10 groups. The class is shown in the following formula:

[0087]

[0088]

[0089] This embodiment uses a bottom-up agglomerative hierarchical clustering algorithm, which uses the shortest distance between classes as the connection criterion, and gradually merges the two closest classes until the termination condition is met.

[0090] The number of clusters The specific strategy for determining the number of clusters can be any of the following methods: Method 1: Preset an upper limit on the number of clusters. max (e.g.) (max = 4), merge from bottom to top until the number of clusters equals 4. Stop merging when the maximum value is reached; Method 2: Traverse Incrementing from 2 to a preset upper limit, each increment is... Calculate the class after The mean profile coefficient under the given value is selected to maximize the mean profile coefficient. The final number of clusters is used; Method 3: a preset inter-cluster merging distance threshold dmerge is used, and merging stops when the inter-cluster distance in the next merge exceeds dmerge. This embodiment preferably uses Method 2.

[0091] For a single segment, the contour coefficient is defined as follows:

[0092]

[0093] in Point The average distance to other points of the same type Point The minimum average distance to all points of other classes. Profile coefficient. The closer it is to 1, the more important it is. The more compact the cluster, the better the separation between clusters.

[0094] The minimum distance between adjacent classes is defined as follows:

[0095]

[0096] That is, the first The minimum value of the class and the first The difference between the maximum values ​​of the -1 class. The larger this index is, the wider the blank band between the two adjacent classes, and the stronger the distinguishability between the two classes.

[0097] Assuming a single segment length is And clustered into The class sets the criteria for judging sorting errors, as shown in the following formula:

[0098]

[0099] According to the following formula:

[0100]

[0101] in:

[0102]

[0103] , These represent preset threshold values. If either of the two criteria is met, it indicates a signal sorting error. All secondary truncation segments generated by the scaling transformation in step two are iterated over. If any segment contains a signal sorting error, then a signal sorting error exists.

[0104] Example

[0105] The following is a specific numerical example to illustrate the feasibility of this invention and the rationality of the parameter values. It should be noted that the following parameter values ​​are typical recommended values; specific values ​​need to be adjusted according to the actual system parameters and application scenarios.

[0106] Simulation scenario: Two identical radiation source platforms move in close formation, with their direction of arrival relative to the observation and receiving system at angles of arrival of approximately 100° and 100° respectively. and The surrounding area changes slowly, and the difference in orientation between the two is only about This is less than the angular resolution of a typical monopulse direction finding system. Using a conventional DOA-based clustering sorting algorithm, two radiation sources are misclassified as a single radiation source, thus triggering the error detection process of this invention.

[0107] Typical values ​​for the implementation parameters are as follows:

[0108]

[0109] Recommended values ​​for threshold parameters:

[0110]

[0111] Under the above parameters, steps one through five of this invention are executed, traversing all secondary truncated segments in the scale space; when the sorting result actually contains errors, the maximum profile coefficient of at least one segment in the scale space exceeds... or the minimum distance between adjacent classes is greater than This triggers the basis for judgment, correctly identifying the sorting error.

[0112] Comparative Example

[0113] In contrast, the following are the results of comparison using the traditional DOA clustering and sorting method instead of the method of this invention.

[0114] Comparative Example 1: Direct clustering of the original DOA sequence using only K-means clustering, without scaling transformation and principal direction rotation, causes the DOA differences between the two radiation sources to be overwhelmed by noise. The clustering result mistakenly merges the two radiation sources into one class, resulting in a silhouette coefficient... The maximum value is only Not achieved The threshold was not met, and sorting errors were not detected.

[0115] Comparative Example 2: Hierarchical clustering is performed using only a single window length truncation (without constructing a scale space). When the time window in which the error occurs does not match the truncation position, the clustering results cannot reflect the existence of the error, and the sorting error is also not detected.

[0116] It can be seen that the present invention can effectively detect DOA sorting errors in formation scenarios through the overall synergistic effect of four innovative technologies: multi-scale truncation, scaling transformation, SVD main direction rotation, and dual-criteria traversal.

[0117] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements 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 signal sorting error detection method based on multidimensional scaling transformation, characterized in that, Used to classify the first of the multiple sorted radiation sources The method for self-checking errors in the angle of arrival sequence of several radiation sources includes the following steps: Step 1: Cut off, using a rectangular window The sorted first sequence of angles of arrival of radiation sources After truncating once, the truncated sequence is obtained, represented as: ； Step 2: Scale transformation, using... Layers, rectangular windows of different sizes on each layer and The truncated sequence is further truncated to obtain a scale space composed of multiple pairs of truncated segments, wherein Indicates the layer number of the second truncation, Indicates the first The segment number within the rectangular window is represented as follows: ； Step 3: Scaling transformation. For each quadratic truncated segment in the scale space, scale it by a scaling factor. The time axis and amplitude axis are scaled as a whole, with the time axis being placed at equal intervals according to the original segment length and then multiplied by . After normalizing the arrival angle values ​​of the amplitude axis, it is mapped to... Interval and multiply by the whole This is done to amplify the difference in the angle of arrival between multiple radiation sources within each truncated segment, resulting in a two-dimensional point set after scaling transformation. Step 4: Rotate in the principal direction and calculate the covariance matrix for each two-dimensional point set after the scaling transformation. and Then, singular value decomposition is performed, and each two-dimensional point set is rotated along the principal direction determined by the right singular vector matrix V to obtain the rotated fragment. and This is to convert the difference in the angle of arrival between radiation sources into a difference in the intercept of the rotated space; Step 5: Sorting error detection. For each rotated segment, check its second dimension component. , Hierarchical clustering is performed on the data, assuming that a single fragment is clustered into... Class, and calculate the minimum distance between adjacent classes. and contour coefficient ; Traverse all secondary truncated segments generated in step two within the scale space, as long as any segment satisfies criterion 1: Or, based on judgment 2: Then determine the first The sorting results for the radiation sources contained errors; among them , , and These are preset threshold values. The length of a single segment; the minimum distance between adjacent classes. For the first The minimum value of the class and the first The difference between the maximum values ​​of the -1 class, the silhouette coefficient Defined as: ； in For point The average distance to other points of the same type For point The minimum average distance to all points of other classes.

2. The signal sorting error detection method based on multidimensional scale transformation according to claim 1, characterized in that, The rectangular window function in step one Defined as: ； in This indicates the initial time of the intercept. Indicates the length of the rectangular window.

3. The signal sorting error detection method based on multidimensional scaling transformation according to claim 1, characterized in that, The two sets of quadratic truncated rectangular window functions in step two are defined as follows: ； ； By taking different values ​​at each level The values ​​constitute the segmentation of the original truncated sequence across multiple time scales.

4. The signal sorting error detection method based on multidimensional scaling transformation according to claim 1, characterized in that, The scaling transformation in step three is performed according to the following formula: ； ； in This is the scaling factor, applied to both the time axis and the amplitude axis. This is the upper limit of the amplitude mapping.

5. The signal sorting error detection method based on multidimensional scaling transformation according to claim 1, characterized in that, In step four, the covariance matrix of each two-dimensional point set is constructed according to the following formula, and singular value decomposition is performed: ； ； ； ； Rotating the segment along the main direction is represented as: ； 。 6. The signal sorting error detection method based on multidimensional scaling transformation according to claim 1, characterized in that, The hierarchical clustering in step five is a bottom-up agglomerative hierarchical clustering; individual segments are clustered as... A class, represented as: ； 。 7. The signal sorting error detection method based on multidimensional scaling transformation according to claim 1, characterized in that, The specific form of the minimum distance between adjacent classes in step five is as follows: ； During the traversal decision, if there exists any quadratic truncation segment such that... or If true, then determine the first [number]th ... The sorting result of the first radiation source is incorrect; conversely, if all segments in the scale space do not meet the above two criteria, then the first radiation source is determined to be incorrect. The results of the radiation source sorting were correct.

8. The signal sorting error detection method based on multidimensional scaling transformation according to claim 1, characterized in that, The threshold The range of values ​​is The threshold The range of values ​​is The amplitude mapping upper limit value The range of values ​​is The number of secondary cut-off layers The range of values ​​is .

9. The signal sorting error detection method based on multidimensional scaling transformation according to claim 1, characterized in that, Independent error detection is performed on each of the multiple radiation sources, that is, steps one to five are performed sequentially for each radiation source's angle of arrival sequence obtained from the sorting.

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