CN114895248A - Sinusoidal frequency modulation signal parameter estimation method, system and medium - Google Patents
Sinusoidal frequency modulation signal parameter estimation method, system and medium Download PDFInfo
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Abstract
The invention discloses a sinusoidal frequency modulation signal parameter estimation method, a system and a medium, wherein the method comprises the following steps: acquiring a sinusoidal frequency modulation signal, calculating an instantaneous frequency after performing differential calculation on the sinusoidal frequency modulation signal, performing down-sampling on the instantaneous frequency according to a preset maximum period number, and calculating a frequency spectrum of the down-sampled instantaneous frequency; calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the maximum value in the frequency spectrum me Based on the frequency estimate f me Calculating the period of the sinusoidal signal in the sinusoidal FM signal, and estimating the value f according to the period, instantaneous frequency and frequency of the sinusoidal signal me Calculating an instantaneous phase weighted cumulative value y, and calculating a modulation index estimation value m according to the instantaneous phase weighted cumulative value y f And a sinusoidal frequency modulation signal bandwidth estimation value Bw, estimating according to the modulation indexEvaluating m f And frequency estimation value f me Calculating carrier frequency estimated value f of sine frequency modulation signal 0 . The algorithm of the invention has simple logic and can better estimate various parameters of the sinusoidal frequency modulation signal.
Description
Technical Field
The invention relates to the field of signal processing, in particular to a sinusoidal frequency modulation signal parameter estimation method, a sinusoidal frequency modulation signal parameter estimation system and a sinusoidal frequency modulation signal parameter estimation medium.
Background
The sinusoidal frequency modulation signal is a typical nonlinear frequency modulation signal, has the characteristics of low interception rate, high range resolution and the like, and is widely applied to the fields of radar, communication, sonar and the like.
Detection and parameter estimation of sinusoidal frequency modulation signals have become a hot research problem in current radar and communication signal processing. The current main method is to use a redistribution smooth pseudo Wigne-Ville distribution (RSPWVD) method or use Hough transformation to estimate parameters of sinusoidal frequency modulation signals, but the method has the problems of high computational complexity and inaccurate estimation of the parameters of the signals by cross terms. The latter scholars estimate signal parameters by fitting a high order polynomial model to the sinusoidal fm signal, but are limited by the modulation index coefficients.
Patent CN110737868A discloses a sinusoidal frequency modulation signal parameter estimation method, which is to estimate sinusoidal signal parameters based on baseband signals, that is, carrier frequency signals of signals need to be accurately estimated first when estimating time signals. And the value range of the modulation index mu is assumed to be
When the algorithm and modulation index are greater than
The adopted methods are different, and finally, a method with higher precision is selected as a final estimation result, so that the algorithm of the method is high in complexity and high in calculation redundancy. Greatly limiting the application range.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the technical problems in the prior art, the invention provides a sinusoidal frequency modulation signal parameter estimation method, a system and a medium, the algorithm logic is simple, and various parameters of the sinusoidal frequency modulation signal can be better estimated.
In order to solve the technical problems, the technical scheme provided by the invention is as follows:
a sinusoidal frequency modulation signal parameter estimation method comprises the following steps:
acquiring a sine frequency modulation signal, calculating an instantaneous frequency after performing differential calculation on the sine frequency modulation signal, performing down-sampling on the instantaneous frequency according to a preset maximum period number, and calculating a frequency spectrum of the down-sampled instantaneous frequency;
calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the position of the maximum value in the frequency spectrum me And further based on the frequency estimation value f me And estimating the period of a sinusoidal signal in the sinusoidal frequency modulation signal by using the signal pulse width; according to the period and instantaneous frequency of the sinusoidal signal in the sinusoidal frequency modulation signal and the frequency estimation value f me Calculating an instantaneous phase weighted cumulative value y; calculating a modulation index estimation value m according to the instantaneous phase weighted accumulation value y f And a sinusoidal frequency modulation signal bandwidth estimation value Bw; according to the modulation index estimated value m f And frequency estimation value f me Calculating the carrier frequency estimated value f of the sine frequency modulation signal 0 。
Further, the step of down-sampling the instantaneous frequency according to a preset maximum number of cycles, and then obtaining the frequency spectrum of the down-sampled instantaneous frequency specifically includes: multiplying the system sampling rate Fs by the pulse width Pw of the sine frequency modulation signal, then dividing by the preset maximum period number, rounding the calculation result downwards to obtain a sampling multiple K, downsampling the instantaneous frequency according to the sampling multiple K, and performing preset N-point Fourier transform on the downsampled instantaneous frequency to obtain a corresponding frequency spectrum.
Further, according to the position of the maximum value in the frequency spectrum, calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal me The method specifically comprises the following steps:
finding the position idx of the maximum amplitude in the spectrum max According to said position idx max Calculating the initial frequency estimation value of the sinusoidal signal in the sinusoidal frequency modulation signal according to the deviation of the frequency spectrum center, the original signal sampling rate Fs' and the decimation multiple K；
Rounding the product of the initial frequency estimation value and the pulse width Pw of the sinusoidal frequency modulation signal to obtain the initial period estimation number M of the sinusoidal signal in the sinusoidal frequency modulation signal e ；
Initially estimating the number M by using the period e Dividing the pulse width Pw of the sinusoidal frequency modulation signal to obtain a frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal me 。
Further, the function expression of the initial frequency estimation value of the sinusoidal signal in the sinusoidal frequency modulation signal is as follows:
in the above formula, idx max The position of the maximum amplitude value in the frequency spectrum is shown, N is the number of points of Fourier transform, Fs 'is the original sampling rate of the signal, and K' is a preset extraction multiple.
Further, according to the period and instantaneous frequency of the sinusoidal signal in the sinusoidal frequency modulation signal and the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal me Calculating the instantaneous phase weighted cumulative value y comprises the following steps:
dividing the pulse width Pw of the sine frequency modulation signal by the period of the sine frequency modulation signal, and rounding down the calculation result to obtain the number N of the periods containing the sine signal in a single pulse;
selecting a target period from the N periods, and according to the instantaneous frequency and the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal me Respectively calculating instantaneous phase weighted cumulative value in each period of the target period, and if only one period of the sinusoidal signal exists in the target period, the modulation index estimated value m f Estimating by using an instantaneous phase weighted accumulation value y in a single period, and if the target period comprises at least two periods of sinusoidal signals, modulating an index estimation value m f The average value Y of the plurality of period instantaneous phase weighted accumulation values is used for estimation.
Further, the modulation index estimated value m f The functional expression of (a) is:
when there is only one period of the sinusoidal signal in the target period:
m f ＝2|y|
when the target period includes at least two periods of the sinusoidal signal:
m f ＝2|Y|
in the above formula, Y is the instantaneous phase weighted accumulation value in a single cycle, and Y is the average value of the instantaneous phase weighted accumulation values.
Further, the functional expression of the sinusoidal frequency modulation signal bandwidth estimation value Bw is as follows:
when there is only one period of the sinusoidal signal in the target period:
when the target period includes at least two periods of the sinusoidal signal:
in the above formula, Y is an instantaneous phase weighted accumulation value in a single period, Y is an average value of the instantaneous phase weighted accumulation values, and T is a period of a sinusoidal signal in the sinusoidal frequency modulation signal.
Further, according to the modulation index estimated value m f And frequency estimation value f me Calculating the carrier frequency estimated value f of the sine frequency modulation signal 0 The method comprises the following specific steps: selecting a target period from the N periods, integrating instantaneous frequency of each period in the target period, and dividing the integration result by the period of the sinusoidal frequency modulation signal to obtain a carrier frequency estimation value of each period in the target period, wherein if only one period exists in the target period, the carrier frequency estimation value is a carrier frequency estimation value f 0 If the target period includes at least two consecutive periods, the average of all carrier frequency estimated valuesThe value is the estimated carrier frequency value f 0 The value of (c).
The invention also provides a sinusoidal frequency modulation signal parameter estimation system, which comprises:
the signal processing unit is used for acquiring a sine frequency modulation signal, calculating the difference of the sine frequency modulation signal, then calculating the instantaneous frequency, down-sampling the instantaneous frequency according to the preset maximum period number, and then calculating the frequency spectrum of the down-sampled instantaneous frequency;
a parameter estimation unit for calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the position of the maximum value in the frequency spectrum me And further based on the frequency estimation value f me Calculating the period of the sine signal in the sine frequency modulation signal, and estimating the frequency f of the sine signal in the sine frequency modulation signal according to the period and the instantaneous frequency of the sine signal in the sine frequency modulation signal me Calculating an instantaneous phase weighted accumulation value y, and calculating a modulation index estimation value m according to the instantaneous phase weighted accumulation value y f And a bandwidth estimation value Bw of the sine frequency modulation signal according to a frequency modulation index m of the sine frequency modulation signal f And frequency f of the sinusoidal signal me Calculating the carrier frequency estimated value f of the sine frequency modulation signal 0 。
The present invention also provides a computer readable storage medium storing a computer program programmed or configured to perform any of the sinusoidal chirp signal parameter estimation methods.
Compared with the prior art, the invention has the advantages that:
according to the invention, the instantaneous frequency is obtained after differential calculation of sinusoidal frequency modulation signals, the instantaneous frequency is a single carrier signal, the sinusoidal frequency modulation signals are modulated on a frequency band, frequency domain analysis is convenient to carry out, the instantaneous frequency is sampled, the frequency resolution is improved, the influence of the frequency of the sinusoidal frequency modulation signals on the normalization error of parameter estimation is reduced, Fourier analysis is carried out on the instantaneous frequency after down conversion, a spectrogram can be obtained, the frequency estimation value of the sinusoidal frequency modulation signals can be conveniently obtained on the spectrogram, and convenience is provided for the estimation of other parameters such as bandwidth and carrier frequency of the sinusoidal frequency modulation signals. In addition, the invention obtains the bandwidth estimation value and the carrier frequency estimation value of the sinusoidal frequency modulation signal by averaging the estimation values in a plurality of periods, thereby reducing the influence of noise on the estimation and improving the estimation precision.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a graph of bandwidth estimation error of sinusoidal frequency modulation signal in an embodiment of the invention.
Fig. 3 is a graph of carrier frequency estimation error of sinusoidal frequency modulation signal in an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the drawings and specific preferred embodiments of the description, without thereby limiting the scope of protection of the invention.
The expression of the sine frequency modulation signal is as follows:
where s (t) is the received sinusoidal FM signal, f 0 For the carrier frequency to be estimated, m f For the modulation index to be estimated, f m The frequency of a sinusoidal signal in the sinusoidal frequency modulation signal to be estimated is theta, the initial phase of the sinusoidal signal in the sinusoidal frequency modulation signal is theta, j is an imaginary unit in a complex domain, and A is the signal amplitude of the sinusoidal frequency modulation signal.
The difference is calculated for the sinusoidal frequency modulation signal, that is, the conjugate product is calculated for the sinusoidal frequency modulation signals at two different time instants, so as to obtain:
wherein s (t) and s (t-1) are sinusoidal frequency modulation signals received at two different time instants, f 0 For the carrier frequency to be estimated, m f For the modulation index to be estimated, f m For the frequency of the sinusoidal signal in the sinusoidal FM signal to be estimated, theta is the sineThe initial phase of a sinusoidal signal in the frequency modulation signal, j is an imaginary unit in a complex domain, and A is the signal amplitude of the sinusoidal frequency modulation signal;
then, the instantaneous phase of the differentiated signal s (t) s (t-1) is obtained, and the instantaneous frequency can be calculated as:
the following can be obtained:
wherein m is f '＝m f f m ，f 0 For the carrier frequency to be estimated, m f For the modulation index to be estimated, f m The frequency of the sinusoidal signal in the sinusoidal frequency modulation signal to be estimated is theta, the initial phase of the sinusoidal signal in the sinusoidal frequency modulation signal is theta, and j is an imaginary unit in a complex domain.
From equation (4), the instantaneous frequency
The sinusoidal signal is a time-domain waveform of a sinusoidal signal in a sinusoidal frequency modulation signal, and is a single-carrier signal which has a single spectral line on a frequency spectrum. I.e. to instantaneous frequency
Fourier transform is carried out to obtain a corresponding spectrogram, and the position corresponding to the maximum amplitude value in the frequency spectrum is searched, so that the frequency f of a sinusoidal signal in a sinusoidal frequency modulation signal can be obtained m Is expressed as f me 。
However, under the unknown condition of the sinusoidal FM signal, the frequency f of the sinusoidal signal in the sinusoidal FM signal m Since the system sampling rate is fixed to Fs, the number of fourier transform points is also fixed, and the spectral resolution is also fixed. According to different frequencies f m Resulting in an estimated value f me The normalized error has a large difference。
For example, Fs is 4800MHz, the number of fourier transform points N is 16384, and the corresponding spectral resolution is
When f is m 100MHz, the spectral resolution results in an estimation error of df 0.00146484375MHz, when f is m At 1MHz, the corresponding normalized error is df 0.146484375MHz, which has a large impact on subsequent estimation.
Therefore, we further improve on the basis and provide a sinusoidal frequency modulation signal parameter estimation method for the instantaneous frequency
The down-sampling is performed to reduce the sampling rate and improve the frequency resolution, as shown in fig. 1, and the method comprises the following steps:
s1) acquiring a sine frequency modulation signal, calculating instantaneous frequency after performing differential calculation on the sine frequency modulation signal, namely time domain waveform of the sine signal in the sine frequency modulation signal, down-sampling the instantaneous frequency according to a preset maximum cycle number M _ max, and performing Fourier transform on the down-sampled instantaneous frequency to obtain a corresponding frequency spectrum;
s2) calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the position of the maximum value in the frequency spectrum me And further based on the frequency estimation value f me Estimating the period of a sinusoidal signal in the sinusoidal frequency modulation signal; according to the period and instantaneous frequency of the sinusoidal signal in the sinusoidal frequency modulation signal and the frequency estimation value f me Calculating an instantaneous phase weighted cumulative value y; calculating a modulation index estimation value m according to the instantaneous phase weighted accumulation value y f And a sinusoidal frequency modulation signal bandwidth estimation value Bw; according to the modulation index estimated value m f And frequency estimation value f me Calculating the carrier frequency estimated value f of the sine frequency modulation signal 0 。
In this embodiment, the step S1) of down-sampling the instantaneous frequency according to the preset maximum number of cycles, and then obtaining the corresponding frequency spectrum by performing the down-sampled instantaneous frequency conversion specifically includes:
s1.1) multiplying a system sampling rate Fs and the pulse width Pw of the sine frequency modulation signal to obtain the total sampling point number of the pulse signal, then dividing the total sampling point number by twice of a preset maximum period number M _ max to obtain a down-sampling multiple K, wherein the down-sampling multiple K can be known through a formula (5), and the extracted signal is still compounded with the Nyquist sampling theorem as long as the period number of the signal is less than or equal to the preset period number; the sampling multiple K is calculated as follows:
in the above formula, the first and second carbon atoms are,
indicating rounding-down, wherein Fs is a system sampling rate, Pw is a pulse width of the sinusoidal frequency modulation signal, and M _ max is a preset maximum cycle number;
s1.2) according to the sampling multiple K to the instantaneous frequency
Down-sampling;
s1.3) carrying out N-point Fourier transform on the down-sampled instantaneous frequency to obtain a corresponding frequency spectrum.
In this embodiment, in step S2), the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal is calculated according to the position of the maximum value in the frequency spectrum me The method specifically comprises the following steps:
s2.1a) finding the position idx of the maximum amplitude value in the frequency spectrum max According to said position idx max Calculating to obtain an initial estimated value f ' of the frequency of the sinusoidal signal in the sinusoidal frequency modulation signal relative to the deviation of the center of the frequency spectrum, the original signal sampling rate Fs ' and the extraction multiple K ' me The calculation formula is as follows:
in the above formula, idx max The position of the maximum amplitude value in the frequency spectrum, N is the number of points of Fourier transform, Fs 'is the original sampling rate of the signal, and K' is a preset extraction multiple;
s2.1b) initial estimation value f 'of frequency' me And rounding the product of the pulse width Pw of the sine frequency modulation signal to obtain the initial cycle estimation number M of the sine signal in the sine frequency modulation signal e The calculation formula is as follows:
M e ＝round(f′ me ·Pw) (7)
in the above formula, round represents rounding, f' me The method comprises the following steps of (1) obtaining an initial frequency estimation value of a sinusoidal signal in a sinusoidal frequency modulation signal, wherein Pw is the pulse width of the sinusoidal frequency modulation signal;
s2.1c) using the initial number M of the period estimation e Dividing the pulse width Pw of the sinusoidal frequency modulation signal to obtain a frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal me Frequency estimation f of sinusoidal signals in sinusoidal FM signals me The function of (a) is expressed as follows:
in the above formula, M e The number of the sine signals in the sine frequency modulation signals is initially estimated, and Pw is the pulse width of the sine frequency modulation signals.
Obtaining the frequency estimation value f of the sine signal in the sine frequency modulation signal me Thereafter, the period of the sinusoidal signal in the sinusoidal FM signal can be estimated, i.e. the period of the sinusoidal signal in the sinusoidal FM signal is estimated
In this embodiment, the frequency of the sinusoidal signal in the sinusoidal FM signal is estimated according to the period and the instantaneous frequency of the sinusoidal signal in the sinusoidal FM signal and the frequency estimation value f of the sinusoidal signal in the sinusoidal FM signal me Calculating the instantaneous phase weighted cumulative value y comprises the following steps:
s2.2a) dividing the pulse width Pw of the sine frequency modulation signal by the period of the sine signal in the sine frequency modulation signal, and rounding down the calculation result to obtain the number N of the periods of the sine signal contained in a single pulse, wherein the calculation formula is as follows:
in the above formula, the first and second carbon atoms are,
representing a rounding-down, T being the period of a sinusoidal signal in said sinusoidal FM signal, f me The frequency estimation value of the sine signal in the sine frequency modulation signal is Pw, and Pw is the pulse width of the sine frequency modulation signal;
s2.2b) selecting a target period from the N periods, and according to the instantaneous frequency and the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal me Respectively calculating instantaneous phase weighted cumulative value in each period of the target period, and if only one period of the sinusoidal signal exists in the target period, the modulation index estimated value m f Estimating by using an instantaneous phase weighted accumulation value y in a single period, and if the target period comprises at least two periods of sinusoidal signals, modulating an index estimation value m f The average value Y of the plurality of period instantaneous phase weighted accumulation values is used for estimation.
In this embodiment, the functional expression of the instantaneous phase weighted cumulative value y is:
in the above formula
Is the instantaneous frequency, f me And the frequency estimation value of the sinusoidal signal in the sinusoidal frequency modulation signal is obtained.
In this embodiment, the function expression of the average value Y of the instantaneous phase weighted cumulative value is:
in the above formula, k is 1 to M, M is the number of accumulation periods, and y (kT) is the instantaneous phase weighted accumulation value in the k-th period.
For instantaneous phase weighted accumulation value y and modulation index estimation value m f And the relation of the bandwidth estimation value Bw of the sinusoidal frequency modulation signal is derived as follows:
in the above formula, m f '＝m f f m ，m f For the modulation index to be estimated, f m The method comprises the steps that the frequency of a sinusoidal signal to be estimated in a sinusoidal frequency modulation signal is obtained, theta is the initial phase of the sinusoidal signal in the sinusoidal frequency modulation signal, j is an imaginary unit in a complex domain, and T is the period of the sinusoidal signal in the sinusoidal frequency modulation signal;
as can be seen from the nature of the sine function,
in the above formula, T is the period of the sinusoidal signal in the sinusoidal frequency modulation signal, and ω is the angular frequency of the sinusoidal signal in the sinusoidal frequency modulation signal.
Then it can be obtained from equations (12) and (13):
in the above formula, m f '＝m f f m ，m f For the modulation index to be estimated, f m Is the frequency of a sinusoidal signal to be estimated in the sinusoidal frequency-modulated signal, theta is the initial phase of the sinusoidal signal in the sinusoidal frequency-modulated signal, T is the period of the sinusoidal signal in the sinusoidal frequency-modulated signal, y (kT) is the instantaneous phase in each periodAnd (4) weighting the accumulated value.
Therefore, step s2.2b) of the present embodiment is followed by modulation index estimation m based on the instantaneous phase weighted sum average Y f The specific steps of the bandwidth estimation value Bw of the sinusoidal frequency modulation signal comprise: step S2.2c) obtains the modulation index estimated value m according to the formula (11) and the formula (14) f And a bandwidth estimation value Bw of the sinusoidal frequency modulation signal, wherein the modulation index estimation value m f And the bandwidth estimation value Bw of the sine frequency modulation signal has a function expression as follows:
when there is only one period of the sinusoidal signal in the target period:
m f ＝2|y| (15)
when the target period includes at least two periods of the sinusoidal signal:
in equations (15) to (18), Y is an instantaneous phase weighted accumulation value in a single period, Y is an average value of instantaneous phase weighted accumulation values in a plurality of periods, and T is a period of a sinusoidal signal in the sinusoidal frequency modulation signal.
In this embodiment, the modulation index estimation value m is used as the basis f And frequency estimation value f me Calculating the carrier frequency estimated value f of the sine frequency modulation signal 0 The method comprises the following specific steps:
s2.3) selecting a target period from the N periods, and carrying out instantaneous frequency treatment on each period in the target period
Integrating and dividing the integration result byThe periods of the sinusoidal frequency modulation signals are used for obtaining a carrier frequency estimation value f (kT) of each period in the target period, and if only one period exists in the target period, the carrier frequency estimation value f (kT) is the carrier frequency estimation value f 0 If the target period includes at least two continuous periods, the average value of all carrier frequency estimated values f (kT) is the carrier frequency estimated value f 0 The value of (c).
For instantaneous frequency
Period T and carrier frequency estimated value f of sinusoidal frequency modulation signal 0 The relationship of (a) is derived as follows:
within one period T there are:
in the above formula, the first and second carbon atoms are,
is instantaneous frequency, T is the period of the sine signal in the sine frequency modulation signal;
substituting formula (4) for formula (19) yields:
in the above formula, m f '＝m f f m ，f 0 For the carrier frequency to be estimated, m f Is a modulation index, f m Is the frequency of a sine signal in a sine frequency-modulated signal, T is the period of the sine signal in the sine frequency-modulated signal, m f 、f m And T has been estimated by the preceding steps;
thus, the carrier frequency f 0 The estimated values of (c) are:
in the above formula, a is an integration result of instantaneous frequency in a period, and T is the period of the sinusoidal frequency modulation signal;
based on equation (21), the function expression of the carrier frequency estimated value f (kt) is:
in the above formula, k is 1 to M, M is the number of accumulation periods,
t is the period of the sinusoidal signal in the sinusoidal FM signal.
In step S2) of this embodiment, the target period may only include a period of one sinusoidal signal, which is suitable for a case where the requirement for estimation accuracy is not high, and the system estimation performance is satisfied while reducing the system overhead, and achieving the balance between speed and accuracy, the target period includes a period of at least two sinusoidal signals which is suitable for a case where the requirement for accuracy is high, and the estimation accuracy is improved by calculating estimated values in a plurality of periods and taking an average value thereof as a final estimation result, thereby reducing the influence of noise on estimation.
The results obtained by simulating the method in this embodiment under the condition of the signal-to-noise ratio of 5-15dB are shown in fig. 2 and fig. 3, and it can be seen that when the signal-to-noise ratio is lower than 8dB, both the carrier frequency of the sinusoidal frequency modulation signal and the normalized error of the bandwidth estimation are less than 10 -3 . The signal-to-noise ratio of about 8dB is the detection threshold of the uncooperative detection system for the pulse signal, and under the signal-to-noise ratio, the method of the embodiment can better estimate the signal parameters, is low in complexity and has extremely high use value.
For the sine wave frequency of the sine frequency modulation signal in the embodiment, the first estimation precision is related to the number of points of fourier transform, the error caused by fourier transform is small, and the normalization error caused by down-sampling the instantaneous frequency is less than 0.1. While an error of 0.1 is not sufficient to affect the number of cycles M e Is estimated, i.e. M e Is estimated with f me First estimation ofThe value is independent and only dependent on the pulse width Pw. Meanwhile, as shown in equation (6), the frequency estimation value f in this embodiment me The estimation accuracy is linearly related to the pulse width Pw only, so that the influence of other parameters is eliminated, and the estimation accuracy is improved.
This embodiment also provides a sinusoidal frequency modulation signal parameter estimation system, including:
the signal processing unit is used for acquiring a sine frequency modulation signal, calculating the difference of the sine frequency modulation signal, then calculating the instantaneous frequency, down-sampling the instantaneous frequency according to the preset maximum period number, and then calculating the frequency spectrum of the down-sampled instantaneous frequency;
a parameter estimation unit for calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the position of the maximum value in the frequency spectrum me And further based on the frequency estimation value f me And calculating the period of the sinusoidal signal in the sinusoidal frequency modulation signal according to the signal pulse width, the instantaneous frequency and the frequency estimation value f me Calculating an instantaneous phase weighted accumulation value y, and calculating a modulation index estimation value m according to the instantaneous phase weighted accumulation value y f And a sinusoidal frequency modulation signal bandwidth estimation value Bw according to the frequency estimation value f me Modulation index estimation value m f Calculating the carrier frequency estimated value f of the sine frequency modulation signal 0 。
The present embodiment also provides a computer-readable storage medium storing a computer program programmed or configured to execute the sinusoidal chirp parameter estimation method of the present embodiment.
The foregoing is considered as illustrative of the preferred embodiments of the invention and is not to be construed as limiting the invention in any way. Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical spirit of the present invention should fall within the protection scope of the technical scheme of the present invention, unless the technical spirit of the present invention departs from the content of the technical scheme of the present invention.
Claims (10)
1. A sinusoidal frequency modulation signal parameter estimation method is characterized by comprising the following steps:
acquiring a sine frequency modulation signal, calculating an instantaneous frequency after performing differential calculation on the sine frequency modulation signal, performing down-sampling on the instantaneous frequency according to a preset maximum period number, and calculating a frequency spectrum of the down-sampled instantaneous frequency;
calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the position of the maximum value in the frequency spectrum me And further based on the frequency estimation value f me Estimating the period of a sinusoidal signal in the sinusoidal frequency modulation signal; according to the period and instantaneous frequency of the sinusoidal signal in the sinusoidal frequency modulation signal and the frequency estimation value f me Calculating an instantaneous phase weighted cumulative value y; calculating a modulation index estimation value m according to the instantaneous phase weighted accumulation value y f And a sinusoidal frequency modulation signal bandwidth estimation value Bw; according to the modulation index estimated value m f And frequency estimation value f me Calculating the carrier frequency estimated value f of the sine frequency modulation signal 0 。
2. The method according to claim 1, wherein the step of down-sampling the instantaneous frequency according to a predetermined maximum number of cycles and then obtaining the frequency spectrum of the down-sampled instantaneous frequency comprises: multiplying the system sampling rate Fs by the pulse width Pw of the sine frequency modulation signal, then dividing by the preset maximum period number, rounding the calculation result downwards to obtain a sampling multiple K, downsampling the instantaneous frequency according to the sampling multiple K, and performing preset N-point Fourier transform on the downsampled instantaneous frequency to obtain a corresponding frequency spectrum.
3. The sinusoidal FM signal parameter estimation method according to claim 2, wherein a frequency estimation value f of a sinusoidal signal in said sinusoidal FM signal is calculated according to a position of a maximum value in said frequency spectrum me The method specifically comprises the following steps:
finding the position idx of the maximum amplitude in the spectrum max According to said position idx max Calculating relative to the deviation of the frequency spectrum center, the original signal sampling rate Fs 'and the extraction multiple K' to obtain an initial frequency estimation value of the sinusoidal signal in the sinusoidal frequency modulation signal;
rounding the product of the initial frequency estimation value and the pulse width Pw of the sinusoidal frequency modulation signal to obtain the initial period estimation number M of the sinusoidal signal in the sinusoidal frequency modulation signal e ；
Initially estimating the number M by using the period e Dividing the pulse width Pw of the sinusoidal frequency modulation signal to obtain a frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal me 。
4. The method according to claim 3, wherein the function of the initial estimate of the frequency of the sinusoidal signal in the sinusoidal modulated frequency signal is expressed as follows:
in the above formula, idx max The position of the maximum amplitude value in the frequency spectrum is shown, N is the number of points of Fourier transform, Fs 'is the original sampling rate of the signal, and K' is a preset extraction multiple.
5. The method according to claim 1, wherein the sinusoidal FM signal parameter estimation method is based on the period, instantaneous frequency and frequency estimation value f of sinusoidal signal in the sinusoidal FM signal me Calculating the instantaneous phase weighted running total y comprises the following steps:
dividing the pulse width Pw of the sine frequency modulation signal by the period of the sine frequency modulation signal, and rounding down the calculation result to obtain the number N of the periods containing the sine signal in a single pulse;
selecting a target period from the N periods according to the instantaneous frequency and the sine toneFrequency estimation f of sinusoidal signals in frequency signals me Respectively calculating instantaneous phase weighted cumulative value in each period of the target period, and if only one period of the sinusoidal signal exists in the target period, the modulation index estimated value m f Estimating by using an instantaneous phase weighted cumulative value y in a single period, and if the target period comprises at least two periods of sinusoidal signals, estimating a modulation index value m f The average value Y of the plurality of period instantaneous phase weighted accumulation values is used for estimation.
6. Method for sinusoidal FM signal parameter estimation according to claim 5, wherein said modulation index estimation m f The functional expression of (a) is:
when there is only one period of the sinusoidal signal in the target period:
m f ＝2|y|；
when the target period includes at least two periods of the sinusoidal signal:
m f ＝2|Y|
in the above formula, Y is the instantaneous phase weighted accumulation value in a single cycle, and Y is the average value of the instantaneous phase weighted accumulation values.
7. The method of claim 5 wherein the sinusoidal FM signal bandwidth estimation value Bw is expressed as a function of:
when there is only one period of the sinusoidal signal in the target period:
when the target period includes at least two periods of the sinusoidal signal:
in the above formula, Y is an instantaneous phase weighted cumulative value in a single period, Y is an average value of the instantaneous phase weighted cumulative values, and T is a period of a sinusoidal signal in the sinusoidal frequency modulation signal.
8. Method for sinusoidal FM signal parameter estimation according to claim 5, characterized by estimating value m from said modulation index f And frequency estimation value f me Calculating the carrier frequency estimated value f of the sine frequency modulation signal 0 The method comprises the following specific steps: selecting a target period from the N periods, integrating instantaneous frequency of each period in the target period, and dividing the integration result by the period of the sinusoidal frequency modulation signal to obtain a carrier frequency estimation value of each period in the target period, wherein if only one period exists in the target period, the carrier frequency estimation value is a carrier frequency estimation value f 0 If the target period includes at least two continuous periods, the average value of all carrier frequency estimated values is the carrier frequency estimated value f 0 The value of (c).
9. A sinusoidal chirp signal parameter estimation system, comprising:
the signal processing unit is used for acquiring a sine frequency modulation signal, calculating the difference of the sine frequency modulation signal, then calculating the instantaneous frequency, down-sampling the instantaneous frequency according to the preset maximum period number, and then calculating the frequency spectrum of the down-sampled instantaneous frequency;
a parameter estimation unit for calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the position of the maximum value in the frequency spectrum me And further based on the frequency estimation value f me Calculating the period of the sine signal in the sine frequency modulation signal, and estimating the frequency f of the sine signal in the sine frequency modulation signal according to the period and the instantaneous frequency of the sine signal in the sine frequency modulation signal me Calculating an instantaneous phase weighted accumulation value y, and calculating a modulation index estimation value m according to the instantaneous phase weighted accumulation value y f And a bandwidth estimation value Bw of the sine frequency modulation signal according to a frequency modulation index m of the sine frequency modulation signal f And frequency of sinusoidal signalsRate f me Calculating the carrier frequency estimation value f of the sine frequency modulation signal 0 。
10. A computer-readable storage medium storing a computer program programmed or configured to perform the method of sinusoidal fm signal parameter estimation according to any of claims 1-8.
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| CN116256738A (en) * | 2023-03-22 | 2023-06-13 | 哈尔滨工程大学 | Sine frequency modulation signal detection method and device under large Doppler condition |
| CN116256738B (en) * | 2023-03-22 | 2023-11-24 | 哈尔滨工程大学 | Sine frequency modulation signal detection method and device under large Doppler condition |
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