A cross-protocol group interworking mapping learning method and system

Abstract

The application is a cross-system group intercommunication mapping learning method and system, relating to the technical field of communication network, comprising: a signaling phase space reconstruction module; a dynamic feature extraction module; a chaotic synchronization determination module; a mapping relationship evolution module; and an intercommunication instruction issuing module. In the application, network group call control signaling is converted into phase space trajectory and essential dynamic features are extracted, so that adaptive learning of different system group communication behaviors can be realized without relying on a large amount of labeled training data, effectively reducing data acquisition cost and model training complexity; a two-stage determination architecture combining Mahalanobis distance coarse screening and phase synchronization index fine determination is adopted, which can quickly screen out potential mapping candidate group pairs, improve system processing efficiency, accurately depict the internal correlation degree of different group communication behaviors, and ensure the accuracy of mapping determination.

Description

Technical Field

[0001] This invention relates to the field of communication network technology, and in particular to a cross-system group interoperability mapping learning method and system. Background Technology

[0002] With the deepening of digital transformation in key industries such as emergency communications, public safety, and rail transit, the long-term complementary coexistence of broadband trunking communication systems and traditional narrowband trunking communication systems has become an industry consensus. Broadband trunking, with its advantages of high-speed data transmission and multimedia service support, can meet the modern business needs of video backhaul and real-time data interaction; narrowband trunking, with its wide coverage, strong resilience, and reliable voice communication, plays an irreplaceable role in extreme environments and basic voice dispatching scenarios. In actual collaborative operation scenarios, end users under different network standards often need to perform unified communication dispatching across groups and networks. Therefore, achieving efficient interoperability between broadband and narrowband trunking has become a key requirement for improving the industry's communication assurance capabilities.

[0003] Currently, cross-system group interoperability technology has formed a relatively mature technical system. Among them, static mapping method has been widely used in early small-scale networks due to its simplicity and stable operation. As network scale continues to expand and business scenarios become increasingly complex, the industry is also gradually exploring dynamic mapping technology, attempting to improve the adaptive adjustment capability of mapping relationships by introducing methods such as rule matching and machine learning.

[0004] However, in actual deployment, existing dynamic mapping methods still face some technical challenges: Rule-based matching methods require customized development for different business scenarios and are difficult to fully cover complex and ever-changing communication behaviors; traditional machine learning methods rely heavily on labeled data, but the cost of obtaining high-quality labeled data in communication networks is high, and the generalization ability of the models needs to be further improved. Summary of the Invention

[0005] The purpose of this invention is to provide a cross-system group interoperability mapping learning method and system to solve the above-mentioned problems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A cross-format group interoperability mapping learning system includes: The signaling phase space reconstruction module is used to collect network group call control signaling, generate a one-dimensional discrete time series by statistically analyzing the activity scalar value according to the time window, calculate the delay time and embedding dimension, and transform the one-dimensional discrete time series into a phase space trajectory matrix. The dynamic feature extraction module is used to receive the phase space trajectory matrix, extract the maximum Lyapunov exponent, correlation dimension and Kolmogorov entropy from the phase space trajectory matrix, and construct a dynamic feature vector. The chaotic synchronization determination module is used to receive a one-dimensional discrete time series and dynamic feature vectors, calculate the Mahalanobis distance between the broadband and narrowband group feature vectors for coarse screening, extract the instantaneous phase of the one-dimensional discrete time series that passes the coarse screening and calculate the phase synchronization index to determine whether a chaotic synchronization state has been reached. The mapping relationship evolution module is used to receive the phase synchronization index, convert the phase synchronization index into an external driving force, substitute it into the competitive evolution differential equation to calculate the mapping probability matrix, and combine it with the dual threshold judgment mechanism to drive the mapping state machine to generate mapping establishment or dismantling events. The interoperability instruction distribution module is used to receive mapping establishment or teardown events, perform signaling semantic mapping and cross-domain half-duplex voice right arbitration, perform media stream transcoding and phase alignment through an adaptive jitter buffer mechanism, perform rate limiting, and distribute routing table entries.

[0007] Preferably, in the signaling phase space reconstruction module, the specific method for generating a one-dimensional discrete-time sequence and converting it into a phase space trajectory matrix is ​​as follows: Within the basic time window, the total number of signaling interaction bytes and the absolute frequency of signaling arrival generated by specific group identifiers are traversed and counted. Different weight coefficients are assigned to the total number of signaling interaction bytes and the absolute frequency of signaling arrival, and the weighted sum is formed to form an activity scalar value. The activity scalar values ​​are spliced ​​together in chronological order of the time window. The maximum and minimum values ​​are found. The minimum value is subtracted from each activity scalar value and then divided by the difference between the maximum and minimum values. Range standardization is then performed to generate a one-dimensional discrete time series. A circular buffer is constructed in memory. When new signaling data arrives and generates new time series data points, the oldest data points are overwritten, keeping the total amount of data in the circular buffer constant. The delay time and embedding dimension are recalculated using the latest time series fragments in the circular buffer according to the set update cycle, and the phase space trajectory matrix is ​​dynamically updated.

[0008] Preferably, when calculating the embedding dimension, the false nearest neighbor method is used to determine false nearest neighbors, and the specific logic is as follows: The spatial index data structure is used to find the nearest neighbor of the phase vector in the current embedding dimension phase space, and the sum of the squares of the coordinate differences between the phase vector and the nearest neighbor in each dimension is calculated as the initial squared Euclidean distance. After adding one dimension to the embedding dimension, the squared Euclidean distance is obtained by adding the squared difference between the coordinates of the phase vector and the nearest neighbor in the new dimension to the squared initial Euclidean distance. The ratio of the absolute coordinate difference on the newly added dimension to the initial Euclidean distance is calculated as a relative increment index. The ratio of the new Euclidean distance to the standard deviation of the original time series is also calculated. If the relative increment index is greater than the set distance change rate threshold, or the ratio of the new Euclidean distance to the standard deviation of the original time series is greater than the set attractor size threshold, then it is determined to be a false nearest neighbor.

[0009] Preferably, in the dynamic feature extraction module, the specific evolution and replacement logic for extracting the maximum Lyapunov exponent from the phase space trajectory matrix is ​​as follows: In the phase space trajectory matrix, an initial reference phase point is selected, and neighboring points whose time interval with the initial reference phase point is greater than the average orbital period are found. The initial Euclidean distance between the initial reference phase point and its neighboring points in the multidimensional space is calculated at the initial moment. After a set evolution time step, the divergent Euclidean distance between the evolved reference phase point and its evolved neighboring points is calculated. When searching for a new replacement point in the neighborhood of the evolved reference phase point, distance constraints and angle constraints are satisfied. The distance constraint is that the Euclidean distance between the new replacement point and the evolved reference phase point is minimized. The angle constraint is that the angle between the vector direction from the evolved reference phase point to the new replacement point and the direction of the original divergence vector is less than a set angle threshold. The distance between the new replacement point and the evolved reference phase point is used as the new initial distance to continue the evolution. The specific processing logic for extracting the correlation dimension is as follows: Calculate the Chebyshev distance between any two state vectors in the phase space trajectory matrix, select the maximum distance and minimum non-zero distance of point pairs in the phase space, select a series of spatial scale radii at logarithmic intervals within the interval of the maximum distance and minimum non-zero distance, and obtain the correlation integral by statistically analyzing the proportion of point pairs whose distance is less than the spatial scale radius. The natural logarithm of both sides of the power law relationship between the correlation integral and the spatial scale radius is taken, and the local slope between adjacent points is calculated using the built-in linearity detection algorithm. Noise interference areas with drastic fluctuations in local slope and boundary saturation areas with local slope approaching zero are eliminated. The global slope is extracted as the correlation dimension within the continuous interval where the Pearson correlation coefficient is greater than a set threshold.

[0010] Preferably, the specific process by which the chaotic synchronization determination module extracts the instantaneous phase of the one-dimensional discrete-time sequence that has passed the coarse screening is as follows: A window function is applied to a one-dimensional discrete time series to suppress spectral leakage, and a fast Fourier transform is performed on the windowed time series to obtain the complex spectrum. In the frequency domain, the amplitude corresponding to the negative frequency part of the complex spectrum is forcibly set to zero, the amplitude corresponding to the positive frequency part is multiplied by two, and the amplitudes of the DC component and the Nyquist frequency component remain unchanged. Perform an inverse fast Fourier transform on the filtered complex spectrum to obtain the analytic signal. Extract the imaginary and real parts of the complex values ​​of the analytic signal. Calculate the quotient of the imaginary part divided by the real part and use the arctangent function to obtain the arctangent angle as the instantaneous phase. Calculate the sum of the squares of the real and imaginary parts and take the square root to obtain the instantaneous amplitude.

[0011] Preferably, the formula for calculating the phase synchronization index is: ; in, For phase synchronization index, This represents the total number of data points within the sliding time window. For the current time variable, For broadband groups and narrowband groups in Phase difference at any given moment; The process of calculating the phase synchronization index is as follows: A first-in-first-out sliding time window queue is maintained in memory. The phase difference calculated at each moment is mapped to a direction vector on the unit circle of the complex plane. The cosine and sine values ​​of the phase difference are calculated respectively. The cosine values ​​corresponding to all moments in the sliding time window queue are summed and divided by the total number of data points to obtain the average value of the real axis projection. The sine values ​​corresponding to all moments are summed and divided by the total number of data points to obtain the average value of the imaginary axis projection. The square of the average value of the real axis projection and the square of the average value of the imaginary axis projection are added together and the square root is taken to obtain the average length of the phase difference vector on the unit circle of the complex plane.

[0012] Preferably, the formula for calculating the mapping probability matrix by substituting the mapping relationship evolution module into the competitive evolution differential equation is as follows: ; in, Let the rate of change of the mapping probability be over time. For endogenous growth rate, For broadband groups With narrowband groups The mapping probability, For the traversal index of the narrowband group, This represents the total number of active groups on the narrowband network side. These are elements in the competition coefficient matrix. For broadband groups With narrowband groups The mapping probability, To drive the weighting coefficients, As an external driving force, The attenuation coefficient; The specific solution process for calculating the mapping probability matrix based on the competitive evolution differential equation is as follows: The fourth-order Runge-Kutta numerical integration algorithm is used to iteratively solve the problem within the discrete time step. The initial change slope is calculated based on the current state of the mapping probability matrix. The temporary states of the mapping probability after half a time step and the full time step are predicted in sequence, and the second, third and fourth change slopes are calculated. The four change slopes are weighted and averaged to obtain the equivalent average change rate, and the mapping probability matrix at the next time step is updated.

[0013] Preferably, the specific transition logic of the mapping state machine driven by the dual threshold determination mechanism is as follows: A high threshold and a low threshold are set. When the mapping probability first exceeds the low threshold, the state machine transitions from the unmapped state to the ready-to-map state and allocates an observation timer in memory to start a countdown. When the mapping probability exceeds the high threshold and the duration exceeds the set hold time, the state machine transitions to the active mapping state and generates a mapping establishment event. If the mapping probability falls back below the low threshold during the observation period, the state machine performs a rollback operation and destroys the observation timer. When the mapping probability falls below the high threshold but remains above the low threshold, the mapping relationship is not physically broken, the state machine transitions to the decaying mapping state and starts the decay timer; if the mapping probability breaks through the high threshold again during the buffer period, the state machine returns to the active mapping state and destroys the decay timer; when the mapping probability continues to decay and falls below the low threshold, the state machine transitions to the unmapped state and generates a map removal event.

[0014] Preferably, the specific control logic for cross-domain half-duplex call right arbitration and rate limiting by the interoperability command issuing module is as follows: The underlying hardware interrupt mechanism is used to stamp the arrival timestamps of broadband request messages and narrowband request control frames and calculate the algebraic difference. The average one-way transmission delay difference is calculated by periodic heartbeat detection messages as the delay compensation value. The delay compensation value is subtracted from the algebraic difference to obtain the calibrated real time difference. The right of speech is determined based on the positive or negative sign of the real time difference. Deploy a leaky bucket rate limiting algorithm based on dual-rate three-color marking at the exit of the issued routing table entry, construct a commitment bucket and a peak bucket, compare the byte length of the interoperability instruction data packet with the number of remaining tokens in the peak bucket, and if it is greater, mark it as red and discard it; If the remaining tokens are less than or equal to the remaining tokens in the peak bucket but greater than the remaining tokens in the commitment bucket, the tokens are marked in yellow and allowed to be issued while deducting tokens from the peak bucket. If the remaining tokens are less than or equal to the remaining tokens in the commitment bucket, the tokens are marked in green and allowed to be issued while deducting tokens from both the commitment bucket and the peak bucket.

[0015] A cross-format group interoperability mapping learning method includes: Collect network group call control signaling, statistically analyze the activity scalar value according to the time window and standardize the range to generate a one-dimensional discrete time series, calculate the delay time and embedding dimension and then convert it into a phase space trajectory matrix; Receive the phase space trajectory matrix, extract the maximum Lyapunov exponent, correlation dimension and Kolmogorov entropy from it, and construct the dynamic feature vector; Receive a one-dimensional discrete time series and a dynamic feature vector. First, calculate the Mahalanobis distance between the broadband and narrowband group feature vectors for coarse screening. Extract the instantaneous phase from the one-dimensional discrete time series that passes the coarse screening and calculate the phase synchronization index. Receive the phase synchronization index, convert it into an external driving force, and then input it into the competitive evolution differential equation to solve the mapping probability matrix. Combine the dual threshold judgment mechanism to drive the mapping state machine and generate mapping establishment or dismantling events. Receive mapping establishment or teardown events, perform signaling semantic mapping and cross-domain half-duplex voice right arbitration, perform media stream transcoding and phase alignment through adaptive jitter buffer, and issue routing table entries after completing rate limiting.

[0016] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. This invention transforms network group call control signaling into phase space trajectories and extracts essential dynamic features, enabling adaptive learning of different group communication behaviors without relying on a large amount of labeled training data. This effectively reduces data acquisition costs and model training complexity. The invention employs a two-level decision architecture that combines Mahalanobis distance coarse screening with phase synchronization index fine judgment. This architecture can quickly screen potential mapping candidate group pairs, improving system processing efficiency, and accurately characterize the intrinsic correlation of different group communication behaviors, ensuring the accuracy of mapping determination.

[0017] 2. This invention dynamically calculates the mapping probability matrix through competitive evolution differential equations, naturally simulating the competitive relationship between different narrowband groups and broadband group interconnection resources. This enables dynamic optimization of interconnection resource allocation and improves the overall system resource utilization. Combined with a dual-threshold judgment mechanism driving the mapping state machine, it effectively smooths instantaneous fluctuations in mapping probabilities, avoids frequent establishment and dismantling of mapping relationships, and enhances system stability. The interconnection command issuance module integrates signaling semantic mapping, cross-domain voice arbitration, media stream phase alignment, and flow control functions, effectively adapting to the transmission characteristics of different networks, ensuring smooth cross-standard communication, and improving the user's communication experience. Attached Figure Description

[0018] Further details, features, and advantages of this application are disclosed in the following description of exemplary embodiments in conjunction with the accompanying drawings, in which: Figure 1 This is a system structure diagram of the present invention; Figure 2 This is a flowchart of the method of the present invention. Detailed Implementation

[0019] Several embodiments of this application will now be described in more detail with reference to the accompanying drawings to enable those skilled in the art to implement this application. This application may be embodied in many different forms and for various purposes and should not be limited to the embodiments set forth herein. These embodiments are provided to make this application thorough and complete, and to fully convey the scope of this application to those skilled in the art. The embodiments described do not limit this application.

[0020] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It will be further understood that terms such as those defined in commonly used dictionaries shall be interpreted as having a meaning consistent with their meaning in the relevant field and / or the context of this specification, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0021] Example 1

[0022] Its specific implementation method is combined with the appendix Figure 1 and attached Figure 2 Please provide a detailed explanation.

[0023] Appendix Figure 1 This invention provides a structural block diagram of a cross-system group interoperability mapping learning system, which shows the connection relationship between the signaling phase space reconstruction module and the interoperability instruction issuance module, and marks the main functional interaction flow of each module.

[0024] Appendix Figure 2 The flowchart of a cross-system group interoperability mapping learning method provided in this embodiment of the invention illustrates the complete steps from signaling phase space reconstruction to interoperability command issuance.

[0025] In this embodiment, it includes: The signaling phase space reconstruction module is used to collect network group call control signaling, generate a one-dimensional discrete time series by statistically analyzing the activity scalar value according to the time window, calculate the delay time and embedding dimension, and transform the one-dimensional discrete time series into a phase space trajectory matrix. The core function of this module is to transform the seemingly chaotic and highly bursty group communication signaling in cross-system networks (such as broadband LTE / 5G systems and narrowband TETRA / PDT systems) into geometric trajectories in a high-dimensional phase space.

[0026] By employing phase space reconstruction techniques in nonlinear dynamics, this module reveals the true dynamic evolution of group communication systems hidden behind one-dimensional time series data, providing a purely mathematical physical state space for subsequent mapping learning. The specific operational mechanism and engineering implementation details of this module are as follows: The system first bypasses high-precision data packet sniffing probes on the signaling plane and media plane control nodes of the cross-standard gateway.

[0027] To avoid disrupting the real-time forwarding of existing communication services, the probe employs port mirroring or optical splitters for non-intrusive data acquisition. Real-time bypass acquisition of group call control signaling in different network standards is performed. For broadband systems (e.g., LTE or 5G core networks based on the IP Multimedia Subsystem (IMS) architecture), the acquired signaling includes, but is not limited to, Session Initiation Protocol (SIP) INVITE, 200 OK, and ACK messages, as well as Real-Time Transmission Control Protocol (RTCP) activity reports and sender / receiver statistics. For narrowband systems (e.g., TETRA or PDT digital trunking communication systems), the acquired signaling includes Inter-System Interface (ISI) group establishment requests, group call assignments, talk rights request (TXDEMAND), and talk rights release (TXCEASED) signaling.

[0028] Since some signaling may be encrypted, the probe in this module only performs deep analysis of the plaintext header information of the network layer and transport layer, as well as the unencrypted signaling control fields, so as to obtain the necessary activity data while ensuring communication security.

[0029] To transform these highly discrete, bursty, and structurally heterogeneous signaling data into continuous time series suitable for nonlinear dynamics analysis, this module introduces a signaling density statistical algorithm with a fixed time window. The system sets a base time window length in memory. (For example, a fixed value between 10 milliseconds and 50 milliseconds, the specific value depends on the processing frequency of the gateway's central processor and the clock interrupt precision of the underlying operating system). Within each time window, the system iterates and counts the total number of signaling bytes generated by a specific group identifier (such as the Group Uniform Resource Identifier URI for broadband or the Group Short User Identifier GSSI for narrowband) and the absolute frequency of signaling arrival.

[0030] The system assigns different weighting coefficients to the number of bytes and frequency, and then sums these two physical quantities with weights to form a scalar value of the group's activity within the current time window. This weighted summation method takes into account both the density of signaling and the size of data packets, and can more realistically reflect the group's communication load.

[0031] Over time, for any given group to be analyzed... The system concatenates the activity scalar values ​​calculated within each time window according to their chronological order, generating a one-dimensional discrete time series. ,in The length of the time series represents the total number of observation time windows. Indicates group In the The activity scalar value within a time window.

[0032] To eliminate the dimensional differences in signaling packet size between different network standards (for example, broadband SIP signaling is typically in text format of hundreds of bytes, while narrowband ISI signaling is typically in binary format of tens of bytes), this module performs time series... Range standardization is performed. The system finds the maximum and minimum values ​​in the time series, subtracts the minimum value from each data point, and then divides by the difference between the maximum and minimum values, thereby linearly mapping it to the dimensionless interval [0,1] to ensure the numerical stability and computational accuracy of subsequent phase space reconstruction.

[0033] After obtaining the one-dimensional time series, according to the Takens embedding theorem, an appropriate delay time needs to be selected. and embedding dimension To reconstruct the phase space.

[0034] If the delay time If the value is too small, the values ​​of adjacent coordinates in phase space will be very close, causing the reconstructed trajectory to be squeezed near the diagonal, making it impossible to unfold the true dynamic characteristics of the system; if If the selection is too large, the correlation between adjacent coordinates will be lost, resulting in the reconstructed trajectory being completely randomly scattered in phase space and losing its geometric structure.

[0035] This module uses mutual information to calculate the appropriate delay time. Mutual information, based on information theory, can effectively measure the degree of nonlinear correlation of time series under different delays.

[0036] The specific calculation process is as follows: For time series to delay Subsequent time series As a unified system.

[0037] Calculate the mutual information function between the two. Its core formula is: ; in: For discrete-time indexing; The set delay time steps; State in time series The marginal probability of occurrence; For the state in the delayed sequence The marginal probability of occurrence; For state and The joint probability of simultaneous occurrence.

[0038] In engineering implementation, this module uses the equidistant histogram estimation method to efficiently calculate the aforementioned marginal probabilities and joint probabilities.

[0039] The system first uniformly divides the standardized time series value range [0,1] into... A series of equally wide intervals (infinite elements), in which The value of is usually determined by the length of the time series according to Sturges' rule or square root selection method. It is determined dynamically.

[0040] The system traverses the entire time series and performs statistics. The frequency of each one-dimensional interval is counted, and this frequency is divided by the total number of data points to obtain the marginal probability. The unbiased estimate. Similarly, the system constructs an Two-dimensional grid, statistical coordinate pairs The frequency of falling into each two-dimensional grid cell is divided by the total logarithm to obtain the joint probability. The estimated value.

[0041] To avoid situations where the probability is zero, rendering logarithmic calculations meaningless, the system introduces a Laplace smoothing mechanism in histogram statistics, pre-assigning a very small non-zero fundamental frequency to each interval.

[0042] The system starts from the delay time steps. Start by gradually increasing the step size by 1. The value of the histogram estimation method is used to calculate the corresponding mutual information function in real time. .along with The increase in correlation is due to the gradual decrease in correlation within the time series. It typically exhibits a downward trend with fluctuations. This module sets up a derivative monitor in memory to find the mutual information function. The first local minimum point.

[0043] When the monitor detects that the condition is met and When the condition is met, it indicates that the mutual information has reached a relatively stable low point for the first time after an initial rapid decline. At this point, the system will... The value is locked as the target delay time for reconstructing the phase space of the time series of this group.

[0044] This information theory-based method fully considers the nonlinear characteristics of the signaling sequence, ensures the information independence between the reconstructed coordinates, and avoids the misjudgments that may be caused by the linear autocorrelation function method.

[0045] Determined delay time Next, the embedding dimension of the phase space needs to be determined. .if If the value is too small, the trajectories that were originally separated in the high-dimensional space will overlap and intersect in the low-dimensional projection, producing "false" adjacent points; if... If the value is too large, it will introduce excessive computational noise and exponentially increase the computational burden on the system.

[0046] This module uses the spurious nearest neighbor method to determine the appropriate embedding dimension. The basic idea is that as the embedding dimension gradually increases from low to high, the false neighboring points caused by projection will gradually separate; when the dimension increases to a level that can fully accommodate the dynamic characteristics of the system, the proportion of false neighboring points will approach zero.

[0047] The specific calculation steps are as follows: Assume the current embedding dimension is d. In the d-dimensional phase space, the system reconstructs the phase point vectors based on the one-dimensional time series. The i-th phase point vector is a multi-dimensional coordinate composed of the value at the current time point and d data points that are subsequently taken sequentially according to the calculated delay time step. After constructing all phase points in the d-dimensional space, the system uses spatial index data structures such as KD-trees or ball trees to efficiently traverse and find the nearest neighbor to the phase point vector. After finding the nearest neighbor, the system calculates the sum of the squares of the coordinate differences between the two points in each dimension, using this as the initial squared Euclidean distance.

[0048] The system will increase the embedding dimension from the current d dimensions to d plus 1 dimension.

[0049] After introducing this new dimension, the system needs to re-evaluate the geometric relationship between the two points that were originally closest to each other in the d-dimensional space in the new space.

[0050] At this point, the squared distance between these two points in the new dimension space is mathematically exact equal to the squared Euclidean distance calculated in the original d-dimensional space, plus the squared difference of their coordinates in this newly added dimension (i.e., the d-th delay point shifted backward according to the delay time step).

[0051] To rigorously determine whether these two points are merely spurious nearest neighbors due to low-dimensional projection, this module sets a specific distance change rate threshold in its engineering implementation (based on the statistical characteristics of a large amount of cross-standard signaling data, this threshold is typically between 10 and 15). The system calculates the ratio of the absolute coordinate difference in the newly added dimension to the Euclidean distance in the original d-dimensional space, using this as the relative increment of the distance.

[0052] If the calculated relative increment is greater than the distance change rate threshold set by the system, it means that the distance between the two points has changed drastically after the dimension increases. The original "adjacent" is just an illusion of overlap when the high-dimensional trajectory is projected into the low-dimensional space. Therefore, the system can determine that they are false nearest neighbors in d-dimensional space due to projection overlap.

[0053] The system traverses all points in the phase space, counts the total number of spurious nearest neighbors that satisfy any of the above conditions, and calculates the proportion of these spurious nearest neighbors to the total number of points. .

[0054] The system from Start increasing dimension by dimension, when The percentage drops to a very small set threshold (e.g., less than 5%), or when Follow When the increase in no longer results in a significant decrease (i.e., the curve tends to flatten), it indicates that the current dimension is sufficient to fully unfold the dynamic trajectory of the system, and the system will then... The value is determined as the target embedding dimension. .

[0055] After obtaining the delay time and embedding dimension Next, this module formally constructs the phase space matrix of the group signaling. For a length of... time series The reconstructed phase space contains A state vector.

[0056] That is, the i-th state vector is a multi-dimensional vector formed by sequentially arranging m data points extracted from the time series starting from the i-th data point, strictly according to the calculated delay time step, and sampling at equal intervals.

[0057] The system arranges all generated state vectors in chronological order, row by row, thereby generating a two-dimensional phase space trajectory matrix in memory with the number of rows M equal to the total number of state vectors and the number of columns equal to the embedding dimension m.

[0058] This matrix fully characterizes the geometric topology of group communication behavior in multidimensional space, transforming the originally invisible temporal evolution into visible spatial geometric features.

[0059] To adapt to real-time changes in group states across different network standards, this module employs a circular buffer in memory to dynamically maintain the phase space matrix. When new signaling data arrives and generates new time-series data points, the circular buffer automatically overwrites the oldest data points, maintaining a constant total amount of data within the buffer.

[0060] The system sets an update cycle, and at fixed time intervals (e.g., every second), it re-executes the above process using the latest time series segment in the buffer. and The calculation process updates the phase space matrix. This sliding window mechanism ensures that the phase space reconstruction can track the nonlinear and non-stationary evolution of group communication behavior in real time, and can quickly adapt even when the group's business patterns change abruptly, providing a high-fidelity mathematical model foundation for subsequent dynamic feature extraction.

[0061] The dynamic feature extraction module, connected to the signaling phase space reconstruction module, is used to receive the phase space trajectory matrix, extract the maximum Lyapunov exponent, correlation dimension and Kolmogorov entropy from the phase space trajectory matrix, and construct the dynamic feature vector. After the signaling phase space reconstruction module transforms the one-dimensional time series into a high-dimensional phase space trajectory matrix, this module is responsible for extracting nonlinear dynamic invariants from these high-dimensional geometric structures that can characterize the essential properties of group communication behavior.

[0062] These invariants are unaffected by initial conditions and coordinate transformations, and are core indicators for characterizing the intrinsic evolutionary laws of cross-system groups. This module mainly extracts three dynamic features: the maximum Lyapunov exponent, the correlation dimension, and the Kolmogorov entropy.

[0063] The specific extraction mechanism is as follows: The Lyapunov exponent (LE) is used to quantitatively describe the exponential divergence or convergence rate of adjacent trajectories in phase space over time. In group communication scenarios, if the signaling interactions of a group exhibit high burstiness and unpredictability (e.g., multiple parties competing for calls during emergency rescue), its phase space trajectory will show extreme sensitivity to initial conditions. In this case, the maximum Lyapunov exponent is greater than zero, and the system is in a chaotic state. Conversely, if the group is in a silent or periodically maintained heartbeat state, the trajectory will converge to a fixed point or a limiting cycle, and the maximum Lyapunov exponent will be less than or equal to zero.

[0064] This module employs an improved small-data method (an evolution of the Wolf algorithm) to calculate the maximum Lyapunov exponent. .

[0065] The specific steps are as follows: In the reconstructed phase space matrix, an initial reference phase point is selected. The nearest neighbor to this reference phase point is found in the phase space. To eliminate temporal correlation interference between adjacent points on the same trajectory, the system requires that the time interval between these two points must be greater than the average orbital period to ensure they are located on different trajectory branches. The system calculates the initial Euclidean distance between these two phase points in multidimensional space at the initial moment.

[0066] As time progresses, the two phase points evolve along their respective trajectories in phase space. After a predetermined evolution time step, the reference phase point evolves to a new position, and its neighboring points also evolve to new positions. At this point, the system calculates the divergent Euclidean distance between these two new positions after evolution.

[0067] Due to the local divergence characteristics of chaotic systems, the evolved distance is usually greater than the initial distance. To prevent the distance divergence from being too large and causing the two points to leave the same local tangent space (i.e., exceeding the effective range of the linear approximation), this module searches for a new alternative point in the neighborhood of the evolved reference point.

[0068] The alternative point must satisfy two geometric constraints: First, the distance constraint, that is, the Euclidean distance between the new replacement point and the current reference point must be as small as possible to ensure that they are in the same small neighborhood; Second, the angle constraint means that the direction of the vector pointing from the current reference point to the new replacement point must be as consistent as possible with the direction of the original divergence vector. The system calculates the angle between the two vectors and requires that the angle be less than the set angle threshold (e.g., 15 degrees) to ensure that the replacement operation does not change the original direction of the trajectory divergence.

[0069] After finding a suitable replacement point, the distance between the new replacement point and the reference point is used as the new initial distance, and the set time step is continued to evolve forward.

[0070] Repeat the above process of evolution, distance calculation, and finding alternative points until the reference trajectory has traversed the entire phase space data sequence.

[0071] Assuming a total of The second replacement operation results in the maximum Lyapunov exponent. The calculation formula is: ; in: This represents the total number of replacements during the evolutionary process. This represents the time step size for each evolution. For the first The divergence distance at the end of the step evolution; For the first The initial distance determined after the step replacement.

[0072] Calculated As a key dynamic characteristic, it directly reflects the degree of chaos and the severity of sudden changes in the current communication state of the group. When The larger the value, the stronger the suddenness and unpredictability of the group signaling, and the more computing resources the system needs to allocate to maintain the synchronization of the mapping relationship.

[0073] Correlation dimension ( The correlation dimension is a measure of the geometric complexity of attractors in phase space. In cross-system mappings, the correlation dimension reflects the effective degrees of freedom occupied by group communication behavior. If a group's communication pattern is very simple (e.g., only one-way broadcasting), its correlation dimension is low; if there is complex interaction logic within the group (e.g., multi-level command and dispatch, concurrent data transmission), its correlation dimension will increase.

[0074] This module uses the Grassberger-Procaccia (GP) algorithm to accurately calculate the correlation dimension. This algorithm is based on the spatial distribution statistics of the distances between point pairs in phase space.

[0075] The specific calculation process is as follows: For the phase space matrix Given a state vector, the system calculates any two vectors. and The Chebyshev distance between them (i.e., the maximum absolute value of the difference between the coordinates in each dimension) is denoted as Using Chebyshev distance instead of Euclidean distance can significantly reduce the multiplication and square root operation overhead of distance calculation in high-dimensional space, thereby improving the real-time processing performance of the gateway.

[0076] Set a spatial scale parameter In statistical phase space, the distance is less than The number of point pairs is calculated, and its proportion to the total number of all possible point pairs is called the correlation integral. The formula is: ; in: The total number of state vectors in the phase space; For a given spatial scale radius; For vectors and The distance between them; Let be the Heaviside step function. When the independent variable is greater than or equal to 0, the function value is 1; when the independent variable is less than 0, the function value is 0.

[0077] To determine the correlation dimension, the system continuously changes the scaling parameter within a certain range. The value of is typically chosen by the system based on the maximum distance between point pairs in phase space. and minimum nonzero distance In the interval Select a series of logarithmically equal intervals within the inner range Value, and calculate the corresponding This logarithmically spaced sampling method ensures a sufficiently dense number of observation points in small-scale regions, thereby capturing the details of fractal structures more accurately.

[0078] According to fractal geometry theory, within a suitable scale-free region, there is a power-law relationship between the correlation integral and the scale.

[0079] To extract this feature, the system takes the natural logarithm of both sides of the power-law relation, thus obtaining a linear equation: That is, the natural logarithm of the correlation integral is equal to the correlation dimension multiplied by the natural logarithm of the spatial scale, plus a constant term.

[0080] This module plots the corresponding scatter plot in a two-dimensional coordinate system. The system uses the least squares method to fit a straight line to the linear region (i.e., the scale-free region) in the scatter plot. The slope of this fitted line is the desired correlation dimension. .

[0081] To ensure the accuracy of the fit, the system incorporates a linearity detection algorithm that automatically calculates the local slope between adjacent points and eliminates errors caused by linearity issues. The noise interference zone caused by an excessively small slope (severe fluctuations in local slope) and The boundary saturation region caused by excessive size (where the local slope approaches zero) is used to extract the global slope only in continuous intervals where the Pearson correlation coefficient is greater than 0.98, thereby obtaining high-precision correlation dimension features.

[0082] Kolmogorov entropy ( Entropy is used to measure the rate at which a system loses information as it evolves over time, or in other words, the rate at which a system generates new information. In group mapping scenarios, the magnitude of entropy directly corresponds to the unpredictability of the group state.

[0083] High entropy values ​​mean that the group state changes rapidly, requiring more frequent mapping synchronization; low entropy values ​​indicate that the group state is stable, which can reduce the signaling overhead of mapping synchronization.

[0084] This module utilizes the correlation integral already obtained when calculating the correlation dimension. To estimate the second-order Kolmogorov entropy .

[0085] According to theoretical derivation, when the embedding dimension Large enough, and spatial scale When the size is sufficiently small, the second-order entropy can be approximated by the ratio of correlation integrals under different embedding dimensions. This strategy of reusing the results of correlation integral calculations greatly saves the overall computational cost of the system.

[0086] The theoretical calculation method for second-order Kolmogorov entropy is as follows: under the limiting conditions where the spatial scale approaches zero and the embedding dimension approaches infinity, take the natural logarithm of the ratio of the correlation integral in the m-dimensional phase space to the correlation integral in the m+1-dimensional phase space, and then divide it by the delay time determined during phase space reconstruction.

[0087] In actual engineering calculations, since the system cannot truly reach the limit of infinity or zero, this module selects a suitable spatial scale value within the defined scale-free region and uses the currently determined embedding dimension to perform high-precision approximate calculations, thereby obtaining stable and reliable entropy characteristics.

[0088] After completing the calculations of the three major dynamic invariants mentioned above, this module will calculate the maximum Lyapunov exponent. Correlation dimension and Kolmogorov entropy By combining these features, a dynamic feature vector describing the current communication state of the group can be constructed. .

[0089] These three feature components, from the three orthogonal dimensions of trajectory divergence rate, geometric complexity, and information generation rate, comprehensively characterize the nonlinear nature of group communication behavior.

[0090] For each active group in a cross-standard network, whether it belongs to a broadband LTE system or a narrowband TETRA system, this module will transform its underlying heterogeneous signaling into a unified, purely mathematical dynamic feature vector.

[0091] This transformation completely eliminates the physical barriers between different communication standards in terms of protocol stack, signaling format, and bearer mechanism. It cleverly transforms the interoperability problem across standard groups into a mathematical comparison and synchronization problem in a unified dynamic feature space, providing standardized input data for the subsequent chaotic synchronization determination module.

[0092] The chaotic synchronization determination module is connected to the signaling phase space reconstruction module and the dynamic feature extraction module, respectively. It is used to receive a one-dimensional discrete time sequence and a dynamic feature vector, calculate the Mahalanobis distance between the broadband and narrowband group feature vectors for coarse screening, extract the instantaneous phase of the one-dimensional discrete time sequence that passes the coarse screening and calculate the phase synchronization index to determine whether a chaotic synchronization state has been reached. After the dynamic feature extraction module transforms the group signaling in the cross-system network into a unified dynamic feature vector, the core task of this module is to find the intrinsic correlation between different system groups in this purely mathematical feature space.

[0093] In nonlinear dynamics theory, when two independent chaotic systems are coupled under certain conditions (in communication scenarios, this manifests as potential correlations between cross-standard services), their state trajectories will gradually approach and maintain a certain definite functional relationship. This phenomenon is called chaotic synchronization.

[0094] This module uses rigorous mathematical calculations to determine whether broadband groups and narrowband groups have achieved generalized synchronization or phase synchronization, thus providing a solid physical and mathematical basis for establishing cross-system mapping.

[0095] Cross-band gateways typically connect to hundreds or thousands of groups simultaneously. Performing complex synchronization calculations on all possible broadband and narrowband group pairs would lead to combinatorial explosion, exhausting the system's computing resources.

[0096] This module first utilizes the dynamic feature vector output by Module 2 to perform distance measurement in the feature space, thereby implementing rapid coarse screening.

[0097] Suppose a group in a broadband network The dynamic eigenvectors are A group in a narrowband network The feature vector is .

[0098] Since the maximum Lyapunov exponent, correlation dimension, and Kolmogorov entropy have different physical dimensions and numerical ranges, directly calculating the Euclidean distance will lead to the feature with the larger value dominating the judgment result.

[0099] This module uses Mahalanobis distance to measure the similarity between two feature vectors. Mahalanobis distance effectively eliminates differences in dimensions and takes into account the correlation between feature components.

[0100] The formula is: ; in: and These are the feature vectors of the wideband and narrowband groups to be compared, respectively. It is the transpose of the difference between the eigenvectors; is the inverse of the covariance matrix.

[0101] In engineering implementation, the process of constructing the covariance matrix and solving for its inverse is as follows: The system allocates a dedicated contiguous storage area in memory to continuously collect the dynamic feature vectors of all active groups (including broadband and narrowband) during historical operation, forming a huge historical feature sample library.

[0102] The system first traverses the sample database, sums up the maximum Lyapunov exponents of all samples and divides them by the total number of samples to obtain the global average value of the feature component; similarly, it calculates the global average value of the correlation dimension and Kolmogorov entropy.

[0103] The system calculates the expected value of the product of each feature component and its deviation from its mean, thus constructing a third-order symmetric covariance matrix. The three elements on the main diagonal of this matrix represent the variances of the maximum Lyapunov exponent, the correlation dimension, and the Kolmogorov entropy itself, reflecting the dispersion of each feature in the sample database; while the elements on the off-diagonal represent the covariances between different features, reflecting the linear correlation between features.

[0104] The system uses Gaussian-Jordan elimination or LU decomposition to obtain the inverse matrix of the covariance matrix in the floating-point unit (FPU).

[0105] When calculating the specific Mahalanobis distance, the system first performs element-wise subtraction between the broadband group feature vector and the narrowband group feature vector to obtain a three-dimensional difference column vector containing three elements.

[0106] The difference column vector is transposed to obtain a row vector. The system then performs matrix multiplication on this row vector, the inverse of the pre-calculated covariance matrix, and the difference column vector to obtain a scalar value. Taking the square root of this scalar value yields the Mahalanobis distance between the two groups in the dynamic characteristic space.

[0107] The system calculates the Mahalanobis distance for all wideband and narrowband group pairs. Set a dynamic coarse screening distance threshold. (This threshold can be adaptively adjusted according to the current CPU load rate of the gateway. When the load is high, the threshold is reduced to enhance filtering.)

[0108] when When this occurs, it indicates that the two groups differ greatly in their macroscopic dynamic characteristics, and they are directly judged to be asynchronous and removed from the candidate pool; Only when Only then are these two groups considered to have potential for synchronization and proceed to the next stage of deep phase synchronization determination.

[0109] For the group pairs that pass the coarse screening, this module needs to further analyze their micro-synchronization characteristics in terms of temporal evolution.

[0110] In chaotic communication theory, even if the amplitudes of two systems exhibit great irregularity and difference, their phases may remain locked due to the inherent business logic correlation, which is phase synchronization.

[0111] To extract the instantaneous phase of the group signaling time series, this module introduces the Hilbert transform. For group... Standardized signaling activity time series Its Hilbert transform Defined as the original signal and function The convolution formula is: ; in: The current time variable; For integration variables; This indicates that the integral takes the Cauchy principal value to avoid [the following]. A singularity is generated at that point.

[0112] In engineering implementation, directly calculating the convolution integral in the time domain would consume a large amount of computational resources and could easily lead to boundary truncation effects. This module utilizes the Fast Fourier Transform (FFT) instruction set supported by the underlying hardware to efficiently construct the analytic signal and extract the instantaneous phase in the frequency domain.

[0113] The specific operating steps are as follows: The system applies a Hamming window or a Hanning window to the one-dimensional signaling activity time series of the group to suppress spectral leakage.

[0114] The system performs a Fast Fourier Transform on the windowed time series, transforming it from the time domain to the frequency domain to obtain the complex spectral representation of the time series.

[0115] The system performs a specific asymmetric filtering operation on the spectrum in the frequency domain: The system iterates through the spectrum array, forcing the amplitude of all negative frequency components to zero; multiplying the amplitude of all positive frequency components by 2 (i.e. shifting it one bit to the left); and leaving the amplitude unchanged for DC components (i.e., the zero-frequency components) and Nyquist frequency components.

[0116] The system performs an inverse fast Fourier transform (IFFT) on the spectrum after the above filtering process, converting it back to the time domain. The resulting time-domain signal is no longer a real number signal, but a complex number signal, which is the analytic signal of the original time series.

[0117] In this analytical signal, the real part is completely equivalent to the original signaling activity time series, while its imaginary part corresponds precisely to the result of the original time series after Hilbert transform. The two are strictly orthogonal at 90 degrees in phase.

[0118] To extract the instantaneous phase, the system extracts the imaginary and real parts of the complex value of the analytic signal at each time point. The system calculates the quotient of the imaginary part divided by the real part and calls the arctangent function (usually the atan2 function) from the underlying mathematical library to ensure that the phase corner is in the correct quadrant.

[0119] The obtained arctangent angle value is the instantaneous phase of the signaling time series of that group at the current moment. The system calculates the sum of the squares of the real part and the squares of the imaginary part, and then takes the square root of the sum to obtain the instantaneous amplitude at that moment.

[0120] Through this purely mathematical signal processing method, this module successfully strips away the apparent differences in amplitude levels such as packet size and frequency in cross-system signaling, directly addressing the phase essence of its evolution over time.

[0121] Obtained broadband group instantaneous phase and narrowband groups instantaneous phase Next, this module calculates the phase difference between the two: ; Under ideal phase synchronization, the phase difference It should be kept constant. However, due to transmission delay jitter, packet loss, and inherent dynamic noise in cross-system networks, the phase difference will fluctuate around this constant, and may even exhibit variations. Phase jump.

[0122] To quantitatively assess the degree of phase synchronization in the presence of noise interference, this module calculates the Phase Synchronization Index (PSI).

[0123] PSI is statistically based on the distribution characteristics of phase difference on the unit circle, and the formula is: ; in: This represents the total number of data points within the sliding time window used to calculate the synchronization index. for The phase difference at any given moment.

[0124] The physical and geometric meaning of the formula and the specific calculation process are as follows: The system maintains a length of in memory... First-in-first-out sliding time window queue.

[0125] The system maps the phase difference calculated at each moment to a direction vector on the unit circle of the complex plane. The system calculates the cosine value (representing the projection length of the vector on the real axis) and the sine value (representing the projection length of the vector on the imaginary axis) of the phase difference.

[0126] Within the set sliding time window, the system iterates through all elements in the queue, sums up the cosine values ​​corresponding to all times, and divides the sum by the total number of data points within the time window to obtain the average value of the real axis projection; similarly, the system sums up the sine values ​​corresponding to all times and divides the sum by the total number of data points to obtain the average value of the imaginary axis projection.

[0127] The system adds the square of the average value of the real axis projection to the square of the average value of the imaginary axis projection, and then performs a square root operation on the sum. Essentially, this series of operations calculates the average length of all phase difference vectors within the time window.

[0128] Phase synchronization index The value of strictly falls within the interval [0,1]. When the communication behaviors of two groups are completely independent and unrelated, their phase difference is uniformly distributed within [0,2π], the vectors on the unit circle cancel each other out, and the average length of the vectors approaches 0; when there is a strong service mapping relationship between the two groups, and their dynamic trajectories are attracted to the same synchronous manifold, the phase difference remains constant, the vectors on the unit circle are superimposed in the same direction, and the average length of the vectors approaches 1.

[0129] The system sets a strict phase synchronization determination threshold. (For example, 0.85). When the calculated value is... At that time, this module formally determines the broadband group. With narrowband groups Dynamically, it achieved a state of chaotic synchronization.

[0130] This determination, as highly confident mathematical evidence, is output to the downstream mapping relationship evolution module.

[0131] The mapping relationship evolution module, connected to the chaotic synchronization determination module, is used to receive the phase synchronization index, convert the phase synchronization index into an external driving force, substitute it into the competitive evolution differential equation to calculate the mapping probability matrix, and combine it with the dual threshold determination mechanism to drive the mapping state machine to generate mapping establishment or demolition events. Although the chaotic synchronization determination module identifies group pairs with high dynamic correlation, the network topology is dynamically changing in actual cross-system private network convergence scenarios.

[0132] A broadband group may exhibit a certain degree of synchronization with multiple narrowband groups at a given moment (e.g., due to a complex hierarchical command structure leading to multiple responses to a single call), or false synchronization peaks may occur due to instantaneous bursts in signaling. If routing is rigidly bound based solely on synchronization determination at a single moment, it is highly likely to cause signaling loops or frequent mapping switching.

[0133] This module introduces a competitive evolution mechanism and a state machine model from nonlinear dynamics. The mapping relationship between cross-system groups is regarded as a probability distribution that evolves dynamically over time. Through the numerical solution of differential equations, the real mapping relationship gradually emerges and stabilizes in the competition, while false or outdated mapping relationships decay naturally, thereby achieving flexible and adaptive learning of the mapping relationship.

[0134] The system maintains a global mapping probability matrix in memory. Assume that the current broadband network has... Several active groups, narrowband network side has If there are 1 active group, then the matrix The dimension is Elements in the matrix Indicates in At any time, broadband groups With narrowband groups The probability confidence level for establishing a true interoperability mapping between them is in the range of [0,1].

[0135] When the system is initially started or a new group is added, the corresponding probability element is initialized to a minimum value (e.g., 0.01).

[0136] This module receives the phase synchronization index matrix output from the chaotic synchronization determination module. (The dimension is also) ).

[0137] To differentiate between high-synchronous steady-state pairs and low-synchronous noise pairs and suppress underlying dynamic noise, this module does not directly use... Instead of converting the value, it transforms it into an external driving force through a sigmoid-type nonlinear excitation function. The formula is: ; in: This is the gain coefficient, which controls the steepness of the nonlinear curve. The larger the value, the higher the discrimination near the threshold. This is a bias parameter, typically set slightly below the synchronization determination threshold. The value is used to set the center point of the excitation.

[0138] The specific operation logic of the nonlinear excitation function is as follows: the system first subtracts the set bias parameter from the input phase synchronization index to obtain a difference value.

[0139] If the difference is negative, it indicates that the synchronization index is below the center point; if it is positive, it indicates that it is above the center point. The system multiplies this difference by the gain coefficient and takes its negative value as the exponent of the natural constant e. The system calls the underlying mathematical library to calculate this exponent of the natural constant e, adds it to the constant 1, and finally takes the reciprocal of the sum to obtain the final external driving force value. Through this nonlinear excitation function, only when the synchronization index... Significantly higher than Only then will a strong positive driving force be generated; Conversely, the driving force will decay exponentially to near zero.

[0140] To address the fuzzy synchronization problem in "one-to-many" or "many-to-many" relationships, this module draws upon the Lotka-Volterra dynamics model, which describes species competition in ecology, to construct a competitive evolution differential equation for cross-mode group mapping. For broadband groups... In other words, all narrowband groups that have potential synchronization relationships with it. Equivalent to being in a competitive group The "mapping resources".

[0141] Mapping probability The evolution over time follows the following nonlinear ordinary differential equation: ; The physical and mathematical meanings of each term in this equation are as follows: The rate of change of the mapping probability over time.

[0142] Endogenous growth rate. Represents the rate at which the mapped probability self-reinforces in the absence of external competition.

[0143] Logistic constraint. Ensures that the probability value does not grow indefinitely, and at most approaches 1.

[0144] : Traversal index of narrowband group.

[0145] Lateral suppression of competing terms. These are elements in the competition coefficient matrix. When the broadband group... Other narrowband groups mapping probability When the value is high, it will affect the current group. The mapping probability exerts a suppressive effect. This lateral suppression mechanism can effectively break symmetry, forcing the system to "collapse" from multiple candidate mappings to a dominant and unique mapping.

[0146] External driver item. To drive the weighting coefficients, This is the nonlinear excitation force calculated above. It is the driving force behind the increase in mapping probability.

[0147] : Natural decay term. This is the decay coefficient. If two groups do not interact with each other for a long time, causing the synchronization exponent to decrease and the external driving force to disappear, this term will cause the mapping probability to decay exponentially over time, thereby achieving automatic cleanup of expired mapping relationships.

[0148] In engineering implementation, due to the high nonlinearity and coupling of this system of differential equations, an analytical solution cannot be obtained. This module employs a fourth-order Runge-Kutta numerical integration algorithm for iterative solution within discrete time steps.

[0149] The system performs the following four prediction and correction calculations within each discrete time step: The first step is to directly substitute the current state of the mapping probability matrix into the above differential equation to calculate the initial slope of change at the current moment. The second step is to use the initial slope to predict the temporary state of the mapping probability after half a time step, and then substitute the temporary state back into the differential equation to calculate the second change slope. Third, the system uses the second slope of change to re-predict the temporary state of the mapping probability after half a time step, and substitutes it into the differential equation to calculate the third slope of change. Fourth, the system uses the third slope of change to predict the temporary state of the mapped probability one full time step ahead, and substitutes it into the differential equation to calculate the fourth slope of change. The system then performs a weighted average of these four slopes according to specific weights (usually the initial slope and the fourth slope have a weight of 1, and the two middle slopes have a weight of 2) to obtain the equivalent average rate of change within that time step. The system adds the equivalent average rate of change multiplied by the time step to the mapped probability value at the current moment, thereby updating the mapped probability matrix for the next moment with high precision.

[0150] The dynamic mapping probability matrix is ​​calculated using the competitive evolution equation. Then, this module needs to convert it into specific route mapping instructions that can be executed by the gateway.

[0151] To prevent the frequent establishment and dismantling of mapping relationships (i.e., the "ping-pong effect") caused by small fluctuations in probability values ​​near the threshold, this module designs a four-state mapping state machine with hysteresis characteristics.

[0152] For any pair of wideband and narrowband groups Its mapping state is defined as follows: Unmapped state: The initial state, where there is no routing association between the two parties.

[0153] Preparatory mapping state: Observation state, indicating that both parties are beginning to show a synchronization trend.

[0154] Active mapping state: In the formal interconnection state, the gateway will forward signaling and media streams bidirectionally between the two parties.

[0155] Decline mapping state: The state remains unchanged, indicating that the synchronous trend is weakening, but the route is temporarily not disconnected in case of sudden recovery.

[0156] The state machine's transition logic strictly relies on a dual-threshold decision mechanism (high threshold). and low threshold ,and And time holder: From unmapped state to pre-mapped state: when evolution probability First breakthrough of low threshold The event is triggered at a specific time. The system allocates a watch timer for the group in memory and starts a countdown.

[0157] From pre-mapping state to active mapping state: when Continue to grow and break through high thresholds Furthermore, the duration above this high threshold exceeds the set holding time. Triggered at time.

[0158] At this point, this module officially confirms the mapping relationship and generates an internal event for establishing the mapping, which is then sent to the downstream module through the inter-process communication mechanism.

[0159] From pre-mapped state to unmapped state: if within the observation period Falling back to The following explains that the previous synchronization was an illusion caused by underlying network noise. The state machine performs a rollback operation and destroys the observation timer.

[0160] From active mapping state to decaying mapping state: This occurs when group communication ends or a switch happens. Falling below the high threshold However, it is still higher than the low threshold. Triggered at time.

[0161] At this point, the mapping relationship is not physically broken, and the system enters the decay buffer period, at which point the decay timer is started.

[0162] Declining state to active state: If the group becomes active again during the buffer period, resulting in... Breakthrough The state quickly returns to active, destroying the decay timer and avoiding the signaling overhead of re-establishing the mapping.

[0163] Decaying from mapped state to unmapped state: when It continued to decline, eventually falling below the low threshold. Triggered at time.

[0164] At this point, this module confirms that the mapping relationship is invalid, generates an internal event to tear down the mapping, and notifies the underlying forwarding plane to clear the routing table entry.

[0165] Through this mechanism that combines competitive dynamics evolution with hysteresis state machines, this module smoothly and stably transforms the complex and uncertain chaotic synchronization characteristics at the underlying level into a deterministic cross-system group mapping topology, providing a reliable decision center for the final interoperability command issuance.

[0166] The interoperability instruction distribution module is connected to the mapping relationship evolution module. It is used to receive mapping establishment or teardown events, perform signaling semantic mapping and cross-domain half-duplex voice right arbitration, perform media stream transcoding and phase alignment through an adaptive jitter buffer mechanism, perform rate limiting and distribute routing table entries. After the mapping relationship evolution module establishes or dismantles events through the deterministic mapping of competitive dynamics and hysteresis state machine outputs, this module undertakes the core task of transforming these high-level logical decisions into specific physical instructions that can be executed by the underlying network devices.

[0167] Due to the significant heterogeneity between broadband networks (such as IP-based LTE / 5G systems) and narrowband networks (such as circuit-switched or proprietary packet-based TETRA / PDT systems) in terms of protocol stack architecture, signaling interaction timing, talk control mechanisms, and media encoding formats, this module must perform in-depth protocol conversion, timing alignment, and state synchronization to ensure smooth and stable interoperability across different standards and groups.

[0168] When a "establish mapping" event (containing the broadband group identifier) ​​is received from the mapping relationship evolution module, and narrowband group identifier When this occurs, this module first starts the signaling semantic mapping engine. This engine is responsible for bidirectional semantic translation between the broadband Session Initiation Protocol (SIP) and the narrowband Inter-System Interface (ISI) protocol.

[0169] For group calls originating from broadband to narrowband, this module intercepts the SIPINVITE request sent from the broadband side. This request contains the Uniform Resource Identifier (URI) of the broadband group and Session Description Protocol (SDP) parameters (such as media port and codec type).

[0170] This module parses these parameters and constructs the corresponding narrowband ISIPDU (Protocol Data Unit) based on the mapping relationship. This module generates an ISI-SETUPPDU, fills the target address field with the mapped Narrowband Group Short User Identifier (GSSI), sets the call type to "Group Call", and maps the broadband-side SDP media parameters to the bearer capability information unit supported by the narrowband side.

[0171] Conversely, for group calls originating from narrowband to broadband, this module intercepts the ISI-SETUP request on the narrowband side and extracts the calling party's Individual Short User Identifier (ISSI) and the called party's GSSI. Based on the mapping relationship, this module generates a standard SIPIVITE request. In this request, the Request-URI is set to the broadband group. The address is specified, with the From header field set to the broadband virtual identity corresponding to the narrowband caller's ISSI, and the To header field set to the broadband group address. This module constructs an SDP in the SIP message body, declaring the IP address and RTP port number used by the gateway to receive broadband media streams.

[0172] To ensure the reliability of signaling interactions, this module maintains a signaling transaction context in memory for each pair of active mapping groups.

[0173] This context records the current signaling interaction status (e.g., call attempt, ringing, established, released), sequence number (CSeq), and timer status. In the engineering implementation, the system allocates an independent hardware-level timer in memory for each signaling transaction. This timer starts immediately and begins counting down after the system sends the initial call setup signaling to the peer network. If the gateway does not receive any response signaling from the peer network within the system-defined base timeout period (e.g., a 200 OK message on the broadband side or a CONNECT message on the narrowband side), the system will trigger the first signaling retransmission mechanism.

[0174] The system that triggers a retransmission will set the next timeout period to twice the current base timeout period. This retransmission mechanism based on the exponential backoff algorithm can effectively prevent gateways from frequently sending retransmission signaling when congestion occurs in cross-standard networks, thereby further exacerbating network signaling storms. If the number of consecutive retransmissions of a signaling transaction reaches the system's preset maximum retransmission threshold, the system will determine that the cross-standard call establishment has failed.

[0175] At this point, the system will forcibly remove the transaction context in memory, release the occupied port resources, and actively send a release signaling message with a specific reason value to the source network that initiated the call (e.g., send a SIP408RequestTimeout message to the broadband side, or send an ISI-DISCONNECT message to the narrowband side), while notifying the upper-layer mapping relationship evolution module to perform state rollback.

[0176] Narrowband trunking communication systems typically employ a strict half-duplex button-based speaking mechanism, meaning that only one member in the group can have the floor privilege and send voice messages at any given time. While broadband systems also support MCPTT, they often face complex issues at the interconnection gateway, such as asynchronous talk privilege states and call-grabbing conflicts between the two ends.

[0177] This module designs a cross-domain voice rights arbitration subsystem, which manages voice rights through a deterministic state transition matrix.

[0178] Define the talk right state space for cross-system group interoperability ,in: Idle state: No one speaks on either the wide or narrow band.

[0179] Broadband occupancy status: A member on the broadband side holds the right to speak, and media streams flow from broadband to narrowband.

[0180] Narrowband occupancy: A member on the narrowband side holds the right to speak, and the media stream flows from narrowband to broadband.

[0181] In a conflict state, members on both the wide and narrow bands almost simultaneously request the right to speak.

[0182] This module drives the state machine to operate based on the received right-of-way control signaling from both sides (such as FloorRequest and FloorRelease for broadband, and TXDEMAND and TXCEASED for narrowband). When the system is in... If a FloorRequest is received from the broadband side first, the state transitions to [state name]. .

[0183] At this time, this module replies with FloorGranted to the broadband side and simultaneously sends ISI-TXDEMAND signaling to the narrowband side, requesting the narrowband base station to allocate a downlink radio channel for this group. When the system is in... In this state, if a TXDEMAND is received from the narrowband side (i.e., a narrowband user is attempting to preempt the call), this module will arbitrate according to a preset priority policy. If the narrowband user's priority is... Higher priority than current broadband speaking users This module sends a FloorRevoke signaling message to the broadband side to forcibly deprive it of its talk rights, and replies with TXGRANTED to the narrowband side, transitioning to a new state. ;if This module replies with TXREJECT to the narrowband side, and the state remains unchanged. .

[0184] To handle conflicts caused by concurrent requests within a very small time window This module introduces a timestamp-based arbitration algorithm. When processing concurrent talk rights requests within a very small time window, the system heavily relies on the high-precision clock provided by the gateway's underlying network interface card (NIC).

[0185] When a request message for voice rights from the broadband side or a control frame from the narrowband side arrives at the physical network card interface of the gateway, the underlying driver of the network card will use the hardware interrupt mechanism to immediately add an arrival timestamp with nanosecond precision to the data packet.

[0186] The system extracts the two timestamps, representing broadband and narrowband applications respectively, from the underlying layer and calculates the algebraic difference between them. To eliminate the unfairness caused by the inherent transmission delay asymmetry between broadband IP networks and narrowband wireless networks, the system introduces a network delay compensation mechanism before comparing the timestamps.

[0187] The system uses periodic heartbeat probe messages to calculate the average one-way transmission delay on both the broadband and narrowband sides in real time, and calculates the difference between the two as a delay compensation value. The system subtracts this delay compensation value from the extracted timestamp algebraic difference to obtain a calibrated true time difference.

[0188] If the calibrated true time difference is less than zero, the system logically and definitively determines that the physical key press action of the broadband user occurred first, thus awarding the call right to the broadband side, and the state machine transitions to the broadband occupied state. If the calibrated true time difference is greater than zero, the system determines that the key press action of the narrowband user occurred first, thus awarding the call right to the narrowband side, and the state machine transitions to the narrowband occupied state. In the extremely rare case where the true time difference is strictly equal to zero, the system will make a mandatory ruling based on a pre-configured default preference strategy (e.g., the narrowband command center has absolute priority by default). Through this rigorous call right arbitration mechanism, this module effectively avoids media stream chaos and signaling deadlock in cross-system interoperability.

[0189] After signaling establishment and voice rights allocation are completed, cross-standard groups enter the media stream interoperability phase. Broadband systems typically use high-bandwidth vocoders (such as AMR-WB and EVS), while narrowband systems, limited by wireless bandwidth, use low-rate vocoders (such as TETRA's ACELP and PDT's NVOC). This module incorporates a digital signal processor (DSP) array or a CPU-based soft transcoding engine, responsible for real-time decoding and re-encoding between different encoding formats.

[0190] During transcoding, due to the significant differences in transmission latency and jitter characteristics between broadband and narrowband networks, directly forwarding media packets can lead to severe audio stuttering or distortion. This module incorporates an adaptive jitter buffering mechanism to achieve phase alignment of heterogeneous media streams.

[0191] For the RTP media stream received from the broadband side, this module extracts the sequence number of each RTP packet. and timestamp The received media packets are stored in the broadband-side jitter buffer. The current depth of the buffer is... Adjust dynamically according to network jitter.

[0192] This module calculates the moving average of network latency. and delay variance Target depth of the jitter buffer The calculation formula is: ; in The safety factor is used to control the level of conservatism in the buffer.

[0193] In the underlying queue management mechanism of the adaptive jitter buffer, the system allocates an independent circular memory queue for each active cross-format media stream.

[0194] When a new media data packet is received, the system first rigorously checks the sequence number in its header. If the extracted sequence number is less than the sequence number the system expects to receive, it means that the data packet is an out-of-order packet that has experienced severe delays during network transmission. In order to ensure the real-time nature of the voice, the system will directly discard the packet. If the sequence number meets or exceeds the expectation, the system will precisely insert the data packet into the corresponding physical memory address of the circular queue according to the offset of the sequence number.

[0195] When the number of media packets accumulated in the circular queue reaches the target depth calculated by the above formula, the system starts the decoding engine to convert the wideband speech decoding into a linear pulse code modulation (PCM) audio stream. The PCM audio stream is then fed into a narrowband encoder, where it is re-sliced ​​and packaged strictly according to the inherent frame length of the narrowband system (e.g., 30 milliseconds per frame). During the repackaging process to generate narrowband media frames, a purely software-implemented phase-locked loop (PLL) mechanism is used to maintain the absolute continuity of the speech on the time axis.

[0196] The system uses the actual arrival rate of broadband media packets as the reference frequency and the transmission rate of locally generated narrowband media frames as the controlled frequency. The system calculates the phase error between these two frequencies in real time and inputs this error value into a proportional-integral filter for smoothing.

[0197] The filter output is used to fine-tune the step value of the local transmission clock. Through this dynamic fine-tuning, the transmission rhythm of narrowband media frames can smoothly track the arrival rhythm of broadband media streams like a spring, thereby effectively absorbing and eliminating voice interruption problems caused by sudden jitter in broadband IP networks without losing voice information.

[0198] Finally, the encapsulated narrowband media frame is sent to the narrowband switching control node (SCN) via the underlying UDP / IP socket.

[0199] To achieve efficient media stream forwarding, this module needs to send the determined mapping relationship to the underlying data forwarding plane of the gateway after completing the signaling negotiation.

[0200] This module generates a five-tuple routing table entry containing source IP, source port, destination IP, destination port, protocol type, and transcoding rule index. Through the internal high-speed inter-process communication (IPC) mechanism, it writes the entry into the hardware forwarding table in the forwarding plane or the Netfilter connection tracking table in kernel mode.

[0201] Subsequent media streams can be forwarded and transcoded at high speed directly at the underlying layer, without having to be sent to the application layer for processing each time, which greatly reduces the system's forwarding latency.

[0202] Furthermore, during public safety emergencies, cross-network systems may generate a massive amount of group connection establishment, disconnection, and voice rights request signaling instantaneously. If this module were to issue all of these commands without restraint, it could easily lead to CPU overload or network congestion in the underlying gateway devices, triggering a signaling storm. To address this, this module deploys a leaky bucket rate limiting algorithm based on dual-rate, three-color labeling at the command issuance exit point.

[0203] Set the committed information rate and peak information rate, as well as the corresponding committed burst size and peak burst size.

[0204] In the underlying logic implementation of the dual-rate, three-color tagging rate limiting mechanism, the system constructs two virtual token bucket data structures in memory, named the commitment bucket and the peak bucket, respectively. The system relies on a high-frequency triggered background timer task to uniformly accumulate tokens into the commitment bucket at a pre-set commitment information rate until the number of tokens in the bucket reaches the upper limit of the commitment burst size. Simultaneously, the same timer task uniformly accumulates tokens into the peak bucket at a set peak information rate until the upper limit of the peak burst size is reached.

[0205] When the system generates an interoperability command data packet and prepares to send it to the underlying network, the system first accurately obtains the byte length of the data packet.

[0206] The system executes strict three-level comparison and deduction logic: First-level comparison: The system compares the byte length of the data packet with the number of tokens remaining in the peak bucket. If the byte length is greater than the number of tokens remaining in the peak bucket, it indicates that the current traffic has seriously exceeded the system's limit capacity. The system logically marks the data packet as red and directly performs a discard operation to protect the underlying hardware from traffic surges. Second-level comparison: If the byte length is less than or equal to the remaining tokens in the peak bucket, the system then compares it with the current remaining tokens in the commitment bucket. If the byte length is greater than the remaining tokens in the commitment bucket, it means that the current traffic exceeds the regular committed rate but is still within the peak allowable range. The system marks the packet as yellow and allows it to be sent, but the system must deduct a number of tokens equal to the byte length of the packet from the peak bucket. Third-level comparison: If the byte length is less than or equal to the number of remaining tokens in the commitment bucket, it means that the current traffic is completely within the normal commitment rate. The system marks the packet as green and allows it to be sent out with priority. The system will also deduct a number of tokens equal to the byte length of the packet from both the commitment bucket and the peak bucket.

[0207] Through this rigorous traffic shaping and rate limiting mechanism at the purely logical level, this module ensures the smooth and orderly issuance of interoperability commands, guaranteeing the high availability and robustness of the cross-system group interoperability mapping learning system under extremely high concurrency scenarios. Example

[0208] Please see Figure 2 A cross-system group interoperability mapping learning method includes the following parts: Step 1, Signaling Phase Space Reconstruction: Collect network group call control signaling, statistically analyze the activity scalar value according to the time window and standardize the range to generate a one-dimensional discrete time series, calculate the delay time and embedding dimension and convert it into a phase space trajectory matrix, and output it to the dynamic feature extraction step and the chaotic synchronization determination step respectively. At the same time, output the one-dimensional discrete time series to the chaotic synchronization determination step. Step 2, Dynamic Feature Extraction: Receive the phase space trajectory matrix, extract the maximum Lyapunov exponent, correlation dimension, and Kolmogorov entropy from it, construct a dynamic feature vector, and output the vector to the chaos synchronization determination step; Step 3, Chaotic Synchronization Determination: Receive a one-dimensional discrete time series and dynamic feature vectors. First, calculate the Mahalanobis distance between the broadband and narrowband group feature vectors for coarse screening. Extract the instantaneous phase from the one-dimensional discrete time series that passes the coarse screening and calculate the phase synchronization index. Output the index to the mapping relationship evolution step. Step 4: Evolution of mapping relationship: Receive the phase synchronization index, convert it into an external driving force, input it into the competitive evolution differential equation to solve the mapping probability matrix, combine it with the dual threshold judgment mechanism to drive the mapping state machine, generate the establishment or dismantling of mapping events, and output the event to the intercommunication command issuance step. Step 5, Interoperability Command Issuance: Receive the establishment or teardown of mapping events, perform signaling semantic mapping and cross-domain half-duplex voice right arbitration, perform media stream transcoding and phase alignment through adaptive jitter buffer, and issue routing table entries after completing rate limiting.

[0209] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

[0210] It should be noted that, in this document, the use of relational terms such as "first" and "second" is merely for distinguishing one entity or operation from another, and does not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0211] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0212] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0213] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A cross-system group interoperability mapping learning system, characterized in that, include: The signaling phase space reconstruction module is used to collect network group call control signaling, generate a one-dimensional discrete time series by statistically analyzing the activity scalar value according to the time window, calculate the delay time and embedding dimension, and transform the one-dimensional discrete time series into a phase space trajectory matrix. The dynamic feature extraction module is used to receive the phase space trajectory matrix, extract the maximum Lyapunov exponent, correlation dimension and Kolmogorov entropy from the phase space trajectory matrix, and construct a dynamic feature vector. The chaotic synchronization determination module is used to receive a one-dimensional discrete time series and dynamic feature vectors, calculate the Mahalanobis distance between the broadband and narrowband group feature vectors for coarse screening, extract the instantaneous phase of the one-dimensional discrete time series that passes the coarse screening and calculate the phase synchronization index to determine whether a chaotic synchronization state has been reached. The mapping relationship evolution module is used to receive the phase synchronization index, convert the phase synchronization index into an external driving force, substitute it into the competitive evolution differential equation to calculate the mapping probability matrix, and combine it with the dual threshold judgment mechanism to drive the mapping state machine to generate mapping establishment or dismantling events. The interoperability instruction distribution module is used to receive mapping establishment or teardown events, perform signaling semantic mapping and cross-domain half-duplex voice right arbitration, perform media stream transcoding and phase alignment through an adaptive jitter buffer mechanism, perform rate limiting, and distribute routing table entries.

2. The cross-system group interoperability mapping learning system according to claim 1, characterized in that, In the signaling phase space reconstruction module, the specific method for generating a one-dimensional discrete time series and converting it into a phase space trajectory matrix is ​​as follows: Within the basic time window, the total number of signaling interaction bytes and the absolute frequency of signaling arrival generated by the preset group identifier are traversed and counted. Different weight coefficients are assigned to the total number of signaling interaction bytes and the absolute frequency of signaling arrival, and the weighted sum is formed to form an activity scalar value. The activity scalar values ​​are spliced ​​together in chronological order of the time window. The maximum and minimum values ​​are found. The minimum value is subtracted from each activity scalar value and then divided by the difference between the maximum and minimum values. Range standardization is then performed to generate a one-dimensional discrete time series. A circular buffer is constructed in memory. When new signaling data arrives and generates new time series data points, the oldest data points are overwritten, keeping the total amount of data in the circular buffer constant. The delay time and embedding dimension are recalculated using the latest time series fragments in the circular buffer according to the set update cycle, and the phase space trajectory matrix is ​​dynamically updated.

3. The cross-system group interoperability mapping learning system according to claim 2, characterized in that, When calculating the embedding dimension, the spurious nearest neighbor method is used to determine spurious nearest neighbors. The specific logic is as follows: The spatial index data structure is used to find the nearest neighbor of the phase vector in the current embedding dimension phase space, and the sum of the squares of the coordinate differences between the phase vector and the nearest neighbor in each dimension is calculated as the initial squared Euclidean distance. After adding one dimension to the embedding dimension, the squared Euclidean distance is obtained by adding the squared difference between the coordinates of the phase vector and the nearest neighbor in the new dimension to the squared initial Euclidean distance. The ratio of the absolute coordinate difference on the newly added dimension to the initial Euclidean distance is calculated as a relative increment indicator, and the ratio of the new Euclidean distance to the standard deviation of the original time series is calculated. If the relative increment index is greater than the set distance change rate threshold, or the ratio of the new Euclidean distance to the standard deviation of the original time series is greater than the set attractor size threshold, it is determined to be a false nearest neighbor.

4. The cross-system group interoperability mapping learning system according to claim 1, characterized in that, In the dynamic feature extraction module, the specific evolution and replacement logic for extracting the maximum Lyapunov exponent from the phase space trajectory matrix is ​​as follows: In the phase space trajectory matrix, an initial reference phase point is selected, and neighboring points whose time interval with the initial reference phase point is greater than the average orbital period are found. The initial Euclidean distance between the initial reference phase point and its neighboring points in the multidimensional space is calculated at the initial moment. After a set evolution time step, the divergent Euclidean distance between the evolved reference phase point and its evolved neighboring points is calculated. When searching for a new replacement point in the neighborhood of the evolved reference phase point, distance constraints and angle constraints are satisfied. The distance constraint is that the Euclidean distance between the new replacement point and the evolved reference phase point is minimized. The angle constraint is that the angle between the vector direction from the evolved reference phase point to the new replacement point and the direction of the original divergence vector is less than a set angle threshold. The distance between the new replacement point and the evolved reference phase point is used as the new initial distance to continue the evolution. The specific processing logic for extracting the correlation dimension is as follows: Calculate the Chebyshev distance between any two state vectors in the phase space trajectory matrix, select the maximum distance and minimum non-zero distance of point pairs in the phase space, select a series of spatial scale radii at logarithmic intervals within the interval of the maximum distance and minimum non-zero distance, and obtain the correlation integral by statistically analyzing the proportion of point pairs whose distance is less than the spatial scale radius. The natural logarithm of both sides of the power law relationship between the correlation integral and the spatial scale radius is taken, and the local slope between adjacent points is calculated using the built-in linearity detection algorithm. Noise interference areas with drastic fluctuations in local slope and boundary saturation areas with local slope approaching zero are eliminated. The global slope is extracted as the correlation dimension within the continuous interval where the Pearson correlation coefficient is greater than a set threshold.

5. The cross-system group interoperability mapping learning system according to claim 1, characterized in that, The specific process by which the chaotic synchronization determination module extracts the instantaneous phase of a one-dimensional discrete-time series that has passed the coarse screening is as follows: A window function is applied to a one-dimensional discrete time series to suppress spectral leakage, and a fast Fourier transform is performed on the windowed time series to obtain the complex spectrum. In the frequency domain, the amplitude corresponding to the negative frequency part of the complex spectrum is forcibly set to zero, the amplitude corresponding to the positive frequency part is multiplied by two, and the amplitudes of the DC component and the Nyquist frequency component remain unchanged. Perform an inverse fast Fourier transform on the filtered complex spectrum to obtain the analytic signal. Extract the imaginary and real parts of the complex values ​​of the analytic signal. Calculate the quotient of the imaginary part divided by the real part and use the arctangent function to obtain the arctangent angle as the instantaneous phase. Calculate the sum of the squares of the real and imaginary parts and take the square root to obtain the instantaneous amplitude.

6. The cross-system group interoperability mapping learning system according to claim 5, characterized in that, The formula for calculating the phase synchronization index is: ； in, For phase synchronization index, This represents the total number of data points within the sliding time window. For the current time variable, For broadband groups and narrowband groups in Phase difference at any given moment; The process of calculating the phase synchronization index is as follows: A first-in-first-out sliding time window queue is maintained in memory. The phase difference calculated at each moment is mapped to a direction vector on the unit circle of the complex plane. The cosine and sine values ​​of the phase difference are calculated respectively. The cosine values ​​corresponding to all moments in the sliding time window queue are summed and divided by the total number of data points to obtain the average value of the real axis projection. The sine values ​​corresponding to all moments are summed and divided by the total number of data points to obtain the average value of the imaginary axis projection. The square of the average value of the real axis projection and the square of the average value of the imaginary axis projection are added together and the square root is taken to obtain the average length of the phase difference vector on the unit circle of the complex plane.

7. The cross-system group interoperability mapping learning system according to claim 1, characterized in that, The formula for calculating the mapping probability matrix by substituting the mapping relationship evolution module into the competition evolution differential equation is as follows: ； in, Let the rate of change of the mapping probability be over time. For endogenous growth rate, For broadband groups With narrowband groups The mapping probability, For the traversal index of the narrowband group, This represents the total number of active groups on the narrowband network side. These are elements in the competition coefficient matrix. For broadband groups With narrowband groups The mapping probability, To drive the weighting coefficients, As an external driving force, The attenuation coefficient; The specific solution process for calculating the mapping probability matrix based on the competitive evolution differential equation is as follows: The fourth-order Runge-Kutta numerical integration algorithm is used to iteratively solve the problem within the discrete time step. The initial change slope is calculated based on the current state of the mapping probability matrix. The temporary states of the mapping probability after half a time step and the full time step are predicted in sequence, and the second, third and fourth change slopes are calculated. The four change slopes are weighted and averaged to obtain the equivalent average change rate, and the mapping probability matrix at the next time step is updated.

8. A cross-system group interoperability mapping learning system according to claim 7, characterized in that, The specific transition logic of the mapped state machine driven by the dual threshold determination mechanism is as follows: A high threshold and a low threshold are set. When the mapping probability first exceeds the low threshold, the state machine transitions from the unmapped state to the ready-to-map state and allocates an observation timer in memory to start a countdown. When the mapping probability exceeds the high threshold and the duration exceeds the set hold time, the state machine transitions to the active mapping state and generates a mapping establishment event. If the mapping probability falls back below the low threshold during the observation period, the state machine performs a rollback operation and destroys the observation timer. When the mapping probability falls below the high threshold but remains above the low threshold, the mapping relationship is not physically broken, the state machine transitions to the decaying mapping state and starts the decay timer; if the mapping probability breaks through the high threshold again during the buffer period, the state machine returns to the active mapping state and destroys the decay timer; when the mapping probability continues to decay and falls below the low threshold, the state machine transitions to the unmapped state and generates a map removal event.

9. A cross-system group interoperability mapping learning system according to claim 1, characterized in that, The specific control logic for cross-domain half-duplex call right arbitration and rate limiting in the interoperability command issuance module is as follows: The underlying hardware interrupt mechanism is used to stamp the arrival timestamps of broadband request messages and narrowband request control frames and calculate the algebraic difference. The average one-way transmission delay difference is calculated by periodic heartbeat detection messages as the delay compensation value. The delay compensation value is subtracted from the algebraic difference to obtain the calibrated real time difference. The right of speech is determined based on the positive or negative sign of the real time difference. Deploy a leaky bucket rate limiting algorithm based on dual-rate three-color marking at the exit of the issued routing table entry, construct a commitment bucket and a peak bucket, compare the byte length of the interoperability instruction data packet with the number of remaining tokens in the peak bucket, and if it is greater, mark it as red and discard it; If the remaining tokens are less than or equal to the remaining tokens in the peak bucket but greater than the remaining tokens in the commitment bucket, the tokens are marked in yellow and allowed to be issued while deducting tokens from the peak bucket. If the remaining tokens are less than or equal to the remaining tokens in the commitment bucket, the tokens are marked in green and allowed to be issued while deducting tokens from both the commitment bucket and the peak bucket.

10. A cross-system group interoperability mapping learning method, and a cross-system group interoperability mapping learning system according to any one of claims 1-9, characterized in that, include: Collect network group call control signaling, statistically analyze the activity scalar value according to the time window and standardize the range to generate a one-dimensional discrete time series, calculate the delay time and embedding dimension and then convert it into a phase space trajectory matrix; Receive the phase space trajectory matrix, extract the maximum Lyapunov exponent, correlation dimension and Kolmogorov entropy from it, and construct the dynamic feature vector; Receive a one-dimensional discrete time series and a dynamic feature vector. First, calculate the Mahalanobis distance between the broadband and narrowband group feature vectors for coarse screening. Extract the instantaneous phase from the one-dimensional discrete time series that passes the coarse screening and calculate the phase synchronization index. Receive the phase synchronization index, convert it into an external driving force, and then input it into the competitive evolution differential equation to solve the mapping probability matrix. Combine the dual threshold judgment mechanism to drive the mapping state machine and generate mapping establishment or dismantling events. Receive mapping establishment or teardown events, perform signaling semantic mapping and cross-domain half-duplex voice right arbitration, perform media stream transcoding and phase alignment through adaptive jitter buffer, and issue routing table entries after completing rate limiting.

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