Dynamic non-cooperative very low frequency signal carrier frequency and phase measurement method and system

Abstract

The application discloses a dynamic non-cooperative very low frequency signal carrier frequency and phase measurement system, comprising a high-precision analog-to-digital converter, a high-precision digital-to-analog converter connected with an FPGA module, and a labview host computer connected with the FPGA module, and discloses a dynamic non-cooperative very low frequency signal carrier frequency and phase measurement method. The FPGA module is used for performing carrier frequency estimation and carrier phase rotation correction on MSK signals collected by the high-precision digital-to-analog converter, and the carrier frequency and phase with high precision are transmitted to the labview host computer to be displayed. The application can realize fast and high-precision carrier frequency estimation, has strong noise resistance and a wide estimation range.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and relates to a system for measuring the carrier frequency and phase of dynamic non-cooperative very low frequency signals, as well as a method for measuring the carrier frequency and phase of dynamic non-cooperative very low frequency signals. Background Technology

[0002] In modern communications, parameter estimation is a fundamental aspect of signal processing, with carrier frequency estimation and phase estimation being the core of parameter estimation and crucial components of spectrum detection. The ability to quickly and accurately estimate the signal carrier frequency is critical to subsequent signal processing, such as the successful estimation of signal symbol rate, carrier amplitude, and carrier phase. Carrier frequency and phase estimation are commonly used in non-cooperative scenarios, such as military communication reconnaissance, and are prerequisites for guided jamming. In communication reconnaissance, the detected signal is a non-cooperative signal, and the receiving party knows very little about the enemy signal characteristics; therefore, the first step is to estimate various parameters of the enemy signal to guide the jammer in interfering with the enemy. Among these parameters, the most fundamental and important are carrier frequency and phase. The jamming signal needs to be aligned with the enemy signal in the frequency domain, and carrier frequency estimation directly determines the effectiveness of the jamming. Furthermore, in the rapidly changing battlefield, in addition to requiring accuracy, speed is also crucial for reconnaissance, enabling rapid signal detection in dynamic situations. Detecting the enemy signal earlier increases the chances of victory. Therefore, finding a carrier frequency estimation algorithm that can adapt to dynamic conditions, is fast, and has high accuracy is of great research significance.

[0003] Numerous studies have investigated carrier frequency estimation, which is broadly categorized into data-assisted and non-data-assisted methods based on whether auxiliary sequences are used. Data-assisted methods work by adding extra preamble or training sequences for carrier recovery at the receiver. Common methods include maximum likelihood estimation, the Fitz algorithm, the L&R algorithm, and the M&M algorithm. In addition to these methods, there is the Interpolated Discrete Fourier Transform (IpDFT) algorithm. This type of algorithm typically uses the FFT peak spectral line and its neighboring spectral lines to calculate interpolation relationships, thereby estimating the frequency. IpDFT algorithms are commonly used for estimating the frequency of real sine waves and rarely involve carrier frequency and phase estimation for very low frequency (VLF) signals. The literature "A Multi-channel MSK Signal Carrier Frequency Estimation Method, System, and Application" achieves high-precision frequency estimation by combining amplitude and phase information, but the estimation time is excessively long, reaching 52 seconds. Summary of the Invention

[0004] The purpose of this invention is to provide a system applicable to the measurement of carrier frequency and phase of dynamic non-cooperative very low frequency (VLF) signals, solving the problems of slow carrier frequency estimation speed and low frequency estimation accuracy under noise interference in the prior art. Another purpose of this invention is to provide a method applicable to the measurement of carrier frequency and phase of dynamic non-cooperative VLF signals, using frequency offset correction caused by phase rotation and iterative processing of the signal frequency using algorithms such as Kalman filtering.

[0005] The technical solution adopted in this invention is a system for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal, including a high-precision analog-to-digital converter, an FPGA module connected to the high-precision analog-to-digital converter, a LabVIEW host computer connected to the FPGA module, and the LabVIEW host computer completes the display of the system. The FPGA module (2) is equipped with a memory.

[0006] Another technical solution of the present invention is: a method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal, which uses the above-mentioned dynamic non-cooperative very low frequency signal carrier frequency and phase measurement system, and is specifically carried out according to the following steps: Step 1: The high-precision analog-to-digital converter (1) periodically acquires the MSK signal and transmits the acquired MSK signal data to the memory of the FPGA module (2). The MSK signal data stored in the FPGA module (2) is called... ; Step 2, transfer the MSK signal data stored in the memory of FPGA module (2) After converting to the frequency domain via Fourier transform, the MSK signal carrier frequency is coarsely estimated using the FPGA module (2) through spectrum search, yielding the desired result. carrier frequency of the signal ; Step 3: In the FPGA module, store the MSK signal data. Digital downconversion to intermediate frequency The intermediate frequency signal is obtained. ; Step 4, for the intermediate frequency signal Perform a square transformation to obtain Using the interpolation discrete Fourier transform algorithm to... The carrier frequency of the signal is finely estimated to obtain the finely estimated carrier frequency. ; Step 5, use the finely estimated carrier frequency ,right MSK signal data stored per second Down-convert to intermediate frequency again A new intermediate frequency signal is obtained. ; Step 6, convert the intermediate frequency signal The signal is divided into multiple segments, and a sum-of-squares time-frequency transformation is performed on each segment. The carrier phase information of each segment is then calculated using the FPGA module. Step 7: Using carrier phase information and the least squares method, perform carrier phase rotation correction on the stored MSK signal data. The carrier frequency is accurately estimated to obtain the accurate carrier frequency value. ; Step 8, process the stored MSK signal data. Kalman filtering is applied to the carrier frequency to reduce the estimation error of carrier frequency and phase; Step 9: If the carrier frequency and phase results meet the accuracy requirements, output the carrier frequency and phase to the LabVIEW host computer, which will then display the output carrier frequency and phase images. If the carrier frequency and phase results do not meet the accuracy requirements, continue with steps 5, 6, 7, and 8.

[0007] Step 1 specifically involves the following: In the actual signal acquired by the high-precision analog-to-digital converter, multiple MSK signals of various frequencies may coexist, along with other signals and noise. These acquired signals are collectively referred to as wideband signals, using the sampling rate... The broadband signal is periodically acquired and stored, and the acquired data is stored in the memory of the FPGA module. Here, the acquired MSK signal data is referred to as... MSK signal data acquired by the high-precision analog-to-digital converter It can be represented as: (1) in, For signal amplitude, For carrier frequency, For signal symbol rate, The symbol sequence representing the signal. This is the initial phase sequence of each symbol in MSK at its start time. It is noise. and They are represented as follows: (2) (3) in, For the symbol period, For taking values The One input code element, For the first The phase constant of each symbol, in order to ensure the continuity of the MSK signal phase at symbol transition times, satisfies: (4) in, The symbol phase is the initial moment of the signal.

[0008] Step 2 specifically involves: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] Do Perform a discrete Fourier transform on the points to obtain the amplitude at each frequency point: (5) in, Indicates that FFT is in The magnitude at the frequency point.

[0009] By searching for the positions corresponding to the maxima of the spectrum, we obtain... A coarse estimate of the carrier frequency of the signal, denoted as . : (6) in for The actual carrier frequency of the signal, This represents the estimation error of the current carrier frequency, with a maximum value equal to the frequency resolution. .

[0010] Step 3 specifically involves: a rough estimate carrier frequency of the signal ,Will Down-conversion to intermediate frequency and reduce the sampling rate A new sampling signal is obtained. .

[0011] Step 4 specifically involves: The power spectrum of the MSK signal is continuous and does not have obvious phase-dependent spectral lines. To concentrate the power spectrum energy of the MSK signal on the intermediate frequency signal... Perform a square transformation to concentrate the power spectrum energy on two spectral lines. Let the signal after squaring be... And then conduct Point-based discrete Fourier transform operation. Search signal. Obtain the peak index of the two largest peaks in the spectrum. and Set peak index. The left and right indices are respectively and And the discrete Fourier transform values ​​of these three points are respectively , and Due to the fence effect, here Only integer values ​​are allowed, but the peak index may actually appear in non-integer positions, so a decimal correction term is also needed. At this point, the peak index is obtained by the following formula: (7) Using the interpolation discrete Fourier transform algorithm to Make an estimate: (8) The more accurate subcarrier frequency can be obtained from the following formula. : (9) Similarly, another subcarrier frequency is obtained. ,Bundle and Attached Obtain the intermediate frequency signal Carrier frequency estimate The frequency offset compensation value is then obtained from formula (10): (10) The signal being estimated at this time The estimated carrier frequency is obtained by the following formula: (11) Step 5 specifically involves: estimating the frequency... , will store Seconds of data Down-convert to intermediate frequency again and reduce the sampling rate A new sampling signal is obtained. .

[0012] Step 6 specifically involves: putting point For each segment of data, perform a square transformation, let the first segment be... The signal after segment square transformation is ,in The maximum value is The signal is obtained from the following formula. Two subcarrier frequencies and : (12) Bundle and Substituting into the following formula yields the piecewise signal. The index values ​​of the two subcarrier frequencies and : (13) Then and Substituting into the following formula, perform the discrete Fourier transform of these two single points for each data segment: (14) in, Pick , Pick or .

[0013] The carrier phase value for each segment of data from the two subcarriers is calculated using the following formula: (15) in, To find complex numbers Angle, Indicates the first segment signal The carrier phase value of subcarrier 1 is similar. Let the signal be... No. The start time of the segment data is ,in The range of values ​​is .

[0014] Step 7 is as follows: After the processing of steps 1 to 6, the frequency estimation error is now very small. Frequency offset will cause phase change. In order to further improve the frequency estimation accuracy, the frequency offset is corrected by phase rotation information.

[0015] The signal after frequency conversion carrier frequency and When there is a frequency offset, it will cause phase rotation, and the corresponding frequency offset compensation value... Satisfy the following formula: (16) in This is the initial value of the phase. This represents the current time phase value.

[0016] In step 6 Substituting into equation (16), we get: (17) in, Pick or ( Convert the above equation into matrix form: (18) in, (19) (20) Equation (20) represents the result under ideal conditions. In actual measurements, errors exist, so equation (18) can be modified as follows: (twenty one) in, for The estimated value is obtained by using the least squares method. The minimum and optimal solution is obtained by the following formula: (twenty two) In step 6 and Substituting each into equation (22) yields The frequency offset compensation values ​​for the two subcarriers of the signal are obtained by dividing each of these compensation values ​​by 2. Frequency offset compensation value of the two subcarriers of the signal and To improve the accuracy of carrier frequency estimation for the signal The average of the frequency offset compensation values ​​of the two subcarriers is obtained by the following formula; (twenty three) At this time, the signal The carrier frequency estimate is obtained by the following formula: (twenty four) At this time, the signal The carrier phase is estimated by equation (19) Provided.

[0017] Step 8 specifically involves the following: When noise interference is significant, the frequency and phase estimates will fluctuate. To reduce estimation errors, a Kalman filter is used. The Kalman filter is obtained from the following formula: (25) The first two formulas are for prediction, and the last three formulas are for updating. This is the predicted state value. Here is the state transition matrix. This is the optimal estimate from the previous moment. For the control matrix, The control input to the system at the previous moment. The predicted values ​​of the covariance matrix are... This is the optimal estimate of the covariance matrix at the previous time step. The process noise covariance matrix is... Kalman gain, State observation matrix, Measure the noise covariance matrix. The state estimate, i.e., the signal The final carrier frequency estimate, The observed value is the carrier frequency estimated in step 7. , Covariance matrix estimate It is an identity matrix.

[0018] The beneficial effects of this invention are: 1. Achieve fast and high-precision carrier frequency estimation, with a frequency estimation error of less than 1e-3Hz within 4s.

[0019] 2. It has strong noise immunity. Even when there is a lot of noise interference, it can still perform carrier frequency estimation with high accuracy through Kalman filtering.

[0020] 3. Wide estimation range, performing frequency estimation for MSK signals in the range of 5kHz-60kHz. Attached Figure Description

[0021] Figure 1 This is an architectural diagram of the dynamic non-cooperative very low frequency signal carrier frequency and phase measurement system of the present invention; Figure 2 This is a flowchart of the dynamic non-cooperative very low frequency signal carrier frequency and phase measurement method of the present invention; Figure 3 This is a graph showing the least squares frequency offset compensation fitting curve of the dynamic non-cooperative very low frequency signal carrier frequency and phase measurement method of the present invention. Figure 4 This is a diagram showing the carrier frequency estimation results of the Kalman filter in the dynamic non-cooperative very low frequency signal carrier frequency and phase measurement method of this invention. Detailed Implementation

[0022] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0023] Invent a dynamic non-cooperative very low frequency signal carrier frequency and phase measurement system, such as Figure 1 As shown, it includes an FPGA module 2, which is connected to a high-precision analog-to-digital converter 1 for acquiring MSK signals. The FPGA module 2 is also connected to a LabVIEW host computer 3. The FPGA module 2 sends the processed carrier frequency and phase to the LabVIEW host computer 3.

[0024] The carrier frequency and phase measurement method of this invention operates in a non-cooperative scenario between the transmitter and receiver, and the object being estimated is a very low frequency signal with MSK modulation. In addition to estimating the carrier frequency of the received MSK signal, the receiver also needs to calculate modulation parameters such as symbol rate and carrier phase.

[0025] The MSK signal acquired by the high-precision analog-to-digital converter 1 can be represented as: (1) in, For signal amplitude, For carrier frequency, For signal symbol rate, The symbol sequence representing the signal. This is the initial phase sequence of each symbol in MSK at its start time. It is noise. and They are represented as follows: (2) (3) in, For the symbol period, For taking values The One input code element, For the first The phase constant of each symbol, in order to ensure the continuity of the MSK signal phase at symbol transition times, satisfies: (4) in, The symbol phase is the initial moment of the signal.

[0026] Since the power spectrum of the MSK signal is continuous and there are no obvious phase-dependent spectral lines, the received MSK signal needs to be further transformed. Ignoring the influence of noise, squaring formula (1) yields: (26) Ignoring the influence of DC, substituting equations (2) to (4) into equation (26) yields: (27) Its carrier frequency is ,make (12) From the formula, we can obtain: (28) (29) It is easy to see from the formula that the squared MSK signal has obvious spectral peaks at two carrier frequencies. conduct Perform a discrete Fourier transform on the point to obtain its spectrum: (30) Searching its spectrum, two maxima were found. and Thus, the formula is determined. and : (31) in, The sampling rate. The phases of the two subcarriers of the MSK signal at time t are: (32) in, To find complex numbers The angle. The present invention provides a method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal, such as... Figure 2 As shown, please follow these steps: Step 1: Collect the MSK signal from the high-precision analog-to-digital converter 1. Periodic data acquisition is performed, and the acquired data is stored in the FPGA's external memory. The FPGA then performs digital signal processing. Specifically, it is implemented as follows: The high-precision analog-to-digital converter 1 may receive multiple MSK signals of various frequencies, along with other signals and noise. These received signals are collectively referred to as wideband signals, measured by the sampling rate. The broadband signal is periodically acquired and stored; the stored data is referred to here as... .

[0027] Step 2: Collect and store the signals After converting to the frequency domain, a spectrum search is used to coarsely estimate the signal carrier frequency using FPGA module 2, resulting in... carrier frequency of the signal ; The coarse estimation of the MSK signal carrier frequency is carried out according to the following steps: right Do Perform a discrete Fourier transform on the points to obtain the amplitude at each frequency point: (5) in, Indicates that FFT is in The magnitude at the frequency point.

[0028] The signal is obtained by searching for the positions corresponding to the maxima of the spectrum. A rough estimate of the carrier frequency, denoted as . : (6) in for The actual carrier frequency of the signal, This represents the estimation error of the current carrier frequency, with a maximum value equal to the frequency resolution. .

[0029] Step 3: Based on the coarse estimate of the signal carrier frequency in Step 2, digitally downconvert the acquired signal to an intermediate frequency. The intermediate frequency signal is obtained. ; Specifically, it will be implemented as follows: (roughly estimated) carrier frequency of the signal ,Will Down-conversion to intermediate frequency and reduce the sampling rate New samples were obtained. .

[0030] Step 4, for the intermediate frequency signal from step 3 Perform a square transformation to obtain Using the interpolation discrete Fourier transform algorithm to... The carrier frequency of the signal is estimated in detail.

[0031] The specific implementation shall be as follows: The power spectrum of the MSK signal is continuous and does not have obvious phase-dependent spectral lines. To concentrate the power spectrum energy of the MSK signal on the intermediate frequency signal... Perform a square transformation to concentrate the power spectrum energy on two spectral lines. Let the signal after squaring be... And then conduct Point-based discrete Fourier transform operation. Search signal. Obtain the peak index of the two largest peaks in the spectrum. and Set peak index. The left and right indices are respectively and And the discrete Fourier transform values ​​of these three points are respectively , and Due to the fence effect, here Only integer values ​​are allowed, but the peak index may actually appear in non-integer positions, so a decimal correction term is also needed. At this point, the peak index is obtained by the following formula: (7) Using the interpolation discrete Fourier transform algorithm to Make an estimate: (8) The more accurate subcarrier frequency can be obtained from the following formula. : (9) Similarly, another subcarrier frequency is obtained. ,Bundle and Attached Obtain the intermediate frequency signal Carrier frequency estimate The frequency offset compensation value is then obtained from formula (10): (10) The signal being estimated at this time The estimated carrier frequency is obtained by the following formula: (11) Step 5, using the frequencies estimated in Step 4, for The signal is down-converted to an intermediate frequency again to obtain a new sampled signal. ; The specific implementation shall be as follows: Estimated frequency , will store Seconds of data Down-convert to intermediate frequency again and reduce the sampling rate A new sampling signal is obtained. .

[0032] Step 6, convert the intermediate frequency signal from step 5 to... The signal is divided into multiple segments, and a sum-of-squares time-frequency transformation is performed on each segment. The carrier phase information of each segment is calculated by FPGA module 2. The specific implementation shall be as follows: Bundle point For each segment of data, perform a square transformation, let the first segment be... The signal after segment square transformation is ,in The maximum value is ; In equation (12), using replace Signals can be obtained Two subcarrier frequencies and ,Bundle and Substituting into the following formula yields the piecewise signal. The index values ​​of the two subcarrier frequencies and : (13) Then, the index values ​​of the two subcarrier frequencies and Substituting into the following formula, perform the discrete Fourier transform of these two single points for each data segment: (14) in, Pick , Pick or .

[0033] The carrier phase value for each segment of data from the two subcarriers is calculated using the following formula: (15) in, To find complex numbers Angle, Indicates the first segment signal The carrier phase value of subcarrier 1 is similar. Let the signal be... No. The start time of the segment data is ,in The range of values ​​is .

[0034] Step 7: Utilizing the phase rotation information and combining it with the least squares method, perform carrier phase rotation correction to achieve... Accurate estimation of signal carrier frequency; The specific implementation shall be as follows: After the previous processing, the frequency estimation error is now very small. Frequency offset will cause a change in phase. In order to further improve the accuracy of frequency estimation, the frequency offset is corrected by phase rotation information.

[0035] The signal after frequency conversion carrier frequency and When there is a frequency offset, it will cause phase rotation, and the corresponding frequency offset compensation value... Satisfy the following formula: (16) in This is the initial value of the phase. This represents the current time phase value.

[0036] In step 6 Substituting into equation (16), we get: (17) in, Pick or ( Convert the above equation into matrix form: (18) in, (19) (20) Equation (20) represents the result under ideal conditions. In actual measurements, errors exist, so equation (18) can be modified as follows: (twenty one) in, for The estimated value is obtained by using the least squares method. The minimum and optimal solution is obtained by the following formula: (twenty two) In step 6 and Substituting each into equation (22) yields The frequency offset compensation values ​​for the two subcarriers of the signal are obtained by dividing each of these compensation values ​​by 2. Frequency offset compensation value of the two subcarriers of the signal and To improve the accuracy of carrier frequency estimation for the signal The average of the frequency offset compensation values ​​of the two subcarriers is obtained by the following formula; (twenty three) The MSK signal stored at this time The carrier frequency estimate is obtained by the following formula: (twenty four) The MSK signal stored at this time The carrier phase is estimated by equation (19) Provided.

[0037] Step 8, for Kalman filtering is applied to the signal carrier frequency to improve its noise immunity. The specific implementation shall be as follows: When noise interference is significant, the frequency and phase estimates will fluctuate. To reduce estimation errors, Kalman filtering is used. Kalman filtering is obtained from the following formula: (25) The first two formulas are for prediction, and the last three formulas are for updating. This is the predicted state value. Here is the state transition matrix. This is the optimal estimate from the previous moment. For the control matrix, The control input to the system at the previous moment. The predicted values ​​of the covariance matrix are... This is the optimal estimate of the covariance matrix at the previous time step. The process noise covariance matrix is... Kalman gain, State observation matrix, Measure the noise covariance matrix. The state estimate, i.e., the signal The final carrier frequency estimate, The observed value is the carrier frequency estimated in step 7. , Covariance matrix estimate It is an identity matrix.

[0038] Step 9: If the carrier frequency estimation result meets the accuracy requirements, output the carrier frequency and phase to the LabVIEW host computer 3; otherwise, continue with steps 5, 6, 7, and 8.

[0039] In the dynamic non-cooperative very low frequency signal carrier frequency and phase measurement method of the present invention: Pure digital processing is employed, with data collected only once and processed iteratively to shorten the estimation time. An interpolation Discrete Fourier Transform (DFT) algorithm is used to initially perform a fast and relatively accurate carrier frequency estimation, followed by carrier phase rotation correction, which significantly reduces the estimation time. Down-conversion lowers the signal variation value to a lower intermediate frequency, further reducing the sampling rate and the number of DFT points, decreasing computational complexity, and shortening the DFT computation time.

[0040] A combination of interpolation discrete Fourier transform algorithm and carrier phase rotation correction algorithm is used to achieve high-precision carrier frequency and phase estimation.

[0041] In the phase rotation correction algorithm, the least squares method is used to fit the frequency offset compensation curve, which improves the noise immunity. Kalman filtering is applied to the final estimated frequency and phase to make the estimation results converge, which further improves the noise immunity and obtains a higher accuracy carrier frequency and phase estimate.

[0042] In the coarse carrier frequency estimation stage, a higher sampling rate and an appropriate number of discrete Fourier transform points are selected to perform error estimation on the MSK signal in the 5kHz-60kHz range. A coarse frequency estimate (Hz) is performed. After the coarse estimate, a down-conversion is performed to perform a fine frequency estimate. Combining the coarse and fine estimates results in a more accurate frequency and phase estimate over a wider range.

[0043] like Figure 3 The graph shows the fitting curve of the least squares frequency offset compensation method, with the horizontal axis representing time. The vertical axis represents the phase; the number of data segments. Taking 10, the 10 dots and 10 intersections in the diagram represent the phase values ​​of 10 data subcarriers 1 and 2. The dashed and dotted line segments are the frequency offset compensation fitting curves for subcarriers 1 and 2, respectively. The solid line is the combined frequency offset compensation fitting curve for subcarriers 1 and 2. The slope of the curve divided by 360° is the frequency offset compensation value. Under noise-free conditions, the phase should change linearly. Figure 3 The results show that under noise interference, the phase fluctuates and is not a straight line. The noise immunity of the system is improved by fitting the curve using the least squares method.

[0044] like Figure 4 The graph shows the carrier frequency estimation results using Kalman filtering. The horizontal axis represents the number of Kalman filter iterations, and the vertical axis represents the frequency. Gaussian white noise with a signal-to-noise ratio of 10dB has been added to the signal. The dashed lines with larger fluctuations represent the measured carrier frequency input to the Kalman filter, while the solid lines with smaller fluctuations represent the frequency value after Kalman filtering. The dotted and straight lines represent the actual carrier frequency value. Figure 4 The results show that the carrier frequency estimation error fluctuation is significantly reduced after filtering, demonstrating the good noise resistance of the present invention; the estimation speed of the present invention is relatively fast, and the output results basically converge in the second iteration (4s).

[0045]

[0046] Table 1 Carrier frequency estimation results Table 1 shows the carrier frequency estimation results of this invention. Gaussian white noise with a signal-to-noise ratio of 10dB was added to the signal, and 50 iterations were performed for each frequency. As can be seen from Table 1, the maximum error after 5 iterations is 0.001Hz, and the mean absolute error and RMSE are both better than 0.001Hz, indicating that this invention still has high accuracy in carrier frequency estimation under noise interference.

Claims

1. A method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal, characterized in that, This method uses a dynamic non-cooperative very low frequency signal carrier frequency and phase measurement system, and is implemented according to the following steps: Step 1: The high-precision analog-to-digital converter (1) periodically acquires the MSK signal and transmits the acquired MSK signal data to the memory of the FPGA module (2). The MSK signal data stored in the FPGA module (2) is called... ; Step 2, transfer the MSK signal data stored in the memory of FPGA module (2) After being converted to the frequency domain by Fourier transform, the MSK signal carrier frequency is roughly estimated by using the FPGA module (2) through spectrum search, and the result is obtained. carrier frequency of the signal ; Step 3: In the FPGA module (2), store the MSK signal data. Digital downconversion to intermediate frequency The intermediate frequency signal is obtained. ; Step 4, for the intermediate frequency signal Perform a square transformation to obtain Using the interpolation discrete Fourier transform algorithm to... The carrier frequency of the signal is finely estimated to obtain the finely estimated carrier frequency. ; Step 5, use the finely estimated carrier frequency ,right MSK signal data stored per second Down-convert to intermediate frequency again A new intermediate frequency signal is obtained. ; Step 6, convert the intermediate frequency signal Divide the signal into multiple segments, perform a sum-of-squares time-frequency transformation on each segment, and calculate the carrier phase information of each segment using the FPGA module (2). Step 7: Using carrier phase information and the least squares method, perform carrier phase rotation correction on the stored MSK signal data. The carrier frequency is accurately estimated to obtain the accurate carrier frequency value. ; Step 8, process the stored MSK signal data. Kalman filtering is applied to the carrier frequency to reduce the estimation error of carrier frequency and phase; Step 9: If the carrier frequency and phase results meet the accuracy requirements, output the carrier frequency and phase to the LabVIEW host computer (3). The LabVIEW host computer (3) will then display the output carrier frequency and phase images. If the carrier frequency and phase results do not meet the accuracy requirements, continue with steps 5, 6, 7 and 8. The dynamic non-cooperative very low frequency signal carrier frequency and phase measurement system includes a high-precision analog-to-digital converter (1), which is connected to an FPGA module (2). The FPGA module (2) is connected to a LabVIEW host computer (3), and the FPGA module (2) is equipped with a memory.

2. The method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal according to claim 1, characterized in that, Step 1 specifically involves: a high-precision analog-to-digital converter (1) where multiple frequencies of MSK signals, other signals, and noise may coexist in the actual acquired signal. These acquired signals are collectively referred to as broadband signals, with the sampling rate... The broadband signal is periodically acquired and stored, and the acquired data is stored in the memory of the FPGA module (2). Here, the acquired MSK signal data is referred to as... The MSK signal data acquired by the high-precision analog-to-digital converter (1) It can be represented as: （1） in, For signal amplitude, For carrier frequency, For signal symbol rate, The symbol sequence representing the signal. This is the initial phase sequence of each symbol in MSK at its start time. For noise, and They are represented as follows: （2） （3） in, For the symbol period, For taking values The One input code element, For the first The phase constant of each symbol, in order to ensure the continuity of the MSK signal phase at symbol transition times, satisfies: （4） in, The symbol phase is the initial moment of the signal.

3. The method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal according to claim 1, characterized in that, The coarse estimation of the signal carrier frequency in step 2 is specifically as follows: right Do Perform a discrete Fourier transform on the points to obtain the amplitude at each frequency point: （5） in, Indicates that FFT is in The magnitude at the frequency point; By searching for the positions corresponding to the maxima of the spectrum, we obtain... A coarse estimate of the carrier frequency of the signal, denoted as . : （6） in for The actual carrier frequency of the signal, This represents the estimation error of the current carrier frequency, with a maximum value equal to the frequency resolution. .

4. The method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal according to claim 1, characterized in that, Step 3 specifically involves: a rough estimate. carrier frequency of the signal ,Will Down-conversion to intermediate frequency and reduce the sampling rate A new sampling signal is obtained. .

5. The method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal according to claim 1, characterized in that, Step 4 specifically involves: the power spectrum of the MSK signal is continuous and has no obvious phase-dependent spectral lines; in order to concentrate the energy of the MSK power spectrum on the intermediate frequency signal... Perform a square transformation to concentrate the power spectrum energy on two spectral lines. Let the signal after squaring be... And then conduct Point-based discrete Fourier transform operation, searching for the signal Obtain the peak index of the two largest peaks in the spectrum. and Set peak index The left and right indices are respectively and And the discrete Fourier transform values ​​of these three points are respectively , and Due to the fence effect, here Only integer values ​​are allowed, but the peak index may actually appear in non-integer positions, so a decimal correction term is also needed. At this point, the peak index is obtained by the following formula: （7） Using the interpolation discrete Fourier transform algorithm to Make an estimate: （8） The more accurate subcarrier frequency can be obtained from the following formula. : （9） Similarly, another subcarrier frequency is obtained. ,Bundle and Attached The intermediate frequency signal is obtained from Carrier frequency estimate At this point, the frequency offset compensation value is obtained from formula (10): （10） The signal being estimated at this time The estimated carrier frequency is obtained by the following formula: （11）。 6. The method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal according to claim 1, characterized in that, Step 5 specifically involves estimating the frequency. , will store Seconds of data Down-convert to intermediate frequency again and reduce the sampling rate A new sampling signal is obtained. .

7. The method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal according to claim 1, characterized in that, Step 6 specifically involves: putting... point For each segment of data, perform a square transformation, let the first segment be... The signal after segment square transformation is ,in The maximum value is The signal is obtained from the following formula. Two subcarrier frequencies and : （12） subcarrier frequency and Substituting into the following formula yields the piecewise signal. The index values ​​of the two subcarrier frequencies and : （13） Then and Substituting into the following formula, perform the discrete Fourier transform of these two single points for each data segment: （14） in, Pick , Pick or ; The carrier phase value for each segment of data from the two subcarriers is calculated using the following formula: （15） in, To find complex numbers Angle, Indicates the first segment signal The carrier phase value of subcarrier 1 is similar. Let the signal No. The start time of the segment data is ,in The range of values ​​is .

8. The method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal according to claim 1, characterized in that, Step 7 specifically involves the following steps: After processing in steps 1-6, the frequency estimation error is now very small. Frequency offset will cause a change in phase. In order to further improve the frequency estimation accuracy, the frequency offset is corrected by using phase rotation information. The signal after frequency conversion carrier frequency and When there is a frequency offset, it will cause phase rotation, and the corresponding frequency offset compensation value... Satisfy the following formula: （16） in This is the initial value of the phase. This represents the current time phase value. In step 6 Substituting into equation (16), we get: （17） in, Pick or ( Convert the above equation into matrix form: （18） in, （19） （20） Equation (20) represents the result under ideal conditions. In actual measurements, errors exist, so equation (18) can be modified as follows: （21） in, for The estimated value is obtained by using the least squares method. The minimum and optimal solution is obtained by the following formula: （22） In step 6 and Substituting each into equation (22) yields The frequency offset compensation values ​​for the two subcarriers of the signal are obtained by dividing each of these compensation values ​​by 2. Frequency offset compensation value of the two subcarriers of the signal and To improve the accuracy of carrier frequency estimation for the signal The average of the frequency offset compensation values ​​of the two subcarriers is obtained by the following formula; （23） At this time, the signal The carrier frequency estimate is obtained by the following formula: （24） At this time, the signal The carrier phase is estimated by equation (19) Provided.

9. The method for measuring the carrier frequency and phase of a dynamic non-cooperative very low frequency signal according to claim 1, characterized in that, Step 8 specifically involves: when noise interference is significant, the frequency and phase estimates will fluctuate. To reduce estimation errors, a Kalman filter is used. The Kalman filter is obtained from the following formula: （25） The first two formulas are for prediction, and the last three formulas are for updating. This is the predicted state value. Here is the state transition matrix. This is the optimal estimate from the previous moment. For the control matrix, The control input to the system at the previous moment. The predicted values ​​of the covariance matrix are... This is the optimal estimate of the covariance matrix at the previous time step. The process noise covariance matrix is... Kalman gain, State observation matrix, Measure the noise covariance matrix. The state estimate, i.e., the signal The final carrier frequency estimate, The observed value is the carrier frequency estimated in step 7. , Covariance matrix estimate It is an identity matrix.

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