Parameter estimation method of UAV frequency hopping signal based on GSACMP

Abstract

The present invention discloses a method for estimating the parameters of a UAV frequency hopping signal based on GSACMP, which mainly solves the problem in the prior art that the amount of data required to estimate the key parameters of a non-cooperative UAV frequency hopping signal is large and is affected by non-Gaussian noise. Its implementation scheme includes: establishing the intercepted UAV frequency hopping signal under the influence of non-Gaussian noise as a segmented form model; based on the generalized sparsity adaptive correlation entropy matching pursuit algorithm, weighting the selection process of atoms in the iterative process to obtain sparse vectors corresponding to all segmented signals; obtaining the center frequency of each segmented signal based on the sparse vector and the signal characteristics of the compressed domain; and estimating the frequency hopping time of the non-cooperative UAV frequency hopping signal by differentiating the center frequency of each segmented signal and using the sliding window method. The present invention optimizes the sparse vector estimation process, improves the estimation performance of the UAV frequency hopping signal parameters under non-Gaussian noise, and can be used in a non-cooperative UAV frequency hopping communication system or a corresponding software radio communication system.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing technology, and in particular relates to a method for estimating parameters of a frequency hopping signal of an unmanned aerial vehicle (UAV), which can be used in a non-cooperative UAV communication system. Background Art

[0002] Drones originated in the military field. With the continuous advancement of flight control and radio communication equipment, drones have begun to develop in a miniaturized and diversified direction. The global drone market is enormous, with civilian infrastructure expected to dominate the drone market, exceeding $45 billion in value. In recent years, drone applications have grown exponentially, finding widespread application in a wide range of fields, including healthcare and social assistance, arts and entertainment, public administration, logistics and transportation, and educational services, generating significant economic and social benefits. China's drone market has developed rapidly, currently accounting for half of the global drone industry. In addition to leading companies such as DJI, ZeroTech, and EHang, Chinese internet companies such as Xiaomi, Alibaba, and JD.com have also invested in drone-related industries, including aerial photography, drone farming, and cargo delivery.

[0003] While the widespread use of drones has driven economic and social development, it has also led to the frequent occurrence of "illegal flights," posing serious safety risks and significant challenges to aviation safety and government regulation. Current mainstream drone systems typically consist of an aircraft and a remote controller, with communication between them primarily relying on frequency-hopping spread spectrum (FHSS) technology in the 2.4 GHz industrial, scientific, and medical (ISM) band. Extracting and identifying key characteristic parameters of drone frequency-hopping signals, such as the hopping timing and hopping frequency, could effectively prevent illegal flights and mitigate unnecessary risks. Frequency-hopping communication offers advantages such as anti-interference and anti-interception capabilities, and intercepted signals from actual drone communications are subject to non-Gaussian noise. Without prior information about the frequency-hopping signal and non-Gaussian noise, existing parameter estimation algorithms based on time-frequency analysis and compressed sensing struggle to effectively decipher key signal parameters. Therefore, accurately estimating frequency-hopping signal parameters is crucial for identifying and countering non-cooperative drones and is crucial for effectively addressing the security risks posed by these drones.

[0004] In existing research, parameter estimation methods for frequency-hopping signals are primarily based on time-frequency analysis and compressed sensing. Time-frequency analysis, a simple and intuitive method for describing the time-frequency characteristics of a signal, is based on the Nyquist sampling theorem and requires high-sampling-rate analog-to-digital converters to process high-frequency signal components. This poses a significant challenge to signal receiving equipment and leads to limitations in processing high-frequency frequency-hopping signals transmitted by devices such as drones. The theory of compressed sensing offers a promising solution to this problem. Algorithms based on this theory include sparse linear regression and sparse Bayesian learning. While these algorithms are theoretically capable of efficiently processing high-dimensional signals and extracting sparse features, they often suffer from high computational complexity in practical applications. In recent years, researchers have combined the advantages of linear programming algorithms to propose a variety of greedy algorithms that offer lower computational complexity and higher signal reconstruction speeds.

[0005] In a study published in the journal Electronics in 2019, Su et al. proposed a method that combines short-time Fourier transform (STFT) and l p -norm algorithm is used to improve the parameter estimation accuracy in impulse noise environment. Although this method has some improvements in robustness, the algorithm is based on Nyquist sampling theorem to sample the signal and the iterative process is relatively complex.

[0006] In their 2023 article published in the journal Sensors, Zhu et al. proposed a compressed-domain frequency-hopping signal parameter estimation algorithm based on an improved atomic dictionary. This algorithm uses the maximum dot product method to estimate the center frequency of a signal segment and uses the improved atomic dictionary to process the center frequency variations of the signal segment to estimate the frequency-hopping time. However, because this method uses the mean square error (MSE) criterion, which assumes a Gaussian noise distribution, it may experience performance degradation when dealing with bursty impulse noise.

[0007] In a study published in IEEE Transactions on Medical Imaging in 2018, Zhang et al. proposed a method that improves the accuracy of selected atoms by using the correlation entropy induced metric (CIM) in an iterative process, overcoming the sensitivity of traditional matching pursuit algorithms to non-Gaussian noise. However, improper parameter selection during the iterative process may lead to performance degradation.

[0008] In an article published in "Engineering Applications of Artificial Intelligence" in 2020, Shen et al. designed a quantitative version of the generalized maximum correlation entropy algorithm. This algorithm not only maintains the ability to resist non-Gaussian noise, but also significantly improves the execution efficiency of the algorithm. However, when using generalized correlation entropy as the loss function, it may face non-convex optimization problems, which increases the difficulty of finding the global optimal solution. Summary of the Invention

[0009] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a compressed domain UAV frequency hopping signal parameter estimation method based on generalized sparse adaptive correlation entropy matching pursuit (GSACMP) to achieve a more robust estimation performance under the condition that the background noise is non-Gaussian while reducing the amount of sampling data.

[0010] To achieve the above object, the technical solution of the present invention includes the following steps:

[0011] (1) The frequency hopping signal intercepted by the receiver in non-cooperative UAV communication is x(t), which is evenly divided into M non-overlapping segments of length E. The mathematical model of the segmented UAV frequency hopping signal is obtained as follows:

[0012] y(t)=[x(t1),x(t2),....,x(t m ),..,x(t M )],

[0013] where x(t m ) is the mth segment signal, m=1,2,...M.

[0014] (2) The sparse vector is obtained based on the generalized sparse adaptive correlation entropy matching pursuit GSACMP algorithm:

[0015] (2a) Initialize the index set B0 to be an empty set, set the initial number of iterations k = 1, and the maximum number of iterations k max , the initial step size L = 1, the measurement matrix Φ is a Gaussian random measurement matrix, and the compressed sampling signal, that is, the initial residual, is set to r0 = Φx(t m ), the length is Q, the sparse basis matrix Ψ is the Fourier orthogonal basis matrix, the sensing matrix A = ΦΨ, and the initial weight vector w is the unit vector of E×1;

[0016] (2b) Calculate each column of the sensor matrix The first k largest inner products with the weighted residuals λ k , and add it to index set B k In the equation, we get the support set A of the corresponding atom t ;

[0017] (2c) In the support set A t Solve vector The vector The L items with the largest absolute value are added to the index set B tL , the new support set A of the corresponding atoms is obtained tL ;

[0018] (2d) Using the new support set A tL Update the weight vector, weighted least squares solution, and residual to obtain the current weight vector w k , the current weighted least squares solution is θ k , the current residual is r k ;

[0019] (2e) Determine whether the current number of iterations k and the residual ratio P of the current and previous iterations meet the set threshold k max or P < 1 × 10 -2 Conditions:

[0020] If yes, proceed to step (3);

[0021] Otherwise, update the number of iterations to set k = k + 1, L = L + 1, and return to step (2b);

[0022] (3) Estimate the center frequency set F of all M segments based on the sparse vector and compressed domain signal characteristics;

[0023] (4) According to the sparse vector and the segment center frequency f, the set of transition times T of all d observed objects is estimated.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] First, low cost

[0026] The present invention compresses and samples the signal based on the principle of compressed sensing. According to the sparse characteristics of the UAV frequency-hopping signal in the frequency domain, the original signal can be accurately restored through a small number of sampling values. Therefore, the method of the present invention avoids the receiver's need for an ultra-high sampling rate analog-to-digital converter. Compared with existing time-frequency analysis methods based on the Nyquist sampling theorem, the system's hardware requirements are reduced, thereby effectively reducing equipment costs.

[0027] Second, strong robustness

[0028] Under conditions of compressed sampling and non-Gaussian noise, the present invention minimizes the residual using a loss function based on the generalized correlation entropy induced metric (GCIM) to optimize the weighting during the iterative process, enabling better selection of characteristic atoms. Compared to minimization strategies based on the correlation entropy loss function and the mean squared error (MSE), the present invention provides more flexible and accurate selection of characteristic atoms. Consequently, the present invention achieves improved robustness when estimating parameters for drone frequency-hopping signals affected by non-Gaussian noise under compressed sampling conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Flowchart for the implementation of the present invention;

[0030] Figure 2 A signal spectrum diagram of a segmented signal reconstructed using the present invention and the existing SAMP method;

[0031] Figure 3 This is a graph of the reconstruction success probability of the present invention under different shape parameter u changes;

[0032] Figure 4 This is a graph of the reconstruction success probability of the present invention under different scale parameter v changes;

[0033] Figure 5 The comparison of mean square error of frequency hopping frequency estimation using the present invention and the existing SAMP-based method when the pulse intensity α is 1.5 is shown;

[0034] Figure 6 The comparison of mean square error of frequency hopping time estimation using the present invention and the existing SAMP-based method when the pulse intensity α is 1.5 is shown;

[0035] Figure 7 The comparison of mean square error of frequency hopping frequency estimation using the present invention and the SAMP method when the pulse intensity α is 1;

[0036] Figure 8 The comparison of mean square error of frequency hopping time estimation using the present invention and the SAMP method when the pulse intensity α is 1;

[0037] Figure 9 The figure compares the mean square error of frequency hopping time estimation using the present invention and the SAMP method under different compression ratios. DETAILED DESCRIPTION

[0038] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0039] It should be noted that the step numbers in the specification and claims of the present invention are only for the purpose of clearly describing the embodiments of the present invention and facilitating understanding, and the order of the step numbers is not limited.

[0040] This example assumes that the hopping frequency and hopping time of the UAV frequency hopping signal affected by non-Gaussian noise intercepted under non-cooperative conditions are unknown, and is estimated based on generalized sparse adaptive correlation entropy matching pursuit (GSACMP) and compressed domain signal features.

[0041] Reference Figure 1 , the implementation steps of this example are as follows:

[0042] Step 1: Build a segmented model for the intercepted signal.

[0043] 1.1) In non-cooperative UAV communication, the frequency hopping signal y(t) transmitted by the non-cooperative UAV has a mathematical model as follows:

[0044]

[0045] Where E is the signal power, T h is the frequency hopping period, t0 is the starting time, f c Indicates the frequency hopping frequency, N h is the frequency hopping frequency, θ c is the initial frequency;

[0046] 1.2) The receiver intercepts the non-cooperative UAV frequency hopping signal x(t). Since x(t) is affected by the non-Gaussian noise n(t) in the channel during actual communication, the mathematical model of the intercepted non-cooperative UAV frequency hopping signal x(t) is:

[0047] x(t)=y(t)+n(t),

[0048] Among them, the Alpha stable distribution model is used to fit n(t). According to the characteristic function of the Alpha stable distribution, n(t) can be described as:

[0049]

[0050] Where sgn(t) represents the sign function, α∈(0,2] is the pulse intensity, β∈(-1,1) is the symmetry coefficient, and γ>0 is the dispersion coefficient. As the position parameter, the characteristic function of an Alpha stable distribution noise is determined by the four parameters α, β, γ, and η. α (β,γ,η);

[0051] 1.3) The frequency hopping signal x(t) is evenly divided into M non-overlapping segments of length E, and the mathematical model of the segmented UAV frequency hopping signal is obtained:

[0052] X=[x(t1),x(t2),....,x(t m ),..,x(t M )]

[0053] Among them, x(t m ) is the mth segment signal, m=1,2,...M.

[0054] Step 2: Initialize the compressed sensing model.

[0055] 2.1) Based on the mathematical model X of the segmented UAV frequency hopping signal, the index set B0 is initialized to an empty set, the initial iteration number k = 1, and the maximum iteration number k max , the initial step size L = 1, the initial weight vector w is a unit vector of E × 1, the compression ratio is λ, and the sparse vector θ0 is initialized to 0;

[0056] 2.2) The mth segment signal x(t m ) is projected onto the Fourier orthogonal basis Ψ∈R E×E Above, it is expressed as:

[0057] x(t m )=Ψθ m

[0058] Among them, the y-th column of the Fourier orthogonal basis Ψ is θ m is a sparse vector;

[0059] 2.3) Assume that the size of the Gaussian random measurement matrix Φ is And satisfy the RIP characteristics, the segmented signal is compressed and sampled to obtain the compressed sampling signal: r0=Φx(t m ), whose length is Q,

[0060] 2.4) The mth segment signal x(t m ) into the compressed sampling signal r0=Φx(t m ), we can get another representation of the compressed sampling signal:

[0061] r0=Φx(t m )=ΦΨθ m =Aθ m

[0062] Wherein, A=ΦΨ is the sensing matrix.

[0063] Step 3: Get the support set of the corresponding atoms.

[0064] 3.1) Calculate the columns of the sensor matrix A The first k largest inner products with the weighted residuals λ k :

[0065]

[0066] Among them, w k-1 is the weight vector obtained in the last iteration, r k-1 is the residual obtained from the last iteration;

[0067] 3.2) According to λ k Update atomic index set B k , B k =B k ∪{λ k}, set B k Each column in the sensor matrix A corresponding to the index in the form of the support set A of the corresponding atom t :

[0068]

[0069] Among them, j is the index set B k Medium elements, is the j-th column atom in the sensing matrix A.

[0070] Step 4: Support set A t Perform the least squares operation to obtain the new support set.

[0071] In the support set A t Solve the least squares problem above:

[0072] from Select the L item with the largest absolute value, which corresponds to A t The index set of L columns in B tL , the new support set A of the corresponding atoms is obtained tL :

[0073]

[0074] Among them, b is the index set B tL Medium elements, is the atom in column b in the sensing matrix A.

[0075] Step 5: Update weights, least squares solution, and residuals.

[0076] 5.1) Calculate the error vector:

[0077] e(q)=r k-1 (q)-(A tL θ k-1 )(q),q=1,2,...,Q

[0078] where θ k-1 is the sparse vector of the last iteration;

[0079] 5.2) Substitute the error vector e(q) into the loss function J based on the generalized correlation entropy induced metric GCIM loss In order to reduce the influence of non-Gaussian noise, it is expressed as:

[0080]

[0081] in is the normalization constant, Γ(·) is the gamma function, u>0 is the shape parameter, v>0 is the scale parameter, λ=v -u is the kernel parameter;

[0082] 5.3) Set p(q) to be an exponential function and, according to the semi-quadratic minimization theory, minimize the loss function J based on the auxiliary function σ(p(q)) loss , get the minimum value J of the loss function loss-min :

[0083]

[0084] 5.4) Substitute the minimum value J in the above formula loss-min It is expressed as the following weighted least squares model:

[0085]

[0086] 5.5) Given p(q) = -exp(-λe(q) u ), according to the semi-quadratic minimization theory, the weighted least squares solution of the least squares model exists in w k =-p(q)λe(q) u-2 At this point, bring p(q) and e(q) into w k Get the current weight vector w k for:

[0087] w k =v -u |r k-1 -A tL θk-1 u-2 exp(-v -u |(r k-1 -A tL θ k-1 ) u );

[0088] 5.6) According to the above weighted least squares model and the current weight vector w k , find the current weighted least squares solution θ k and the current residual r k for:

[0089] θ k =(A tL T diag(w k )A tL ) -1 A tL T diag(w k )r0,

[0090] r k =r0-A tL θ k .

[0091] Step 6: Check whether the iteration termination condition is met.

[0092] Determine whether the current number of iterations k and the residual ratio P of the current and previous iterations meet the set threshold k max or P < 1 × 10 -2 Conditions:

[0093] If yes, proceed to step (7);

[0094] Otherwise, update the parameters, i.e. set k = k + 1, L = L + 1, and return to step (3);

[0095] Step 7: Estimate the segment center frequency to obtain the center frequencies of all segments.

[0096] 7.1) Calculate the position pos of the maximum non-zero coefficient of the sparse vector:

[0097]

[0098] Where W is the segment signal length, w k-1 is the weight vector at the end of the iteration, r k-1 The residual at the end of the iteration

[0099] 7.2) According to the position pos and sampling frequency f s The relationship between the current segment center frequency f m:

[0100]

[0101] 7.3) Perform steps 7.1)-7.2) for all M segments to obtain the center frequency set F:

[0102] F=[f1,...,f m ,...,f M ].

[0103] Step 8: Obtain the frequency hopping time set according to the center frequency set.

[0104] 8.1) Initialize the observation object set D to be an empty set, and take the difference between the center frequency of each segment in F and the previous segment to obtain the difference value Δf m =f m -f m-1 , treat the segment whose difference value is not 0 and the previous segment as one observation object, and put a total of d observation objects into the set D;

[0105] 8.2) The i-th element D in the observation set D i Add rectangular window function ζ on the left N (n), which takes the value of 1 within the window and 0 outside the window, and is represented as follows:

[0106] Where N is the length of the window function and n is the point in the window function;

[0107] 8.3) Initialize the amplitude ratio set Z to be an empty set. Suppose the frequencies of the signal before and after the window function jump are f1 and f2 respectively. The length of the signal segment with frequency f1 is N1, and the length of the signal segment with frequency f2 is N2. Then N = N1 + N2. The angular frequencies corresponding to the frequencies f1 and f2 are w1 = 2πf1 and w2 = 2πf2 respectively, and the corresponding amplitudes are:

[0108] 8.4) Perform steps 2-5 on the signal within the window function and calculate the ratio b of the amplitudes |F1(w)| and |F2(w)|, and store it in the amplitude ratio set Z;

[0109] 8.5) Let the initial sliding number be h = 0, and the i-th element D in the observation object set D i Slide the rectangular window function ζ with a step size μ N (n), update the number of slides, and execute step 8.4) until the number of slides is

[0110] 8.6) Find the number of slides h1 when the value is closest to 1 in the amplitude ratio set Z, and get the observed object D i The transition time t i for:

[0111]

[0112] Among them, t m-1 is the observed object D i The start time of

[0113] 8.7) Perform steps 8.2)-8.6) for all d observation objects to obtain the transition time set T:

[0114] T=[t1,...,t i ,...,t d ], i=1,2,...,d.

[0115] At this point, the key parameter estimation results of the non-cooperative UAV frequency hopping signal are obtained: the center frequency set F and the hopping time set T.

[0116] The effect of the present invention can be further illustrated by the following simulation experiments:

[0117] 1. Simulation conditions

[0118] The simulation experiment of the present invention was performed on an AMD Ryzen 7 7840H with Radeon 780M Graphics 3.80GHz, a 64-bit Windows operating system, and MATLAB R2023b as the simulation software. The simulation parameters were set as follows:

[0119] Assume that a non-cooperative UAV transmits a 2.4GHz frequency hopping signal with a signal bandwidth within 100MHz. The receiver intercepts the non-cooperative frequency hopping signal and down-converts it to the range of 0-100MHz for processing. The frequency hopping frequency set is set to f i ={8,15,23}MHz, the sampling frequency is f k =50MHz, the frequency hopping period is T h =63×10 -6 s, the noise environment uses the standard Alpha stable distribution S α (0,1,0), the corresponding parameters are β=0,γ=1,η=0, the maximum number of iterations is k max =50, the compression ratio is λ=3, and the estimation performance is evaluated using the normalized mean square error obtained from 100 Monte Carlo experiments.

[0120] 2. Simulation content

[0121] Simulation 1: Under the above conditions, the signal spectrum is reconstructed using the present invention and the existing SAMP-based method, as shown in Figure 2 As shown, Figure 2 (a) is a signal spectrum diagram reconstructed using the present invention, Figure 2 (b) in the figure is the signal spectrum reconstructed using the SAMP method.

[0122] from Figure 2 It can be seen that the signal spectrum diagram reconstructed by the present invention has a clear and prominent peak, which corresponds to the frequency information of the segmented signal; the signal spectrum diagram reconstructed in the existing method has its spectral characteristics obscured by multiple scattered and messy peak points, and the true frequency information of the signal is seriously confused by the noise signal. Figure 2 The comparison results of (a) and (b) show that the present invention has higher estimation accuracy.

[0123] Simulation 2: Under the above conditions, the present invention is used to simulate the reconstruction of signals under different shape parameters u, and the probability of successful reconstruction is calculated. That is, when the error between the main frequency component of the reconstructed signal and the original signal is less than 1×10 -2 This experiment is considered a successful reconstruction experiment. Figure 3 , where the solid line represents the probability of successful reconstruction when the segmented signal contains one frequency information K=1, the short dashed line represents the probability of successful reconstruction when the signal segment contains the center frequency before and after the jump K=2, and the long dashed line represents the overall probability of successful reconstruction.

[0124] Comparing the three curves in the figure, it can be seen that as the value of u increases, the probabilities of K=1, K=2 and overall reconstruction success all decrease. When u is 1.1, the probability of reconstruction success is the highest. Therefore, the present invention selects the fixed parameter u value of 1.1.

[0125] Simulation 3: Under the above conditions, the present invention is used to simulate the reconstruction of the signal under different scale parameters v, and the probability of successful reconstruction is calculated, as shown in FIG. Figure 4 As shown in the figure, by comparing the three curves, it can be seen that with the increase of u value, the reconstruction success probability of K=1, K=2 and the overall value increases first and then decreases. The reconstruction success probability is highest when v is 2.25. Therefore, the present invention selects the fixed parameter u value of 2.25.

[0126] Simulation 4: Under the above conditions, the present invention and the existing SAMP-based method are used to estimate the frequency hopping frequency at different generalized signal-to-noise ratios (GSNRs) when the pulse intensity α is 1.5, and the mean square error is used to evaluate the respective estimation effects. The results are shown in Figure 4. Figure 5As shown, the dotted line represents the mean square error of the frequency hopping frequency estimated by the present invention under different generalized signal-to-noise ratios GSNR, and the solid line represents the mean square error of the frequency hopping frequency estimated by the SAMP method under different generalized signal-to-noise ratios GSNR. Figure 5 It can be seen that the present invention can realize the signal hopping frequency estimation when the generalized signal-to-noise ratio GSNR is greater than or equal to 2dB, while the SAMP-based method can only realize the signal hopping frequency estimation when the generalized signal-to-noise ratio GSNR is greater than or equal to 3dB; when the generalized signal-to-noise ratio GSNR is less than 2dB, although the estimation performance of both methods decreases, the estimation accuracy of the present invention is higher than that of the existing SAMP-based method at the same signal-to-noise ratio.

[0127] Simulation 5: Under the above conditions, the present invention and the existing SAMP-based method are used to estimate the frequency hopping time at different generalized signal-to-noise ratios (GSNRs) when the pulse intensity α is 1.5, and the mean square error is used to evaluate the respective estimation effects. The results are shown in Figure 5. Figure 6 As shown. Figure 6 It can be seen that the present invention can realize signal transition time estimation when the generalized signal-to-noise ratio GSNR is greater than or equal to 2dB, while the SAMP-based method can only realize signal transition time estimation when the generalized signal-to-noise ratio GSNR is greater than or equal to 3dB. When the generalized signal-to-noise ratio GSNR is less than 2dB, although the estimation performance of both methods decreases, the estimation accuracy of the present invention is higher than that of the existing SAMP-based method at the same signal-to-noise ratio.

[0128] Simulation 6, under the above conditions, the present invention and the existing SAMP-based method are used to estimate the frequency hopping frequency at different generalized signal-to-noise ratios (GSNRs) when the pulse intensity α is 1, and the mean square error is used to evaluate the respective estimation effects. The results are shown in FIG. Figure 7 As shown. Figure 7 It can be seen that the present invention can realize the signal hopping frequency estimation when the generalized signal-to-noise ratio GSNR is greater than or equal to 4dB, while the SAMP-based method can only realize the signal hopping frequency estimation when the generalized signal-to-noise ratio GSNR is greater than or equal to 4dB. When the generalized signal-to-noise ratio GSNR is less than 4dB, the estimation performance of both methods decreases, but the estimation accuracy of the present invention is higher than that of the existing SAMP-based method at the same signal-to-noise ratio.

[0129] Simulation 7, under the above conditions, the present invention and the existing SAMP-based method are used to estimate the frequency hopping time at different generalized signal-to-noise ratios (GSNR) when the pulse intensity α is 1, and the mean square error is used to evaluate the respective estimation effects. The results are shown in FIG. Figure 8 As shown. Figure 8It can be seen that the present invention can realize the signal transition time estimation when the generalized signal-to-noise ratio GSNR is greater than or equal to 4dB, while the SAMP-based method can only realize the signal transition time estimation when the generalized signal-to-noise ratio GSNR is greater than or equal to 4dB. When the generalized signal-to-noise ratio GSNR is less than 4dB, the estimation performance of both methods decreases, but the estimation accuracy of the present invention is higher than that of the existing SAMP-based method at the same signal-to-noise ratio.

[0130] Simulation 8, under the above conditions, the frequency hopping time is estimated using the present invention and the existing SAMP-based method at different compression ratios, and the mean square error is used to evaluate the respective estimation effects. The results are as follows: Figure 9 As shown. Figure 9 It can be seen that as the compression ratio increases, the useful signal components obtained by compressed sampling decrease, and the mean square error of the jump time estimation gradually increases. However, the estimation accuracy of the present invention is higher than that of the existing SAMP-based method at the same compression ratio.

[0131] The above simulation results show that when estimating the key parameters of the frequency hopping signal of a non-cooperative UAV under the influence of non-Gaussian noise, the present invention can obtain good estimation performance with less sampled data.

Claims

1. A compressed domain UAV frequency hopping signal parameter estimation method based on GSACMP, characterized by: These include: (1) The frequency hopping signal intercepted by the receiver in non-cooperative UAV communication is x(t), which is evenly divided into M non-overlapping segments of length E. The mathematical model of the segmented UAV frequency hopping signal is obtained as follows: X=[x(t1),x(t2),....,x(t m ),..,x(t M )], where x(t m ) is the mth segment signal, m=1,2,...M; (2) Based on the generalized sparse adaptive correlation entropy matching pursuit GSACMP algorithm, the sparse vector is obtained: (2a) Initialize the index set B0 to be an empty set, set the initial number of iterations k = 1, and the maximum number of iterations k max , the initial step size L = 1, the measurement matrix Φ is a Gaussian random measurement matrix, and the compressed sampling signal, that is, the initial residual, is set to r0 = Φx(t m ), the length is Q, the sparse basis matrix Ψ is the Fourier orthogonal basis matrix, the sensing matrix A = ΦΨ, and the initial weight vector w is the unit vector of E×1; (2b) Calculate each column of the sensor matrix The first k largest inner products with the weighted residuals λ k , and add it to index set B k In the equation, we get the support set A of the corresponding atom t ; (2c) In the support set A t Solve vector The vector The L items with the largest absolute value are added to the index set B tL , the new support set A of the corresponding atoms is obtained tL ; (2d) Using the new support set A tL Update the weight vector, weighted least squares solution, and residual to obtain the current weight vector w k , the current weighted least squares solution is θ k , the current residual is r k ; (2e) Determine whether the current number of iterations k and the residual ratio P of the current and previous iterations meet the set threshold k max or P < 1 × 10 -2 Conditions: If yes, proceed to step (3); Otherwise, update the number of iterations to set k = k + 1, L = L + 1, and return to step (2b); (3) Estimate the center frequency set F of all M segments based on the sparse vector and compressed domain signal characteristics; (4) According to the sparse vector and the segment center frequency f, the set of transition times T of all d observed objects is estimated.

2. The method according to claim 1, characterized in that The frequency hopping signal intercepted by the receiver in the non-cooperative UAV communication in step (1) is x(t), which is expressed as follows: Where E is the signal power, T h is the frequency hopping period, t0 is the starting time, f c Indicates the frequency hopping frequency, N h is the frequency hopping frequency, θ c is the initial frequency, and n(t) is the channel non-Gaussian noise.

3. The method according to claim 1, characterized in that In step (2b), the atomic number of each column of the sensing matrix is ​​calculated. The first k largest inner products with the weighted residuals λ k And the support matrix A of the corresponding index t , the formula is as follows: Among them, w k-1 is the weight vector obtained in the last iteration, r k-1 is the residual obtained from the last iteration, j is the index set B k Medium elements, is the j-th column atom in the sensing matrix A.

4. The method according to claim 1, wherein The support matrix A of the new corresponding index is obtained in step (2c) tL , which is expressed as follows: Among them, b is the index set B tL Medium elements, is the atom in column b in the sensing matrix A.

5. The method according to claim 1, wherein In step (2d), the new support set A is used tL Update the weight vector, weighted least squares solution, and residual to obtain the current weight vector w k , the current weighted least squares solution is θ k , the current residual is r k , implemented as follows: (2d1) Substitute the error vector e(q) into the loss function J based on the generalized correlation entropy induced metric GCIM loss In order to reduce the influence of non-Gaussian noise, it is expressed as: in is the normalization constant, Γ(·) is the gamma function, u>0 is the shape parameter, v>0 is the scale parameter, λ=v -u is the kernel parameter, e(q)=r k-1 (q)-(A tL θ k-1 )(q), q=1,2,...,Q; (2d2) Set p(q) as an exponential function and minimize the loss function J based on the auxiliary function σ(p(q)) according to the semi-quadratic minimization theory. loss , get the minimum value J of the loss function loss-min : (2d3)The above equation can be expressed as the following weighted least squares model: (2d4) Given p(q) = -exp(-λe(q) u ), then the minimum value exists in w k =-p(q)λe(q) u-2 At, we get the current weight vector w k for: w k =v -u |r k-1 -A tL θ k-1 | u-2 exp(-v -u |(r k-1 -A tL θ k-1 )| u ); (2d4) According to the above least squares model and the current weight vector w k , find the current weighted least squares solution θ k and the current residual r k for: θ k (A tL T diag(w k )AM tL ) -1 AM tL T diag(w k )r0, r k Zr0-A tL θ k 。 。 6. The method according to claim 1, wherein In step (3), the center frequency set F of all M segments is estimated based on the sparse vector and compressed domain signal characteristics, which is implemented as follows: (3a) According to the position pos of the largest non-zero coefficient of the sparse vector and the sampling frequency f s Get the center frequency f of the segment m : Where T is the segment signal length, w k-1 is the weight vector at the end of the iteration, r k-1 is the residual at the end of the iteration; (3b) Execute step (3a) for all M segments to obtain the center frequency set: F=[f1,...,f m ,...,f M ],m=1,2,...M。 7. The method according to claim 1, characterized in that In step (4), the transition time set T of all d observation objects is estimated based on the sparse vector and the segment center frequency f, which is implemented as follows: (4a) Initialize the observation object set D to be an empty set, and differentiate the center frequency of each segment from the previous segment to obtain the differential value Δf m =f m -f m-1 , treat the segment whose difference value is not 0 and the previous segment as one observation object, and put a total of d observation objects into the set D; (4b) The i-th element D in the observation set D i Add rectangular window function ζ on the left N (n), which takes the value of 1 inside the window and 0 outside the window, N (n) is represented as follows: Where N is the length of the window function and n is the point in the window function; (4c) Assume that the frequencies of the signal before and after the jump in the window function are f1 and f2 respectively, the length of the signal segment with frequency f1 is N1, and the length of the signal segment with frequency f2 is N2, then N = N1 + N2, and the angular frequencies corresponding to the frequencies f1 and f2 are w1 = 2πf1 and w2 = 2πf2, respectively, and the corresponding amplitudes are: Initialize the amplitude ratio set Z to an empty set; (4d) executing step (2) on the signal within the window function and calculating the ratio b of the amplitudes |F1(w)| and |F2(w)|, and storing it in the amplitude ratio set Z; (4e) Assume that the initial sliding number is h = 0, and i Slide the rectangular window function ζ with a step size μ N (n), update the number of slides, and execute step (4d) until the number of slides is (4f) Find the sliding number h1 when its value is closest to 1 in the amplitude ratio set Z, and get the observed object D i The transition time t i for: Among them, t m-1 is the observed object D i The start time of (4g) Execute steps (4b)-(4f) for all d observation objects to obtain the transition time set T: T=[t1,...,t i ,...,t d ], i=1,2,...,d.

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