CN112162152B - Frequency estimation method of sine wave coherent pulse train signal based on phase straight line fitting - Google Patents

Abstract

The invention discloses a sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting. The method comprises the following steps: FFT operation is performed on each of a plurality of pulses of an input complex-analysis digital signal, and an average value of initial estimation values of the frequency of each pulse is denoted as f _e The method comprises the steps of carrying out a first treatment on the surface of the By f _e Performing down-conversion processing on the input complex analysis digital signal, and extracting phase angle information of each pulse; preprocessing the obtained phase angle data and adjusting an initial phase angle; extracting the phase mean value and the center moment of each pulse; performing linear fitting operation on the phase average value of each pulse, and calculating a frequency estimation error delta f according to the result of linear approximation _e The method comprises the steps of carrying out a first treatment on the surface of the When Deltaf _e When the frequency is not smaller than the set threshold value, the frequency estimated value f _e Adjusted to f _e ＝f _e +△f _e Performing down-conversion again, extracting phase angle information of each pulse again, and repeating the steps; otherwise directly output f _e As a final estimate of the frequency. The frequency estimation method has better frequency estimation precision and wider application range.

Description

Frequency estimation method of sine wave coherent pulse train signal based on phase straight line fitting

Technical field

The invention relates to the technical field of digital signal processing, in particular to a frequency estimation method of sine wave coherent pulse train signals based on phase straight line fitting.

Background technique

In many engineering application fields, such as radar/sonar signal processing, communication signal processing, passive positioning, measurement and testing, etc., high-precision frequency estimation of sine wave coherent pulse train signals is required. Performing an FFT operation on the signal and using the frequency corresponding to the strongest amplitude spectrum peak as the frequency estimate is a commonly used frequency estimation method for sine wave coherent pulse train signals (hereinafter referred to as the FFT algorithm). In addition to being restricted by the detection signal-to-noise ratio, the frequency estimation performance of the FFT algorithm is also restricted by its digital resolution f _s /M (f _s and M are the sampling frequency and the number of FFT operation points respectively). When f _s is constant, every time the digital resolution is doubled, the amount of data storage and calculation will be doubled accordingly. Therefore, the FFT algorithm is usually not suitable for high-precision frequency estimation of sine wave coherent pulse train signals. occasion.

To solve this problem, people have proposed a variety of solutions. One of the solutions is to first use the FFT algorithm to obtain a rough estimate of the frequency, and then use the maximum likelihood estimation method to find the frequency within a certain range around the frequency estimate. precise estimate. When the error of the rough frequency estimate is large, the calculation amount of this frequency estimation method is still very large. Another effective solution proposed by people is to first use the FFT algorithm to obtain a rough estimate of the frequency, then use the estimate to downconvert each coherent pulse, and find the mean value of each pulse signal after downconversion, and then , and then use the FFT algorithm to estimate the frequency error from the mean sequence of each pulse signal, and use the frequency error estimate to correct the rough frequency estimate (hereinafter referred to as the two-level FFT algorithm). The computational complexity of the two-level FFT algorithm is relatively small, but it is only suitable for frequency estimation of coherent pulse trains with fixed repetition frequencies, and its frequency estimation performance is still restricted by the detection signal-to-noise ratio and digital resolution.

Contents of the invention

The purpose of the present invention is to provide a high-precision iterative estimation method for the frequency of sine wave coherent pulse train signals based on the combination of FFT algorithm and phase linear fitting, which can be used for high-precision estimation of sine wave coherent pulse train signals with arbitrary changes in repetition frequency. Precision frequency estimation.

The technical solution to achieve the purpose of the present invention is: a frequency estimation method of sine wave coherent pulse train signals based on phase straight line fitting, which includes the following steps:

Step 1: Perform FFT operations on multiple pulses of the input complex analytical digital signal, and use the frequency value corresponding to the strongest spectral line as the initial estimate of each pulse frequency. The average value of the initial estimate of each pulse frequency is recorded as f _e ;

Step 2: Use the average value f _e of the initial estimated value of each pulse frequency to perform down-conversion processing on the input complex analytical digital signal;

Step 3: Extract the phase angle information of each pulse from the down-converted complex analytical digital signal;

Step 4: Preprocess the obtained phase angle data and adjust the initial phase angle;

Step 5: Extract the phase mean and center time of each pulse;

Step 6: Perform a straight line fitting operation on the phase mean value of each pulse, and then calculate the frequency estimation error Δf _e based on the straight line fitting results;

Step 7: Compare Δf _e with the set threshold: when Δf _e is less than the set threshold, directly output f _e as the final estimated value of the frequency, otherwise go to step 8;

Step 8: Adjust the frequency estimate f _e to f _e = f _e + Δf _e , use Δf _e to perform down-conversion processing again on the input complex analytical digital signal that has been down-converted and adjusted by the initial phase, and then go to step 3 .

Further, as described in step 1, perform FFT operations on the multiple pulses of the input complex analytical digital signal, and use the frequency value corresponding to the strongest spectral line as the initial estimated value of each pulse frequency, and use the initial estimated value of each pulse frequency to The average value is denoted as f _e , as follows:

remember is the noisy complex analytical sine wave coherent pulse train signal to be processed, where 0≤t≤T; w(t) is the observation white noise with zero mean; f ₀ , θ, T, _Ti , τ _i and P They are the signal frequency, initial phase, duration, the center moment of the i-th pulse, the duration of the i-th pulse and the number of pulses;/> is a rectangular pulse with duration τ _i and time center T _i ; f ₀ is the quantity to be estimated; at the same time, the sampling frequency and number of sampling points of signal s ₀ (t) are f _s and N respectively, and the signal sequence obtained after sampling is s ₀ (n), n=1,2,3,…,N-1;

Perform M-point FFT operation on the i-th pulse signal. M is greater than the number of sampling points of the i-th pulse signal. The frequency value corresponding to the strongest spectral line As an initial estimate of each pulse frequency, find all/> After that, the average value of the initial estimated value of each pulse frequency is recorded as f _e , then/>

Further, as described in step 2, the average value f _e of the initial estimated value of each pulse frequency is used to perform down-conversion processing on the input complex analytical digital signal, specifically as follows:

The sampling signal sequence s ₀ (n) is down-converted using f _e . In the subsequent signal processing process, the part other than the duration of each pulse is set to zero, that is Get the sampled signal sequence after downconversion/> n=1, 2, 3,..., N-1.

Further, as described in step 3, the phase angle information of each pulse is extracted from the complex analytical digital signal after downconversion processing, as follows:

Compute data series The phase angle _information θ _i (n) of each pulse signal _in Number of sampling points; record the sampling data sequence of the i-th pulse as/> then/> -π≤θ _i (n)≤π, n=0, 1, 2, ..., Q _i -1.

Further, as described in step 4, preprocess the obtained phase angle data and adjust the initial phase angle, specifically as follows:

1) First determine whether the percentage of phase folding phenomena in the pulses of each extracted pulse phase data sequence exceeds the threshold: if more than 75% of the pulse phase data in the pulses have phase folding phenomena, adjust the initial phase angle of the signal, and Re-extract the phase data sequence of each pulse, and the specific adjustment method is as follows: n = 0, 1, 2,..., N-1; then, extract the phase data sequence of each pulse; if the number of pulses with phase folding phenomenon in the phase data in the pulse is less than 75%, then the pulses with phase folding phenomenon will be Perform de-phase folding operation on internal phase data;

2) Eliminate the phase data whose intra-pulse phase estimation value does not meet the requirements. The specific method is: first calculate ψ _i (n) = θ _i (n+1)-θ _i (n), n = 0, 1, 2 ,..., Q-1, and then find the mean and standard deviation of ψ(n). When the difference between ψ(n) and its mean is greater than 3 times its standard deviation, use ψ(n-1) or ψ(n+1 ) instead of ψ(n).

Further, as described in step 5, extract the phase mean value and center moment of each pulse, as follows;

Calculate the center time t _ci of each pulse after phase preprocessing and the mean value Θ _i of each pulse phase data sequence to obtain a new phase data sequence Θ _i (t _ci ), i=1, 2,...,P.

Further, perform a straight line fitting operation on the phase mean value of each pulse as described in step 6, and then calculate the frequency estimation error Δf _e based on the straight line fitting result, as follows:

Perform a straight line fitting operation on the phase data sequence Θ _i (t _ci ), i=p, p+1, p+2,..., L-1, p and L respectively correspond to the largest phase data segment without phase folding. The index number of the starting pulse and the final pulse;

Assume that the fitted straight line is Θ(t _ci )=2πΔf _e t _ci +θ ₀ , i=p, p+1, p+2,..., L-1, then Δf _e is the frequency estimation error.

Further, as described in step 8, use Δf _e to perform down-conversion processing again on the input complex analytical digital signal that has been down-converted and adjusted by the initial phase. The formula is as follows:

Among them, n=0, 1, 2,..., N-1.

Compared with the existing technology, the significant advantages of this invention are: (1) performing necessary preprocessing operations on intra-pulse and inter-pulse phase data, and the frequency estimation accuracy is better; (2) using intra-pulse phase data to perform phase straight line When fitting, there are no constraints on the inter-pulse interval; (3) It can be used for high-precision frequency estimation of sine wave coherent pulse train signals with fixed repetition frequency, and can also be used for sine wave coherent pulse train signals with arbitrary repetition frequency. High-precision frequency estimation has a wider range of applications.

Description of the drawings

Figure 1 is a flow chart of the frequency estimation method of sine wave coherent pulse train signals based on phase straight line fitting according to the present invention.

Figure 2 is a schematic diagram of each pulse phase data sequence extracted in step 3 in the embodiment of the present invention.

Figure 3 is a schematic diagram of each pulse phase data sequence extracted in step 3 in the embodiment of the present invention.

Figure 4 is a schematic diagram of the mean sequence of each pulse phase data sequence extracted in step 5 in the embodiment of the present invention.

FIG. 5 is a schematic diagram of each pulse phase data sequence extracted in step 3 after performing a phase straight line fitting using the phase mean sequence shown in FIG. 4 in the embodiment of the present invention.

FIG. 6 is a schematic diagram of each pulse phase mean sequence extracted from each pulse phase data sequence shown in FIG. 4 in an embodiment of the present invention.

Figure 7 is a comparison chart of the estimated performance simulation results of the method provided by the present invention and the two-level FFT algorithm under several input signal-to-noise ratio conditions.

Detailed ways

The present invention is a sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting. The steps are as follows:

Step 1: Perform FFT operations on multiple pulses of the input complex analytical digital signal, and use the frequency value corresponding to the strongest spectral line as the initial estimate of each pulse frequency. The average value of the initial estimate of each pulse frequency is recorded as f _e ;

Step 2: Use the average value f _e of the initial estimated value of each pulse frequency to perform down-conversion processing on the input complex analytical digital signal;

Step 3: Extract the phase angle information of each pulse from the down-converted complex analytical digital signal;

Step 4: Preprocess the obtained phase angle data and adjust the initial phase angle;

Step 5: Extract the phase mean and center time of each pulse;

Step 6: Perform a straight line fitting operation on the phase mean value of each pulse, and then calculate the frequency estimation error Δf _e based on the straight line fitting results;

Step 7: Compare Δf _e with the set threshold (the threshold is determined by the required estimation accuracy): when Δf _e is less than the set threshold, directly output f _e as the final estimated value of the frequency, otherwise go to step 8;

Step 8: Adjust the frequency estimate f _e to f _e = f _e + Δf _e , use Δf _e to perform down-conversion processing again on the input complex analytical digital signal that has been down-converted and adjusted by the initial phase, and then go to step 3 .

Further, as described in step 1, perform FFT operations on the multiple pulses of the input complex analytical digital signal, and use the frequency value corresponding to the strongest spectral line as the initial estimated value of each pulse frequency, and use the initial estimated value of each pulse frequency to The average value is denoted as f _e , as follows:

remember is the noisy complex analytical sine wave coherent pulse train signal to be processed, where 0≤t≤T; w(t) is the observation white noise with zero mean; f ₀ , θ, T, _Ti , τ _i and P They are the signal frequency, initial phase, duration, center moment of the i-th pulse, duration of the i-th pulse and number of pulses respectively; i=1, 2, 3,...,P; is a rectangular pulse with duration τ _i and time center T _i ; f ₀ is the quantity to be estimated; at the same time, the sampling frequency and number of sampling points of signal s ₀ (t) are f _s and N respectively, and the signal sequence obtained after sampling is s ₀ (n), n=1, 2, 3,..., N-1;

Perform M-point FFT operation on the i-th pulse signal (M should be greater than the number of sampling points of the i-th pulse signal, but in order to improve the accuracy of frequency estimation, the value of M should be increased as much as possible; in order to avoid a low input signal-to-noise ratio Under certain conditions, pure reception noise signals are introduced due to inaccurate estimation of the start and end times of each pulse. A more conservative estimate of the pulse start and end times should be used to ensure that pure reception noise signals are not introduced). The frequency value corresponding to the strongest spectral line As an initial estimate of each pulse frequency, find all After that, the average value of the initial estimated value of each pulse frequency is recorded as f _e , then/> When the input signal-to-noise ratio is high, such as greater than 10dB, in order to reduce the amount of calculations, it is only necessary to calculate the frequency estimates of a small number of pulses and then average them.

Further, as described in step 2, the average value f _e of the initial estimated value of each pulse frequency is used to perform down-conversion processing on the input complex analytical digital signal, specifically as follows:

The sampling signal sequence s ₀ (n) is down-converted using f _e . In the subsequent signal processing process, the part other than the duration of each pulse is set to zero, that is Get the sampled signal sequence after downconversion/> n=1, 2, 3,..., N-1.

Further, as described in step 3, the phase angle information of each pulse is extracted from the complex analytical digital signal after downconversion processing, as follows:

Compute data series The phase angle _information θ _i (n) of each pulse signal _in The number of sampling points; record the sampling data sequence of the i-th pulse as then/> -π≤θ _i (n)≤π, n=0, 1, 2, ..., Q _i -1.

Further, as described in step 4, preprocess the obtained phase angle data and adjust the initial phase angle, specifically as follows:

1) First determine whether the percentage of phase folding phenomena in the pulses of each extracted pulse phase data sequence exceeds the threshold: if more than 75% of the pulse phase data in the pulses have phase folding phenomena, adjust the initial phase angle of the signal, and Re-extract the phase data sequence of each pulse, and the specific adjustment method is as follows: n = 0, 1, 2,..., N-1; then, extract the phase data sequence of each pulse; if the number of pulses with phase folding phenomenon in the phase data in the pulse is less than 75%, then the pulses with phase folding phenomenon will be Perform de-phase folding operation on internal phase data;

2) Eliminate the phase data whose intra-pulse phase estimation value does not meet the requirements. The specific method is: first calculate ψ _i (n) = θ _i (n+1)-θ _i (n), n = 0, 1, 2 ,..., Q-1, and then find the mean and standard deviation of ψ(n). When the difference between ψ(n) and its mean is greater than 3 times its standard deviation, use ψ(n-1) or ψ(n+1 ) instead of ψ(n).

Further, as described in step 5, extract the phase mean value and center moment of each pulse, as follows;

Calculate the center time t _ci of each pulse after phase preprocessing and the mean value Θ _i of each pulse phase data sequence to obtain a new phase data sequence Θ _i (t _ci ), i=1, 2,...,P.

Further, perform a straight line fitting operation on the phase mean value of each pulse as described in step 6, and then calculate the frequency estimation error Δf _e based on the straight line fitting result, as follows:

Perform a straight line fitting operation on the phase data sequence Θ _i (t _ci ), i=p, p+1, p+2,..., L-1, p and L respectively correspond to the largest phase data segment without phase folding. The index number of the starting pulse and the final pulse;

Assume that the fitted straight line is Θ(t _ci )=2πΔf _e t _ci +θ ₀ , i=p, p+1, p+2,..., L-1, then Δf _e is the frequency estimation error.

Before proceeding to step 6, you can also linearize the phase data sequence Θ _i (t _ci ) (i = 1, 2,..., P) obtained in step 6, that is, solve the phase folding operation, so as to make more The pulse phase data participates in the straight line fitting operation.

Further, as described in step 8, use Δf _e to perform down-conversion processing again on the input complex analytical digital signal that has been down-converted and adjusted by the initial phase. The formula is as follows:

Among them, n=0, 1, 2,..., N-1.

Compared with the two-level FFT algorithm, although the calculation complexity of the present invention is increased, its frequency estimation accuracy is better, and it overcomes the limitations of the two-level FFT algorithm, and can be used for fixed repetition frequency sine wave coherent pulse trains. The high-precision frequency estimation of the signal can also be used for the high-precision frequency estimation of the sine wave coherent pulse train signal with arbitrary changes in repetition frequency, so it has a wider application range.

The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

Example

Figure 1 shows the specific processing steps of the single sine wave coherent pulse train signal frequency estimation method adopted in the present invention. The noisy complex analytical sinusoidal coherent pulse train signal to be processed in the present invention can be expressed in the form shown in formula (1).

In formula (1), w(t) is the observation white noise with zero mean; f ₀ , θ, T, _Ti , τ _i and P are the signal frequency, initial phase, duration and center of the i-th pulse respectively. time, duration of the i-th pulse and number of pulses; is a rectangular pulse with duration τ _i and time center T _i ; f ₀ is the quantity to be estimated. At the same time, the sampling frequency and number of sampling points of the signal s ₀ (t) are recorded as f _s and N respectively, and the signal sequence obtained after sampling is s ₀ (n) (n=1, 2, 3,..., N-1). The phase of the signal sequence can be expressed in the form shown in Equation (2) (Although the present invention processes sampled digital signals, the continuous time variable t is still used to represent the correspondence between the signal phase and time, which does not affect description of the invention).

In formula (2), is the phase noise generated by w(t). When w(t) is random noise with zero mean,/> It is also random noise with zero mean. Theoretically, ignore/> The influence of φ(t) changes linearly with time t, whether within each pulse duration or throughout the entire observation time. However, when performing numerical calculations on φ(t), φ(t) can only take values within the range of (-π, π). Therefore, during the entire observation time, φ(t) should actually change periodically linearly. , unless the sine wave coherent pulse train signal to be processed only changes within one cycle during the entire observation time. When/> Cannot ignore untied time unless/> Strong enough to submerge φ(t), otherwise this change pattern of φ(t) should still be observed.

Perform M-point FFT operation on the i-th (i=1, 2, 3,...,P) pulse signal (M should be greater than the number of sampling points of the i-th pulse signal, but in order to improve the frequency estimation accuracy, it should be increased as much as possible The value of M; in order to avoid the introduction of pure reception noise signals due to inaccurate estimation of the start and end times of each pulse under low input signal-to-noise ratio conditions, a more conservative estimate of the pulse start and end times should be used to ensure that the pure reception noise signal portion is not introduced) , the frequency value corresponding to the strongest spectral line is obtained, recorded as Find all After that, get a rough estimate of frequency/>

After using f _e to perform down-conversion processing on the signal sequence s ₀ (n) (n = 1, 2, 3,..., N-1), the extracted signal phase information can be expressed in the form shown in equation (3).

In formula (3), Δf=f ₀ -f _e . Since the frequency estimation error Δf is usually much smaller than f ₀ , the extracted signal phase information may no longer change periodically, or at least the change period will increase significantly.

affected by phase noise And the influence of the value of the initial phase value θ, the intra-pulse phase information extracted after down-conversion processing of the signal sequence s ₀ (n) (n = 1, 2, 3,..., N-1) may have out-of-tolerance or phase-folded data. Necessary preprocessing of the extracted phase data is necessary to obtain high-precision frequency estimates.

Figure 2 shows the results extracted in this embodiment after down-converting the signal sequence s ₀ (n) (n=1, 2, 3,..., N-1) using _fe (the signal sequence after frequency conversion is recorded as) Each pulse phase data sequence. It can be seen from Figure 2 that phase folding occurs in each extracted pulse phase data sequence. In this case, the signal sequence obtained after downconversion should be multiplied by a factor e ^jπ , and then the phase data sequence of each pulse should be re-extracted. Figure 3 shows each pulse phase data sequence extracted in this embodiment after down-converting the signal sequence s ₀ (n) (n = 1, 2, 3, ..., N-1) using _fe . As can be seen from Figure 3, phase folding occurs in the phase data sequence of the second half of the pulse. While phase folding does not occur in the phase data sequence of the first half of the pulse, individual phase estimation values are obviously out of tolerance. In this case, if only a few phase estimates in the pulse are significantly out of tolerance, the estimated value can be eliminated so that it does not participate in the subsequent calculation process. For data with both phase folding and individual phase out-of-tolerance occurring within the pulse, the phase folding should be resolved first, and then the individual phase out-of-tolerance data should be eliminated.

After preprocessing the extracted intra-pulse phase data, calculate the intra-pulse phase mean value of each pulse to obtain the intra-pulse phase mean data sequence.

In formula (4), is the noise part in the phase mean value,/> FIG. 4 shows the intra-pulse phase mean sequence extracted by the present invention after preprocessing the intra-pulse phase data sequence shown in FIG. 3 . It can be seen from Figure 4 that a phase folding phenomenon occurs in this phase mean sequence.

When performing straight line fitting on the pulse phase mean sequence shown in Figure 4, the following two methods can be used: one is to perform a phase folding operation on the pulse phase mean sequence where phase folding occurs, and then perform straight line fitting; The second is to take the maximum intra-pulse phase mean sequence without phase folding. For example, perform straight line fitting on the first 11 intra-pulse phase mean sequences in Figure 4.

After performing straight line fitting on the intra-pulse phase mean sequence and obtaining the frequency difference estimate Δf _e , if Δf _e is less than or equal to a given threshold value, the frequency estimate value f _e is output, and the frequency estimation process ends. When Δf _e is greater than a given threshold value, on the one hand, the frequency estimate is adjusted according to equation (5), and on the other hand, Δf _e is used to adjust the down-converted signal sequence. (n = 0, 1, 2, ..., N-1), the frequency is down-converted again, and then the extraction and preprocessing of each pulse phase data sequence, the extraction of the intra-pulse phase mean sequence, and the iterative estimation of the frequency difference are performed again, until The frequency difference estimate is less than a given threshold. Usually, the frequency estimation process can be completed after two iterative operations of the frequency error estimate.

Figures 5 and 6 respectively show the frequency difference estimate Δf _e obtained after performing a phase straight line fitting using the phase mean data of the first 11 pulses shown in Figure 4 (correspondingly, f _e =f _e +Δf _e ) , and then use this estimated value to estimate the downconverted signal sequence (n=0, 1, 2, ..., N-1) Each pulse phase data sequence and the intra-pulse phase mean sequence extracted after down-conversion again.

Figure 7 shows a comparison chart of the estimated performance simulation results of the method provided by the present invention and the two-stage FFT algorithm under several input signal-to-noise ratio conditions (signal sampling frequency, coherent pulse train duration, pulse repetition frequency and pulse width respectively are 100MHz, 1ms, 20kHz and 2μs; the signal frequency to be estimated takes uniform values within the range of 5MHz±1.05kHz; the number of simulations under single input signal-to-noise ratio conditions is 500 times; the method provided by the invention and the secondary FFT algorithm use the same Rough estimate of the frequency; when the secondary FFT algorithm estimates the frequency error, the digital resolution of the FFT algorithm used is 7.3Hz; during simulation calculations, it is assumed that the start and end time of each pulse is known). It can be seen from Figure 7 that within a given input signal-to-noise ratio range, the estimation performance of the frequency estimation method provided by the present invention is better than the two-stage FFT algorithm; as the input signal-to-noise ratio decreases, the estimation performance of the two frequency estimation methods closer and closer.

The present invention performs necessary preprocessing operations on intra-pulse and inter-pulse phase data, and the frequency estimation accuracy is better; when using intra-pulse phase data for phase straight line fitting, there are no constraints on the inter-pulse interval; it can be used to fix heavy It can also be used for high-precision frequency estimation of sine wave coherent pulse train signals with arbitrary repetition frequency, and has a wider application range.

Claims (7)

1. A sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting is characterized by comprising the following steps:

step 1, opposite transfusionPerforming FFT operation on multiple pulses of the input complex analysis digital signal, taking the frequency value corresponding to the strongest spectral line as the initial estimation value of each pulse frequency, and recording the average value of the initial estimation values of each pulse frequency as f _e ；

Step 2, using the average value f of the primary estimation values of each pulse frequency _e Performing down-conversion processing on the input complex analysis digital signal;

step 3, extracting phase angle information of each pulse from the complex analysis digital signal after the down-conversion treatment;

and 4, preprocessing the obtained phase angle data, and adjusting an initial phase angle, wherein the method comprises the following steps of:

1) Firstly, judging whether the percentage of the phase folding phenomenon occurring in the pulse exceeds a threshold value or not according to the extracted pulse phase data sequences: if the phase folding phenomenon occurs in the pulse phase data of more than 75% of the pulses, the signal initial phase angle is adjusted, the phase data sequence of each pulse is re-extracted, and the specific adjustment method is as follows: down-converted sample signal sequenceThen, extracting the phase data sequence of each pulse; if the pulse number of the phase folding phenomenon of the phase data in the pulse is less than 75%, performing the phase folding operation on the phase data in the pulse with the phase folding phenomenon;

2) The method for eliminating the phase data of which the phase estimation value does not meet the requirement in each pulse comprises the following specific steps: first calculate psi _i (n)＝θ _i (n+1)-θ _i (n), n=0, 1,2, …, Q-1, i=1, 2,3, …, P representing the number of pulses, θ _i (n) is a sequencePhase angle information of each pulse signal; then solving the mean value and standard deviation of the phi (n), and replacing the phi (n) by the phi (n-1) or the phi (n+1) when the difference between the phi (n) and the mean value is more than 3 times of the standard deviation;

step 5, extracting the phase mean value and the center moment of each pulse;

step (a)6, carrying out linear fitting operation on the phase average value of each pulse, and calculating a frequency estimation error delta f according to the linear fitting result _e ；

Step 7, Δf _e Comparing with a set threshold: when Deltaf _e When the value is smaller than the set threshold value, directly outputting f _e As the final estimated value of the frequency, otherwise, go to step 8;

step 8, frequency estimation value f _e Adjusted to f _e ＝f _e +Δf _e By Δf _e And (3) performing down-conversion treatment on the input complex analysis digital signal subjected to down-conversion and initial phase adjustment, and then turning to step (3).

2. The method for estimating frequency of sine wave coherent pulse train signal based on phase straight line fitting as set forth in claim 1, wherein in step 1, the plurality of pulses of the input complex analysis digital signal are subjected to FFT operation, and a frequency value corresponding to a strongest spectral line is used as an initial estimate value of each pulse frequency, and an average value of the initial estimate values of each pulse frequency is denoted as f _e The method is characterized by comprising the following steps:

recording deviceThe method comprises the steps of analyzing sine wave coherent pulse train signals for noise-containing complex to be processed, wherein T is more than or equal to 0 and less than or equal to T; w (t) is observed white noise with a mean value of zero; f (f) ₀ 、θ、T、T _i 、τ _i And P is the signal frequency, initial phase, duration, central time of the ith pulse, duration of the ith pulse and pulse number respectively; i=1, 2,3, …, P; />Is of duration tau _i The time center is T _i Is a rectangular pulse of (2); f (f) ₀ The measurement is to be estimated; at the same time, signal s is recorded ₀ The sampling frequency and the sampling point number of (t) are f respectively _s N, the signal sequence obtained after sampling is s ₀ (n)，n＝1,2,3,…,N-1；

For the ith pulse signalM-point FFT operation, M is greater than the sampling point number of the ith pulse signal, and the frequency value corresponding to the strongest spectral lineAll +.>Then, the average value of the primary estimation values of the pulse frequencies is denoted as f _e Then->

3. The method for estimating a frequency of a sinusoidal coherent pulse train signal based on phase straight line fitting according to claim 2, wherein the average value f of the initial estimation values of each pulse frequency is used in step 2 _e The down-conversion processing is carried out on the input complex analysis digital signal, and the down-conversion processing is concretely as follows:

by f _e For a sequence of sampled signals s ₀ (n) down-conversion processing, in which the portions other than the pulse durations are set to zero in the subsequent signal processing, i.eObtain a down-converted sample signal sequence +.>

4. The method for estimating frequency of sinusoidal coherent pulse train signal based on phase straight line fitting according to claim 3, wherein in step 3, the phase angle information of each pulse is extracted from the complex analysis digital signal after the down-conversion processing, specifically as follows:

computing a data sequencePhase angle information θ of each pulse signal in (a) _i (n)，n＝0,1,2,…,Q _i -1, i=1, 2,3, …, P; wherein Q is _i The number of sampling points for the ith pulse; the sampling data sequence of the ith pulse is marked as +.>Then->-π≤θ _i (n)≤π，n＝0,1,2,…,Q _i -1。

5. The method for estimating a frequency of a sinusoidal coherent pulse train signal based on phase straight line fitting according to claim 4, wherein the step 5 is characterized by extracting a phase mean value and a center moment of each pulse, specifically as follows;

calculating the central moment t of each pulse after phase preprocessing _ci And the average value theta of each pulse phase data sequence _i Obtaining a new phase data sequence theta _i (t _ci )，i＝1,2,…,P。

6. The method for estimating a frequency of a sinusoidal coherent pulse train signal based on phase straight line fitting according to claim 5, wherein in step 6, a straight line fitting operation is performed on the phase average value of each pulse, and then a frequency estimation error Δf is calculated according to the result of the straight line fitting _e The method is characterized by comprising the following steps:

for phase data sequence theta _i (t _ci ) Performing linear fitting operation, wherein i=p, p+1, p+2, …, L-1, p and L are index numbers of a start pulse and a final pulse corresponding to a phase data segment with no phase folding at maximum respectively;

assume that the resulting fitted line is Θ (t _ci )＝2πΔf _e t _ci +θ ₀ I=p, p+1, p+2, …, L-1, Δf _e I.e. the frequency estimation error.

7. According to claimThe method for estimating a frequency of a sinusoidal coherent pulse train signal based on phase line fitting as set forth in claim 6, wherein said step 8 uses Δf _e And (3) performing down-conversion treatment on the down-converted and initially-phase-adjusted input complex analysis digital signal again, wherein the formula is as follows:

where n=0, 1,2, …, N-1.