CN116886124B - Frequency hopping signal tracking and suppressing method - Google Patents

Frequency hopping signal tracking and suppressing method Download PDF

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CN116886124B
CN116886124B CN202311132750.XA CN202311132750A CN116886124B CN 116886124 B CN116886124 B CN 116886124B CN 202311132750 A CN202311132750 A CN 202311132750A CN 116886124 B CN116886124 B CN 116886124B
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frequency hopping
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time
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CN116886124A (en
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宁涛
程寒珂
李高东
吴骏杰
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Chengdu Jiuhua Yuantong Technology Development Co Ltd
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B1/00Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69Spread spectrum techniques
    • H04B1/713Spread spectrum techniques using frequency hopping
    • H04B1/715Interference-related aspects
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B1/00Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/66Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission for reducing bandwidth of signals; for improving efficiency of transmission
    • H04B1/667Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission for reducing bandwidth of signals; for improving efficiency of transmission using a division in frequency subbands
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B1/00Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69Spread spectrum techniques
    • H04B1/713Spread spectrum techniques using frequency hopping
    • H04B1/715Interference-related aspects
    • H04B2001/7152Interference-related aspects with means for suppressing interference
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B1/00Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69Spread spectrum techniques
    • H04B1/713Spread spectrum techniques using frequency hopping
    • H04B1/7156Arrangements for sequence synchronisation
    • H04B2001/71566Tracking

Abstract

The invention discloses a frequency hopping signal tracking and suppressing method, which comprises the following steps: s1, broadband scanning; s2, signal frequency hopping detection and analysis; s3, frequency hopping tracking pressing. Wherein, the step S2 comprises the following substeps: s21, noise reduction and binarization; s22, extracting image information; s23, clustering and feature extraction; s24, frequency hopping detection; s25, frequency hopping sorting and parameter estimation; the step S25 includes the sub-steps of: s251, extracting a frequency hopping interval; s252, extracting T according to frequency hopping intervals C The method comprises the steps of carrying out a first treatment on the surface of the S253, parameter estimation; the parameters include: bandwidth per hop, residence time, hop speed, hop period, hop pattern. The invention effectively solves the problems of high energy consumption, easy skip and low interference success rate in the prior art.

Description

Frequency hopping signal tracking and suppressing method
Technical Field
The invention relates to the technical field of signal processing, in particular to a frequency hopping signal tracking and suppressing method.
Background
At present, the suppression method for the frequency hopping signal comprises blocking interference, sweep frequency interference, preselected frequency interference, tracking interference and the like. Blocking interference directly transmits broadband signals, does not need to consider a frequency hopping frequency set, and interferes the whole frequency hopping frequency band, but has extremely high energy consumption; the frequency sweep interference emits a narrow-band frequency sweep signal, a frequency hopping frequency set is not considered, the energy consumption is low, but the frequency hopping is easy to leak or the interference time for each hop is insufficient, and the interference success rate is not high; the pre-selected frequency interference is detected and reflected according to a user-defined frequency set, if a signal appears, a signal with a corresponding bandwidth is transmitted to perform interference, and if no signal appears, an interference signal is not transmitted, so that the frequency-hopping signal is more energy-saving than the frequency-sweeping interference, and is easy to leak and hop; the tracking interference firstly estimates the frequency hopping parameter, then carries out the reactive interference according to the parameter in a targeted way, and has higher interference success rate and low energy consumption.
Disclosure of Invention
The invention provides a frequency hopping signal tracking and suppressing method, which comprises the following steps: s1, broadband scanning: the method comprises the steps of performing quick scanning in an extremely wide target frequency band, and automatically searching out a frequency band suspected to contain a frequency hopping signal; s2, signal frequency hopping detection and analysis; s3, frequency hopping tracking pressing.
Further, the step S1 includes the following substeps: s11, using f s Sampling rate is T seconds sampling on the ith frequency band, N data are collected altogether, and n=tf s The method comprises the steps of carrying out a first treatment on the surface of the S12, overlapping every N samples in T seconds fft Point-adding Hanning window short-time Fourier transform operation, sharingA FFT operation, resulting in a time-frequency plot S (T, f) of T seconds samples, t=1, …, K, where f=1, …, N fft ;N fft Is a positive integer.
Further, the step S2 includes the following substeps: s21, noise reduction and binarization; s22, extracting image information; s23, clustering and feature extraction; s24, frequency hopping detection; s25, frequency hopping sorting and parameter estimation.
Further, the step S21 includes the substeps of: s211, comparing the time-frequency diagram with a threshold th to obtain a binarized time-frequency diagram:wherein t=1, …, K; f=1, …, N fft The method comprises the steps of carrying out a first treatment on the surface of the S212, performing two-dimensional median filtering operation on the time direction and the frequency direction of the time-frequency diagram to obtain a noise reduction binarization time-frequency diagram.
Further, the step S22 is to separate the non-stick shapes in all the binarized time-frequency diagrams by adopting a field programmable gate array,and calculating parameters of the shape; the parameters include: maximum number of pixels N on time axis t Maximum number of pixels N on frequency axis f Centroid of shape (T) C ,F C ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein T is C ,F C The average number of pixels on the time axis and the average number of pixels on the frequency axis, respectively.
Further, each shape corresponds to a signal, wherein the signal residence timeThe method comprises the following steps: />The method comprises the steps of carrying out a first treatment on the surface of the Bandwidth per hop of signal>The method comprises the following steps: />The method comprises the steps of carrying out a first treatment on the surface of the Center frequency per hop of signal>The method comprises the following steps: />
Further, the step S23 includes the following substeps: s231, extracting parameters of each shape from the binarization time-frequency diagram, and performing blind clustering by using a flooding-based algorithm to obtain a similar signal setM is a positive integer; s232, extracting characteristics of parameters in each class G (k), wherein the extracted characteristics are as follows: f (F) C Distributed information quantity I (k) and ordered T C The square of the coefficient of variation V (k) of the difference;
wherein, the calculation formula of I (k) is:the method comprises the steps of carrying out a first treatment on the surface of the Wherein P is n (k) Is F C The probability mass function of the distribution, I (k), ranges from: />N is the number of sub-bands of the average segment in the mid-band width, < >>M is a positive integer;
the calculation formula of V (k) is as follows:wherein->And->Ordered T of k signal sets respectively C Variance and expectation of the difference of (c).
Further, the central node parameter in the clustering algorithm is (N t,c ,N f,c ) The parameter of the i-th node within the radius r range is (N t,i ,N f,i ) The search direction is (a, b), and the search range is:the method comprises the steps of carrying out a first treatment on the surface of the The calculation formula of the search direction (a, b) is as follows: />
Further, the step S24 is performed by combining F C Distributed information quantity I (k) and ordered T C The difference coefficient square V (k) of the current frequency band is compared with a threshold to determine a frequency hopping signal in the current frequency band; the information amount range of the frequency hopping signal is as follows:wherein f IF The intermediate frequency bandwidth is B, the bandwidth of each sub-frequency band in the intermediate frequency bandwidth is B, and N is the number of the sub-frequency bands.
Further, the step S25 includes the substeps of: s251, extracting a frequency hopping interval; s252, extracting T according to frequency hopping intervals C The method comprises the steps of carrying out a first treatment on the surface of the S253, parameter estimation; the parameters include: bandwidth per hop, residenceA dwell time, a hop rate, a hop period, and a hop pattern.
The invention provides a frequency hopping signal tracking and suppressing method, which effectively solves the problems of high energy consumption, easy skip leakage and low interference success rate in the prior art.
Drawings
Fig. 1 is a flowchart of a method for tracking and suppressing a frequency hopping signal provided by the present invention;
fig. 2 is a flow chart of a blind clustering algorithm based on flooding of the frequency hopping signal tracking and suppressing method provided by the invention;
fig. 3 is a flowchart of a frequency hopping sorting algorithm of a frequency hopping signal tracking and suppressing method provided by the invention;
fig. 4 is an extracted frequency hopping T of the method for tracking and suppressing frequency hopping signals according to the present invention C Algorithm flow chart of the sequence.
Detailed Description
The following detailed description of embodiments of the invention, taken in conjunction with the accompanying drawings, illustrates only some, but not all embodiments, and for the sake of clarity, illustration and description not related to the invention is omitted in the drawings and description.
As shown in fig. 1, the present invention provides a method for tracking and suppressing a frequency hopping signal, which includes the following steps: s1, broadband scanning; s2, signal frequency hopping detection and analysis; s3, frequency hopping tracking pressing. Wherein, the step S2 comprises the following substeps: s21, noise reduction and binarization; s22, extracting image information; s23, clustering and feature extraction; s24, frequency hopping detection; s25, frequency hopping sorting and parameter estimation; the step S25 includes the sub-steps of: s251, extracting a frequency hopping interval; s252, extracting T according to frequency hopping intervals C The method comprises the steps of carrying out a first treatment on the surface of the S253, parameter estimation; the parameters include: bandwidth per hop, residence time, hop speed, hop period, hop pattern.
In step S1, broadband scanning uses f s Sample rate of =204.8mhz for T seconds on the ith band, then n=tf total s The intermediate frequency bandwidth is 80MHz, and in order to meet the frequency resolution requirement (25 kHz), the FPGA performs non-overlapping N on every 8192 samples in T seconds fft =8192 points plus Hanning window shortTime Fourier Transform (STFT) operations, in commonThe FFT operation is performed to obtain ∈>Time-frequency diagram of second sampling->Because the sampling amount is small, the time-frequency diagram data amount is small, and the time-frequency diagram data amount can be directly stored in the FPGA. And then comparing the time-frequency diagram with a threshold th to obtain a binarized time-frequency diagram:. Wherein, using the duty ratio to judge whether there is a frequency hopping signal, if any f, d is satisfied 0 <D(f)<d 1 If yes, the suspected frequency hopping signal is considered to exist; the duty cycle is calculated as:
in step S2, f is also used for frequency hopping detection s The sampling rate=204.8mhz samples for T seconds on the frequency band detected to be suspected to contain frequency hopping, T is longer than the sampling time per frequency band in the wideband scanning phase, the intermediate frequency bandwidth is 80MHz, and the fft point number is 8192. And the time-frequency diagram is obtained by using the FPGA in the same mode in the broadband scanning stage, and the data of the time-frequency diagram is stored in the DDR due to the large sampling quantity and the large data quantity of the time-frequency diagram.
In the step S21, the time-frequency diagram obtained by short-time Fourier transform has larger noise energy, the time direction and the frequency direction of the time-frequency diagram are subjected to median filtering in order to obtain a cleaner binarized time-frequency diagram, and the filter length is set to be 3 in order to prevent median filtering from filtering out frequency hopping signals with extremely narrow bandwidth (2-3 pixels) or extremely short residence time (2-3 pixels). After median filtering, useAnd obtaining a binarized time-frequency diagram. The binarized time-frequency diagram still contains a large amount of salt and pepper noise, and the median filtering operation amount is large again, which is thatThe secondary noise reduction with higher efficiency is achieved, and the useObtaining a time-frequency diagram of secondary noise reduction; wherein (1)>For corrosion operator +.>For the dilation operator, M is a predefined shape for the erosion and dilation operations on the image, since the signal is presented mainly in a rectangle in the video map, M is defined as a rectangle, the time direction of which is defined as 3 pixels, the frequency direction as 2 pixels, all pixel values as 1, based on the same considerations in the median filtering. The corrosion expansion operation can reduce noise, shape shaping, corner grinding and pattern weak connection part breaking, and is ready for the next image information extraction; this step uses FPGA operations.
In step S22, the image information extraction uses FPGA to separate all non-adhered shapes in the binarized time-frequency diagram, and calculates the parameters of the shapes, wherein the parameters comprise the maximum pixel number N on the time axis t Maximum number of pixels N on frequency axis f Centroid of shape (T) C ,F C ),T C ,F C The average number of pixels on the time axis and the average number of pixels on the frequency axis, respectively. Each shape corresponds to a signal, the signal dwell time being:the method comprises the steps of carrying out a first treatment on the surface of the The bandwidth per hop of the signal is: />The method comprises the steps of carrying out a first treatment on the surface of the The center frequency of each hop of the signal is: />
In step S23, as shown in FIG. 2, after extracting the parameters of each shape from the binarized time-frequency graph, a blind clustering algorithm is used to base on (N t ,N f ) Information pairSignals are classified as having a similarity (N t ,N f ) The signal types of the parameters are unknown, and blind clustering is carried out by adopting a flooding-based algorithm: starting from an unviewed node, searching for distance in the direction defined by (a, b) centered on the nodeAnd (3) dividing the nodes into a class, starting from the nodes, searching again in the direction facing away from the front center, performing recursive operation until the nodes are not searched or the nodes are sparsely distributed, dividing all the accessed nodes into the class at the moment, and repeating the whole operation until all the nodes are accessed. The search direction and sparse distribution in the algorithm are set for cutting off weak connection, if the process is absent, the blind clustering algorithm based on flooding can combine two types with relatively close distance into one type by connecting intermediate nodes; let the parameters of the current center node be (N) t,c ,N f,c ) The parameter of the i-th node within the radius r range is (N t,i ,N f,i ) According to the search direction (a, b), the search range of the current center node isThe search azimuth (a, b) has the following calculation formula: />. The judgment condition of sparse node distribution in the search azimuth is that the average distance from the current center node to all nodes in the range is smaller than r/2. To reduce unnecessary recursive computation, the algorithm only finds the maximum N among all nodes in the node search range t,i (node R), minimum N t,i (node L), maximum N f,i (node U), minimum N f,i (node B) these four nodes operate recursively as the next central node.
Clustering algorithm to obtain similar signal setM is a positive integer, G (k) comprises (T) C ,F C ) Parameters, extracting characteristics for the parameters in each class G (k), are used as the basis of frequency hopping detection and parameter estimation. The extracted characteristic is F C Distributed information quantity I (k) and ordered T C The square of the coefficient of variation V (k) of the difference of (c). Feature I (k) characterizes F C The greater I (k), the greater F C The more dispersed and uniform the distribution, the opposite F C The more concentrated the distribution. Extracting features I (k), by calculating F C Probability mass function of distribution->Dividing the whole frequency band into N segments, and calculating the probability of signal occurrence of each segment, namely F C The probability of occurrence in each segment is then calculated as feature I (k), calculated as:wherein the range of I (k) is: />N is the number of sub-bands of the average segment in the mid-band width, < >>. If F C The distribution is very concentrated, I (k) is close to 0 if the frequency signal is fixed; if F C Uniformly distributed P n (k) For all n equal, then->. F of frequency-hopping signal in general C The distribution is relatively diffuse, which can be separated from the fixed frequency signal by I (k), but it is possible to treat similar spurious signals whose center frequencies are relatively diffuse as frequency hopping. To distinguish the frequency hopping from spurious signals, a feature V (k) needs to be introduced. The square of the coefficient of variation, V (k), is calculated as: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->Ordered T of k signal sets respectively C Variance and expectation of the difference of (c). The feature V (k) characterizes the degree of dispersion of the adjacent signal time differences and takes into account the influence of the mean. The interval between two hops of the frequency hopping signal is generally constant, the average value is larger, the variance is smaller, the V (k) value is small, the average value of the time difference between adjacent signals of the spurious signals is not constant, but the variance is larger, and the V (k) value is generally larger than that of the frequency hopping signal.
In step S24, the presence of the frequency hopping signal of the current frequency band can be determined by comparing the characteristics I (k) and V (k) with a threshold. The selection of the I (k) threshold is related to the total frequency hopping bandwidth B and the frequency band segmentation number N, and the information quantity range of the center frequency of each hop of the frequency hopping signal is as followsThe method comprises the steps of carrying out a first treatment on the surface of the Wherein f IF For the intermediate frequency bandwidth, B is the bandwidth of each sub-band in the intermediate frequency bandwidth, N is the number of sub-bands, and when the frequency hopping is only carried out with two central frequencies F C The information amount is 1 when F C The information amount is maximum when the distribution of the total bandwidth of the frequency hopping is uniform. The frequency set length of the frequency hopping signal is typically much longer than 2, and taking into account F C Will not be evenly distributed, set the I (k) threshold to 2, at this time, the +.>Is not recognized, other frequency hopping signals may not be recognized, depending on F C Is a distribution of the (b). The value of the characteristic V (k) has a plurality of influencing factors, does not have good threshold selection criteria, and a threshold empirical value of 1 is selected through a plurality of experiments. Combining features I (k) and V (k), when V (k)<1 and I (k)>2, the signal set k is identified as frequency hopping.
In step S25, as shown in FIG. 3 and FIG. 4, the frequency hopping sorting algorithm mainly uses the characteristic that the same frequency hopping signal has equal time intervals per hop, and continuously selects the candidate T C Extracting equidistant ordered T C Every time a group T is extracted C Then from candidate T C Excluding the extracted T C Considered as signals of the same frequency hopping station. The core of the algorithm comprises two steps: extracting frequency hopping interval according to hoppingFrequency interval extraction T C . The algorithm for extracting the frequency hopping interval is improved based on the algorithm for searching the longest arithmetic series, all possible difference values are calculated firstly, then a series conforming to each difference value is calculated, and finally the corresponding difference value of the longest series is extracted; algorithm by using ordered T C The ratio of the difference of the sequences to each possible difference value extracts the frequency hopping. After extracting each hop interval, from the ordered T with N numbers based on the interval value C The first number of sequences starts to find, and if the difference between the latter number and the current number is a multiple of the interval value dT and within a tolerance, the latter number is included in the hopping set T h And then, the latter number is used as the current number to continue searching backwards, N sequences are obtained by searching from all N numbers, and the longest one is determined as frequency hopping.
The hopping parameter estimates include bandwidth per hop, residence time, hop speed, hop period, hop pattern, etc. The bandwidth and residence time per hop can be used separatelyAnd->The hop speed is estimated by the inverse of the interval time per hop. The estimation method of the hopping period and hopping pattern is as follows, assuming time-ordered F C The sequence comprises a plurality of frequency hopping periods, and a small continuous frequency sequence without leakage hopping and F can be intercepted C The sequences are mutually correlated, so that a frequency hopping period is found, then a plurality of periods are compared with each other, and the leakage hopping is compensated to the maximum extent, so that a frequency hopping pattern is obtained. For the still existing frequency-hopping in the frequency-hopping pattern, searching the frequency range of the most possible frequency-hopping signal in the time-frequency diagram according to the corresponding time, each frequency-hopping bandwidth and residence time of the frequency-hopping. F (F) C The relation with the true frequency value is +.>. If a complete frequency hopping period cannot be found, only an incomplete frequency hopping center frequency set can be obtained, and the frequency hopping signals need to be extracted and supplemented by subsequent collected data.
While the foregoing is directed to embodiments of the present invention, other and further details of the invention may be had by the present invention, it should be understood that the foregoing description is merely illustrative of the present invention and that no limitations are intended to the scope of the invention, except insofar as modifications, equivalents, improvements or modifications are within the spirit and principles of the invention.

Claims (5)

1. The frequency hopping signal tracking and suppressing method is characterized by comprising the following steps of:
s1, broadband scanning: the method comprises the steps of performing quick scanning in an extremely wide target frequency band, and automatically searching out a frequency band suspected to contain a frequency hopping signal;
s2, signal frequency hopping detection and analysis;
s3, frequency hopping tracking pressing;
the step S1 comprises the following substeps:
s11, using f s Sampling rate is T seconds sampling on the ith frequency band, N data are collected altogether, and n=tf s
S12, overlapping every N samples in T seconds fft Performing short-time Fourier transform operation of a dot-plus-Hanning window, and obtaining a time-frequency diagram S (T, f) of T second sampling by K FFT operations in total; wherein,;t=1,…,K; f=1,…,N fft ;N fft is a positive integer;
the step S2 comprises the following substeps:
s21, noise reduction and binarization;
s22, extracting image information;
s23, clustering and feature extraction;
s24, frequency hopping detection;
s25, frequency hopping sorting and parameter estimation;
the step S23 comprises the following substeps:
s231, extracting parameters of each shape from the binarized time-frequency diagram, and performing blind clustering by using a flooding-based algorithm to obtain a similar signal set G= { G (k), wherein k=1, 2, & gt, M }, and M is a positive integer;
s232, extracting characteristics of parameters in each class G (k), wherein the extracted characteristics are as follows: f (F) C Distributed information quantity I (k) and average pixel number T on ordered time axis C The square of the coefficient of variation V (k) of the difference;
the calculation formula of the I (k) is as follows:
wherein P is n (k) Is F C The probability mass function of the distribution, I (k), ranges from: i (k) is more than or equal to 0 and log is more than or equal to 2 N, N is the number of equally segmented sub-bands within the mid-band bandwidth, n=1, 2,..n, k=1, 2,..m, M is a positive integer;
the calculation formula of V (k) is as follows:wherein σ is 2 (k) And μ (k) is the ordered T of the k signal sets, respectively C Variance and expectation of the difference of (2);
the central node parameter in the clustering algorithm is (N) t,c ,N f,c ) The parameter of the i-th node within the radius r range is (N t,i ,N f,i ) The search direction is (a, b), and the search range is:the method comprises the steps of carrying out a first treatment on the surface of the The calculation formula of the search direction (a, b) is as follows:the method comprises the steps of carrying out a first treatment on the surface of the Wherein t=1, …, K; f=1, …, N fft The method comprises the steps of carrying out a first treatment on the surface of the c is a central node;
the step S24 is performed by combining F C Distributed information quantity I h (k) And ordered T C The difference coefficient square V (k) of the current frequency band is compared with a threshold to determine a frequency hopping signal in the current frequency band; the information amount range of the frequency hopping signal is as follows:wherein f IF Is the intermediate frequency bandwidth, B is the bandwidth of each sub-frequency band in the intermediate frequency bandwidth, N is the number of sub-frequency bands, T C ,F C The average number of pixels on the time axis and the average number of pixels on the frequency axis, respectively.
2. The method of frequency hopping signal tracking hold-down as claimed in claim 1, wherein said step S21 comprises the sub-steps of:
s211, comparing the time-frequency diagram S (t, f) with a threshold th to obtain a binarized time-frequency diagram:wherein t=1, …, K; f=1, …, N fft
S212, performing two-dimensional median filtering operation on the time direction and the frequency direction of the time-frequency diagram to obtain a noise reduction binarization time-frequency diagram.
3. The method for tracking and suppressing a frequency hopping signal according to claim 1, wherein said step S22 is to separate all non-stick shapes in the binarized time-frequency chart by using a field programmable gate array, and calculate parameters of the shapes; the parameters include: maximum number of pixels N on time axis t Maximum number of pixels on frequency axis, shape centroid (T C ,F C ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein T is C ,F C The average number of pixels on the time axis and the average number of pixels on the frequency axis, respectively.
4. A method of frequency hopping signal tracking hold-down as claimed in claim 3, wherein each shape corresponds to a signal, wherein the signal dwell timeThe method comprises the following steps: />The method comprises the steps of carrying out a first treatment on the surface of the Bandwidth per hop of signal>The method comprises the following steps: />The method comprises the steps of carrying out a first treatment on the surface of the Center frequency per hop of signal>The method comprises the following steps: />
5. The method of frequency hopping signal tracking hold-down as claimed in claim 1, wherein said step S25 comprises the sub-steps of: s251, extracting a frequency hopping interval; s252, extracting T according to frequency hopping intervals C The method comprises the steps of carrying out a first treatment on the surface of the S253, parameter estimation; the parameters include: bandwidth per hop, residence time, hop speed, hop period, hop pattern; wherein T is C Is the average number of pixels on the time axis.
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