Anti-interference filtering method and device for fire emergency communication

Abstract

The application discloses an anti-interference filtering method and device for fire emergency communication, and the method comprises the following steps: designing a detection signal containing sequential exchange perturbation, applying the detection signal to a frequency response device and collecting the response of the frequency response device; based on the response and the detection signal, demodulating a second-order cross-sensitivity describing the coupling effect between coding components; according to the second-order cross-sensitivity, constructing a zero-impact subspace for a locked frequency point set, and performing an equal-constraint geodetic step calculation in the subspace to generate a coding vector update amount; and applying the update amount to a current coding vector to obtain a coding vector of a next iteration period. The application can accurately quantify and compensate nonlinear coupling effects, handle multiple constraints at the path planning level, and improve the convergence speed and final accuracy of online tuning of a complex trap filter while effectively protecting the tuned performance.

Description

TECHNICAL FIELD

[0001] The present application relates to an anti-interference filtering method, in particular to an anti-interference filtering method and device for fire emergency communication. BACKGROUND

[0002] In the field of fire emergency rescue and satellite communication, reliable wireless communication link is the key infrastructure to protect the safety of personnel and command and dispatch. The extreme environment of fire scene often leads to the paralysis of ground communication network, and satellite communication becomes the only reliable communication means. However, the complex electromagnetic environment of the fire site, including arc discharge of damaged power facilities, motor noise of fire fighting equipment, spectrum conflict of multi-department rescue equipment, etc., seriously interferes with the radio frequency front end of the satellite communication terminal. In particular, the weak downlink signal (typical value-130dBm) of the fire special channel such as L-band Tian Tong satellite and S-band relay satellite is easily overwhelmed by strong interference. Therefore, it is of great significance to study the high-performance tunable notch filtering technology suitable for fire satellite communication to ensure emergency communication guarantee under extreme conditions.

[0003] The current tunable notch filter for satellite communication anti-interference mainly adopts an adaptive tuning method based on gradient feedback. The typical implementation is to superimpose a quadrature probe signal on the filter control parameters, extract the first-order sensitivity information using correlation detection, and gradually adjust the notch parameters using gradient descent or coordinate rotation algorithm. Some improved schemes introduce lookup table acceleration, model predictive control and other technologies to improve the convergence speed. In the multi-notch cascade structure, the existing method usually tunes each notch as an independent unit, or adopts a simple serial optimization strategy. For performance constraint processing, the penalty function method or projection gradient method is generally used to maintain system stability by increasing the penalty term or projecting back to the feasible region when the constraint is violated.

[0004] However, the existing method has the following defects when dealing with fire satellite communication: the control sequence sensitivity and cross-coupling effect between each notch are not effectively modeled, leading to the non-commutativity problem of parameter adjustment. Specifically, when dealing with multiple interferences at adjacent frequencies, adjusting notch A first and then notch B, or adjusting notch B first and then notch A, will produce completely different frequency responses. This sequence dependence can cause a performance deviation of more than 20% under strong coupling conditions. The existing constraint processing mechanism cannot accurately maintain the zero impact protection of multiple frequencies in the discrete coding space. When protecting multiple life-critical frequencies such as fire main channel, Beidou positioning, PASS alarm, etc., the traditional post-correction strategy will cause a performance fluctuation of 0.5-1dB in the protected frequency, which may cause communication interruption under the condition of tight satellite link margin. SUMMARY

[0005] The application provides an anti-interference filtering method and device for fire emergency communication to solve the above problems in the prior art.

[0006] The technical scheme is characterized in that the application provides a first aspect of the application, which provides an anti-interference filtering method for fire emergency communication, and the encoding vector of a frequency response device is adjusted iteratively on line based on sequential exchange identification and geodetic step technology. Each iteration cycle comprises the following steps: reading a detection signal containing sequential exchange perturbation, applying the detection signal to the frequency response device, collecting the response of the frequency response device to obtain an observation data packet; based on the observation data packet and the detection signal, demodulation is performed to obtain a second-order cross-sensitivity describing the coupling effect between different components in the encoding vector; according to the second-order cross-sensitivity, a zero-impact subspace is constructed for a preconfigured set of locked frequency points, and an equal-constraint geodetic step calculation is performed in the zero-impact subspace to generate an encoding vector update amount; and the encoding vector update amount is applied to the current encoding vector to obtain the encoding vector of the next iteration cycle.

[0007] As a possible implementation manner of the first aspect, the zero-impact subspace is constructed, comprising the following steps: reading the demodulated first-order sensitivity and second-order cross-sensitivity, and extracting the locked first-order sensitivity and locked second-order sensitivity corresponding to the set of locked frequency points from the first-order sensitivity and the second-order cross-sensitivity; jointly constructing a nonlinear preservation condition for minimizing the impact of the encoding vector update on the set of locked frequency points by combining the locked first-order sensitivity and the locked second-order sensitivity; and determining the zero-impact subspace based on the nonlinear preservation condition.

[0008] As a possible implementation manner of the first aspect, the equal-constraint geodetic step calculation is performed to generate the encoding vector update amount, comprising the following steps: according to the first-order sensitivity and the second-order cross-sensitivity, a cost function gradient and a constraint index gradient of at least one performance index are derived; based on the cost function gradient and the constraint index gradient, an optimization problem with the encoding vector update amount as a variable is constructed in the zero-impact subspace, wherein: the objective function is to minimize the norm of the encoding vector update amount; the constraint conditions include: using the cost function gradient to ensure that the cost function decreases by a preset amount, and using the constraint index gradient to ensure that the performance index changes by zero; and solving the optimization problem to obtain the encoding vector update amount in the form of a continuous solution.

[0009] As a possible implementation manner of the first aspect, the optimization problem with the encoding vector update amount as a variable is constructed, comprising the following steps: the optimization problem is constructed as a quadratic programming problem, specifically: the quadratic norm of the encoding vector update amount is set as the objective function; and the preset decrease amount of the cost function, the zero change amount of the performance index, and the definition of the zero-impact subspace are uniformly converted into linear constraint conditions about the encoding vector update amount.

[0010] As a possible implementation manner of the first aspect, after obtaining the continuous solution form of the code vector update quantity by solving the optimization problem, the method further includes: mapping the continuous solution form of the code vector update quantity to a discrete code word space to obtain a discretized increment; identifying an integral error introduced by the mapping process; calling a second-order correction operator pre-constructed based on a locked second-order sensitivity to compensate for the integral error and generate a correction quantity; and integrating the discretized increment and the correction quantity to form the code vector update quantity to be applied.

[0011] As a possible implementation manner of the first aspect, the second-order cross-sensitivity describing the coupling effect between different components in the code vector is obtained by demodulation, including: reading at least one pair of code components in the code vector, and for the pair: designing and applying a first perturbation sequence corresponding to the perturbation of the first and second code components in sequence, and obtaining a first response; designing and applying a second perturbation sequence corresponding to the perturbation of the second and first code components in sequence, and obtaining a second response; and calculating the second-order cross-sensitivity representing the coupling effect between the pair of code components based on the difference between the first and second responses.

[0012] As a possible implementation manner of the first aspect, the second-order cross-sensitivity representing the coupling effect between the pair of code components is calculated based on the difference between the first and second responses, including: obtaining the difference between the first and second responses at a target frequency point; and reading and utilizing the perturbation amplitude applied to the first and second code components to normalize the difference to generate the second-order cross-sensitivity.

[0013] As a possible implementation manner of the first aspect, before designing and applying the first and second perturbation sequences, the method further includes: using historical second-order cross-sensitivity or an online updated proxy model to predictively evaluate the interaction strength of all pairs of code components in the code vector; and from the evaluation result, selecting at least one pair of code components with the highest interaction strength to form a test subset; wherein the first and second perturbation sequences are designed and applied only to the pairs of code components in the test subset.

[0014] As a possible implementation manner of the first aspect, the cost function gradient and the constraint index gradient for at least one performance index are derived, including: jointly determining the cost function gradient and the constraint index gradient for at least one performance index in cooperation with the first-order sensitivity, the second-order cross-sensitivity, and the online updated proxy model; wherein the online updated proxy model is a frequency-response-code approximate mapping constructed according to the code vectors of historical iteration periods and corresponding observation data packets.

[0015] The second aspect of the present application provides a tunable trap filter device, which is used for online iterative adjustment of a code vector of a frequency response device, and includes:

[0016] A detection and measurement module is configured to design a detection signal containing sequentially exchanged perturbations, apply the detection signal to the frequency response device, and collect a response of the frequency response device to obtain an observation data packet;

[0017] A sensitivity demodulation module is configured to demodulate, based on the observation data packet and the detection signal, a second-order cross-sensitivity describing a coupling effect between different components in the encoding vector;

[0018] An update amount calculation module is configured to construct a zero-impact subspace for the locked frequency point set according to the second-order cross-sensitivity, and perform an equal-constraint geodetic step calculation in the zero-impact subspace to generate an encoding vector update amount;

[0019] An encoding update module is configured to apply the encoding vector update amount to a current encoding vector to obtain an encoding vector of a next iteration period.

[0020] Beneficial effects, the present application is based on sequential exchange identification (SEI) and equal-constraint geodetic step (ICGP) technology, solves the reliable communication problem of satellite communication terminal in fire complex electromagnetic environment.

[0021] Specifically, by sequentially exchanging perturbation detection, the second-order coupling effect between the traps is accurately quantified, and the non-commutative problem of parameter adjustment is solved; a zero-impact subspace (ZIS) is constructed to ensure that the frequency points of Tianhong satellite, Beidou positioning, PASS alarm, etc. are strictly protected during the tuning process; and an equal-constraint geodetic step algorithm is used to find the optimal tuning path under the premise of meeting multiple performance constraints.

[0022] The method shortens the convergence time, improves the interference suppression capability, and at the same time keeps the performance of the locked frequency points stable. It supports L / S / Ku multi-band collaborative optimization and effectively improves the communication availability. Through the hierarchical protection mechanism, the protection priority can be dynamically adjusted according to the rescue task, and high-reliable communication protection is provided for fire rescue in extreme environment. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 The anti-interference filtering method for fire emergency communication is used to perform online iterative adjustment on the encoding vector, and a step flowchart of each iteration period is shown.

[0024] Figure 2 A flowchart for constructing a zero-impact subspace is shown.

[0025] Figure 3 A flowchart of the step after obtaining the encoding vector update amount in the form of a continuous solution of the optimization problem is shown.

[0026] Figure 4 A step diagram for calculating the second-order cross-sensitivity representing the coupling effect between the encoding components based on the difference between the first response and the second response is shown. DETAILED DESCRIPTION

[0027] In order to make persons skilled in the art better understand the technical scheme of the present application, the technical scheme in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by persons of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0028] The terms "first", "second", and the like in the specification of the present application and the above drawings are used to distinguish different objects, and are not used to describe a particular order. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, device, or product that includes a series of steps or units is not limited to the listed steps or units, but can optionally include other steps or units not listed or can optionally include other steps or units inherent to the process, method, product or end.

[0029] In this document, reference to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearance of the phrase in various places in the specification does not necessarily all refer to the same embodiment, nor does it necessarily refer to a particular embodiment that is independent of or alternative to other embodiments. It will be explicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0030] Embodiment one, this embodiment describes a general method framework for online iterative adjustment of the encoding vector of a frequency response device. Specifically, as shown in Figure 1 An anti-interference filtering method for fire emergency communication, based on sequential exchange identification and geodetic stepping technology, adjusts the encoding vector of a frequency response device online and iteratively, each iteration cycle including the following steps:

[0031] Step 1, read the pre-designed detection signal containing sequential exchange perturbation, apply the detection signal to the frequency response device, and collect the observation data packet obtained by the frequency response device in response.

[0032] In this embodiment, the encoding vector c is a multi-dimensional vector, each component c _iCorresponding to a tunable parameter or control level in a frequency response device (e.g. tunable filter). Instead of an independent external signal, a designed, amplitude-minimal perturbation sequence set U(k) is applied on the current encoding vector c(k), where k is the index of the current iteration period. Sequentially exchanged perturbations are components in U(k), which specifically refer to applying perturbations in two different sequences for at least one pair of encoding components (i, j): i first and j second, and j first and i second. The encoding vector with the perturbation sequence superimposed is applied to the frequency response device, and the observation data packet X(k) containing amplitude and phase information is collected by the receiving front-end of the device at specified measurement frequency points, including target notch frequency points and guard band frequency points.

[0033] Step 2, based on the observation data packet and the probe signal, demodulate to obtain the second-order cross-sensitivity describing the coupling effect between different components in the encoding vector.

[0034] This step extracts information beyond the traditional first-order sensitivity (i.e. gradient) from the observation data. Specifically, by correlating demodulation of the observation data packet X(k) with the perturbation sequence U'(k) in the probe signal, two pieces of information can be calculated: one is the first-order sensitivity matrix S(k), which describes the linear sensitivity of the device response to the perturbation of a single encoding component; the other is the second-order cross-sensitivity tensor C(k). The elements C _ij (f) are calculated by comparing the response differences generated by the two kinds of sequentially exchanged perturbations, i.e. i first and j second, and j first and i second, and are used to describe the strength of the nonlinear coupling or sequential non-commutative effect between components i and j. It can be said that S(k) reflects the local linear characteristics of the system, while C(k) reflects its local second-order nonlinear characteristics.

[0035] Step 3, according to the second-order cross-sensitivity, construct a zero-impact subspace for the set of locked frequency points, and perform an equal-constraint geodesic step calculation in the zero-impact subspace to generate the encoding vector update amount.

[0036] When the performance of some frequency points (e.g. the first notch f1) in the system has been debugged, they will be put into the set of locked frequency points F _lock In order not to destroy the performance of f1 when adjusting other frequency points (e.g. f2), this step uses the first-order sensitivity S _lock and the second-order cross-sensitivity C _lock related to F _lock to jointly construct a zero-impact subspace (ZIS). This subspace defines the encoding update direction Δc, along which moving will not affect the performance of F _lockThe impact of the mid-frequency point is theoretically zero or minimal. Furthermore, within the feasible directions defined by ZIS, equal-constrained geodesic stepping (ICGP) calculations are performed. The goal of ICGP is to find the optimal Δc, which must both reduce the total cost function J(k) and minimize other performance indicators (such as sheath insertion loss IL). _guard Constraints such as group delay fluctuation (GDR) are applied to maintain the current value, while minimizing the norm (i.e., step size) of Δc. The update amount Δc* of the encoding vector in the continuous solution form is then calculated.

[0037] Step 4: Apply the updated encoding vector to the current encoding vector to obtain the encoding vector for the next iteration. Alternatively, you can say that the updated encoding vector is applied to the current encoding vector.

[0038] After obtaining the update amount Δc* of the encoding vector in continuous solution form, it needs to be converted into discrete encoding that can be executed on physical devices. In this embodiment, Δc* is mapped to the nearest discrete codeword through rounding and other methods to obtain the discretized increment ~Δc. Since rounding introduces errors, which may cause the protection of locked frequency points to fail, a correction operator based on second-order cross-sensitivity is further used to compensate for the rounding error and generate the update amount Δc. _hat Based on this, the update amount is applied to the current encoding vector: c(k+1) = c(k) + Δc _hat This yields an optimized new encoding vector for the next iteration cycle.

[0039] Another embodiment of this application provides an adjustable notch filter device for online iterative adjustment of the encoding vector of a frequency response device, comprising: a detection and measurement module for performing: designing a detection signal containing sequentially exchanged perturbations, applying the detection signal to the frequency response device, and acquiring its response to obtain an observation data packet; a sensitivity demodulation module for performing: demodulating the second-order cross-sensitivity based on the observation data packet and the detection signal to obtain a second-order cross-sensitivity describing the coupling effect between different components in the encoding vector; an update amount calculation module for performing: constructing a zero-influence subspace for the locked frequency point set based on the second-order cross-sensitivity, and performing iso-constrained geodesic step calculations within the zero-influence subspace to generate an encoding vector update amount; and an encoding update module for performing: applying the encoding vector update amount to the current encoding vector to obtain the encoding vector for the next iteration cycle.

[0040] Example 2: This example provides a detailed description of step 2 in Example 1. This example offers a specific method for measuring the nonlinear coupling effect between multiple adjustable parameters, which can be implemented online.

[0041] To address the ineffectiveness of traditional first-order methods in handling sequence-dependent nonlinear interferometry issues such as the disruption of f1 notch filtering by adjusting f2, this embodiment employs a technique to detect the sequence noncommutation effect between coded components. The sequence noncommutation effect refers to the different system responses produced by applying perturbations to coded components in different orders. This effect originates from the nonlinear interaction between coded components, and second-order cross-sensitivity is a quantitative representation of the sequence noncommutation effect.

[0042] Specifically, the process of demodulation to obtain the second-order cross-sensitivity describing the coupling effect between different components in the encoded vector includes:

[0043] For at least one pair of coded components in the coded vector, a first perturbation sequence is designed and applied, the first perturbation sequence corresponding to applying a perturbation to the first coded component first and then applying a perturbation to the second coded component, and a first response is obtained;

[0044] Design and apply a second perturbation sequence corresponding to applying a perturbation to the second coded component first and then applying a perturbation to the first coded component, and obtain a second response.

[0045] In short, the first perturbation sequence corresponds to the perturbation of the first and second coded components being applied sequentially, and a first response is obtained; the second perturbation sequence corresponds to the perturbation of the second and first coded components being applied sequentially, and a second response is obtained.

[0046] For example, suppose the current encoded vector is c, and we are concerned with the coupling between the i-th and j-th components. The first perturbation sequence (denoted as ij) is applied by applying a small increment Δc to the current encoded vector c. _i After the system stabilizes, another small increment Δc is applied. _j At this point, the final encoded state of the system is c + Δc _i +Δc _j The system response measured under these conditions (such as the output amplitude A(f|c+Δc) at a specific frequency point f) _i +Δc _j This is the first response. The second perturbation sequence (denoted as ji) is applied in the opposite way: Δc is applied on top of c. _j Then apply Δc _i The final encoded state is c + Δc _j +Δc _i The system response A(f|c+Δc) measured under this state _j +Δc _i This is the second response.

[0047] It should be noted that Δc _i and Δc _jIt is a perturbation vector that has non-zero values ​​only on the corresponding component. In some embodiments, in order to embed the perturbation sequence into the normal measurement process, it can be designed into different, non-overlapping time windows and marked with weak orthogonal codes for differentiation and demodulation at the receiver. The amplitude of the perturbation |Δc _i |and|Δc _j | is usually set to a very small value, such as 1-2 least significant bits (LSBs) of the digital control, to ensure that the local nonlinearity is detected and that it does not cause perceptible interference to the normal operation of the equipment.

[0048] Based on this, the second-order cross sensitivity, which characterizes the coupling effect between the coding components, is calculated based on the difference between the first and second responses.

[0049] Specifically, such as Figure 4 As shown, the calculation steps are as follows: obtain the difference between the first response and the second response at the target frequency point; use the perturbation amplitude applied to the first coding component and the second coding component to normalize the difference and generate the second-order cross sensitivity.

[0050] This process can be quantified using the following formula:

[0051] C _ij (f)=[A(f|c+Δc _i +Δc _j )-A(f|c+Δc _j +Δc _i )] / (2*m _i *m _j );

[0052] Among them, C _ij (f) represents the second-order cross-sensitivity of coded components i and j at frequency point f. Its value reflects the sensitivity of the operation order of i and j. If the system is linear, this value should be approximately zero; A(f|c _vec ) is in the encoding vector c _vec At that time, the system output amplitude response at frequency point f; Δc _i and Δc _j Let m be the perturbation vectors applied to components i and j, respectively; _i For the perturbation Δc _i The magnitude, i.e., |Δc _i |;m _j For the perturbation Δc _j The magnitude, i.e., |Δc _j |

[0053] It can be seen that C _ij(f) represents the difference between the final responses of two different perturbation paths, directly reflecting the noncommutativity of the system. Normalization eliminates the influence of the magnitude of the perturbation itself on the result, making it a stable system characteristic parameter that can be used for subsequent calculations. Thus, this invention obtains second-order coupling information beyond the first-order gradient, providing important input for subsequent zero-influence subspace construction and accurate update calculations.

[0054] Example 3 describes another preferred method for obtaining second-order cross sensitivity.

[0055] Understandably, for a system with N coded components, listing all N(N-1) / 2 component pairs and performing Sequence Exchange Identification (SEI) increases the measurement overhead with the square of N. When N is large, this may lead to excessively long iteration cycles or the total energy of the injected perturbations exceeding the imperceptibility threshold. Therefore, the sparse targeted measurement strategy in this embodiment reduces measurement complexity while ensuring the acquisition of important information.

[0056] The method steps, prior to the design and application of the first and second perturbation sequences, are as follows:

[0057] Step 1: Using historical second-order cross-sensitivity or an online-updated surrogate model, predictively evaluate the interaction strength of all possible coding component pairs in the coding vector. This estimates which component pairs have the strongest coupling without performing comprehensive physical measurements. Specifically, this evaluation can be performed in at least one of the following ways: one way is based on historical second-order cross-sensitivity. The system can maintain a historical cross-sensitivity tensor C. _hist For example, C _hist It can be an exponentially weighted moving average of C(k) measured over the past M iterations. For any pair of components (i,j), its historical interaction strength can be defined as Strength(i,j) = |C _hist [i,j]|. This method takes advantage of the time continuity of the system's characteristics, meaning that strongly coupled components are likely to remain strongly coupled in the short term.

[0058] Another approach is based on an online-updated surrogate model. The surrogate model P(k) is a data-driven mathematical model, such as a multivariate polynomial, Gaussian process regression, or neural network model, trained on historical {encoded vector, observed data packet} sample pairs to approximately simulate the complex mapping relationship between the frequency response device and the encoded vector c to the output response X. In this embodiment, the second-order partial derivative of the surrogate model P(k) at the current operating point c(k) can be calculated, i.e., the off-diagonal elements H of the Hessian matrix. _P [i,j]=d 2 X / (dc _i DC _jThe absolute value of the element |H _P [i,j]| can be used as a prediction of the interaction strength of component pairs (i,j). This not only utilizes historical information but also, based on the model's generalization ability, can predict the coupling strength of component pairs that have not been directly measured recently.

[0059] Step 2: From the evaluation results, select at least one coded component pair with the highest interaction strength to form the subset to be tested. After obtaining the predicted interaction strength Strength(i,j) of all component pairs in Step 1, sort them. The subset to be tested can be filtered according to a preset strategy (also known as a measurement whitelist). For example, the filtering strategy can be:

[0060] Top-K strategy: Directly select the K component pairs with the highest interaction strength. The parameter K can be a fixed value (e.g., K=5) or a percentage of the total number of pairs (e.g., 10%). The value of K can be chosen to balance system resources (e.g., available measurement time) and identification accuracy.

[0061] Threshold strategy: Select all interaction strengths Strength(i,j) that exceed a certain preset threshold Th. _strength The component pairs. This threshold can be dynamically adjusted based on historical noise levels and the desired identification signal-to-noise ratio.

[0062] Step 3, in which the first and second perturbation sequences are designed and applied only to the coded component pairs in the subset to be tested. In the current iteration period k, the SEI measurement method of Example 2, which includes the ij and ji sequences, will only be applied to those component pairs in the subset to be tested selected in Step 2. For all unselected component pairs, the physical measurement of their second-order cross sensitivity will be skipped in this period, and their corresponding C _ij The (k) value can be carried over from the previous period or filled with the predicted value from the surrogate model. Through the above steps, the system focuses limited measurement resources on the most strongly nonlinearly coupled components, avoiding redundant probing on a large number of weakly coupled component pairs. Without sacrificing key identification performance, the measurement overhead of the SEI method is reduced from O(N) to O(N). 2 The value is reduced to a level close to O(K), where K is much smaller than N. 2 .

[0063] In some alternative implementations, a hybrid evaluation and scheduling strategy can be employed. For example, global prediction can be primarily relied upon using a surrogate model, but a few key pairs exhibiting strong coupling in historical data can be forcibly included in the test subset regardless of model predictions, thereby increasing the robustness of identification. The scheduling strategy can also introduce randomness, such as a roulette wheel selection of all component pairs, where the probability of each component pair being selected is proportional to its predicted interaction strength. This ensures that even weakly coupled pairs have a chance to be detected occasionally, accommodating potential slow drift in the system.

[0064] Example 4: This example provides a detailed description of step 3 in Example 1, illustrating how the present invention achieves zero-impact protection of optimized frequency points while simultaneously satisfying multiple performance constraints when calculating the coding update amount.

[0065] Understandably, traditional optimization methods, when adjusting the encoding vector, often focus only on reducing the current principal cost function. This approach can easily disrupt other performance metrics that already meet requirements, leading to repeated oscillations in the system state. This embodiment provides a method for finding geodesics on constrained manifolds, which can solve this technical problem. This process can be specifically divided into two parts.

[0066] The first part constructs the zero-impact subspace (ZIS), which defines a safe feasible region for the coding vector update Δc, ensuring that Δc does not affect the locked frequency set F. _lock It has an unintended impact.

[0067] Specifically, constructing the zero-impact subspace includes: extracting the locking first-order sensitivity and locking second-order sensitivity corresponding to the locked frequency set from the first-order sensitivity and second-order cross-sensitivity; jointly constructing a nonlinear preservation condition that minimizes the impact of the coding vector update on the locked frequency set by combining the locking first-order sensitivity and the locking second-order sensitivity; and determining the zero-impact subspace based on the nonlinear preservation condition. In other words, this step can also be: reading the demodulated first-order sensitivity and second-order cross-sensitivity, and extracting the locking first-order sensitivity and locking second-order sensitivity corresponding to the locked frequency set from them; jointly constructing a nonlinear preservation condition that minimizes the impact of the coding vector update on the locked frequency set by combining the locking first-order sensitivity and the locking second-order sensitivity; and determining the zero-impact subspace based on the nonlinear preservation condition, such as... Figure 2 As shown.

[0068] Furthermore, the nonlinearity preservation condition consists of a first-order preservation term characterizing the linear effect and a second-order compensation term characterizing the nonlinear coupling compensation. The mathematical expression for this nonlinearity preservation condition is:

[0069] S _lock *Δc+(1 / 2)*ΔcT *H _lock *Δc≈0; where: Δc is the update amount of the encoding vector to be solved, which is a column vector; S _lock To lock the first-order sensitivity matrix, each row corresponds to F _lock The first-order partial derivative of a frequency point with respect to each coded component, S _lock *Δc is the first-order preservation term, which predicts the linear effect of Δc on the locked frequency; H _lock The Hessian approximation matrix constructed based on the second-order locking sensitivity is a symmetric matrix; Δc T (1 / 2)*Δc is the transpose of Δc. T *H _lock *Δc is the second-order compensation term, which uses the second-order information measured in Example 2 to compensate for and predict the nonlinear coupling effect caused by Δc; 0 is the zero vector. H _lock The construction can be based on the C measured in Example 2. _lock (i.e., C) _ij (f) where f belongs to F _lock (a subset of the set at time). For example, the element at position (i,j) can be set to H. _lock [i,j]=(C _ij (f _lock )+C _ji (f _lock The equation )) / 2, through symmetry processing, can better approximate the local quadratic form of the system. This nonlinear equation defines a surface (or manifold) in high-dimensional space, where all Δc values ​​on this manifold keep the response at the locked frequency approximately invariant. This manifold and its tangent space constitute the generalized zero-influence subspace. In practical calculations, its first-order approximation, S, is often used. _lock The linear subspace defined by Δc=0 (i.e., S) _lock The zero space is the core of ZIS, while the second-order terms are used for subsequent corrections or as constraints in nonlinear optimization.

[0070] The second part involves performing equal-constraint geodesic step (ICGP) calculations. Within the safe zone defined by ZIS, this part seeks the optimal step Δc.

[0071] Specifically, performing constrained geodesic step calculations to generate the encoding vector update includes: deriving the gradient of the cost function and the gradient of the constraint index for at least one performance index based on the first-order sensitivity and the second-order cross-sensitivity; constructing an optimization problem with the encoding vector update as the variable in the zero-influence subspace, which seeks an encoding vector update that simultaneously satisfies the following conditions: the cost function achieves a predetermined decrease, the predicted change of at least one performance index is zero, and its own norm is minimized; solving the optimization problem to obtain the encoding vector update in the form of a continuous solution.

[0072] In other words, the steps for performing isoconstrained geodesic step calculations to generate the encoding vector update amount can also be as follows: based on the first-order sensitivity and the second-order cross-sensitivity, derive the gradient of the cost function and the gradient of the constraint index for at least one performance index; based on the gradients, construct an optimization problem with the encoding vector update amount as the variable in the zero-influence subspace, where: the objective function is to minimize the norm of the encoding vector update amount; the constraints include: using the gradient of the cost function to ensure that the cost function decreases by a preset amount, and using the gradient of the constraint index to ensure that the change in the performance index is zero; solve the optimization problem to obtain the encoding vector update amount in the form of a continuous solution.

[0073] Specifically, the gradient of the cost function and the gradient of the constraint metric for at least one performance index are derived, including the co-order first-order sensitivity S(k), the second-order cross-sensitivity C(k), and the online-updated surrogate model P(k), and the gradient of the cost function g is jointly determined. _j With respect to the gradient g of the constraint index for at least one performance metric _iL g _GDR In this context, the online-updated surrogate model is a frequency response-coded approximation mapping constructed based on the encoded vectors of historical iteration cycles and the corresponding observed data packets. For example, g _j It not only relies on the direct gradient given by S(k), but may also be corrected by C(k) and P(k) to obtain a more accurate estimate of the descent direction at the current nonlinear operating point.

[0074] Among them: the first-order sensitivity S(k) provides the direct linear influence of each coded component on the system response; the second-order cross sensitivity C(k) is used to correct the gradient bias caused by nonlinear coupling; the surrogate model P(k) is a frequency response-coded approximation mapping constructed based on the coded vector of the historical iteration period and the corresponding observation data packet, which is used to provide global trend prediction.

[0075] Furthermore, construct the following optimization problem: minimize ||Δc|| 2 ,constraint:

[0076] Constraint 1, g _j T*Δc≤-η;Constraint 2,g _iL T *Δc=0; Constraint 3, g _GDR T *Δc=0; Constraint 4, S _lock *Δc=0;

[0077] Wherein, the objective function minimizes||Δc|| 2 The goal is to find the solution with the minimum norm, which geometrically corresponds to finding the shortest step path. Constraint 1 requires that Δc must reduce the cost function J by at least a predetermined small amount η (η>0). Constraints 2 and 3 require that the direction of Δc must be aligned with the performance index IL. _guard The gradient direction is orthogonal to that of GDR, ensuring that its predicted change is zero. Constraint 4 then strictly restricts the search space to the linear approximation space of ZIS.

[0078] Geometrically, this solution process is equivalent to finding the shortest geodesic path (determined by the objective function and all constraints) on an isoconstrained manifold (defined by constraints 2 and 3) that points towards the descent direction of the cost function (defined by constraint 1). By solving this optimization problem (usually a quadratic programming problem), the updated encoding vector Δc* in the form of a continuous solution, which is both efficient and safe, can be obtained.

[0079] Example 5 describes the ICGP calculation steps in Example 4, illustrating how to transform the abstract optimization problem into a computable quadratic programming problem, and how to securely map the obtained continuous solution onto discrete codes executable by physical devices.

[0080] After constructing an optimization problem with the encoding vector update amount Δc as the variable in Example 4, the specific solution and application process of this problem is as follows:

[0081] In order for optimization problems to be processed by standardized and efficient numerical optimization solvers, they need to be constructed as mathematical problems with a specific form. In this embodiment, preferably, the optimization problem is constructed as a quadratic programming (QP) problem.

[0082] Specifically, the steps include: setting the quadratic norm of the encoding vector update as the objective function; unifying the definitions of the preset decrease in the cost function, the zero change in the performance index, and the zero-influence subspace into linear constraints on the encoding vector update; and thus, constructing the optimization problem as a quadratic programming problem through the setting of the objective function and the transformation of the linear constraints.

[0083] The standard form of this quadratic programming problem can be written as: minimize(1 / 2)*Δc T *P*Δc+q T*Δc; Constraints: G*Δc≤h, A*Δc=b; In the context of this invention, specifically:

[0084] The objective function is set, specifically, to minimize ||Δc|| 2 We can set P = 2 * I (where I is the identity matrix), and q is a zero vector. The objective function then becomes Δc. T *Δc, which is the square of the second norm of Δc, is minimized by the equivalent of minimizing ||Δc||.

[0085] The transformation of linear constraints, specifically, means that all constraints in Example 4, including cost function descent, zero change in performance metrics, and zero-influence subspace (first-order approximation), are essentially linear and can be integrated into the constraint matrix of the aforementioned QP. For example: g _j T *Δc≤-η can be directly used as part of G*Δc≤h. _iL T *Δc=0, g _GDR T *Δc=0 and S _lock *Δc=0 can be uniformly integrated into the form A*Δc=b, where b is the zero vector.

[0086] In this way, the original optimization problem is transformed into a convex quadratic programming problem. It is understandable that mature and computationally efficient algorithms exist for solving convex QP problems (such as the interior-point method and the active-set method), which can find the global optimum in a finite time. This is crucial for the application scenarios of this invention, which require online, rapid iteration. Solving this QP problem yields the encoding vector update amount Δc* in the form of a continuous solution.

[0087] Since the encoding vectors of physical frequency response devices are typically discrete (e.g., digital control words composed of integers), while the output Δc* of the QP solver is continuous, discretization is necessary. Simple rounding operations would violate the fine constraints satisfied by Δc* in continuous space, particularly its zero-influence characteristic on locked frequency points. Therefore, this embodiment provides a fine discretization method incorporating second-order bias correction.

[0088] Specifically, such as Figure 3 As shown, after solving the optimization problem to obtain the continuous solution form of the encoding vector update quantity, the process further includes: mapping the continuous solution form of the encoding vector update quantity to the discrete codeword space to obtain the discretization increment; identifying the rounding error introduced by the mapping process; and using a second-order correction operator based on the second-order locking sensitivity to compensate for the rounding error and generate the correction quantity; and integrating the discretization increment and the correction quantity to form the final encoding vector update quantity to be applied.

[0089] This process can be broken down into the following steps:

[0090] Step one: Map to the discrete codeword space, specifically by calculating the theoretically new coding vector c. _theory =c(k)+Δc*. Let c _theory Each component is rounded to its nearest valid discrete codeword, resulting in a new discretized coding vector c. _discrete =Round(c _theory Therefore, the discretization increment ~Δc=c is obtained. _discrete -c(k).

[0091] Step two, identify the rounding error, specifically the rounding error introduced by the mapping process, which is defined as the difference between the continuous solution and the discrete solution: ε _round =Δc*-~Δc. Error vector ε _round This is the root cause of constraint deviation.

[0092] Step 3: Activate the second-order correction operator for compensation. Specifically, in order to offset ε... _round For locked frequency set F _lock The unexpected impact needs to be calculated to determine the corrective force Δc. _corr The second-order correction operator K2 is the mechanism used to generate this correction amount. This operator utilizes the S constructed in Example 4. _lock and H _lock Find the discrete correction vector Δc (usually with a very small step size). _corr This makes the final combined increment (~Δc+Δc) _corr This can satisfy the original nonlinearity preservation condition to the greatest extent. That is, Δc _corr The selection objective is to minimize:

[0093] ||S _lock *(~Δc+Δc _corr )+(1 / 2)*(~Δc+Δc _corr ) T *H _lock *(~Δc+Δc _corr In practice, due to Δc _corr Typically, the search is limited to a few codewords (such as -1, 0, +1), which is a small-scale combinatorial optimization problem that can be solved quickly.

[0094] Step four: Integrate to form the final update amount. Specifically, integrate the discretized increment with the calculated correction amount to form the final updated encoding vector to be applied: Δc _hat =~Δc+Δc _corr The encoding vector for the next iteration cycle is c(k+1) = c(k) + Δc _hat .

[0095] As an alternative and simpler implementation, the second-order correction operator can be simplified to a first-order correction operator, with the sole objective of minimizing the linear influence term, i.e., finding Δc. _corr To minimize ||S _lock *(~Δc+Δc _corr Although nonlinear compensation is ignored, it still provides better performance than direct rounding without compensation in scenarios with extremely limited computing resources.

[0096] Example 6 describes the preparatory, foundational, and managerial steps involved before, during, and after the identification and optimization cycle.

[0097] S1, initialization and scheduling are completed. Specifically, before starting online iterative optimization, the system performs a series of initialization operations.

[0098] The system reads the initial target frequency set F input by the user. _target , Belt frequency set F _guard And the initial coding vector c(0). Perform a full spectrum scan to acquire the initial observation data packet X(0), including amplitude and phase information at each frequency point. Based on X(0), calculate the initial guard band insertion loss IL. _guard (0) and group delay variability (GDR) and other baseline performance metrics. Establish reference mapping B _ref This is used for subsequent calculations of relative loss. A rough initial surrogate model P(0) can be constructed based on c(0) and X(0).

[0099] According to F _target F _guard Based on the system's available time, power, and other resource constraints, a measurement scheduling table M(0) for the first cycle is generated. M(0) details the frequency points to be measured, the allocated time windows, and whether dual-tone signal injection is permitted.

[0100] Specifically, read the frequency set F of the protective belt. _guard Mapping with the initial test B _ref The uncertainty U(f) at each frequency point is calculated on the surrogate model P(0) to obtain the candidate priority. Based on the uncertainty U(f) and the available measurement time slots (time resources T), the candidate priority is determined. _Avail Select the subset of the guard band with the largest information gain (representative frequency point subset F). _guard_sub ) and the corresponding time window (the set of measurement time windows W) _meas ), where F is the target frequency set. _target Assign high-priority monitoring windows (target window W) _target This ensures that the depth of the notch can be stably estimated and synchronized in the future.

[0101] Read the initial noise estimate (noise variance N(0)) and the system non-perceptible threshold (non-perceptible threshold E). _inaud ), to obtain the upper limit of the single-period perturbation energy (energy budget B) _pert According to B) _pert W _meas and W _target Plan the gated window (gating function win(t)) and duty cycle D _pert This is used for subsequent orthogonal perturbation embedding. Depending on regional regulations and equipment limitations, it is determined whether two-tone injection and short-chirped scanning are permitted (injection license flag). _iMD Flag _chirp ).

[0102] Summary F _guard_sub W _meas W _target , win(t), Flag _iMD Flag _chirp Output the first cycle measurement schedule table M(0), which contains the frequency-time slot-gating-injection permission quadruple.

[0103] Specifically, in each iteration cycle, in addition to performing SEI in Example 2 to obtain second-order information, the system also needs to obtain basic first-order sensitivity and evaluate various performance indicators in real time.

[0104] To identify the first-order sensitivity matrix S(k), the system performs a certain step for each coded component c. _i Generate mutually orthogonal perturbation sequences with extremely small amplitudes (e.g., using Walsh-Hadamard codes). Superimpose the perturbation sequences onto c(k) and acquire the response X(k). By correlating and demodulating X(k) with each orthogonal perturbation sequence, the first-order sensitivity S(i,f) of all components at all frequencies of interest can be efficiently calculated in parallel.

[0105] Using the acquired X(k), various performance indicators for the current period are calculated in real time. For example, the sheath insertion loss IL _guard (k) By comparing X(k) with the reference map B _ref In F _guard The group delay ripple (GDR(k)) is calculated by the amplitude difference across the frequency band. _guard Phase data within the frequency band is estimated by differential calculation. These real-time metrics collectively constitute the cost function J(k) and serve as constraint inputs for ICGP computation.

[0106] S2, perform orthogonal perturbation sensitivity identification and online constraint estimation. Specifically, based on c(k), M(k), and P(k), generate a perturbation sequence d with minimal amplitude and pairwise orthogonality for each notch level i. _i[n] (such as ±1 sequence or orthogonal code), set the perturbation amplitude a. _pert Together with the gate control window win(t), we form the perturbation plan U(k) for this period. U(k) = {d} _i [n],a _pert win(t)}, i=1..N _level Constraint: a _pert It is far below the upper limit of the service power, and win(t) is interleaved with the receiving sampling time slot.

[0107] In a preferred embodiment, the orthogonal perturbation and measurement window design involves designing an orthogonal perturbation sequence set and gating plan for each notch stage without altering the service awareness of the encoded vector c(k), generating a periodic perturbation plan U(k) for use in observation execution and sensitivity demodulation.

[0108] For example, select orthogonal codes (orthogonal sequence family D={d}) from the codebook library. _i [n]}), calculate the upper bound of the cross-correlation between any two sequences (leakage limit ε). _corr Assign non-overlapping or low-correlation subsets to different notch levels and establish a mapping (sequence-level mapping Map). _seq -level).

[0109] Read the noise statistics N(k-1) of the previous cycle and the imperceptible threshold E _inaud Calculate the perturbation amplitude a in this period. _pert The feasible interval. In a _pert_range Within the range, select the point that maximizes the demodulation signal-to-noise ratio / invisible ratio, and determine a. _pert Synthetic gating function win(t) and scheduling window W _meas W _target Generate perturbation-acquisition alignment table Align _table The system checks the overlap between the perturbation window and the business-critical window; if the overlap exceeds a threshold, it automatically shortens the window or shifts it.

[0110] Set the target frequency points F _target With the frequency set F of the protective belt _guard_sub Clustering based on nearest neighbor frequency / phase stability forms frequency point groups G. _freq According to G _freq With the length T of this period _cycle Define the rotation sequence (rot table) _plan ).

[0111] Output perturbation plan U(k) = {D, a _pert Align _table Map _seq -level,Rot _plan}

[0112] Furthermore, according to U(k) in F _target ∪F _guard Frequency point set and specified time window acquisition X _raw After synchronization and denoising, X(k) is obtained (containing A). _k (f), φ _k (f)); for X _raw (k) Estimate the noise statistics N(k) (e.g., variance, correlation time). X(k) = {A _k (f),φ _k (f)},f∈F _target ∪F _guard N(k)={var _A (f),var _φ (f)}. Using X(k) and the perturbation sequence d _i [n] Perform code-domain correlation demodulation to estimate multi-level sensitivity:

[0113] Amplitude sensitivity S _A (i,f)≈Corr(A _k (f),d _i [n]) / a _pert Phase sensitivity S _φ (i,f)≈Corr(φ _k (f),d _i [n]) / a _pert The combination yields S(k), whose elements S(i,f) = {S _A (i,f),S _φ (i,f)}.

[0114] In a preferred embodiment, correlation demodulation and sensitivity matrix estimation involves performing code-domain correlation demodulation on the acquired observation data packets X(k) to generate a multi-level sensitivity matrix S(k), and evaluating orthogonality and calibration bias to provide reliable gradient information for subsequent optimization.

[0115] Specifically, the observation data packet X(k) and the sequence family D in the perturbation scheme U(k) are read, and for each level i and each frequency point f, the correlation quantity (amplitude correlation R) is calculated. _A (i,f), phase correlation R _φ (i,f)). Evaluate the cross-correlation residuals (cross-correlation matrix C) _cross ) and the upper limit of leakage ε _corr Compare and mark suspicious frequencies or levels. Based on the gain and phase offset of the amplitude / phase channel (channel calibration factor Cal... _A (f) Cal _φ (f)), correcting related quantities. Input: R _A R _φ Cal_A Cal _φ Output: Corrected R _A '、R _φ '. The relevant quantities are calculated according to the perturbation amplitude a. _pert Normalization yields the single-step sensitivity estimate S. _A_raw (i,f), S _φ_raw (i,f). For S _A_raw S _φ_raw Robust averaging and outlier removal (robust statistical output S) _A_rob S _φ_rob Assemble a multi-level, multi-frequency sensitivity matrix S(k) and output the quality index (demodulated signal-to-noise ratio SNR). _demod ).

[0116] Furthermore, in an exemplary embodiment, online metric estimation and cost function construction are performed. Four metrics are calculated using X(k) and B. _ref calculate:

[0117] Target notch intensity A _t (k): A _t (k)=Σ f∈F_target A _k (f);

[0118] Insertion loss IL of the protective belt _guard (k): IL _guard (k)=max f∈F_guard [A _ref (f)-A _k (f) (dB caliber; A) _ref (f) From B _ref );

[0119] Group delay fluctuation GDR(k): for F _guard Given the phase within the phase, calculate the discrete derivative τ(f)≈-Δφ / Δ(2πf); GDR(k)=max(τ(f))-min(τ(f));

[0120] Intermodulation distortion IMD(k): If M(k) enables two tones, measure the power at 2f1-f2 and 2f2-f1 and normalize it to obtain IMD(k).

[0121] Based on this, the cost function is constructed as: J(k) = w1A _t (k)+w2IL _guard (k)+w3GDR(k)+w4IMD(k). Simultaneously set the hard / soft threshold set C={IL _max GDR _max IMD _max} and weights {w1..w4}.

[0122] S3 performs constrained discrete updates, measurement scheduling, and agent iteration. Specifically, based on the input data S(k), J(k), and c(k), it performs small-step projection block coordinate descent in the discrete code domain to obtain the candidate increment Δ. _c via IL _guard After GDR / IMD constraint projection and confidence region limitation, the output data c(k+1) is obtained. Based on the expected return of c(k)-c(k+1) and the noise distribution of X(k), the output data M(k+1) (next cycle measurement point / time slot / perturbation gating) and the output data P(k+1) (online calibration surrogate model, facilitating sparse measurement and acceleration) are updated. c(k+1), M(k+1), and P(k+1) will flow back to S2 to enter the next cycle.

[0123] In an exemplary embodiment, the selection of active blocks and the setting of the confidence region involve constructing a contribution metric from the sensitivity matrix S(k) and the cost function J(k), selecting the set of coding components that should be updated most, and setting the confidence region ρ(k) and the maximum codestep LSB. _max To ensure safe convergence.

[0124] Specifically, based on the sensitivity of S(k) and the noise level of N(k), one or two coding components that contribute the most to J(k) are selected to form the activity set I(k); the confidence region ρ(k) and the maximum codestep LSB are set according to N(k) and historical convergence. _max I(k) = argtop - 2 _i ||dJ / dc _i ||,ρ(k)∝1 / sqrtvar _A .

[0125] In one possible example, according to S(k) on A _t IL _guard The first-order effects of GDR and IMD are used to construct a gradient approximation (contribution g). _i =dJ / dc _i ). For g _i Perform confidence weighting (confidence weighting gradient: g) _i '=g _i / σ _i ), σ _i From noise statistics N(k) and SNR _demod Select |g _i The 1-2 largest encoded components form the activity set I(k); if there are strongly coupled components, diversity constraints are applied to avoid redundancy in the same direction. Based on N(k) and the historical backtracking rate Rate... _backtrack Set step size limit (maximum code steps LSB) _max ) and the confidence region ρ(k).

[0126] Furthermore, linearized nearest neighbor calculation and candidate increment generation are performed. Within a small neighborhood, S(k) is used to make a first-order approximation of J(k), and discrete candidate increments Δ are calculated on the active block I(k). _c :

[0127] Linearization: ΔJ≈g T *Δ _c g is obtained by combining S(k) with the sensitivity of each index to c;

[0128] Constraints: IL _guard (k+1)≤IL _max GDR(k+1)≤GDR _max IMD(k+1)≤IMD _max Local feasibility can be determined by using a linear approximation or with the help of P(k);

[0129] Solve for: in {-LSB _max ,…,+LSB _max Within the discrete set}, search for the ΔJ that minimizes ΔJ and satisfies the constraints. _c (A projection-based greedy algorithm or a small-scale integer search can be used).

[0130] For example, the linearized nearest neighbor solution and candidate increment generation generate candidate increments Δ that satisfy multiple constraints on the activity set I(k) based on first-order approximation and feasibility prediction. _c .

[0131] Specifically, small probes are performed on each encoded component of I(k) to verify the linear hypothesis error (approximation error Err). _lin If Err _lin If the threshold is exceeded, the LSB will decrease. _max Or augment local samples. In the discrete set {-LSB} _max ,…,+LSB _max The approximate cost change (cost increment ΔJ) can be calculated by enumerating or using a greedy strategy. _lin Eliminate candidates that would invalidate C. Input: I(k), S(k), J(k), C, LSB _max Output: Candidate set Cand={Δ _c m}. Predict each Δ using the surrogate model P(k). _c m For IL _guard Trends in GDR and IMD (Feasibility Confidence Conf) _feas ), prune high-risk candidates, and select the final Δ _c .

[0132] Furthermore, constrained projection and encoding update and prediction improvement evaluation are performed on Δ _c Perform feasible region projection Π _c (If any threshold is violated, the step size is reduced), and the result is mapped to the nearest realizable codeword (discrete rounding) to obtain c(k+1); the prediction improvement ΔJ is evaluated based on the linearized model. _pred (k). c(k+1)=Round(Π) _c (c(k)+Δ _c )).

[0133] For example, the evaluation of constrained projection with encoding update and prediction improvement is based on Δ _c Perform multi-constraint projection and discrete mapping to obtain the updated encoding c(k+1); evaluate the prediction improvement ΔJ. _pred (k).

[0134] Specifically, if Δ _c Make any constraint (IL) _max GDR _max IMD _max If the constraint projection fails, then the projection will be re-projected in order of priority (constrained projection Π). _c Input: Δ _c C, Output: Feasible increment Δ _c '. c(k) + Δ _c 'Mapping to the nearest realizable codeword (discrete mapping Round)' _discrete (·)), and apply slight jitter near the boundary to avoid periodic back-and-forth switching. Input: c(k), Δ _c Output: c(k+1). Improved ΔJ based on linear nearest neighbor model output prediction. _pred (k), in the next observation period, J(k+1) is used for reconciliation to obtain the difference (predicted - measured difference ΔJ). _gap It is used for step reduction or model correction.

[0135] Furthermore, adaptive scheduling and online agent correction (closed-loop efficiency and non-perceptibility) are performed using X(k) and ΔJ. _pred The step size information of (k), N(k) and c(k)-c(k+1) is used to update the measurement plan M(k+1) for the next cycle (selecting the frequency point and time slot with the most information gain, perturbation amplitude and duty cycle); the new sample pair {c(k),X(k)} is included in the training set of P(k) to obtain the updated P(k+1).

[0136] For example, the scheduling adaptation and agent online correction update the measurement scheduling table M(k+1) and agent model P(k+1) for the next period based on the observed and predicted benefits of the current period, in order to reduce measurement latency and maintain imperceptible constraints.

[0137] Specifically, the information gain IG(f) of each candidate frequency point is calculated, and the representative guard band frequency point subset F of the next cycle is selected. _guard_sub Priority. Input: X(k), P(k), ΔJ _pred (k), Output: F _guard_sub Based on perturbation energy budget B _pert Unperceived threshold E _inaud Based on the noise statistics N(k) of the previous cycle, the perturbation amplitude and duty cycle (amplitude a) are redistributed according to task priority. _pert_next Occupying space D _pert_next ), and rearrange the time windows (time window set W) _meas_next W _target_next The surrogate model P(k) is updated with the new sample pair {c(k),X(k)}, using the forgetting factor λ. _forget Weaken outdated samples and remove outlier samples (outlier score) _next Input: {c(k), X(k)}, P(k), Output: P(k+1).

[0138] This step outputs: Measurement scheduling table M(k+1), surrogate model P(k+1), a _pert_next Resource parameters, etc.

[0139] S4 performs convergence judgment and state management. Specifically, the optimization iteration will not continue indefinitely and needs to have clear termination conditions and subsequent management mechanisms.

[0140] At the end of each cycle, the system checks whether the convergence condition is met. A preferred convergence criterion is: in the nearest K... _conv Within a period (e.g., K) _conv =5), the improvement in cost function J(k) is less than the small threshold ε. _j And all constraint performance metrics (IL) _guard (k), GDR(k), etc.) have all met their respective performance requirement thresholds (IL). _max GDR _max wait).

[0141] Once the convergence condition is met, the current encoding vector c(k) is considered the optimal solution and is fixed as c*. The system then generates a performance report R*, which includes information such as the final performance metrics achieved, the number of iterations, and the perturbation energy consumed, for recording and analysis.

[0142] During long-term system operation, performance drift may occur due to factors such as temperature changes and component aging. To address this, the present invention also includes a drift sentinel mechanism. This mechanism continuously monitors the system's key performance parameters. When a parameter drift is detected to exceed a preset range, a short-cycle micro-calibration process is automatically triggered. This micro-calibration starts with the current optimal solution c*, performs several S2-S3 iterations, and quickly finds a new compensated post-encoding c*' that adapts to the current drift state, ensuring long-term stability of system performance.

[0143] In an exemplary embodiment, the convergence criterion and state solidification, event-triggered recalibration, and final output specifically include the following steps.

[0144] If IL _guard (k)≤IL _max GDR(k)≤GDR _max IMD(k)≤IMD _max If J(k) improves by less than ε within the most recent K periods, then convergence is determined. Input: IL _guard (k), GDR(k), IMD(k), J(k); Output: convergence / non-convergence flag.

[0145] Upon convergence, c(k) is solidified into c*, and R* (target notch depth curve, IL) is summarized. _guard (GDR, IMD, number of iterations, perturbation energy budget, etc.)

[0146] During operation, monitor drift sentinels (such as changes in dA / df and temperature drift); upon triggering, perform a short-cycle S2-S3 micro-calibration starting from c* to obtain c*' and R*'; finally, release c. _final (C* or C*') and Q _final .

[0147] This specification uses a unified convention for symbols and data items. Among them, F... _target Represents the target frequency set; F _guard Let F represent the set of frequency points of the guard band; c(k) represents the coding vector of the k-th period; X(k) represents the frequency point of the guard band. _target ∪F _guard The acquired amplitude and phase observation data packets; S(k) represents the sensitivity matrix, describing the output's sensitivity to perturbations at each stage of coding; IL _guard (k) represents the sheath insertion loss index; GDR(k) represents the group delay fluctuation index; IMD(k) represents the intermodulation distortion index; J(k) represents the cost function; M(k) represents the measurement schedule; P(k) represents the surrogate model; R* represents the final performance report; w1, w2, w3, w4 represent weighted parameters, which are non-negative and weigh the weights of each index.

[0148] Example 7: In a certain scenario, the calculation process of the discrete code update quantity is as follows.

[0149] Suppose a frequency response device is composed of a three-dimensional discrete coding vector c=[c1,c2,c3]. T Control. In the current iteration period k, its encoding vector is c(k)=[50,80,60] T .

[0150] The system's tuning objective is as follows: at f _lock The notch depth at 100MHz must remain constant. This frequency constitutes the locked frequency set F. _lock It needs to be deepened in f. _target The notch filter at 150MHz is used to minimize the amplitude response at that point. The cost function J simplifies to f. _target The magnitude of the change. During the optimization process, the predicted change of a certain key performance indicator (such as the average insertion loss IL within the sheath) must be zero.

[0151] The following system parameters were obtained through prior measurements (such as in Example 6):

[0152] In f _lock First-order sensitivity (locked first-order sensitivity) S _lock :S _lock =[0.2,-0.1,0.05].

[0153] The gradient of the cost function J with respect to the encoding c (in f) _target g (measured at) _j :g _j =[-0.5,-0.8,0.1] T .

[0154] The gradient g of insertion loss IL with respect to encoding c _iL :g _iL =[0.01,0.04,0.02] T .

[0155] Using the Sequence Exchange Identification (SEI) method of Example 2, the result was measured at f _lock At this point, the second-order cross sensitivity between components 1 and 2 is: C _12 (f _lock )=0.08, C _21 (f _lock =0.07. The cross sensitivity between other component pairs is assumed to be zero in this example.

[0156] According to Example 4, it is necessary to construct nonlinear holding conditions based on the sensitivity information of the locked frequency point.

[0157] Specifically, construct the Hessian approximation matrix H. _lock Using the measured second-order cross sensitivity, H is constructed through symmetry processing. _lock The corresponding element in: H _lock [1,2]=H _lock [2,1]=(C _12 +C _21 ) / 2 = (0.08 + 0.07) / 2 = 0.075. Therefore, we obtain the (sparse) Hessian approximation matrix: H _lock =[[0,0.075,0],[0.075,0,0],[0,0,0]].

[0158] Furthermore, the nonlinearity preservation condition is established: S _lock *Δc+(1 / 2)*Δc T *H _lock Substituting *Δc≈0 into the value, we get: [0.2,-0.1,0.05]*Δc+(1 / 2)*Δc T *[[0,0.075,0],[0.075,0,0],[0,0,0]]*Δc≈0.

[0159] Based on this, the linearized ZIS used for optimization is determined, and when constructing the quadratic programming problem, the linearized part of this condition is used as a hard constraint: S _lock *Δc=0, that is, 0.2*Δc1-0.1*Δc2+0.05*Δc3=0.

[0160] According to Example 5, all objectives and constraints are integrated into a standard quadratic programming (QP) problem. The preset decrease in cost function is set to η = 0.1.

[0161] Objective function: minimize||Δc|| 2 That is, minimize(Δc1) 2 +Δc2 2 +Δc3 2 Constraints:

[0162] (Zero-influence constraint) 0.2*Δc1 - 0.1*Δc2 + 0.05*Δc3 = 0;

[0163] (Performance equivalence constraint) 0.01*Δc1+0.04*Δc2+0.02*Δc3=0;

[0164] (Cost function descent constraint) -0.5*Δc1-0.8*Δc2+0.1*Δc3≤-0.1.

[0165] The QP problem described above is input into a standard numerical optimization solver. Understandably, the solver will provide a continuous solution that satisfies all constraints and has the smallest self-norm. In this example, assume the solver obtains a continuous solution of: Δc*=[-0.6,1.3,0.8] T .

[0166] Specifically, mapping to the discrete codeword space, we calculate the theoretically new encoding:

[0167] c _theory =c(k)+Δc*=[50,80,60] T +[-0.6,1.3,0.8] T =[49.4,81.3,60.8] T Performing the rounding mapping yields the discrete code: c _discrete =Round(c _theory =[49,81,61] T The discretization increment is obtained as follows:

[0168] ~Δc=c _discrete -c(k)=[-1,1,1] T .

[0169] Furthermore, the rounding error is identified and second-order correction is performed, and the rounding error is calculated:

[0170] ε _round =Δc*-~Δc=[-0.6,1.3,0.8] T -[-1,1,1] T =[0.4,0.3,-0.2] T .

[0171] To evaluate the deviation of the discrete increment ~Δc from the ZIS, calculate:

[0172] S _lock *~Δc=0.2*(-1)-0.1*(1)+0.05*(1)=-0.2-0.1+0.05=-0.25. It can be seen that directly applying the discrete increment will cause the locked frequency point to produce an unexpected response of -0.25, which seriously violates the ZIS condition.

[0173] To calculate the correction amount, the second-order correction operator is activated, and the correction amount Δc, which has the smallest norm and consists of integers, is found. _corr This allows it to compensate for the aforementioned deviation of -0.25 to the greatest extent possible. That is, S _lock *Δc _corr It should be as close as possible to +0.25. Δc can be found by searching within a small range (e.g., with components taking values ​​in {-1, 0, 1, 2}). _corr =[1,0,1]T It is a preferred solution because S _lock *[1,0,1] T =0.2*(1)-0.1*(0)+0.05*(1)=0.25, which just compensates for the first-order deviation.

[0174] The final update amount is obtained by integrating the data. The final updated encoding vector to be applied is:

[0175] Δc _hat =~Δc+Δc _corr =[-1,1,1] T +[1,0,1] T =[0,1,2] T .

[0176] Apply the corrected discrete update to the current encoding:

[0177] c(k+1)=c(k)+Δc _hat =[50,80,60] T +[0,1,2] T =[50,81,62] T .

[0178] As can be seen, through the complete process of this invention, the system obtains the update quantity in integer form [0,1,2]. T The result is the same as the original rounded result [-1,1,1]. T In comparison, although it differs more from the continuous solution Δc* in form, it has undergone fine correction and can better maintain the performance stability of the locked frequency point, making it the better solution found in the discrete space.

[0179] Example 8 describes how to intelligently plan and adjust measurement tasks to minimize the time and energy costs required for measurement while ensuring identification accuracy, and to ensure that the entire process is imperceptible to the external environment or business operations. This example is a further refinement of the design of the detection signal steps in Example 1, and specifically includes three parts.

[0180] The first part is the initial measurement scheduling based on information gain. In the first iteration after system startup or reset, the selection of measurement points is not uniform or random in order to establish an initial understanding of the system in the most efficient way.

[0181] Specifically, after performing the initial scan (Example 6) and constructing the initial proxy model P(0), the system uses this model to evaluate the frequency point set F of the guardrail. _guardThe uncertainty U(f) is the value of each frequency point f. U(f) can be represented by the prediction variance directly output by the surrogate model (such as Gaussian process regression), or by perturbation analysis of the model. The higher the uncertainty of a frequency point, the less accurate the current model's prediction of the response at that point is, and therefore the greater the information gain that can be obtained by measuring that point.

[0182] Accordingly, the initial measurement scheduling table M(0) will prioritize allocating measurement resources (such as longer time windows or higher sampling rates) to the frequency subsets with the highest U(f), thereby achieving an exploratory intelligent scheduling aimed at maximizing information acquisition.

[0183] The second part is the adaptive perturbation amplitude setting based on energy budget. In order to achieve imperceptible online identification, the strength of the injected perturbation signal must be strictly controlled.

[0184] The system is based on a preset imperceptible threshold E _inaud Based on the initial background noise level, the total energy budget B of the perturbation that can be injected within a single iteration cycle is calculated. _pert E _inaud It defines the degree to which changes in the system output will not be detected externally.

[0185] At the beginning of each iteration period k, the perturbation amplitude a _pert It is not fixed, but rather adaptively adjusted. The system will adjust the total energy budget B based on the noise statistics N(k-1) of the previous cycle k-1. _pert Under the constraint of 'a', choose the option that maximizes the demodulation signal-to-noise ratio / perceived risk ratio. _pert For example, during periods of high environmental noise, the system can appropriately increase a. _pert This ensures that the demodulated sensitivity information is not overwhelmed by noise; while in a very quiet environment, the noise level can be reduced. _pert This makes the detection activities more covert.

[0186] The third part is the closed-loop adaptive update of measurement scheduling. The measurement scheduling of this invention is a dynamically evolving closed-loop system. At the end of period k, the system uses the newly collected data of this period to incrementally learn or online correct the surrogate model P(k) on {c(k),X(k)}, and obtain the updated model P(k+1).

[0187] Optionally, a forgetting factor λ can be introduced into the learning process. _forget This reduces the weight of outdated samples in the model, enabling the model to better track the time-varying characteristics of the system.

[0188] Based on this, the system uses the updated and more accurate surrogate model P(k+1) to recalculate the information gain U(f) of all candidate frequencies. According to the latest information gain ranking and combined with information from the integrated optimization process (ICGP) regarding which regions are more sensitive to performance improvements, a measurement schedule M(k+1) for the next period k+1 is generated. Through this closed loop of measurement-modeling-planning-remeasurement, the system can continuously and dynamically refocus measurement resources on the uncertain or sensitive regions most valuable to the current optimization task, achieving continuous self-optimization of measurement efficiency.

[0189] Example 9 provides a preferred and more robust implementation of the optimization decision-making process of the present invention. It is understood that in real physical environments, measurements are always accompanied by noise, and models always contain errors. An optimization algorithm based solely on ideal assumptions may make erroneous or unstable decisions when faced with uncertainty. This example describes a multi-layered guarantee mechanism to enhance the stability and security of the optimization process. It does not rely on a single technical point, but rather ensures the reliability of the update steps through a chain design of input purification, robust decision-making, and risk prediction. Specifically, it includes three parts.

[0190] The first part is the regularization and stabilization of the sensitivity matrix. The first step in optimization decision-making is to obtain accurate system state information, i.e., the sensitivity matrix S(k). However, the raw sensitivity data obtained directly from correlation demodulation may contain noise and outliers due to transient interference or low signal-to-noise ratio.

[0191] To address this issue, in a preferred embodiment of the present invention, after obtaining the original correlation demodulation results, a sensitivity matrix stabilization process is first performed. Specifically, this process can employ one or a combination of the following methods:

[0192] Instead of the traditional arithmetic mean, a statistical method that is insensitive to outliers is used to calculate the final sensitivity value. For example, median filtering or truncated averaging can be used to aggregate multiple demodulation results within the measurement window, automatically filtering out outlier data points caused by burst noise.

[0193] Based on the prior knowledge that the sensitivity response of a physical system is usually continuous and smooth in frequency, a low-pass filter (such as moving average or Gaussian kernel smoothing) can be applied to the calculated sensitivity matrix S(k) along the frequency axis to suppress high-frequency random noise.

[0194] The process of solving the sensitivity matrix is ​​constructed as a regularized inverse problem. A penalty term (such as L1 or L2 norm) is added during the solution process to obtain a smoother or sparser solution with better physical interpretation.

[0195] Through the above processing, the system obtains a purified and more reliable sensitivity matrix S(k). This process also produces quality evaluation metrics, such as the demodulated signal-to-noise ratio (SNR) for each sensitivity element. _demod This indicator will serve as a source of confidence in subsequent steps.

[0196] The second part is the selection of active blocks based on confidence weighting. When the active blocks of the coding components to be optimized this week are determined (usually 1-2 components), the traditional approach is to select the component with the largest absolute gradient value. However, a seemingly large gradient may simply originate from a noisy measurement.

[0197] To avoid being misled by misleading gradients, this invention preferably employs a confidence-weighted activity block selection strategy. Specifically, the system does not directly use the gradient g of the cost function derived from S(k). _i =dJ / dc _i Instead, first calculate the confidence-weighted gradient g. _i ':g _i '=g _i / σ _i ; where: g _i ' is the confidence-weighted gradient of component i; g _i σ is the original gradient of component i; _i For gradient g _i The uncertainty estimate combines the statistical variance N(k) of the measurement noise and the demodulated signal-to-noise ratio (SNR) of the corresponding element of the gradient obtained in the first part. _demod σ _i The larger the value, the better the gradient g. _i The more uncertain the estimate, the lower its confidence level. Furthermore, the system will select the one with the largest |g... _i The encoded component of '|' is used as the active block. It can be seen that the strategy prioritizes optimization in directions that not only have high descent potential but also have highly reliable measurement results of the descent trend, effectively avoiding ineffective exploration in uncertain directions and improving the robustness of decision-making.

[0198] As a further improvement, the selection process can also introduce diversity constraints. For example, after selecting the first component i with the highest confidence, when selecting the second component, the system queries the second-order cross-sensitivity matrix C(k). If the coupling strength |C| between the candidate component j and the selected component i is high, then the selection process can be improved by considering the following constraints: _ij If the value of | is too high, the system may skip j and choose the next suboptimal component p that is less coupled with i. This is to ensure that the multiple components updated each time have a certain degree of independence, so as to achieve more efficient exploration in the parameter space.

[0199] The third part is feasibility prediction and pruning based on the surrogate model, which obtains the candidate coding update amount Δ through ICGP calculation or other methods. _c Afterwards, the system will not immediately execute the update. Because the linear model used for ICGP calculations is only a local approximation, its prediction accuracy may decrease for updates with slightly larger step sizes, posing a risk of violating performance constraints. To mitigate this risk, this invention preferably introduces a virtual execution and risk prediction stage based on a proxy model. Specifically, in applying Δ... _c Previously, the system first conducted a simulation exercise: calculating the candidate new code c to be applied. _cand =c(k)+Δ _c c _cand As input, it is fed into the more refined nonlinear online surrogate model P(k) mentioned in Example 8. The surrogate model P(k) will output a response to c. _cand The complete system response X _pred The system is based on X. _pred Calculate the predicted values ​​of various constraint performance indicators, such as IL. _guard_pred GDR _pred etc. Compare these predicted values ​​with their respective hard constraint thresholds (IL). _max GDR _max The candidate update value Δ is compared with other values. If any predicted value exceeds or is too close to its constraint boundary, then the candidate update value Δ is... _c It is marked as high risk. Accordingly, the system will prune the candidate, for example, by shortening its overall size by a certain percentage (reducing the step size), or by rejecting the update and triggering a recalculation with a smaller step size.

[0200] The robust optimization method described in this embodiment constructs a progressive safety net by purifying the input data, weighting the decision basis with confidence, and predicting the risk of the decision consequences. This ensures that the optimization algorithm can converge stably, safely, and efficiently in complex real-world environments, thereby improving the practicality and reliability of the present invention.

[0201] According to one aspect of this application, the locked frequency set includes primary fire-fighting channel frequencies and tactical fire-fighting channel frequencies.

[0202] The primary fire-fighting channel frequency is used for communication between the fire command center and on-site commanders, while the tactical fire-fighting channel frequency is used for collaborative communication between on-site firefighters. The zero-impact subspace design ensures that the signal transmission quality of both the primary and tactical fire-fighting channels is not degraded when suppressing interference signals. Performance indicators include the bit error rate (BER) of fire-fighting digital communication; specifically, the BER of vital signs monitoring data is set to a threshold of no more than 10. -6The error rate of GPS positioning data is set to a threshold of no more than 10. -5 The bit error rate for air margin transmission is set to a threshold of no more than 10. -6 The constrained geodesic step calculation uses the bit error rate index as a hard constraint to ensure that the filtering adjustment process will not lead to errors in the transmission of secure data.

[0203] According to one aspect of this application, the method also includes steps for identifying and protecting the characteristic signals of fire-fighting equipment: before implementing the detection signal design, the characteristic signals of fire-fighting equipment within the operating frequency band are scanned and identified; the characteristic signals of fire-fighting equipment include: alarm signals of personal alarm security systems (PASS); data transmission signals of thermal imagers; and remote control signals of fire pumps and smoke exhaust equipment; after the characteristic signals are identified, the frequency points corresponding to the characteristic signals are automatically added to the locked frequency point set, and zero-impact protection is performed in subsequent filtering adjustments.

[0204] The identification of fire equipment characteristic signals is achieved through the following methods: constructing a fire equipment signal characteristic library, which includes the frequency characteristics, modulation methods, and protocol characteristics of various fire equipment; performing feature matching on the collected spectrum data, and determining that a signal is a fire equipment characteristic signal when the matching degree exceeds a preset threshold; for newly identified unknown signals, determining whether they are potential fire-related signals by analyzing their time-frequency characteristics and occurrence patterns, and adopting a conservative protection strategy if so.

[0205] According to one aspect of this application, the method further includes adaptive adjustments for the fire environment: monitoring the dynamic changes in ambient noise levels and interference intensity; automatically increasing the measurement frequency of the second-order cross sensitivity when broadband pulse interference specific to the fire environment is detected, so as to quickly track changes in the nonlinear characteristics of the system; and adaptively increasing the perturbation amplitude of the detection signal when the ambient noise exceeds a preset threshold, but not exceeding the imperceptible threshold of fire communication, so as to ensure identification accuracy.

[0206] According to one aspect of this application, the method further includes emergency priority management: setting priorities for different types of fire communication channels, with life safety-related channels having the highest priority; when system resources are limited, prioritizing the anti-interference performance of high-priority channels; and under extreme interference conditions, automatically activating a degradation mode to sacrifice the performance of some low-priority channels to ensure the smooth operation of life safety channels.

[0207] Example 10 describes the data processing procedure and its advantages in solving the problem of reliable communication via satellite links in the complex electromagnetic environment of a fire scene. It should be noted that this application scenario is merely an example and not restrictive.

[0208] Step S10.01: Design a detection signal containing sequentially exchanged perturbations, apply the detection signal to a frequency response device, and collect its response to obtain an observation data packet.

[0209] In this embodiment, the frequency response device is specifically the radio frequency front-end filter bank of the satellite communication terminal, operating in the L-band (1.5-1.7GHz) and S-band (2.4-2.5GHz). The detection signal is designed with the following parameters: the perturbation amplitude is set to 2-3 times the minimum resolution of the encoder, approximately 0.05dB; the perturbation duration is controlled within 5ms to ensure that it does not affect the frame synchronization of the satellite signal; the sequential exchange interval is set to 100ms to avoid conflict with the satellite beacon period.

[0210] The generation process of the probe signal is as follows: Based on the current encoded vector c(k)=[c1,c2,...,cn], two components to be measured, ci and cj, are selected; the first perturbation sequence is generated, first applying a +δ perturbation to ci, which lasts for 5ms and then recovers, and then applying a +δ perturbation to cj; the second perturbation sequence is generated, with the order reversed so that cj is perturbed first, followed by ci; the total duration of both sequences is 10ms, ensuring completion within the same satellite burst time slot. The observation data packet contains the frequency response amplitude, phase, and signal strength at key frequencies at each perturbation moment, with the sampling rate set to 10kHz to capture rapid changes.

[0211] Satellite downlink signals are typically transmitted using time division multiplexing (TDM) or burst mode, and have regular quiet periods, which can be used to insert probe signals; L-band satellite signals (such as Tiantong-1) have strong anti-interference capabilities, and a brief 5ms disturbance will not cause bit errors; by synchronizing with the satellite frame structure, disturbances can be avoided during the synchronization header or pilot symbols.

[0212] Optionally, for high-frequency satellite communications such as Ku / Ka, the perturbation amplitude can be further reduced to 0.02dB because high-frequency phase noise is more sensitive. For satellite systems using spread spectrum technology (such as GPS), the perturbation amplitude can be appropriately increased to 0.1dB without affecting the signal quality after despreading by utilizing the spread spectrum gain. In extreme interference situations, a fast detection mode can be enabled to compress the perturbation duration to 2ms. Although the measurement accuracy decreases slightly, it can respond to interference changes more quickly.

[0213] Step S10.02: Based on the observed data packet and the probe signal, demodulate to obtain the second-order cross sensitivity that describes the coupling effect between different components in the coding vector.

[0214] Second-order cross sensitivity C _ij In satellite communication systems, the interaction between different notch filters is reflected, which is particularly evident when dealing with interference from adjacent frequencies. The demodulation process employs a differential measurement method: C _ij =(R _ij -R _ji ) / (4*δ2 ), where R _ij R represents the response change after the initial perturbation ci and the subsequent perturbation cj. _ji δ represents the change in response after sequential exchange, and δ is the perturbation amplitude.

[0215] In the practical implementation of satellite communication, the impact of Doppler frequency shift needs to be addressed. The Doppler frequency shift of low-Earth orbit satellites (such as Iridium) can reach ±40kHz, causing drift in the observed frequency. This is addressed by performing Doppler compensation before demodulation and calculating the current frequency offset f using the satellite ephemeris. _doppler Frequency correction is applied to the observed data: f _corrected =f _observed -f _doppler After calibration, the measurement accuracy of second-order cross-sensitivity can reach 0.01 dB / LSB. 2 .

[0216] For TDMA (Time Division Multiple Access) systems, data packets may only appear in specific time slots. Therefore, a valid data detection threshold needs to be set; data is considered valid only when the received power exceeds -110 dBm. By accumulating and averaging measurements from multiple burst cycles, the C... _ij The estimation accuracy was improved. Experiments showed that after accumulating 10 burst cycles, the measurement standard deviation decreased to 0.005 dB / LSB. 2 .

[0217] Furthermore, for broadband satellite communications (such as Ka-band HTS), the coupling characteristics of multiple subcarriers can be measured simultaneously, and a frequency-dependent second-order cross-sensitivity matrix C can be constructed. _ij (f) The expansion of the frequency dimension allows the system to predict the effects of broadband interference more accurately. In a 32-carrier Ka-band system, the complete C _ij (f) The matrix contains 1024 elements, and all measurements can be completed within 200ms through parallel processing.

[0218] Step S10.03: Based on the second-order cross sensitivity, construct a zero-influence subspace for the locked frequency point set, and perform equal-constrained geodesic step calculations within the zero-influence subspace to generate the coding vector update amount.

[0219] In satellite communication applications, the frequency set F has been locked. _lock It includes several key frequency points: the Tiantong-1 main channel (1.6165GHz), the Beidou short message frequency point (1.61568GHz), the GPS L1 frequency point (1.57542GHz), and the emergency beacon frequency point (406MHz). These frequency points carry critical functions such as location information, distress alarms, and command and dispatch, and must be protected with zero impact.

[0220] The construction process of the zero-influence subspace is as follows: calculate the first-order sensitivity matrix S of the locked frequency point. _lock The dimension is m×n, where m is the number of locked frequency points and n is the dimension of the encoding vector; an extended constraint matrix H is constructed by combining second-order cross-sensitivity. _lock =S _lock +C _lock c(k), where C _lock To lock the second-order terms related to the frequency point; through singular value decomposition H _lock =UΣ*V T Take the column vectors in V corresponding to the zero singular values ​​to form the basis of the zero-influence subspace.

[0221] The optimization problem of constrained geodesic stepping is concretized in the satellite scenario as: minimize||Δc|| 2 The constraints include: g _J T Δc ≤ -0.5dB (ensuring interference suppression effect); g _BER T Δc=0 (maintaining the bit error rate without degradation); g _C / N0 T Δc≥0 (carrier-to-noise ratio does not decrease); H _lock Δc=0 (zero effect at locked frequency). Where g _J g is the gradient of the interference power. _BER g represents the gradient of the bit error rate metric. _C / N0 represents the gradient of the carrier-to-noise ratio.

[0222] The solution employs the interior-point method, transforming inequality constraints into equality constraints plus slack variables, and constructing the Lagrangian function L = ||Δc|| 2 +λ1(g _J T Δc+0.5)+λ2(g _C T Δc)+λ3(-g _C / N0 T Δc+s)+μ T (H _lock Δc) is solved using Newton-Raphson iteration to obtain the KKT conditions. In a typical 8-dimensional coding space, convergence to 10 is achieved in 3-5 iterations. -6 The accuracy is high, and the calculation time is approximately 15ms.

[0223] Optionally, when the satellite link margin is sufficient (C / N0>10dB), the carrier-to-noise ratio constraint can be relaxed, allowing a 0.5dB degradation in exchange for stronger interference suppression; in the case of severe rain attenuation, the optimization weight can be dynamically adjusted to prioritize link availability; for military satellite communications, anti-interception constraints can be added to limit out-of-band radiated power.

[0224] Step S10.04: Apply the updated encoding vector to the current encoding vector to obtain the encoding vector for the next iteration cycle.

[0225] The update process employs an adaptive step-size strategy: c(k+1) = c(k) + αΔc, where α is the step-size factor. In satellite communication, the step-size selection needs to consider the link's stability requirements. The initial step-size is set to 0.8. When fluctuations are detected in satellite signal locking indicators (such as carrier locking, frame synchronization locking), the step-size is automatically reduced to 0.5. When all performance indicators are stable for five consecutive cycles, the step-size can be increased to 1.0 to accelerate convergence.

[0226] After the update, a boundary check is required to ensure that the encoded value is within the valid range: c _i ∈[0,2 B-1 ], where B is the number of bits used for encoding, typically 10-12 bits. For components exceeding the boundary, saturation processing is used instead of truncation to preserve direction information. A smooth transition mechanism is also implemented, decomposing the update into four sub-steps, each updating 1 / 4 of the amount, executed at 2ms intervals, to avoid sudden changes impacting the satellite receiver's carrier tracking loop and symbol synchronization loop.

[0227] After the update is completed, the system enters the verification phase, continuously monitoring key indicators within 50ms: Eb / N0 of the satellite signal, bit error rate, carrier frequency offset, and symbol timing deviation. If any indicator becomes abnormal (such as Eb / N0 dropping by more than 1dB), it immediately rolls back to the previous stable state c(k), halves the step size, and retryes. This conservative strategy ensures the high reliability of the satellite link.

[0228] In this embodiment, through 1000 field tests, the update success rate reached 98.5%, the average convergence time was 8 iteration cycles (800ms), the achieved interference suppression was 42-48dB, and the insertion loss change of the locked frequency point was kept to be less than 0.1dB.

[0229] Step S10.05: Identify the characteristic signals of the fire-fighting equipment and implement protection.

[0230] Satellite communication terminals need to identify and protect interconnection signals with firefighting equipment. In addition to satellite links, various wireless devices exist at fire scenes: personal locator beacons (PLB, 406MHz), respirator wireless monitoring (433MHz), thermal imager data transmission (2.4GHz WiFi), and drone control links (5.8GHz). Although these signals are not satellite signals, they are equally important for firefighting and rescue operations.

[0231] The identification process employs a dual mechanism. First, feature database matching: pre-stores the spectral characteristics of various fire-fighting equipment, including center frequency, occupied bandwidth, modulation method, and feature code. For example, a 406MHz PLB signal has a unique 112-bit message format, with the first 24 bits being the synchronization code "011010000101111000000100", which can be quickly identified through relevant detection. Second, behavioral pattern recognition: even if a precise match to the feature database is not possible, if a signal at a certain frequency exhibits characteristics such as periodic bursts, stable power, or continuous presence, it is still marked as a potential protection target.

[0232] After detecting the signal of the fire-fighting equipment, its frequency point is automatically added to the extended protection set F. _protect With satellite locked frequency set F _lock Together, they form a complete set of protected frequencies. The difference is that F... _protect The frequency points in the middle adopt a soft protection strategy, allowing for a 0.5dB variation in insertion loss, while F _lock A robust protection system is employed, requiring strict zero-impact measures. The tiered protection mechanism ensures the protection of critical satellite links while also accommodating the communication needs of other firefighting equipment.

[0233] Optionally, the system can dynamically adjust the protection strategy according to the mission phase. In the initial reconnaissance phase of a fire, priority is given to protecting drone links and video transmission; in the interior attack phase, the focus is on protecting respirator monitoring and personnel location; and in the evacuation phase, the PASS alarm signal receives the highest priority. The protection template is automatically switched through information exchange with the fire command system.

[0234] According to one aspect of this application, satellite links suffer from significant free-space loss, with L-band geostationary satellites experiencing path losses reaching 189 dB and signal power extremely weak, typically around -130 dBm. Therefore, the additional insertion loss of the filter directly impacts the link budget, necessitating optimization.

[0235] The optimization strategy comprises three levels. First, frequency selectivity optimization: targeting the narrowband characteristics of satellite signals (e.g., the Tiantong-1 channel bandwidth is 31.25kHz), an ultra-narrow transition band notch filter is designed, with the transition band controlled within 5kHz to ensure adjacent channels are unaffected. Second, group delay equalization: satellite signals already exhibit significant group delay distortion after long-distance propagation; filters require pre-equalization to control the additional group delay fluctuations within 20ns. Third, temperature compensation: satellite ground stations are often deployed outdoors, with temperature variations ranging from -40℃ to +70℃; temperature sensors are used for real-time monitoring, and table lookups are used to compensate for temperature-induced device parameter drift.

[0236] Different optimization parameters are used for satellites at different orbital altitudes. For geostationary orbit (GEO) satellites, the signal is stable but the power is weak, so the focus is on optimizing insertion loss performance, allowing for a slower adaptation speed (iteration period of 100ms). For low Earth orbit (LEO) satellites, such as the Iridium system, the satellite's overhead time is only 8-10 minutes, requiring rapid adaptation, so the iteration period is shortened to 20ms, while reserving a 40kHz Doppler tolerance. For medium Earth orbit (MEO) satellites, such as the BeiDou system, a balance is achieved between insertion loss and speed, with the iteration period set at 50ms.

[0237] Under extreme weather conditions, such as heavy rain causing Ka-band rain attenuation of up to 20dB, the system automatically switches to rain attenuation countermeasures mode. By increasing the Q value of the notch filter, the 3dB bandwidth is compressed to 1.2 times the bandwidth of the interference signal. Although this increases implementation complexity, it can reduce insertion loss by 0.3-0.5dB, partially compensating for rain attenuation loss. By coordinating the parameters of multiple notch filters and utilizing their coupling effect, a gain peak is generated at a specific frequency, further enhancing the signal strength by 1-2dB.

[0238] Example 11: This example describes the collaborative anti-interference mechanism when multiple frequency band satellites are operating simultaneously, and describes the joint optimization of the L / S / Ku three frequency bands.

[0239] Step S11.01: Construct extended detection signals for multi-band joint observation.

[0240] In fire satellite communication systems, multiple frequency bands are typically used simultaneously: the L-band is used for voice and low-speed data (Tiantong-1 1.6GHz), the S-band is used for telemetry and control (2.2GHz), and the Ku-band is used for broadband data and video backhaul (14 / 12GHz). Although the filters for these frequency bands are physically independent, they are coupled through shared local oscillator and intermediate frequency processing.

[0241] The extended probe signal design employs orthogonal coding, assigning a different Walsh code to each frequency band. The L-band uses W1=[+1,+1,+1,+1], the S-band uses W2=[+1,-1,+1,-1], and the Ku-band uses W4=[+1,+1,-1,-1]. The perturbation signal, modulated with the corresponding Walsh code, is simultaneously applied to each frequency band. The receiver can separate the responses of each band through correlation demodulation. This allows for the simultaneous acquisition of coupling information from all frequency bands in a single probe, reducing the measurement time from 30ms serially to 10ms parallelly.

[0242] The main challenge in multi-band detection is the difference in propagation delay between different frequency bands. Although the L-band and Ku-band use the same satellite, the L-band signal is delayed by approximately 50 ns compared to the Ku-band due to frequency-dependent ionospheric delay. Accurate delay compensation in the baseband is performed to align the observation windows of each frequency band and ensure the synchronization of coupled measurements. The compensation amount is calculated in real-time based on the total electron content (TEC): Δt = 40.3TEC(1 / f) _L 2 -1 / f _Ku 2 ), where TEC is the unit of TECU and frequency is the unit of Hz.

[0243] Step S11.02: Demodulate and obtain the generalized second-order cross-sensitivity matrix across frequency bands.

[0244] Generalized second-order cross-sensitivity includes not only coupling C within the same frequency band _ij LL C _ij SS C _ij KuKu It also includes cross-band coupling C _ij LS C _ij LKu C _ij SKu Cross-band coupling is primarily generated through shared frequency synthesizers and power amplifiers. For example, adjusting an L-band notch filter changes the load impedance of the power amplifier, affecting the gain flatness of the Ku-band.

[0245] Demodulation employs matrix-based least-squares estimation. Assuming the observation vector y contains responses across all frequency bands, and the probe matrix X consists of Walsh codes and perturbation sequences, then the generalized sensitivity matrix C... _general =(X T *X) -1 X T y. For a system with 3 frequency bands and 4 adjustable notch filters per band, C _general It is a 12×12 matrix containing 144 coupling coefficients. By utilizing the sparsity of the matrix (cross-frequency band coupling is usually weak), it can be decomposed into a predominantly diagonal block form, reducing computational complexity.

[0246] Actual measurement data shows that the typical coupling coefficient within the same frequency band is 0.1-0.3 dB / LSB. 2 The cross-band coupling coefficient is typically less than 0.05 dB / LSB. 2 However, in some cases, such as when the power amplifier is close to saturation, cross-band coupling can increase, reaching up to 0.2 dB / LSB. 2The system monitors the power amplifier's output power and automatically increases the weight of the cross-band coupling coefficient when it approaches the 1dB compression point.

[0247] Step S11.03: Construct an extended zero-influence subspace for multi-objective optimization.

[0248] The zero-impact subspace of a multi-band system needs to consider the protection requirements of each band simultaneously. The extended locked frequency set includes: 5 channels in the L-band (1616.0-1616.5MHz, spaced 100kHz apart), 3 channels in the S-band (2200-2290MHz), and 8 carriers in the Ku-band (14.0-14.5GHz, spaced 62.5MHz apart). These 16 locked frequencies form a 16×12 constraint matrix H. _multi .

[0249] The multi-objective optimization problem is extended to: minimize||Δc|| 2 +w _L P _L +w _S P _S +w _Ku P _Ku , where P _L P _S P _Ku These are the performance penalty functions for each frequency band, w _L w _S w _Ku This refers to the weighting coefficient. The weight is dynamically adjusted based on the current service priority, for example, during video transmission. _Ku =0.6, w during voice communication _L =0.7. Constraints include performance constraints for each frequency band and a unified zero-effect constraint H. _multi Δc=0.

[0250] The solution employs a hierarchical optimization strategy. Independent optimization is performed within each frequency band to obtain a local optimum Δc. _L Δc _S Δc _Ku Global optimization is performed through the coordination layer, taking into account the impact of cross-frequency band coupling, to generate the globally optimal solution Δc. _global The ADMM algorithm (Alternating Direction Multiplier Method) is used to decompose the large-scale problem into multiple smaller subproblems, achieving convergence after 5-8 iterations, with the total computation time controlled within 50ms.

[0251] Alternatively, on embedded platforms with limited computing resources, a simplified sequential optimization strategy can be adopted: optimize each frequency band in order of priority, with the results of the previous bands used as fixed constraints for later optimized bands. Although global optimality cannot be guaranteed, computational complexity is reduced, and it performs well in engineering applications.

[0252] Step S11.04: Implement an adaptive multi-band collaborative update strategy.

[0253] Updating multi-band coding vectors requires coordinating the convergence speed of each band. Due to significant differences in signal characteristics and interference environments across different bands, using a uniform step size can lead to slow convergence or oscillations in some bands. This embodiment employs an adaptive asynchronous update strategy, where each band independently adjusts its step size based on its own convergence status.

[0254] Due to the weak signal power and low signal-to-noise ratio in the L-band, a conservative step size α is adopted. _L =0.5, to ensure stability; the S-band signal is stronger, so a standard step size α can be used. _S =0.8; Due to its large bandwidth and sensitivity to group delay, the Ku band adopts a gradual lengthening process, starting from α. _Ku Starting at 0.3, the step size increases by 0.1 each cycle until it reaches 0.8. When a performance degradation is detected in a certain frequency band, the step size for that band is immediately halved, while other frequency bands remain unchanged.

[0255] The filter controllers of each frequency band exchange status information via a high-speed bus (such as PCIe), including the current coding vector, performance metrics, and convergence flags. When the L-band detects strong interference and begins adjustment, it sends a warning message to the S- and Ku-bands, which then fine-tune their parameters in advance to compensate for potential cross-band effects. This feedforward compensation mechanism shortens the overall convergence time of the multi-band system.

[0256] In the field test of this embodiment, facing complex multi-source interference (5 narrowband interferences in the L-band, 2 frequency-sweeping interferences in the S-band, and broadband noise in the Ku-band), the system completed the optimization of all frequency bands within 1.2 seconds, achieving interference suppression levels of 45dB, 42dB, and 38dB for each band, while maintaining performance changes of less than 0.2dB for all locked frequency points. Compared to traditional independent optimization schemes, this improves convergence speed and stability.

[0257] In some alternative implementations, regarding the design of the perturbation sequence, Embodiment 2 describes using step-like small increments Δc to construct the sequential exchange sequence. As an alternative, the perturbation can employ more complex waveforms. For example, it can be applied to each coded component c. _i and c _j Design specific, mutually orthogonal pseudo-random codes or short-duration chirped signals as their perturbation content. Analyzing the intermodulation components of the corresponding codewords or chirped signals in the system response can also extract second-order interaction information. This approach may offer better signal-to-noise ratio identification in noisy environments.

[0258] Regarding the calculation method for cross sensitivity, in Example 2, C is mainly calculated based on the difference in amplitude response A(f). _ij (f). In another alternative implementation, the calculation can be performed in the complex domain. Specifically, the complex form of the system response H(f) can be directly obtained using the I / Q (in-phase / quadrature) data in the observation data packet X(k). In this case, the second-order cross sensitivity is also in the complex form C. _ij_Complex (f), its calculation will be based on the difference in complex responses. Therefore, C _ij_Complex (f) can characterize not only the amplitude coupling between components, but also the phase coupling effect, providing more complete information for the subsequent construction of zero-influence subspaces, and is more effective in constraining phase-sensitive indicators such as group delay.

[0259] Regarding the prediction and evaluation of interaction strength (for sparse scheduling), Example 3 describes using historical data or the Hessian matrix of a surrogate model to predict interaction strength. In another alternative implementation, prediction can be based on first-order sensitivity information. Specifically, if the first-order sensitivity vectors S(i,:) and S(j,:) of two coded components i and j have high correlation or overlap in the frequency domain (i.e., tending to influence the same set of frequencies), it can be determined that there is a high probability of strong coupling between them. Therefore, the cross-correlation or inner product between S(i,:) and S(j,:) can be calculated, and the result can be used as a surrogate index of interaction strength to screen the subset to be tested.

[0260] Regarding the objective function of the optimization problem, in Examples 4 and 5, the objective function is set as minimizing the L2 norm ||Δc|| of the encoding update amount Δc. 2 This tends to produce a smooth solution where each component varies only slightly. In some alternative implementations, the objective function can be replaced by minimizing the L1-norm||Δc|| _1 Understandably, optimization problems that minimize the L1-norm (which can often be transformed into linear programming in this scenario) tend to produce sparse solutions, meaning that only a few components of Δc are non-zero. Therefore, adjusting only the most critical few encoded components in each iteration has a clearer physical meaning and may be easier to implement on some hardware.

[0261] Regarding the solution method for the optimization problem, Example 5 describes constructing the problem as a quadratic programming problem (QP) for solution. Alternatively, the original optimization problem containing nonlinear constraints can be solved directly. Specifically, the complete nonlinearity-preserving condition S from Example 4 can be used... _lock *Δc+(1 / 2)*Δc T *H _lock*Δc≈0 is used as an equality constraint, and a general nonlinear programming solver (such as sequential quadratic programming (SQP) or interior-point method) is employed for solving it. Although this method has higher computational complexity, it provides theoretically more accurate results because it avoids the linearization approximation of the ZIS.

[0262] Regarding discretization, Example 5 describes a two-step method: first solving for the continuous solution, then projecting and correcting the bias. In another optional implementation, the discrete characteristics of the encoded update quantity can be directly incorporated into the optimization model, constructing the problem as a mixed integer quadratic programming (MIQP) problem. In this model, the variable type of Δc is directly declared as an integer. By solving this MIQP problem, the optimal integer update quantity can be obtained directly, without subsequent rounding and bias correction steps. However, the MIQP problem is much more difficult to solve than the QP problem; therefore, this approach is more suitable for scenarios with low real-time requirements or low-dimensional encoded components.

[0263] In an alternative, more robust implementation, an ensemble of surrogate models can be built and maintained. This ensemble consists of multiple models of different structures or types (e.g., multinomial regression models, radial basis function networks, and small neural networks). When making predictions (whether for information gain calculation or feasibility prediction), the results are a weighted average or a vote of the predictions from multiple models. The overall prediction accuracy and stability of the ensemble model are generally better than those of a single model, effectively reducing the risk of overfitting or underfitting from a single model.

[0264] According to one aspect of this application, a lightweight alternative can be adopted in scenarios with extremely stringent computational speed requirements. The system can provide performance metrics requiring hard constraints (such as IL) for each metric. _guard Train a dedicated sentinel model with a very simple structure. The function of this sentinel model is not to predict the specific value of the metric, but simply to act as a classifier to determine the candidate update value Δ. _C Is it safe or high-risk? Because the model is simple and has a specific function, its evaluation speed is much faster than that of a complete frequency response prediction model.

[0265] By introducing an online identification method based on sequence exchange perturbation (SEI), this invention achieves for the first time in the field of online filter tuning a second-order cross-sensitivity C between coded components. _ijDirect measurement and quantification are achieved. By comparing the differences in system responses produced by two perturbation sequences, i followed by j and j followed by i, the sequence-dependent interaction effects originally hidden in the system nonlinearity are made explicit. The system optimization model provides second-order coupling information beyond the traditional first-order gradient, elevating the system model from a local linear approximation to a local quadratic approximation. This allows the optimization algorithm to accurately predict and compensate for non-commutation effects caused by the tuning operation sequence. It solves the tuning instability problem caused by model mismatch, such as adjusting f2 to destroy f1. This enables the algorithm to make more accurate response predictions when facing strongly coupled multi-notch systems, avoiding ineffective iterations and oscillations near the optimal solution, accelerating convergence speed and improving tuning accuracy.

[0266] This invention combines first-order sensitivity S _lock and second-order cross sensitivity H _lock , for the locked frequency set F _lock A nonlinear preservation condition was constructed, and a zero-influence subspace (ZIS) was determined based on it. All subsequent coding updates, Δc, are strictly constrained within this subspace. This invention, from the planning level of the optimization path rather than the ex-post correction level of traditional methods, ensures that the performance impact of the tuning operation on the locked frequency point is theoretically close to zero. This allows the algorithm to adjust other optimization objectives without worrying about the consequences. It solves the problem of iterative, piecemeal adjustments caused by inter-stage coupling, achieving effective decoupling of different notch tuning processes when tuning multi-notch filters, thus improving tuning stability and efficiency.

[0267] This invention integrates zero-influence constraints, equivalent constraints of other performance metrics (such as insertion loss and group delay), and the objective of cost function descent into a unified solution within a quadratic programming (QP) framework of equal-constraint geodesic stepping (ICGP). This method seeks the shortest path (geodesic) on a feasible manifold that satisfies all constraints, pointing towards the objective descent direction. It transforms the traditional sequential, locally optimal strategy of taking one step at a time and then projecting and correcting each step into a parallel, globally optimal strategy of first planning the globally optimal path and then taking steps. The QP solver can find a balanced update direction that simultaneously satisfies all constraints in one go. The objective function that minimizes the step norm suppresses overshoot and avoids traversing back and forth across the feasible region boundary. It solves the problem of oscillation and convergence stagnation near multi-constraint boundaries caused by coarse projection operations in traditional methods, enabling the algorithm to converge smoothly and quickly to the optimal solution that truly satisfies all stringent performance metrics.

[0268] This invention addresses the discrepancy between the continuous solution Δc* obtained through optimization and the discrete code ~Δc executed by the device by designing a discrete error correction mechanism including second-order correction. This mechanism can accurately identify the error ε introduced by the rounding operation. _roundAnd using the system's second-order model H _lock Calculate the correction amount Δc in integer form. _Corr This is used to compensate for the violation of core constraints (especially ZIS conditions) by the error. Unlike traditional methods that ignore or simply handle rounding errors, this invention treats them as deterministic perturbations that must be actively managed and compensated for. Through second-order correction, the discrete update amount Δc applied to the physical device... _hat The actual physical effects produced are, to some extent, brought back to the effect that the ideal continuous solution Δc* should produce. This solves the problem of the optimization results failing at the last mile due to discretization errors, ensuring the superiority of theoretical calculations, which can be truly translated into high performance of physical devices, and guaranteeing the accuracy and feasibility of the tuning results.

[0269] Strong electromagnetic interference in fire environments often originates from damaged power facilities, high-power firefighting equipment, and rescue equipment from multiple departments, which can clog communication links. This invention, by rapidly generating deep notch filters, can accurately filter out interfering frequencies within milliseconds while keeping adjacent useful signals unaffected. Zero-impact subspace technology ensures that key frequencies such as the primary firefighting channel and tactical channel remain stable throughout the tuning process, avoiding the instantaneous interruptions that may occur with traditional tuning methods.

[0270] Satellite downlink signals are weak and easily overwhelmed by strong ground interference. By modeling second-order cross-sensitivity and employing a differential measurement mechanism based on sequential exchange identification, the system can converge rapidly in high-noise environments, effectively suppressing measurement noise and maintaining stable adaptive tuning capabilities. For satellite terminals using multiple frequency bands simultaneously, this invention achieves collaborative optimization through online identification of cross-band coupling matrices, improving overall anti-interference performance.

[0271] While suppressing interference, the system actively maintains the group delay flatness and phase linearity of the channel, ensuring reliable transmission of data such as vital sign monitoring, air margin, and location information. This multi-objective integrated optimization capability is crucial for modern fire communication systems that carry complex digital information.

[0272] Faced with the rapidly changing interference environment of a fire scene, the system can dynamically adjust its protection strategy according to different stages of the rescue mission, achieving optimal configuration with limited resources. Even under extreme conditions such as high temperature and strong electromagnetic pulse, it can maintain stable operation, providing reliable communication support for fire rescue operations.

[0273] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. An anti-interference filtering method for fire emergency communication, characterized in that, based on sequential exchange identification and geodetic stepping technology, the encoding vector of frequency response equipment is iteratively adjusted online, Each iteration cycle includes: The probe signal containing the sequential exchange perturbation is read, applied to the frequency response device, and the response of the frequency response device is collected to obtain the observation data packet; Based on the observed data packets and the probe signals, the second-order cross sensitivity describing the coupling effect between different components in the coded vector is obtained by demodulation. Based on the second-order cross sensitivity, a zero-influence subspace is constructed for the pre-configured locked frequency point set, and an equal-constraint geodesic step calculation is performed within it to generate the coding vector update amount; The updated encoding vector is applied to the current encoding vector to obtain the encoding vector for the next iteration. The construction of the zero-influence subspace includes: Read the first-order sensitivity and second-order cross sensitivity of the demodulation, and extract the first-order sensitivity and second-order sensitivity corresponding to the locked frequency set. By combining the first-order locking sensitivity and the second-order locking sensitivity, a nonlinear preservation condition that minimizes the impact of the coding vector update on the locked frequency point set is constructed. Based on the nonlinear preservation condition, the zero-influence subspace is determined; The execution of the constrained geodesic step calculation to generate the encoding vector update includes: Based on the first-order sensitivity and the second-order cross-sensitivity, the gradient of the cost function and the gradient of the constraint index for at least one performance index are derived. Based on the gradient of the cost function and the gradient of the constraint index, an optimization problem with the update amount of the encoding vector as the variable is constructed in the zero-influence subspace, where: The objective function is to minimize the norm of the encoding vector update. The constraints include: using the gradient of the cost function to ensure that the cost function decreases by a predetermined amount, and using the gradient of the constraint index to ensure that the change in the performance index is zero; Solve the optimization problem to obtain the update amount of the encoding vector in the form of continuous solutions; The demodulation yields a second-order cross-sensitivity that describes the coupling effect between different components in the coding vector, including: Read at least one pair of coded components from the coded vector, and for them: Design and apply a first perturbation sequence, which corresponds to the perturbation of the first and second coded components applied sequentially, and obtain a first response; Design and apply a second perturbation sequence, which corresponds to the perturbation of the second and first coded components applied sequentially, and obtain a second response; Based on the difference between the first and second responses, the second-order cross sensitivity, which characterizes the coupling effect between the coded components, is calculated.

2. The method according to claim 1, characterized in that, Constructing an optimization problem with the encoding vector update as the variable includes transforming the optimization problem into a quadratic programming problem, specifically: The quadratic norm of the encoding vector update quantity is set as the objective function; The pre-defined decrease in cost function, zero change in performance metrics, and zero-influence subspace are uniformly transformed into linear constraints on the update amount of the encoding vector.

3. The method according to claim 1, characterized in that, After solving the optimization problem to obtain the encoding vector update quantity in the form of continuous solutions, the following is also included: The update amount of the encoding vector in the form of continuous solution is mapped to the discrete codeword space to obtain the discretized increment; Identify rounding errors introduced by the mapping process; The second-order correction operator, pre-built based on the second-order locking sensitivity, is invoked to compensate for the rounding error and generate the correction value. Integrate the discretization increment and the correction amount to form the encoding vector update amount to be applied.

4. The method according to claim 1, characterized in that, Based on the difference between the first and second responses, the second-order cross-sensitivity, characterizing the coupling effect between the coded components, is calculated, including: Obtain the difference between the first and second responses at the target frequency. The difference is normalized by reading and utilizing the perturbation amplitudes applied to the first and second coding components to generate a second-order cross sensitivity.

5. The method according to claim 1, characterized in that, Before designing and applying the first and second perturbation sequences, the following is also included: By utilizing historical second-order cross sensitivity or an online-updated surrogate model, the interaction strength of all coded component pairs in the coded vector is predictively evaluated. From the evaluation results, at least one pair of coded components with the highest interaction strength is selected to form the subset to be tested; Among them, the first and second perturbation sequences are designed and applied only to the coded component pairs in the subset to be tested.

6. The method according to claim 1, characterized in that, The gradients of the cost function and the constraint metrics for at least one performance metric are derived, including: The first-order sensitivity, second-order cross sensitivity, and online-updated surrogate model are used to jointly determine the gradient of the cost function and the gradient of the constraint index for at least one performance index. The online-updated proxy model is a frequency response-coded approximation mapping constructed based on the coding vector of the historical iteration cycle and the corresponding observation data packet.

7. An anti-interference filtering device for fire emergency communication, characterized in that, This device is used for online iterative adjustment of the encoding vector of a frequency response device, including: The detection and measurement module is used to design a detection signal containing sequentially exchanged perturbations, apply the detection signal to a frequency response device, and collect its response to obtain an observation data packet; The sensitivity demodulation module is used to demodulate the second-order cross sensitivity, which describes the coupling effect between different components in the coded vector, based on the observed data packet and the probe signal. The update quantity calculation module is used to construct a zero-influence subspace for the locked frequency point set based on the second-order cross sensitivity, and perform equal-constraint geodesic step calculation within the zero-influence subspace to generate the coding vector update quantity; The encoding update module is used to apply the encoding vector update amount to the current encoding vector to obtain the encoding vector for the next iteration period; The construction of the zero-influence subspace includes: Read the first-order sensitivity and second-order cross sensitivity of the demodulation, and extract the first-order sensitivity and second-order sensitivity corresponding to the locked frequency set. By combining the first-order locking sensitivity and the second-order locking sensitivity, a nonlinear preservation condition that minimizes the impact of the coding vector update on the locked frequency point set is constructed. Based on the nonlinear preservation condition, the zero-influence subspace is determined; The execution of the constrained geodesic step calculation to generate the encoding vector update includes: Based on the first-order sensitivity and the second-order cross-sensitivity, the gradient of the cost function and the gradient of the constraint index for at least one performance index are derived. Based on the gradient of the cost function and the gradient of the constraint index, an optimization problem with the update amount of the encoding vector as the variable is constructed in the zero-influence subspace, where: The objective function is to minimize the norm of the encoding vector update. The constraints include: using the gradient of the cost function to ensure that the cost function decreases by a predetermined amount, and using the gradient of the constraint index to ensure that the change in the performance index is zero; Solve the optimization problem to obtain the code vector update amount in the form of continuous solutions; The demodulation yields a second-order cross-sensitivity that describes the coupling effect between different components in the coding vector, including: Read at least one pair of coded components from the coded vector, and for them: Design and apply a first perturbation sequence, which corresponds to the perturbation of the first and second coded components applied sequentially, and obtain a first response; Design and apply a second perturbation sequence, which corresponds to the perturbation of the second and first coded components applied sequentially, and obtain a second response; Based on the difference between the first and second responses, the second-order cross sensitivity, which characterizes the coupling effect between the coded components, is calculated.

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