A weighted compound track association method and system fusing radio frequency fingerprint and kinematic features

Abstract

The application provides a weighted compound track association method and system fusing radio frequency fingerprints and kinematic characteristics, the method fuses target radio frequency fingerprint characteristic vectors on the basis of kinematic state characteristics, constructs a weighted compound cost function to perform track association, a first dimension cost term of the weighted compound cost function is a normalized Mahalanobis distance, a second dimension cost term is a radio frequency fingerprint cosine distance, and an adaptive weighting coefficient is used as a weight adjustment of the two cost terms, and when the radio frequency fingerprint is unavailable, the weighted compound cost function is automatically degraded into the normalized Mahalanobis distance. The application fundamentally solves the problem that the pure kinematic method cannot continue to maintain correct association after the Mahalanobis distance is invalid due to target concentration or track intersection.

Description

Technical Field

[0001] This invention belongs to the field of multi-sensor trajectory association technology in low-altitude flight, specifically involving a weighted composite association method and system that integrates radio frequency fingerprint features and kinematic features in the trajectory association cost function. It is particularly suitable for UAV trajectory association in scenarios where multiple targets are flying densely or where trajectory intersections lead to blurred kinematic features. Background Technology

[0002] With the rapid development of the low-altitude economy, drones are widely used in logistics, geographic mapping, traffic monitoring, and disaster relief. The typical process for drone management includes detection, identification, tracking, and countermeasures, among which real-time and effective multi-sensor, multi-target detection and tracking are prerequisites for precise countermeasures. During drone target tracking, the number of targets may be unknown. When multiple targets exist, the system may be unable to determine whether the measurement data comes from the tracked target, a false alarm, or another target. Therefore, a data association process is needed to establish the correspondence between sensor measurement data and target sources, thereby improving the reliability of subsequent data fusion processes.

[0003] Data association is generally divided into three types: measurement-to-measurement, measurement-track, and track-to-track association, i.e., point-to-point, point-to-track, and track-to-track association. Among them, track-to-track association (TTTA) is used to determine whether local tracks formed by different sensors (radar / infrared / BeiDou, etc.) originate from the same target. This type of association is generally found in distributed multi-sensor data fusion systems. Track association is a core component of multi-sensor multi-target tracking systems. Its task is to establish correct correspondences between local tracks output by different sensors. The correctness of track association directly affects the accuracy of subsequent track fusion and the continuity of track identity maintenance.

[0004] Track association algorithms are mainly divided into two types: statistical and fuzzy mathematics-based methods. Statistical methods use Mahalanobis distance as a measure of difference between tracks, while fuzzy mathematics-based methods handle the uncertainty in association by constructing membership functions or grey relational functions. Both types of methods utilize the kinematic state information of the target, such as position, velocity, and acceleration. When the trajectories of multiple targets are close or intersect, the information differences brought by the motion features are small, the discriminative power of the association decision decreases significantly, and false associations are very likely to occur.

[0005] Radio frequency (RF) fingerprinting refers to the unique and difficult-to-forge physical layer characteristics left in the transmitted signal by wireless transmitting equipment due to minor differences in hardware manufacturing tolerances, component aging, circuit layout, etc., similar to the device's "electromagnetic DNA" or "electronic ID card." RF fingerprints are typically extracted from the transient or steady-state modulation of the signal upon power-on. Transient features include the rising / falling edge shape of the signal envelope, transient duration, and frequency offset curve at power-on. Steady-state features include carrier frequency offset (CFO), crystal oscillator frequency offset, I / Q imbalance (amplitude / phase imbalance), modulation error vector amplitude (EVM), phase noise spectral density, and nonlinear distortion coefficient. Higher-order statistical features include bispectral analysis and cyclostationary characteristics. RF fingerprints are determined by individual manufacturing differences in the transmitter's analog front-end components, possessing a factory-fixed, physically unique characteristic that is difficult to replicate manually.

[0006] In the field of drone flight, by leveraging the individual manufacturing differences in drone transmitter hardware and extracting the inherent radio frequency fingerprint features of the drone, it is possible to distinguish individual devices of the same model without relying on communication protocol parsing. Currently, several patents disclose drone individual identification methods based on radio frequency fingerprints, such as CN116680631A, CN121193351A, and CN120390223A. These patents mostly focus on drone individual classification or identity authentication at the signal level.

[0007] In addition, CN120103259A discloses a track association method based on multiple radiation sources. It identifies the target by acquiring single-signal track information and then associates the target. Its technical approach is fundamentally different from the method of using radio frequency fingerprint hardware features to distinguish the individual identity of the transmitter. It does not involve the technical solution of introducing radio frequency fingerprint individual features into the track association cost function.

[0008] Therefore, existing multi-sensor track association methods suffer from the following problems: In scenarios where multiple targets are flying densely or tracks intersect, making it impossible to reliably distinguish different targets using kinematic features, the kinematic states of the tracks are statistically indistinguishable. Relying solely on kinematic features is insufficient to make correct association decisions, leading to missed detections and fusion errors in the fused tracks. Furthermore, existing track association methods have yet to find a technical solution that uses radio frequency fingerprint features as an independent criterion dimension, combining them with kinematic features to form a weighted composite cost function for track association. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a weighted composite trajectory association method and system that integrates radio frequency fingerprints and kinematic features. The technical solution of this invention uses radio frequency fingerprint features as an independent criterion dimension and combines them with kinematic features to form a weighted composite cost function for trajectory association.

[0010] On one hand, the present invention provides a weighted composite track association method that integrates radio frequency fingerprints and kinematic features. The method includes the following steps: S1. Preparation of track data to be associated: obtaining a set of tracks to be associated after time synchronization and coordinate transformation. With candidate track set ,in For the first A pending associated flight path For the first There are 10 candidate tracks, each track carrying both kinematic state information and an RFID fingerprint field, wherein the RFID fingerprint field includes an RFID fingerprint feature vector. and validity markers S2. Kinematic Mahalanobis distance calculation: For each pair of tracks to be associated... Calculate the Mahalanobis distance in a common kinematic measurement space; S3. RF fingerprint validity determination: examine each track to be associated. and candidate tracks Their respective validity markers If both parties If both are valid, proceed to step S4. If at least one is valid... If invalid, proceed to step S7; S4. Calculate the track to be associated. With candidate tracks The calculation involves calculating the cosine similarity between the RF fingerprint feature vectors; and an adaptive weighting coefficient based on the ratio of the minimum and second minimum values ​​of the normalized Mahalanobis distance; S5. Weighted composite cost calculation: The calculation uses the normalized Mahalanobis distance as the first-dimensional cost term, the RF fingerprint cosine distance as the second-dimensional cost term, and uses the adaptive weighting coefficient as the weight adjustment to construct a weighted composite cost function. ; S6. Composite threshold decision: With composite threshold If a comparison is made, ,accept Select as a candidate association pair; otherwise reject. Candidate association pairs; after completing the decision, proceed to step S9; S7. RF fingerprint missing rollback processing: The adaptive weighting coefficients are forcibly set to 1 and the process jumps to step S8; S8. Chi-square threshold decision: normalize the Mahalanobis distance. Compared with 1, if ,accept If it is a candidate association pair, then reject it. For candidate association pairs, proceed to step S9; S9. Global optimal allocation: For all candidate association pairs that pass the threshold decision, minimize the total cost. With the goal of finding the globally optimal correspondence scheme, the Hungarian algorithm is used.

[0011] As described above and in any possible implementation, a further implementation is provided, wherein the radio frequency fingerprint feature vector in S1 This includes, but is not limited to, carrier frequency offset, I / Q amplitude imbalance and phase imbalance, power amplifier nonlinear distortion coefficient, constellation diagram distortion characteristics, and phase noise profile.

[0012] As described above, and in accordance with any possible implementation, a further implementation is provided in S3. The valid determination condition is: the radio frequency fingerprint feature vector of the track. In the most recent frame There is at least one direct update from the radio frequency fingerprint feature extraction module.

[0013] As described above, and in any possible implementation, a further implementation is provided, wherein the weighted composite cost function in S5... Represented as: ,in For normalized Markov distance, For radio frequency fingerprint cosine similarity, These are adaptive weighting coefficients.

[0014] It should be further explained that the weighted composite cost function in S5 The feature vector of the cosine similarity term involved is an RF fingerprint rather than an image feature descriptor. This invention is applicable to non-visual multi-sensor systems and differs from other application areas and hardware usage: Image features of visual sensors are CNN appearance descriptors (ReID vectors) extracted from image bounding boxes, representing visual appearances such as clothing, color, and texture. These features are greatly affected by viewing angle, lighting, occlusion, and clothing changes, and do not exist in non-visual sensor scenarios. The RF fingerprint vector of this invention is extracted by the receiver from the RF signal emitted by the target. Typical components include CFO (carrier frequency offset), phase noise, I / Q transients, rising edge, power amplifier nonlinear distortion, etc., originating from differences in transmitter hardware manufacturing. It does not depend on optical visibility, can be attached to radar / electro-optical tracks, and is resistant to MAC / IP spoofing—the RF fingerprint remains stable even when the automatic identification system is lying.

[0015] In addition to the aspects described above and any possible implementations, a further implementation is provided, wherein the normalized Mahalanobis distance is: ,in The Mahalanobis distance calculated in step S2. This is the chi-square threshold corresponding to the kinematic measurement space that is comparable to both parties for this association.

[0016] In addition to the aspects and any possible implementations described above, a further implementation is provided in which the cosine similarity of the radio frequency fingerprint feature vector is: , in These represent the tracks to be associated. and candidate tracks The radio frequency fingerprint feature vector, Represents the dot product of two vectors. express and The product of the L2 norms of their respective radio frequency fingerprint feature vectors; the cosine similarity value ranges from... The larger the value, the more similar the two fingerprint feature vectors are.

[0017] As described above, and in addition to any possible implementation, an implementation with adaptive weighting coefficients is further provided. The calculation formula is as follows: , in For kinematic ambiguity index, The minimum value of the normalized Mahalanobis distance. This is the second smallest value of the normalized Mahalanobis distance. As a normalization reference factor, For adaptive weighting coefficients The lower limit represents the state when the kinematics are completely fuzzy. The minimum value that can be obtained.

[0018] It should be further explained that the adaptive weighting coefficients By association pairs ( This invention uses the ratio of the minimum to the second smallest normalized Mahalanobis distance within the candidate set as the driving force, with a lower bound truncation. Compared to using manually set constants or Mahalanobis distance to adjust observation weights, this invention emphasizes adaptive weighting coefficients. The separation degree changes online with the current candidate set, rather than being tuned offline, and the "minimum / second smallest distance ratio" as an ambiguity metric has not been publicly disclosed in the same way.

[0019] As described above and in any possible implementation, a further implementation is provided, wherein the radio frequency fingerprint feature vector The track fusion operation injects electronic reconnaissance tracks into the fused track. As a persistent attribute field in the track data structure, it is continuously stored and updated throughout the track's lifecycle. When the electronic reconnaissance signal is interrupted, the injected data... exist The feature vector remains valid until the expiration date. When the electronic detection signal returns to normal, the newly extracted feature vector will be valid. With storage Keep it up-to-date by updating with moving averages or medians.

[0020] In addition to the aspects and any possible implementations described above, a further implementation is provided, wherein the system includes: a radar subsystem, an optoelectronic subsystem, an electronic reconnaissance subsystem, and a signal processing subsystem, wherein: the radar subsystem is used to output a radar track, the track containing kinematic states but not carrying a radio frequency fingerprint feature vector F; the optoelectronic subsystem is used to output an optoelectronic track, the optoelectronic track containing kinematic states but not carrying a radio frequency fingerprint feature vector F; The electronic reconnaissance subsystem extracts the radio frequency fingerprint feature vector F from the I / Q baseband data through the built-in radio frequency fingerprint feature extraction module and outputs the electronic reconnaissance track. The electronic reconnaissance track contains the kinematic state and the radio frequency fingerprint feature vector F. The signal processing subsystem includes a track preprocessing unit, a track association unit, a track fusion and management unit, and a fused track output unit.

[0021] In addition to the aspects described above and any possible implementation, a further implementation is provided, wherein the track preprocessing unit is used to perform step S1, which involves time synchronization, coordinate transformation, kinematic state extraction, and RF fingerprint validity determination on the tracks input from each sensor, thus completing the data preparation before association; the track association unit is used to execute the algorithms for the two paths in steps S2-S9, and output the globally optimal association scheme; the track fusion and management unit is used to perform track fusion operations, including F injection, maintenance, expiration and update management, as well as track start, track maintenance and track termination management; and the fused track output unit is used to output the fused track with RF fingerprint identity tag.

[0022] It should be further clarified that the track association object in this invention is track-to-track (T2T) rather than detection-to-track (D2T). Detection-to-track (D2T) requires heterogeneous state projection and covariance construction, and must handle the covariance of two independent filtered tracks, heterogeneous state space projection, and temporal asynchrony registration. D2T, on the other hand, only needs to handle the single-step uncertainty of "prediction-detection". Therefore, both ends of this invention are tracks, each carrying historical filtered state estimates and covariance; the association granularity is increased from "intra-frame detection" to "cross-sensor track lifecycle alignment".

[0023] This invention utilizes the individual uniqueness of the target radio frequency fingerprint as a second-dimensional criterion independent of kinematics to improve the track association cost function, thereby maintaining correct track association relationships even when kinematics are ambiguous. Compared with existing technologies, this invention achieves the following technical effects: (1) Introducing individual feature information of radio frequency fingerprints into the trajectory association cost function breaks through the limitation of existing methods that rely solely on motion features for association decisions. The cosine distance of the radio frequency fingerprint, as a second-dimensional criterion independent of kinematics, has discriminative power derived from the hardware physical differences of the target transmitter and does not change due to changes in the target's spatial position or motion state. In kinematically fuzzy scenarios, since the corresponding weights of the radio frequency fingerprint terms are... , Approaching At that time, the cosine distance term of the radio frequency fingerprint can bear no less than 70% of the decision weight, providing an independent basis for the association decision when kinematics fails. This fundamentally solves the problem that the pure kinematic method cannot continue to maintain the correct association after the Mahalanobis distance fails due to dense targets or cross tracks.

[0024] (2) A dynamic balance between the two criteria dimensions of kinematics and radio frequency fingerprinting is achieved through adaptive weighting coefficients. When the kinematics are highly distinguishable, the method automatically degenerates into the traditional weighted statistical distance method without introducing additional computational burden and is fully compatible with existing systems; when the kinematics are ambiguous, the radio frequency fingerprint is automatically added to the decision without manual switching or intervention. This mechanism enables the method to maintain its original performance in normal scenarios and automatically gain additional distinguishing ability in complex scenarios, that is, without sacrificing the advantages of existing methods, it expands the applicability of track association in dense target scenarios.

[0025] (3) The applicable boundaries of this method are clarified through the radio frequency fingerprint validity determination mechanism. Radar and electro-optical tracks themselves do not carry fingerprint information. When one of the associated parties does not have a valid fingerprint, the method automatically degenerates into pure Mahalanobis distance association—it does not forcibly use non-existent fingerprint information, ensuring that the system can still work normally when fingerprints are missing. This mechanism ensures that this method can operate stably under any sensor configuration, and radio frequency fingerprint enhancement only automatically participates in the decision when conditions are met.

[0026] (4) The radio frequency fingerprint clustering results extracted independently by the electronic reconnaissance terminal can provide an estimate of the number of targets independent of the space sensor. When the space sensor merges multiple spatially close targets into a single track due to insufficient resolution, the radio frequency fingerprint clustering results can be fed back to the track management unit of the fusion center as an independent verification source to help determine the actual number of targets currently existing, and provide physical layer basis for track management decisions such as track splitting, track initiation and deletion. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart of the weighted composite track association method of the present invention; Figure 2 This is a schematic diagram illustrating the construction principle of the weighted composite cost function of this invention; Figure 3 This is the radio frequency fingerprint feature vector of the present invention. A diagram illustrating the injection, retention, expiration, and update mechanisms; Figure 4 This is a schematic diagram of the weighted composite track association system of the present invention. Detailed Implementation

[0029] To facilitate understanding of the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0030] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0031] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0032] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0033] This invention addresses the shortcomings of existing track association methods, such as low association accuracy and lack of individual identity recognition capabilities in scenarios with dense or overlapping targets. It proposes a weighted composite track association method that integrates radio frequency fingerprints and kinematic features.

[0034] This method is based on the heterogeneous weighted statistical distance method. It retains the threshold decision and optimal allocation steps unchanged, and improves its associated cost function by adding the cosine distance of radio frequency fingerprint as an independent cost term on the basis of traditional Mahalanobis distance, and introducing adaptive weighting coefficients to construct a two-dimensional weighted composite cost function.

[0035] See Figure 1The diagram shows the complete processing flow of the method of the present invention, which includes 9 specific steps, including 6 main stages: data preparation, Mahalanobis distance calculation, radio frequency fingerprint validity determination, composite cost calculation, threshold decision and global optimal allocation. Figure 1 Using the diamond node 3 as the branch point: when the two parties to be associated... If both are valid, proceed to the left path, i.e., steps 4-6, to perform weighted composite cost calculation and composite threshold decision; if at least one party... If invalid, proceed to the right path, i.e., steps 7-8, where α=1 is forced to degenerate into normalized Mahalanobis distance and then chi-square threshold decision is performed; the two paths merge in step 9 and the global optimal allocation is performed uniformly.

[0036] The specific nine steps include: Step S1: Preparation of track data to be associated Obtain the set of tracks to be associated after time synchronization and coordinate transformation. With candidate track set ,in For the first There are 100 unrelated flight paths, totaling 100. A pending associated flight path For the first There are 10 candidate tracks, totaling 100. Candidate flight paths, and All are positive integers greater than or equal to 1. Each track carries both of the following types of information: (1a) Kinematic state information: including state estimation vector and its covariance matrix . The state vector dimension and physical meaning of a track are determined by the sensor from which it originates. For example, the state vector measured by Doppler radar includes range, azimuth, radial velocity, etc. The covariance matrix is ​​used in this invention to describe the uncertainty of trajectory estimation. It quantifies the variance of each state estimation vector in different directional components and the correlation between different components.

[0037] (1b) Radio frequency fingerprint field: contains radio frequency fingerprint feature vector and its validity flag . The valid determination condition is: the track's field in recent frame Inside( (Taking 30 to 80 frames, corresponding to 3 to 8 seconds) there is at least one direct update from the radio frequency fingerprint feature extraction module. The extraction method is as follows: the RF fingerprint feature extraction module processes the acquired raw I / Q baseband sampling data to extract subtle RF fingerprint features determined by individual differences in transmitter hardware. These subtle RF fingerprint features include, but are not limited to, the following: carrier frequency offset, I / Q amplitude imbalance and phase imbalance, power amplifier nonlinear distortion coefficient, constellation diagram distortion features, and phase noise profile. The extracted features are then concatenated into a high-dimensional electromagnetic fingerprint feature vector. Output.

[0038] Simultaneously determine two threshold values: the chi-square threshold. Based on the state vector dimension of the common measurement space and the preset saliency level (usually taken as...), Obtained from the chi-square distribution table; composite threshold. The value is 0.5 to 0.7, with a typical value of 0.6.

[0039] Step S2: Calculation of Kinematic Mahalanobis Distance For each pair of related flight paths On both sides (tracks) With track Mahalanobis distance is calculated in a commonly comparable kinematic measurement space between the two tracks (by mapping the motion parameters of the two tracks to the same Cartesian or geographic coordinate system to ensure physical comparability of the data). The Mahalanobis distance between isomorphic data can be calculated directly on their shared state space. (1) in These represent the tracks to be associated. and candidate tracks The state estimation vector, These represent the tracks to be associated. and candidate tracks The covariance matrix, Indicates transpose. It indicates the inverse.

[0040] Heterogeneous data are projected onto a common measurement space through observation equations to construct residual vectors. : (2) in These represent the tracks to be associated. and candidate tracks The projection function from the state space containing the state vector to the common measurement space is used to calculate the Mahalanobis distance of heterogeneous data: (3) Where the covariance matrix It is obtained by summing the covariances of both sides after Jacobian matrix transformation.

[0041] Step S3: Determining the validity of the radio frequency fingerprint Check the track to be associated and candidate tracks Their respective validity markers If both parties If both are valid, proceed to step S4. If at least one is valid... If invalid, proceed to step S7.

[0042] Step S4: Calculation of cosine similarity of RF fingerprint and adaptive weighting coefficient (4a) Calculation of cosine similarity of radio frequency fingerprints calculate and Cosine similarity between the RF fingerprint feature vectors: (4) in These represent the tracks to be associated. and candidate tracks The radio frequency fingerprint feature vector, Represents the dot product of two vectors. express and The cosine similarity is the product of the L2 norms of their respective RF fingerprint feature vectors. The range of cosine similarity values ​​is... The larger the value, the more similar the two fingerprint vectors are.

[0043] (4b) Adaptive weighting coefficients calculate For the current flight path to be associated Calculate its normalized Mahalanobis distance from the candidate track. (5) To determine the chi-square threshold corresponding to the kinematic measurement space that is comparable to both parties for this association, take the trajectory to be associated. With each candidate track Minimum value of normalized Mahalanobis distance and the second smallest value .

[0044] Adaptive weighting coefficients The calculation formula is: , (6) remember For kinematic ambiguity index, The minimum value of the normalized Mahalanobis distance. This is the second smallest value of the normalized Mahalanobis distance, representing the ratio of the normalized Mahalanobis distance between the second-best and best pairings. It reflects the kinematic discriminatory power of the current track to be associated relative to the second-best kinematic match. The range of values ​​is , =1 indicates that the normalized Mahalanobis distances of the best and second-best pairings are completely equal, and the kinematic features cannot distinguish between the two, that is, the kinematics is completely fuzzy; The larger the size, the more obvious the advantage of the best pairing over the second-best pairing, and the higher the kinematic discrimination.

[0045] The purpose of this normalization reference factor is to normalize the kinematic ambiguity index. The numerical range is compressed to adaptive weighting coefficients. The required scale factor for the numerical range, The value of indicates how many times the second-best distance reaches the optimal distance before the kinematic characteristics can be considered sufficiently reliable, by convention. When the distance between two candidates differs by a factor of 4 to 8, the significance of the chi-square test is sufficiently large, indicating that the best pairing is statistically significantly better than the second-best pairing. A typical value can be taken as the midpoint of the range, which is 5.

[0046] The lower bound of the weighting coefficients represents the adaptive weighting coefficients when the kinematics are completely blurred. The minimum value that can be obtained is also the minimum weight of the kinematic term in the composite cost, and the corresponding weight of the RF fingerprint term is... Considering that the kinematics are completely ambiguous, the primary responsibility for judgment should lie with the radio frequency fingerprinting team. ,Right now At the same time, to avoid the system from over-relying on potentially noisy fingerprint information, a minimum weight lower bound needs to be reserved for kinematics, set to 0.2, i.e. The value range is (0.2, 0.5), with the typical value being the midpoint of the range, 0.3.

[0047] It should be noted that, due to and All are adjustable parameter variables, in order to ensure The physical meaning is that it refers to the minimum weight of the kinematic term in the composite cost when the kinematics is completely fuzzy. When adjusting the values ​​of both, extra attention needs to be paid to the range of values. The restrictions.

[0048] Abbreviation of adaptive weighting coefficients The calculation formula is as follows: (7) Analyze the physical meaning of this formula: Time: Kinematic height is distinguishable, , The system fully trusts kinematics, and the composite cost degenerates into the normalized Mahalanobis distance; At that time, the kinematic components can be distinguished. , Follow The decrease is monotonically decreasing, and the kinematics and radio frequency fingerprint share the decision weights proportionally. At that time, the kinematics are fuzzy: , Cut off by the lower limit, RF fingerprint bears the responsibility The decision weights, kinematics only retain The weight.

[0049] In other embodiments, adaptive weighting coefficients The calculation method can be replaced by one based on Binary switching with a fixed threshold (e.g.) hour ,otherwise This simplifies the calculation, but it sacrifices the smoothness of the transition interval.

[0050] Step S5: Weighted Composite Cost Calculation (8) in To normalize the Mahalanobis distance, the Mahalanobis distance is scaled using the chi-square threshold as the baseline, making it comparable in magnitude to the cost term of RF fingerprinting. The cosine distance is the radio frequency fingerprint. Since the association process revolves around the track to be associated... Finding corresponding candidate tracks, therefore adaptive weighting coefficients It is a follow-up trajectory Changing variables. When When the value approaches 1, the composite cost degenerates into the normalized Mahalanobis distance, which is fully compatible with existing weighted statistical distance methods; when Approaching At that time, the radio frequency fingerprint item shall bear no less than 70% of the decision weight, and fusion decision shall be added in the kinematic fuzzy scenario.

[0051] In other embodiments, the radio frequency fingerprint similarity measure in formula (8) can be replaced by Mahalanobis distance instead of cosine distance: (9) in Radio frequency fingerprint feature vector The covariance matrix; when When irreversibility is not possible, pseudo-inverse or diagonal loading regularization methods can be used.

[0052] In other embodiments, the normalized Mahalanobis distance term in formula (8) Alternatively, the P-value method or the degree-of-freedom normalization method can be used to calculate it: For the P-value method From the original Change to , To be Substitute the corresponding degrees of freedom The cumulative probability obtained from the chi-square cumulative distribution function. This represents the dimension of the state vector in the common measurement space. The probability value is [0, 1], and the value decreases as the distance increases. Formula (8) then becomes: (10) For the degree-of-freedom normalization method , Let represent the dimension of the state vector in the common measurement space, then formula (8) becomes: (11) Compared to other embodiments, the algorithm of formula (8) is still the core of the present invention, and it has the best overall performance in terms of versatility, real-time performance and robustness.

[0053] Step S6: Composite Threshold Decision Will With composite threshold Compare. If ,accept Select as a candidate association pair; otherwise reject. This is a candidate association pair. After the decision is made, proceed to step S9.

[0054] Step S7: RF fingerprint missing rollback processing (jump from step S3 to this step) Adaptive weighting coefficients When forced to be 1, the association cost degenerates into pure Mahalanobis distance: (12) Proceed to step S8.

[0055] Step S8: Chi-square threshold decision (jump from step S7 to this step) Will Compare with 1. If (equivalent to) ),accept Select as a candidate association pair; otherwise reject. Candidate association pairs. Proceed to step S9.

[0056] Step S9: Global Optimal Allocation For all candidate association pairs that pass the threshold decision, minimize the total cost. With the goal of finding the globally optimal correspondence and association scheme through the Hungarian algorithm or other optimization algorithms, we can find the unique correspondence and matching scheme with the minimum global cost among all candidate association pairs that have passed the threshold screening, thus avoiding local optima or conflict associations.

[0057] This step avoids situations where the same path to be associated might pass the threshold decision with multiple candidate paths simultaneously, or multiple paths to be associated might pass the threshold decision with the same candidate path simultaneously. Under the premise of satisfying the one-to-one matching constraint (each path can be assigned to at most one target), the total cost that maximizes all selected association pairs is selected. The smallest set of solutions is selected, thus outputting the final conflict-free, globally optimal association result.

[0058] In other embodiments, the Hungarian algorithm can be replaced by an auction algorithm or other optimized algorithms to achieve lower computational complexity, making it suitable for large-scale track association scenarios. Tracks to be associated that are not assigned to any candidate track are marked as "unassociated". The final association results are output.

[0059] The Hungarian algorithm is a classic and widely used combinatorial optimization algorithm specifically designed to find the global optimum in assignment problems. This algorithm is based on row and column reduction operations on the cost or payoff matrix, and by continuously searching and augmenting alternating paths, it ultimately determines a unique corresponding association scheme that minimizes the total cost or maximizes the total payoff. The time complexity of the Hungarian algorithm is... This indicates that as the input size n increases, the algorithm's running time is proportional to the cube of n.

[0060] To further illustrate the algorithm of this invention, Figure 2 This describes the construction method of the weighted composite cost function in this invention. See also... Figure 2 The diagram below illustrates the construction principle of the weighted composite cost function of this invention, which includes four main modules: input features, distance calculation, adaptive weighting coefficient calculation, and weighted composite cost calculation. Among them, (1) Input feature module: inputs kinematic features and radio frequency fingerprint feature vectors, wherein the kinematic features include the track to be associated. and candidate tracks State estimation vector and the corresponding covariance matrix , The radio frequency fingerprint feature vector is the track to be associated. and candidate tracks RF fingerprint feature vector , (2) Distance calculation module: The kinematic characteristics are normalized to obtain the normalized Mahalanobis distance by Mahalanobis distance calculation and chi-square threshold normalization. Radio frequency fingerprint feature vector , After cosine similarity calculation, it is converted into cosine distance of radio frequency fingerprint. (3) Adaptive weighting coefficient calculation module: calculates kinematic ambiguity. And adaptive calculation of weighting coefficients (4) Weighted composite cost module: The two are combined through a weighted composite cost function. Fusion comes at a cost.

[0061] In this invention, the radio frequency fingerprint feature vector The sole source of information in the trajectory system is the radio frequency fingerprint (RF) feature extraction module, which is integrated within the electronic reconnaissance subsystem. Other detection systems, such as radar and photoelectric systems, only provide trajectory information including distance, angle, and velocity measurements; they do not carry RF fingerprint information themselves. The RF fingerprint feature vector F refers to a unique and stable set of digital features extracted from the source of the wireless signal, used to identify and distinguish different physical devices. This vector typically contains multiple dimensions, including but not limited to carrier frequency offset, I / Q amplitude imbalance and phase imbalance, power amplifier nonlinear distortion coefficient, constellation diagram distortion characteristics, and phase noise profile. It needs to be injected into the track system through track fusion operations and persistently transmitted along with the track data structure. This invention relates to the radio frequency fingerprint feature vector. Detailed explanation of injection and inheritance mechanisms: Figure 3 This demonstrates the radio frequency fingerprint feature vector. The complete lifecycle of a trajectory system consists of four stages.

[0062] (1) Injection Tracks with radio frequency fingerprints ( Effective) and non-RF fingerprint track ( (Invalid) After the initial association confirmation, track fusion is performed, and the newly generated fused track inherits the current track. Fields, Once enabled, the injection operation is automatically executed upon completion of the fusion process. Specifically, when a data entry carrying a valid... ( (Effective) electronic reconnaissance tracks and one or more tracks not carrying ( When invalid radar tracks and / or electro-optical tracks are merged into a single fused track using a track fusion algorithm, the newly generated fused track inherits the electronic reconnaissance track's... Fields, Keep it active. The injection operation is performed automatically upon completion of track fusion, without requiring any additional associated processes.

[0063] (2) The maintenance F is a persistent attribute field in the track data structure. When radio frequency fingerprint information is interrupted due to signal blockage or interference, the track only updates its kinematic features, but... and The track remains in the track data structure and can still be used when the track is associated during the interruption. . Specifically: The field is a persistent attribute field in the track data structure. Once the merged track obtains a valid result through injection... Even if the signal of the electronic reconnaissance subsystem is temporarily interrupted due to obstruction, interference, or other reasons, and the track is maintained solely by kinematic prediction based on radar and / or electro-optical measurement data, the fused track... fields and The markers are still retained in the track data structure. Remains valid until consecutively exceeding The frame was not directly updated by the electronic reconnaissance subsystem. During periods of electronic reconnaissance signal interruption, the stored data can still be used when the track participates in association. Performing composite cost calculations (steps S4-S6) requires, on the premise that It has not expired yet.

[0064] (3) Expired When F continuously exceeds When the frame is not directly updated by the fingerprint information of the radio frequency fingerprint feature extraction module, Automatically invalidated, this track association subsequently relies on pure Mahalanobis distance association to prevent... The lack of updates over a long period has rendered the fingerprint entries in the composite cost function virtually useless. Specifically: When the fusion trajectory Fields continuously exceed the most recent frame When the signal is not directly updated by the radio frequency fingerprint feature extraction module (e.g., the target flies out of the effective coverage area of ​​the electronic reconnaissance, or the signal is continuously blocked). Automatically invalidated from valid. Afterwards, when this track is involved in association, it will directly jump to step S7 – association using pure Mahalanobis distance. This expiration mechanism prevents [further issues]. The lack of updates over a long period has rendered the RF fingerprint item in the composite cost practically obsolete.

[0065] Expired frames It can be dynamically adjusted according to the target type and scenario: a smaller value (30 to 50 frames, where the signal changes rapidly) is used for high-speed fixed-wing targets, and a larger value (80 to 100 frames, where the signal is stable) is used for hovering rotor targets.

[0066] (4) Update When the electronic reconnaissance signal is continuously and normally received, the newly extracted feature vector for each frame With stored feature vectors Update using moving average, keep The timeliness and representativeness of vectors. Specifically: When the electronic reconnaissance subsystem continues to receive the target signal normally, the newly extracted feature vector in each fusion processing cycle With the feature vector currently stored in the track Take the moving average: (13) in Alternatively, a value of 0.1 to 0.3 can be used to update the RF fingerprint features with a smaller weight for the signals in the new period, or the median vector of the most recent 5 to 20 frames (the number of frames can be determined based on signal strength) of the RF fingerprint feature vector in the new period can be used for updating. Fields, keep The timeliness and representativeness of vectors.

[0067] [Specific Implementation Example 1] Correlation Recovery After the Crossing of Flight Paths of Two Non-Cooperative UAVs of the Same Model Scene setting: Two identical DIY FPV racing drones, both using encrypted image transmission and with unusable protocol parsing, crossed the monitored area at approximately 15 m / s, with target A traveling from east to west and target B from south to north. Their tracks intersected near the center of the area. The monitored area was equipped with one electronic reconnaissance subsystem (four stations deployed in a diamond-shaped non-coplanar configuration), one radar detection system, and one electro-optical detection system. Before the intersection, target A and target B maintained their own independent fused tracks, FUS_A and FUS_B, respectively. Both tracks had been injected with radio frequency fingerprint feature vectors through track fusion. , Both are valid; after the crossover, the system obtains two new fused tracks, Track_X and Track_Y, which need to be associated with the tracks of target A and target B before the crossover, respectively.

[0068] Steps S1-S2: Data preparation and Mahalanobis distance calculation: The kinematic state Z_A, covariance P_A, and fingerprint F_A are obtained from FUS_A. In this embodiment, three types of features are used: carrier frequency offset CFO, I / Q amplitude imbalance and phase imbalance, and constellation diagram distortion. In fingerprint F_A, the carrier frequency offset CFO is on the order of several kHz, the I / Q amplitude imbalance is on the order of 0.3 dB, and the phase imbalance is on the order of 2°. The corresponding feature values ​​of F_B are significantly different in order of magnitude, with the CFO offset direction being opposite, and the I / Q imbalance and constellation diagram distortion being larger. The states of Track_X and Track_Y are obtained in the same way as the fingerprint. The normalized Mahalanobis distance of the four association pairs is calculated, and the chi-square threshold is used. Normalized Mahalanobis distance calculation results: , , , The fact that the four values ​​are very close indicates that the kinematic features can no longer effectively distinguish between correct and incorrect association pairings after cross-matching.

[0069] Step S3: Determine the validity of the radio frequency fingerprint: Track_X, Track_Y, FUS_A, FUS_B All four tracks are valid; all four tracks are fused tracks and contain radio frequency fingerprint feature vectors. Satisfying both parties If all conditions are valid, proceed to step S4.

[0070] Step S4: Calculate cosine similarity. , , , For Track_X: the best pairing is X→A ( The second best is X→B ( ), For Track_Y: the best pairing is Y→B ( The second best is Y→A ( ), Calculate the adaptive weighting coefficients. ,Pick , :

[0071]

[0072] It can be seen that the kinematics is fuzzy at this point. With the threshold lowered to 0.3, radio frequency fingerprints account for 70% of the decision weight.

[0073] Steps S5-S9 are executed: Composite threshold Using a typical value of 0.6, calculate the weighted composite cost: (Pass threshold 0.6) (reject) (reject) (Pass threshold 0.6) Only the two association pairs (Track_X, FUS_A) and (Track_Y, FUS_B) pass the composite threshold, resulting in 100% association accuracy. If only traditional Mahalanobis distance is used... The normalized Mahalanobis distances of the four associated pairs are 0.23, 0.27, 0.26, and 0.24, respectively. All of them pass the chi-square threshold and their values ​​are very close. The Hungarian algorithm actually randomly selects one of the two pairs, and its accuracy is only 50%.

[0074] This invention also provides a weighted composite track association system that integrates radio frequency fingerprints and kinematic features based on the above method, for... Figure 4 As shown, the system includes: a radar subsystem 1, an optoelectronic subsystem 2, an electronic reconnaissance subsystem 3, and a signal processing subsystem. The signal processing subsystem includes a track preprocessing unit 4, a track association unit 5, a track fusion and management unit 6, and a fused track output unit 7. Specifically: 1- Radar subsystem: Active detection, outputs radar tracks containing kinematic states (including but not limited to position, velocity, acceleration, heading angle, etc.), without carrying F; 2- Optoelectronic subsystem: Passive detection, outputs optoelectronic tracks containing kinematic states (including but not limited to angle, velocity, attitude, etc.), without carrying F; 3- Electronic reconnaissance subsystem: Passive reception, internally includes an RF fingerprint feature extraction module, extracts the RF fingerprint feature vector F from I / Q baseband data, and outputs an electronic reconnaissance track containing kinematic states and the RF fingerprint F; 4- Track preprocessing unit: Executes step S1, performing time synchronization, coordinate transformation, kinematic state extraction, and RF fingerprint validity determination on the tracks input from each sensor, completing data preparation before association; 5- Track association unit: Executes... Figure 1 The steps S2-S9 shown involve two paths, both sides The composite cost path (S4-S6) when both are effective, at least one of them When invalid, the pure Mahalanobis distance backtracking path (S7-S8) is used. The two paths are merged in S9 using the Hungarian algorithm to output the globally optimal correlation scheme; 6- Track fusion and management unit: performs track fusion operation, and track fusion is the only entry point for F injection; including the injection, maintenance, expiration and update management of the radio frequency fingerprint vector F; track start, track maintenance and track termination management; 7- Fusion track output unit: outputs the fused track with radio frequency fingerprint identity tag, carrying kinematic state, radio frequency fingerprint F, Information such as track confidence and target category.

[0075] The beneficial effects of this invention include: (1) Introducing individual feature information of radio frequency fingerprints into the track association cost function breaks through the limitation of existing methods that rely solely on motion features for association decisions. As a second-dimensional criterion independent of kinematics, the cosine similarity of radio frequency fingerprints has the ability to distinguish based on the hardware physical differences of the target transmitters and does not change due to changes in the target's spatial position or motion state. In kinematically ambiguous scenarios, the cosine distance term of radio frequency fingerprints can bear no less than 70% of the decision weight, providing an independent basis for association decisions when kinematics fails. This fundamentally solves the problem that pure kinematic methods cannot maintain correct association after Mahalanobis distance failure due to dense targets or track intersections.

[0076] (2) A dynamic balance between the two criteria dimensions of kinematics and radio frequency fingerprinting is achieved through adaptive weighting coefficients. When the kinematics are highly distinguishable, the method automatically degenerates into the traditional weighted statistical distance method without introducing additional computational burden and is fully compatible with existing systems; when the kinematics are ambiguous, the radio frequency fingerprint is automatically added to the decision without manual switching or intervention. This mechanism enables the method to maintain its original performance in normal scenarios and automatically gain additional distinguishing ability in complex scenarios, that is, without sacrificing the advantages of existing methods, it expands the applicability of track association in dense target scenarios.

[0077] (3) The applicable boundaries of this method are clarified through the radio frequency fingerprint validity determination mechanism. Radar and electro-optical tracks themselves do not carry fingerprint information. When one of the associated parties does not have a valid fingerprint, the method automatically degenerates into pure Mahalanobis distance association—it does not forcibly use non-existent fingerprint information, ensuring that the system can still work normally when fingerprints are missing. This mechanism ensures that this method can operate stably under any sensor configuration, and radio frequency fingerprint enhancement only automatically participates in the decision when conditions are met.

[0078] (4) The radio frequency fingerprint clustering results extracted independently by the electronic reconnaissance terminal can provide an estimate of the number of targets independent of the space sensor. When the space sensor merges multiple spatially close targets into a single track due to insufficient resolution, the radio frequency fingerprint clustering results can be fed back to the track management unit of the fusion center as an independent verification source to help determine the actual number of targets currently existing, and provide physical layer basis for track management decisions such as track splitting, track initiation and deletion.

[0079] The method and system of this application can be used not only in the field of low-altitude flight, but also in track association in other flight and navigation fields.

[0080] The foregoing has provided a detailed description of the weighted composite track association method and system that fuses radio frequency fingerprints and kinematic features, as well as its embodiments. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and its core ideas; furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

[0081] Certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that hardware manufacturers may use different names to refer to the same component. This specification and claims do not distinguish components based on differences in name, but rather on differences in function. The terms "comprising" and "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising / including but not limited to". "Approximately" means that within an acceptable margin of error, those skilled in the art can solve the technical problem and substantially achieve the technical effect within a certain margin of error. The following descriptions in the specification are preferred embodiments for carrying out this application; however, these descriptions are for the purpose of illustrating the general principles of this application and are not intended to limit the scope of this application. The scope of protection of this application shall be determined by the appended claims.

[0082] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or system comprising a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or system. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the product or system that includes said element.

[0083] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0084] The foregoing description illustrates and describes several preferred embodiments of this application. However, as previously stated, it should be understood that this application is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the application concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of this application should be within the protection scope of the appended claims.

Claims

1. A weighted composite track association method integrating radio frequency fingerprints and kinematic features, characterized in that, The method includes the following steps: S1. Preparation of track data to be associated: Obtain the set of tracks to be associated after time synchronization and coordinate transformation. With candidate track set ,in For the first A pending associated flight path For the first There are 10 candidate tracks, each track carrying both kinematic state information and an RFID fingerprint field, wherein the RFID fingerprint field includes an RFID fingerprint feature vector. and validity markers ; S2. Kinematic Mahalanobis distance calculation: For each pair of tracks to be associated... Calculate Mahalanobis distance in a common kinematic measurement space; S3. RFID fingerprint validity determination: Check each track to be associated and candidate tracks Their respective validity markers If both parties If both are valid, proceed to step S4. If at least one is valid... If invalid, proceed to step S7; S4. Calculation of cosine similarity and adaptive weighting coefficients for RF fingerprints: Calculate the track to be associated. With candidate tracks The cosine similarity between the RF fingerprint feature vectors; and the adaptive weighting coefficients calculated based on the ratio of the minimum and second minimum values ​​of the normalized Mahalanobis distance; S5. Weighted Composite Cost Calculation: Step S5 calculates the weighted composite cost function by using normalized Mahalanobis distance as the first-dimensional cost term, cosine distance of RF fingerprint as the second-dimensional cost term, and adaptive weighting coefficients as weight adjustments. ; S6. Composite threshold decision: With composite threshold If a comparison is made, ,accept Select as a candidate association pair; otherwise reject. Candidate association pairs; after completing the judgment, proceed to step S9; S7. RF fingerprint missing rollback handling: [The rest of the text appears to be incomplete and requires further context.] The adaptive weighting coefficients in the code are forcibly set to 1 and the process jumps to step S8. S8. Chi-square threshold decision: Normalized Mahalanobis distance Compared with 1, if ,accept If the pair is a candidate association, it is rejected; otherwise, proceed to step S9. S9. Globally optimal allocation: For all candidate association pairs that pass the threshold decision, minimize the total cost. With the goal of finding the globally optimal correspondence scheme, the Hungarian algorithm is used.

2. The trajectory association method according to claim 1, characterized in that, The radio frequency fingerprint feature vector in S1 This includes, but is not limited to, carrier frequency offset, I / Q amplitude imbalance and phase imbalance, power amplifier nonlinear distortion coefficient, constellation diagram distortion characteristics, and phase noise profile.

3. The trajectory association method according to claim 1, characterized in that, In S3 The valid determination condition is: the radio frequency fingerprint feature vector of the track. In the most recent frame There is at least one direct update from the radio frequency fingerprint feature extraction module.

4. The trajectory association method according to claim 1, characterized in that, The weighted composite cost function in S5 Represented as: in For normalized Markov distance, For radio frequency fingerprint cosine similarity, For adaptive weighting coefficients, The cosine distance of the radio frequency fingerprint.

5. The trajectory association method according to claim 4, characterized in that, The normalized Mahalanobis distance is: in The Mahalanobis distance calculated in step S2. The chi-square threshold is the kinematic measurement space that is comparable to both the track to be associated and the candidate track.

6. The trajectory association method according to claim 4, characterized in that, The cosine similarity of the radio frequency fingerprint is: in These represent the tracks to be associated. and candidate tracks The radio frequency fingerprint feature vector, Represents the dot product of two vectors. express and The product of the L2 norms of their respective radio frequency fingerprint feature vectors; the cosine similarity of the radio frequency fingerprint ranges from... The larger the value, the more similar the feature vectors of the two radio frequency fingerprints are.

7. The track association method according to claim 4, characterized in that, Adaptive weighting coefficients The calculation formula is as follows: ， in For kinematic ambiguity index, The minimum value of the normalized Mahalanobis distance. This is the second smallest value of the normalized Mahalanobis distance. As a normalization reference factor, For adaptive weighting coefficients The lower limit represents the state when the kinematics are completely fuzzy. The minimum value that can be obtained.

8. The trajectory association method according to claim 2, characterized in that, The radio frequency fingerprint feature vector The track fusion operation injects electronic reconnaissance tracks into the fused track. As a persistent attribute field in the track data structure, it is continuously stored and updated throughout the track's lifecycle. When the electronic reconnaissance signal is interrupted, the injected data... exist The feature vector remains valid until the expiration date. When the electronic detection signal returns to normal, the newly extracted feature vector will be valid. With storage Keep it up-to-date by updating with moving averages or medians.

9. A weighted composite track association system integrating radio frequency fingerprinting and kinematic features, characterized in that, The system employs the method described in any one of claims 1-8, and the system comprises: a radar subsystem, an optoelectronic subsystem, an electronic reconnaissance subsystem, and a signal processing subsystem, wherein: The radar subsystem is used to output radar tracks, which include kinematic states but do not carry radio frequency fingerprint feature vectors. ; The optoelectronic subsystem is used to output an optoelectronic track, which includes kinematic states but does not carry radio frequency fingerprint feature vectors. ; The electronic reconnaissance subsystem extracts radio frequency fingerprint feature vectors from I / Q baseband data through a built-in radio frequency fingerprint feature extraction module. The system outputs an electronic reconnaissance track, which includes kinematic state and radio frequency fingerprint feature vector. ; The signal processing subsystem includes a track preprocessing unit, a track association unit, a track fusion and management unit, and a fused track output unit.

10. The trajectory association system according to claim 9, characterized in that, The track preprocessing unit is used to perform step S1, which involves time synchronization, coordinate transformation, kinematic state extraction, and radio frequency fingerprint validity determination of the tracks input from each sensor, thus completing the data preparation before association. The track association unit is used to execute the algorithms for the two paths in steps S2-S9 and output the globally optimal association scheme; The track fusion and management unit is used to perform track fusion operations, including the injection, maintenance, expiration and update management of F, as well as track initiation, track maintenance and track termination management; The fusion track output unit is used to output fusion tracks with RFID fingerprint identification tags.

Images