A target frequency hopping period estimation method based on rotation phase factor
By using a rotation phase factor-based method, the frequency hopping period is directly estimated from the relative time series of the signal, which solves the problems of high computational complexity and stacking errors in the existing technology, and achieves fast and accurate frequency hopping period estimation, which is applicable to a variety of target situations.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- 36TH RES INST OF CETC
- Filing Date
- 2022-01-07
- Publication Date
- 2026-05-19
AI Technical Summary
Existing technologies have high computational complexity in frequency hopping signal period estimation and are prone to estimation errors due to stacking errors, making it difficult to achieve fast and accurate parameter estimation.
A target frequency hopping period estimation method based on rotating phase factor is adopted. By acquiring the relative time series of the signal, an all-zero sequence and a unit pulse sequence are established. The detection results are calculated by combining the rotating phase factor, and the frequency hopping period is directly estimated without the need for clustering.
It achieves fast and accurate period estimation for arbitrary combination of frequency hopping signals, avoids clustering errors, and is applicable to single targets, multiple targets with the same hopping speed, and multiple targets with different hopping speeds. It has high estimation accuracy and engineering application value.
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Figure CN116455423B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of signal processing technology, and in particular to a target frequency hopping period estimation method based on a rotating phase factor. Background Technology
[0002] Frequency hopping communication has been widely used in military communications due to its good anti-interference performance and low probability of interception. With the improvement of technology maturity and the rapid development of electronic devices, civilian equipment such as drones have also begun to use frequency hopping technology for telemetry and control communication on a large scale.
[0003] In spectrum monitoring and communication systems, as a non-cooperative third party, accurate parameter estimation of frequency-hopping signals is a crucial prerequisite for the effective detection of these signals and the realization of system functions and performance. The frequency-hopping signal period is one of the most important characteristic parameters of a frequency-hopping signal; therefore, rapid and accurate estimation of the frequency-hopping period is of great significance for subsequent frequency-hopping signal sorting, frequency-hopping demodulation, and other processes.
[0004] Existing methods require clustering the frequency hopping signal descriptors according to their hopping speed before estimating the hopping period for each cluster. This method has high computational complexity. Furthermore, since clustering is required first, it can easily lead to clustering errors when the target hopping speeds are close, thereby reducing the accuracy of frequency hopping period estimation. Summary of the Invention
[0005] Based on the above analysis, the present invention aims to provide a target frequency hopping period estimation method based on a rotating phase factor, in order to solve the problems of high computational complexity and easy error in frequency hopping period estimation due to stacking errors in existing methods.
[0006] On one hand, embodiments of the present invention provide a target frequency hopping period estimation method based on a rotating phase factor, comprising the following steps:
[0007] Acquire the frequency hopping signal and obtain the relative time series of the signal based on the occurrence time of the frequency hopping signal;
[0008] Based on the duration and time estimation accuracy of the frequency hopping signal, an all-zero sequence is established, and based on the relative time sequence of the signal, a unit pulse sequence is obtained from the all-zero sequence.
[0009] Within the frequency hopping shift value range, for each shift value taken, the detection threshold corresponding to the shift value is obtained according to the duration of the frequency hopping signal; and the unit pulse sequence is shifted according to the shift value to obtain the unit pulse delay sequence. Based on the rotation phase factor, the detection result corresponding to the shift value is obtained according to the unit pulse sequence and the unit pulse delay sequence; if the detection result is greater than the detection threshold, the shift value is used as an estimate of the frequency hopping period of a target; finally, the frequency hopping period estimates of one or more targets in the frequency hopping signal are obtained.
[0010] Based on a further improvement to the above method, a relative time series of the signal is obtained according to the occurrence time of the frequency hopping signal, including:
[0011] The frequency hopping signals are sorted from smallest to largest occurrence time to obtain the signal occurrence time series;
[0012] The relative time series of the signal is obtained by subtracting the first element from each element value in the time series of the signal occurrence.
[0013] Based on further improvements to the above method, the descriptor of the frequency hopping signal includes: signal occurrence time, signal duration, signal center frequency, signal bandwidth, and signal amplitude;
[0014] The duration of the frequency hopping signal is obtained by adding the duration of the signal corresponding to the last element in the signal occurrence time series to the value of the last element in the relative time series.
[0015] Based on a further improvement of the above method, the length of the all-zero sequence is obtained by dividing the duration of the frequency hopping signal by the time estimation accuracy;
[0016] Based on the relative time series of the signal, a unit pulse sequence is obtained from the all-zero sequence, including:
[0017] Divide each element value in the relative time series of the signal by the time estimation precision, and round off to obtain multiple positions to be marked;
[0018] Based on multiple positions to be marked, set 1 at the corresponding positions in the all-zero sequence to obtain the unit pulse sequence.
[0019] Based on further improvements to the above method, the frequency hopping shift value ranges from the preset minimum frequency hopping period value divided by the time estimation accuracy to the maximum frequency hopping period value divided by the time estimation accuracy.
[0020] Based on a further improvement of the above method, for each shift value extracted, the detection threshold corresponding to the shift value is obtained according to the duration of the frequency hopping signal. The calculation formula is:
[0021] M th (τ)=λT L / τ
[0022] Among them, T L The frequency hopping signal duration is represented by τ, the shift value is represented by λ, and the detection threshold adjustment value is represented by 0.2≤λ≤0.6.
[0023] Based on a further improvement of the above method, the unit pulse sequence is shifted according to the shift value to obtain a unit pulse delay sequence, including:
[0024] Subtract the maximum frequency hopping period value from the duration of the frequency hopping period, and then divide by the time estimation accuracy to obtain the maximum shift sequence number.
[0025] Starting from the first element in the unit pulse sequence, a shift value is added to its corresponding index as a delay index. Based on the delay index, the corresponding element value is taken out as the first element value of the unit pulse delay sequence. This process is repeated until the element corresponding to the largest shift index in the unit pulse sequence is shifted to obtain the unit pulse delay sequence.
[0026] Based on the above method, a further improvement is made. Based on the rotation phase factor, the detection result corresponding to the shift value is obtained according to the unit pulse sequence and the unit pulse delay sequence. This includes multiplying the element value at each same position in the unit pulse sequence and the unit pulse delay sequence, and multiplying by the rotation phase factor corresponding to the shift value. The result is obtained by summing the results.
[0027] Based on a further improvement of the above method, the rotation phase factor is related to the shift value, and the calculation formula is:
[0028]
[0029] Where i represents the index variable to be shifted, τ represents the shift value, j represents a complex number, and H min H represents the minimum frequency hopping period value. max T represents the maximum frequency hopping period value. L The duration of the frequency hopping signal is represented by P, and the time estimation accuracy is represented by P.
[0030] Based on further improvements to the above method, the detection result corresponding to the shift value is calculated according to the following formula:
[0031]
[0032] in, S1 represents the rotation phase factor corresponding to the shift value, S2 represents the unit pulse sequence, and S3 represents the unit pulse delay sequence.
[0033] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:
[0034] 1. It can quickly estimate the period of any combination of frequency hopping signals at once, without having to cluster them according to the hopping speed and then estimate the period of each cluster separately, thus effectively avoiding errors in the period estimation caused by clustering errors.
[0035] 2. By introducing a rotating phase factor, the harmonic components of the frequency hopping period estimate can be effectively suppressed, and the accurate estimate of the frequency hopping period can be obtained quickly and effectively.
[0036] 3. The method is simple, has high estimation accuracy, and is applicable to single-target frequency hopping, multiple targets with the same hopping speed, and multiple targets with different hopping speeds, thus having high engineering application value.
[0037] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description
[0038] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.
[0039] Figure 1 This is a flowchart of the target frequency hopping period estimation method based on the rotating phase factor in Embodiment 1 of the present invention;
[0040] Figures 2(a) and 2(b) are the first and second detection results in scenario 1 of embodiment 2 of the present invention, respectively.
[0041] Figure 3 This is a graph showing the change in the second detection result and the corresponding detection threshold in scenario 1 of embodiment 2 of the present invention.
[0042] Figures 4(a) and 4(b) are the first and second detection results in scenario 2 of embodiment 2 of the present invention, respectively.
[0043] Figure 5 This is a graph showing the change in the second detection result and the corresponding detection threshold in scenario 2 of embodiment 2 of the present invention. Detailed Implementation
[0044] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.
[0045] Example 1,
[0046] A specific embodiment of the present invention discloses a target frequency hopping period estimation method based on a rotating phase factor, such as... Figure 1 As shown, it includes the following steps:
[0047] S11: Obtain the frequency hopping signal and obtain the relative time series of the signal based on the occurrence time of the frequency hopping signal;
[0048] It should be noted that the frequency hopping signal is obtained based on time-frequency signal detection, and the descriptor of the frequency hopping signal is obtained, including: signal occurrence time, signal duration, signal center frequency, signal bandwidth and signal amplitude information.
[0049] Based on the occurrence time of the frequency hopping signal, the relative time series of the signal is obtained, including:
[0050] The frequency hopping signals are sorted from smallest to largest occurrence time to obtain the signal occurrence time series;
[0051] The relative time series of the signal is obtained by subtracting the first element from each element value in the time series of the signal occurrence.
[0052] Specifically, the N frequency hopping signals are sorted in ascending order of their occurrence time to obtain the corresponding frequency hopping signal occurrence time sequence T. s =(t0,t1,…,t N-1 ), T s Subtracting the first element t0 from each element yields the relative occurrence time series T of each frequency hopping signal. s0 = (0, t1-t0, t2-t0, ..., t N-1 -t0)=(t′0,t′1,t′2,…t′ N-1 ).
[0053] Compared with existing technologies, the acquired frequency hopping signals do not need to be clustered according to the signal duration. They can be sorted directly according to the signal occurrence time in the descriptor, which is simple and fast.
[0054] S12: Based on the duration of the frequency hopping signal and the time estimation accuracy, establish an all-zero sequence, and based on the relative time sequence of the signal, obtain the unit pulse sequence based on the all-zero sequence;
[0055] It should be noted that the duration of the frequency hopping signal is obtained by adding the signal duration corresponding to the last element in the signal occurrence time series to the value of the last element in the relative time series.
[0056] Based on the duration T of the frequency hopping signal L With time estimation accuracy P, establish a length of T L The sequence of all zeros / P, where the time estimation accuracy P is related to the FPGA (Field Programmable Gate Array) detection algorithm for acquiring the frequency hopping signal. Once the detection algorithm is fixed, this value is determined accordingly. In this embodiment, P is set to 10µs.
[0057] Based on the relative time series of the signal, a unit pulse sequence is obtained from the all-zero sequence, including:
[0058] Divide each element value in the relative time series of the signal by the time estimation precision, and round off to obtain multiple positions to be marked;
[0059] Based on multiple positions to be marked, set 1 at the corresponding positions in the all-zero sequence to obtain the unit pulse sequence.
[0060] Specifically, the unit pulse sequence is represented as:
[0061] S13: Within the frequency hopping shift value range, for each shift value taken out, the detection threshold corresponding to the shift value is obtained according to the duration of the frequency hopping signal; and the unit pulse sequence is shifted according to the shift value to obtain the unit pulse delay sequence. Based on the rotation phase factor, the detection result corresponding to the shift value is obtained according to the unit pulse sequence and the unit pulse delay sequence; if the detection result is greater than the detection threshold, the shift value is used as an estimate of the frequency hopping period of a target; finally, the frequency hopping period estimates of one or more targets in the frequency hopping signal are obtained.
[0062] It should be noted that the frequency hopping shift value ranges from the preset minimum frequency hopping period value divided by the time estimation accuracy to the maximum frequency hopping period value divided by the time estimation accuracy, expressed as: Among them, H min H represents the minimum frequency hopping period value. max This represents the maximum frequency hopping period value. Preferably, the minimum frequency hopping period value is set to 500us, and the maximum frequency hopping period value is set to 10000us.
[0063] Each shift value is sequentially extracted from the frequency hopping shift value range, and the detection threshold and detection result corresponding to each shift value are calculated. Specifically, this includes:
[0064] ① Based on the duration of the frequency hopping signal, the detection threshold corresponding to the shift value is obtained. The calculation formula is:
[0065] M th (τ)=λT L / τ formula (1)
[0066] Among them, T L τ represents the duration of the frequency hopping signal, λ represents the shift value, and λ represents the detection threshold adjustment value. Considering that the actual signal duration and detection results may have false alarms and missed alarms, λ is usually 0.2≤λ≤0.6. Preferably, λ is set to 0.3.
[0067] ② Shift the unit pulse sequence according to the shift value to obtain the unit pulse delay sequence, including:
[0068] Subtract the maximum frequency hopping period value from the duration of the frequency hopping period, and then divide by the time estimation accuracy to obtain the maximum shift sequence number.
[0069] Starting from the first element in the unit pulse sequence, a shift value is added to its corresponding index as a delay index. Based on the delay index, the corresponding element value is taken out as the first element value of the unit pulse delay sequence. This process is repeated until the element corresponding to the largest shift index in the unit pulse sequence is shifted to obtain the unit pulse delay sequence.
[0070] It should be noted that when calculating the maximum shiftable sequence number, the duration of the frequency hopping period is subtracted from the maximum frequency hopping period value. This can prevent the element sequence number of the unit pulse sequence from overflowing after the shift value is added during the shift process, and also ensure that the unit pulse delay sequence length obtained for each shift value is the same, thereby improving the accuracy of the detection result calculation.
[0071] ③ Based on the rotation phase factor, the detection results corresponding to the shift value are obtained according to the unit pulse sequence and the unit pulse delay sequence, including:
[0072] Multiply the unit pulse sequence by the element value at each corresponding position in the unit pulse delay sequence, and simultaneously multiply by the rotation phase factor corresponding to the shift value. Summing these results yields the detection result corresponding to the shift value.
[0073] It should be noted that the rotating phase factor is related to the shift value. By introducing the rotating phase factor, the harmonic components of the frequency hopping period estimate can be effectively suppressed, thereby obtaining an accurate estimate of the frequency hopping period quickly and effectively.
[0074] The formula for calculating the rotation phase factor is:
[0075]
[0076] Where i represents the index variable to be shifted, τ represents the shift value, j represents a complex number, and H min H represents the minimum frequency hopping period value. max T represents the maximum frequency hopping period value. L The duration of the frequency hopping signal is represented by P, and the time estimation accuracy is represented by P.
[0077] Based on the rotation phase factor, the detection result corresponding to the shift value is calculated according to formula (3):
[0078]
[0079] Where S1 represents the unit pulse sequence and S2 represents the unit pulse delay sequence. This represents the rotation phase factor corresponding to the shift value.
[0080] The detection threshold calculated for each shift value is compared with the detection result. If the detection result is greater than the detection threshold, the shift value is used as an estimate of the frequency hopping period of a target. After traversing each shift value in the frequency hopping shift value range, the estimated frequency hopping period of one or more targets in the frequency hopping signal is obtained.
[0081] It should be noted that when only one detection result is greater than the corresponding detection threshold, it means that the currently acquired frequency hopping signal contains only one target with a frequency hopping cycle; when multiple detection results are greater than the corresponding detection threshold, it means that the currently acquired frequency hopping signal contains multiple targets with different frequency hopping cycles.
[0082] Compared with existing technologies, this embodiment provides a target frequency hopping period estimation method based on a rotating phase factor. This method can quickly estimate the period of any combination of frequency hopping signals at once, without the need to cluster the signals according to their hopping speed and then estimate the period of each cluster separately. This effectively avoids errors in frequency hopping period estimation caused by clustering errors. By introducing a rotating phase factor, the harmonic components of the frequency hopping period estimate can be effectively suppressed, and an accurate estimate of the frequency hopping period can be obtained quickly and effectively. The method is simple, has high estimation accuracy, and is applicable to single-target frequency hopping, multiple targets with the same hopping speed, and multiple targets with different hopping speeds. It has high engineering application value.
[0083] Example 2,
[0084] This embodiment uses the target frequency hopping period estimation method based on the rotating phase factor in Embodiment 1 to estimate the target frequency hopping period of the acquired frequency hopping signal.
[0085] Set the frequency hopping signal time estimation accuracy P to 10µs, and the minimum frequency hopping period value H. min The maximum frequency hopping period value H is 500µs. max The detection threshold λ is set to 0.3, with a duration of 10000µs. The frequency hopping signals acquired have start times of 130µs, 20µs, and 216µs, and a duration of 3 seconds. Two scenarios are set: in scenario 1, there are three frequency hopping signals with a hopping period of 1000µs each; in scenario 2, there are three frequency hopping signals with different hopping periods of 1000µs, 2000µs, and 5000µs.
[0086] When estimating the target frequency hopping period, in scenario 1, the rotation phase factor is not introduced first. That is, for each shift value, the element values at the same position in the unit pulse sequence S1 and the unit pulse delay sequence S2 are multiplied and summed to obtain the first detection result corresponding to the current shift value. The first detection result of scenario 1 is shown in Figure 2(a). Then, the rotation phase factor is introduced, and the second detection result of scenario 1 is calculated using formula (3) in embodiment 1, as shown in Figure 2(b).
[0087] As shown in Figure 2(a), multiple peaks appear at the 1000µs position and its integer multiples therein of the potential frequency hopping period. Simultaneously, due to measurement errors, multiple spurious peaks appear around each main peak, leading to incorrect frequency hopping period estimation. However, as shown in Figure 2(b), using the method of Example 1, the detection results based on the rotating phase factor only show a single peak at the estimated frequency hopping period position. Furthermore, the spurious peaks caused by measurement errors in Figure 2(a) are significantly suppressed in Figure 2(b). Introducing the rotating phase factor effectively overcomes the influence of subharmonics and spurious peaks, improving the speed and accuracy of frequency hopping period estimation.
[0088] The curves showing the variation of the second detection result C(τ) based on the rotation phase factor and the corresponding detection threshold Th(τ) in Scenario 1 are as follows: Figure 3 As shown. From Figure 3 As can be seen from the second detection result, there is only one point that exceeds the detection threshold, corresponding to a frequency hopping period estimated value of 1000us, which is consistent with the setting of actual scenario 1.
[0089] Similarly, in scenario 2, the first detection result of scenario 2 without introducing the rotation phase factor is shown in Figure 4(a); the second detection result of scenario 2 with the rotation phase factor is shown in Figure 4(b).
[0090] As shown in Figure 4(a), multiple peaks appear at the potential frequency hopping period positions of 1000µs, 2000µs, and 5000µs, as well as their integer multiples thereof. Simultaneously, due to measurement errors, multiple spurious peaks appear around each main peak, leading to incorrect frequency hopping period estimation. However, as shown in Figure 4(b), using the method of Example 1, the detection results based on the rotating phase factor only show three peaks at the estimated frequency hopping period positions of 1000µs, 2000µs, and 5000µs. Furthermore, the spurious peaks caused by measurement errors in Figure 4(a) are significantly suppressed. By introducing the rotating phase factor, the influence of subharmonics and spurious peaks is effectively overcome, improving the speed and accuracy of frequency hopping period estimation.
[0091] The curves showing the variation of the second detection result C(τ) based on the rotation phase factor and the corresponding detection threshold Th(τ) in scenario 2 are as follows: Figure 5 As shown. From Figure 5 It can be seen that there are 3 points where the second detection result is greater than the detection threshold, and the corresponding frequency hopping period estimates are 1000us, 2000us and 5000us, which are consistent with the actual scenario 2 settings.
[0092] Compared with the prior art, this embodiment effectively suppresses the harmonic components of the frequency hopping period estimate by introducing a rotating phase factor, and is suitable for single-target frequency hopping, multiple targets with the same hopping speed, and multiple targets with different hopping speeds. It achieves fast and accurate estimation of the frequency hopping period of multiple targets, which has obvious advantages.
[0093] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.
[0094] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.
Claims
1. A target frequency hopping period estimation method based on a rotating phase factor, characterized in that, Includes the following steps: Acquire the frequency hopping signal and obtain the relative time series of the signal based on the occurrence time of the frequency hopping signal; A zero sequence is established based on the duration of the frequency hopping signal and the time estimation accuracy. The length of the zero sequence is obtained by dividing the duration of the frequency hopping signal by the time estimation accuracy. Based on the relative time series of the signal, a unit pulse sequence is obtained from the all-zero sequence, including: dividing each element value in the relative time series of the signal by the time estimation precision, rounding to obtain multiple positions to be marked; setting 1 at the corresponding position in the all-zero sequence according to the multiple positions to be marked, thereby obtaining the unit pulse sequence; Within the frequency hopping shift value range, for each shift value taken, a detection threshold corresponding to the shift value is obtained based on the duration of the frequency hopping signal; and the unit pulse sequence is shifted according to the shift value to obtain a unit pulse delay sequence, including: subtracting the maximum frequency hopping period value from the duration of the frequency hopping signal, and then dividing by the time estimation accuracy to obtain the maximum to-be-shifted index; starting from the first element in the unit pulse sequence, the shift value is added to its corresponding index as a delay index; based on the delay index, the corresponding element value is taken as the first element value of the unit pulse delay sequence, until the element corresponding to the maximum to-be-shifted index in the unit pulse sequence is... The process involves shifting the signal to obtain a unit pulse delay sequence. Based on a rotation phase factor, and according to the unit pulse sequence and the unit pulse delay sequence, a detection result corresponding to the shifted value is obtained. This includes multiplying the unit pulse sequence by the element value at each corresponding position in the unit pulse delay sequence, and simultaneously multiplying by the rotation phase factor corresponding to the shifted value. The summation yields the detection result corresponding to the shifted value. If the detection result is greater than a detection threshold, the shifted value is used as an estimate of the frequency hopping period of a target. Finally, an estimate of the frequency hopping period of one or more targets in the frequency hopping signal is obtained. The rotation phase factor is related to the shifted value, and its calculation formula is: in, i This represents the sequence number variable to be shifted. τ Indicates the shift value. j To represent a complex number, H min This represents the minimum frequency hopping period value. H max This represents the maximum frequency hopping period value. T L Indicates the duration of the frequency hopping signal. P Indicates the accuracy of the time estimation.
2. The target frequency hopping period estimation method based on rotating phase factor according to claim 1, characterized in that, The step of obtaining the relative time series of the signal based on the occurrence time of the frequency hopping signal includes: The frequency hopping signals are sorted from smallest to largest occurrence time to obtain the signal occurrence time series; Subtract the first element value from each element value in the time sequence of the signal occurrence to obtain the relative time sequence of the signal.
3. The target frequency hopping period estimation method based on rotating phase factor according to claim 2, characterized in that, The descriptor of the frequency hopping signal includes: signal occurrence time, signal duration, signal center frequency, signal bandwidth, and signal amplitude; The duration of the frequency hopping signal is obtained by adding the duration of the signal corresponding to the last element in the time sequence of the signal occurrence to the value of the last element in the relative time sequence of the signal.
4. The target frequency hopping period estimation method based on rotating phase factor according to claim 1 or 3, characterized in that, The frequency hopping shift value ranges from the preset minimum frequency hopping period value divided by the time estimation accuracy to the maximum frequency hopping period value divided by the time estimation accuracy.
5. The target frequency hopping period estimation method based on rotating phase factor according to claim 4, characterized in that, For each shift value extracted, the detection threshold corresponding to the shift value is obtained based on the duration of the frequency hopping signal. The calculation formula is: M th ( τ )= λT L / τ in, T L Indicates the duration of the frequency hopping signal. τ Indicates the shift value. λ This indicates the detection threshold adjustment value, 0.2≤ λ ≤0.
6.
6. The target frequency hopping period estimation method based on the rotating phase factor according to claim 5, characterized in that, The detection result corresponding to the shift value is calculated according to the following formula: in, This represents the rotation phase factor corresponding to the shift value. S 1 represents a unit pulse sequence. S 2 represents a unit pulse delay sequence.