CN106712720A - Parameter estimation method for multi-component SFM (Sinusoidal Frequency Modulated) signals based on LFBT (Logarithmic Fourier-Bessel Transform) - Google Patents

Abstract

The invention provides a parameter estimation method for multi-component SFM (Sinusoidal Frequency Modulated) signals based on LFBT (Logarithmic Fourier-Bessel Transform). The method comprises the steps of S1, judging whether phase ambiguity exists in the multi-component SFM signals or not, and carrying out phase ambiguity removal if the phase ambiguity exists; S2, selecting suitable LFB series resolutions k and carrying out LFBT on the multi-component SFM signals after ambiguity removal; and S3, calculating the center error frequency of intervals in which two adjacent LFB series are located and correcting estimation frequency, thereby obtaining the estimation frequency of each component. According to the parameter estimation method for the multi-component SFM signal, on the basis of related property analysis of a Bessel function, transform--LFBT is provided; the parameter estimation for the multi-component SFM signals is finished based on the LFBT; and the multi-component SFM signals are separated accurately.

Description

A kind of multi -components SFM signal parameter estimation based on LFBT

Technical field

The present invention relates to Signal and Information Processing technology, and in particular to a kind of parameter Estimation of multi -components sine FM signal Method.

Background technology

Non-stationary signal is widely present among nature.Whether the time statistical property according to non-stationary signal is linear It is divided into linear FM signal and NLFM signal.Sine FM (Sinusoidal Frequency Modulated, SFM) Signal is class NLFM signal most commonly seen in practice, is widely used in radar target feature extraction, biological doctor In medical diagnosis on disease and seismic survey, and generally exist in multi -components form.In radar target feature extraction, SFM signal bags The fine movement information and structural information of radar fine motion target are contained, have been one of important evidence of target identification；In biomedicine In medical diagnosis on disease, eeg signal and NMR signal are all SFM signals, and the different parameters of signal reflect examiner's Health.Therefore, the parameter extraction of SFM signals has important Research Significance.

The parameter Estimation of SFM signals generally is used converted the signal into and carried out on not same area.To solve multi -components SFM signals Parameter Estimation Problem, Sun Zhiguo etc. exists《Multi -components sine FM Signal parameter estimation side based on the conversion of discrete sine frequency modulation Method》(system engineering and electronic technology, 2012,34 (10):In 1973-1979), converted in discrete sine frequency modulation by SFM signals The feature of amassing wealth by heavy taxation in (Discrete Sinusoidal Frequency-Modulated Transform, DSFMT) domain, completes many The Frequency Estimation of component SFM signals.Peng Bo etc. exists《A Sinusoidal Frequency Modulation Fourier Transform for Radar-Based Vehicle Vibration Estimation》(IEEE Transactions on Instrumentation and Measurement,2014,63(9):In 2188-2199), by ORTHOGONAL TRIANGULAR basic function On carry out signal projection, using sine FM Fourier transform (Sinusoidal Frequency Modulation Fourier Transform, SFMFT) carry out the Frequency Estimation of SFM signals.However, except the spectral line of each sub-goal fine motion frequency in the frequency spectrum Outward, while there are some distracter spectral lines, have impact on the accuracy of parameter extraction.

For the Parameter Estimation Problem of multi -components SFM signals, by analyzing the relevant nature of Bessel function, FBT's On the basis of propose logarithm Fourier-bessel transform (Logarithmic Fourier-Bessel Transform, LFBT), Be projected in the phase term of signal on Bessel function by LFBT, and the amplitude attenuation characteristic of Bessel function is allowed it to well Non-stationary signal is used to indicate, and then proposes a kind of multi -components SFM signal parameter estimation based on LFBT, entered exactly The parameter Estimation of each component SFM signal modulation frequencies of row.

The content of the invention

It is an object of the invention to overcome above-mentioned weak point of the prior art, a kind of multi -components based on LFBT are proposed SFM signal parameter estimation, comprises the following steps：

The first step：Multi -components SFM signals are judged with the presence or absence of phase ambiguity, if carrying out Used for Unwrapping Phase Ambiguity treatment in the presence of if；

If the total phase offset of discrete sample signals is excessive, phase ambiguity can be produced；Due to the phase measurement position of signal In on interval (- π, π), therefore phase ambiguity phenomenon is produced when total phase offset is more than 2 π；Total phase offset reaches the whole of 2 π When counting K times, K is phase ambiguity number；Phase ambiguity can be modified by the phase difference value between neighbouring sample point, when adjacent When phase difference value between sampled point is no more than π, can be modified by the following method

Wherein pha (n)=Im [ln s (n)], phar (n) are the difference of revised phase shift and measured value；Therefore, signal is worked as When the phase difference value of neighbouring sample point is no more than π, Used for Unwrapping Phase Ambiguity treatment can be carried out.

Second step：Suitable LFB series resolution ratio k is selected, LFBT is carried out to the multi -components SFM signals after ambiguity solution；

Known sine FM signal model is

S (t)=R exp { j [a sin (ω t)+b cos (ω t)] } (2)

Wherein R is signal amplitude, and a, b are respectively the modulation index of SFM signals, and ω is modulating frequency；

The LFBT of definition signal s (t) is

Wherein J_αT () is first kind α rank Bessel functions, ω is conversion domain variable；Corresponding logarithm Fourier-Bezier Inverse transformation (Inverse Logarithmic Fourier-Bessel Transform, ILFBT) is

Fourier transform (Fourier Transform, FT) shows as fourier series in finite interval, with Fourier Conversion is similar, and LFBT is represented in finite interval with LFB series (LFB Series)；In actual signal treatment, actual signal Discrete sampling is generally gone through, the LFB series of discrete signal shows as the finite term sum on signal phase

Wherein n=1 ..., N, N count for signal sampling, t_sFor signal sampling is spaced and N=T/t_s；M LFB coefficient meter It is

Wherein COEFFICIENT K₁=2/ (N²t_s) it is an imaginary constant, coefficientBecome with LFB number of term in series m Change；Because the positive root of α rank Bessel functions constitutes constant row { J_α,m, therefore { K_2,mAlso for one with the constant of signal intensity Row, generally take α=0；

LFB number of term in series is corresponded with the frequency modulated component of SFM signals, and m LFB series is f in frequency content_m Place obtains maximum

Therefore, after carrying out LFBT conversion to SFM signals, using maximum amplitude LFB series as SFM signal modulation frequencies Estimate；

Wherein

The corresponding frequency-splitting of adjacent two LFB series, i.e. frequency resolution is calculated as

If frequency resolution Δ f_mSmaller, then the corresponding theoretic frequency value difference value of adjacent two LFB series reduces, then estimate Error can also reduce；

LFB series resolution ratio k values are introduced, when LFB series resolution ratio is k

Now frequency resolution is Δ f_m=1/2 π kNt_s, with the increase of LFB series resolution ratio k, frequency resolution also can Increase；Now estimate that frequency is

Wherein maximal term LFB coefficients are

Now, the frequency resolution of adjacent two LFB series is

3rd step：The errors of centration frequency in interval where adjacent two LFB series is calculated, carries out estimating frequency amendment, obtained To the estimation frequency of each component；

By maximal term () the LFB series estimation frequency that calculates SFM signals isNormal conditions Under, estimated frequency error f_biasNo more than the half of frequency resolution

Now actual frequency is adjacent m and m+1 LFB coefficient theory of correspondences frequencies J_0,m/ 2 π T and J_0,m+1/2πT Average value；But such case is only applicable to a frequency content and is only projected on a single spectral line or single series (such as FT)； In LFB series, a frequency content is projected on some rank Bessel series, that is to say, that f_mPeak is obtained in m series Projection amplitude of the value simultaneously in neighbouring some class numbers is not zero；

The frequency separation f that adjacent two LFB series theory of correspondences frequency is constituted_i∈[f_m-1,f_m+1) on, Frequency Estimation Error frequency f centered on the mean value definition of maximum difference and minimal difference_cen, by calculating the errors of centration on the interval frequently Rate come carry out estimate frequency amendment, successively calculate LFB series maximum go forward side by side line parameter estimation, until without obvious LFB Untill series maximum.

The calculating of the errors of centration frequency is divided into three steps：The first step, calculates the corresponding maximal term LFB coefficients of signal, leads to The amplitude maximum for crossing LFB coefficients calculates estimation frequencySecond step, selection m-1 and m+1 LFB series, and calculate Their corresponding theoretic frequency f_m-₁And f_m+1；3rd step, selects suitable step-length, calculates f on frequency separation_i∈[f_m-1,f_m+1) The corresponding estimation frequency of respective LFB coefficient amplitudes maximal termAnd be calculated as below

f_cenAs errors of centration frequency；Therefore, the evaluated error frequency of amendment is

After amendment, evaluated error frequency meets f_bias≤Δf_m/2。

The present invention proposes a kind of conversion on the basis of the relevant nature analysis of Bessel function --- LFBT, Jin Erji The parameter Estimation of multi -components SFM signals is completed in LFBT, the separation of each component SFM signals is carried out exactly.

Brief description of the drawings

Fig. 1 shows flow chart of the invention；

Fig. 2 shows multi -components SFM signal time frequency analysis results；

Fig. 3 shows the LFB series of multi -components SFM signals；

Fig. 4 (a) shows the first component SFM signal time frequency analysis results, and Fig. 4 (b) shows frequency division during second component SFM signals Analysis result, Fig. 4 (c) shows three-component SFM signal time frequency analysis results；

Fig. 5 (a) shows under the conditions of SNR=8dB that the estimation frequency normalization obtained using different LFB series resolution ratio is equal Square error (Normalized Root Mean Square Error, NRMSE) simulation result；Fig. 5 (b) shows SNR=4dB bars Under part, the NRMSE simulation results obtained using different LFB series resolution ratio；Fig. 5 (c) is shown under the conditions of SNR=0dB, using not With the NRMSE simulation results that LFB series resolution ratio is obtained；Fig. 5 (d) is shown under the conditions of SNR=-4dB, using different LFB series The NRMSE simulation results that resolution ratio is obtained.

Specific embodiment

Below in conjunction with the accompanying drawings with example of the invention, the invention will be further described.

As shown in figure 1, the present invention is realized through the following steps：Select suitable LFB series resolution ratio k；Calculate multi -components The LFB series of SFM signals；The errors of centration frequency in interval where the adjacent two LFB series of gained frequency is calculated, enters line frequency Estimate the amendment of parameter；It is described as follows：

The first step：Multi -components SFM signals are judged with the presence or absence of phase ambiguity, if carrying out Used for Unwrapping Phase Ambiguity treatment in the presence of if；

If the total phase offset of discrete sample signals is excessive, phase ambiguity can be produced；Due to the phase measurement position of signal In on interval (- π, π), therefore phase ambiguity phenomenon is produced when total phase offset is more than 2 π；Total phase offset reaches the whole of 2 π When counting K times, K is referred to as phase ambiguity number.Phase ambiguity can be modified by the phase difference value between neighbouring sample point, work as phase When phase difference value between adjacent sampled point is no more than π, can be modified by the following method

Wherein pha (n)=Im [lns (n)], phar (n) are the difference of revised phase shift and measured value；Therefore, signal is worked as When the phase difference value of neighbouring sample point is no more than π, Used for Unwrapping Phase Ambiguity treatment can be carried out.

Second step：Suitable LFB series resolution ratio k is selected, LFBT is carried out to the multi -components SFM signals after ambiguity solution；

Known sine FM signal model is

S (t)=R exp { j [a sin (ω t)+b cos (ω t)] } (2)

Wherein R is signal amplitude, and a, b are respectively the modulation index of SFM signals, and ω is modulating frequency；

The LFBT of definition signal s (t) is

Wherein J_αT () is first kind α rank Bessel functions, ω is conversion domain variable.Corresponding logarithm Fourier-Bezier Inverse transformation (Inverse Logarithmic Fourier-Bessel Transform, ILFBT) is

Fourier transform (Fourier Transform, FT) shows as fourier series in finite interval, with Fourier Conversion is similar, and LFBT is represented in finite interval with LFB series (LFB Series)；In actual signal treatment, actual signal Discrete sampling is generally gone through, the LFB series of discrete signal shows as the finite term sum on signal phase

Wherein n=1 ..., N, N count for signal sampling, t_sFor signal sampling is spaced and N=T/t_s；M LFB coefficient meter It is

Wherein COEFFICIENT K₁=2/ (N²t_s) it is an imaginary constant, coefficientBecome with LFB number of term in series m Change；Because the positive root of α rank Bessel functions constitutes constant row { J_α,m, therefore { K_2,mAlso for one with the constant of signal intensity Row, generally take α=0；

LFB number of term in series is corresponded with the frequency modulated component of SFM signals, and m LFB series is f in frequency content_m Place obtains maximum

Therefore, after carrying out LFBT conversion to SFM signals, using maximum amplitude LFB series as SFM signal modulation frequencies Estimate.

Wherein

The corresponding frequency-splitting of adjacent two LFB series, i.e. frequency resolution is calculated as

If frequency resolution Δ f_mSmaller, then the corresponding theoretic frequency value difference value of adjacent two LFB series reduces, then estimate Error can also reduce；

LFB series resolution ratio k values are introduced, when LFB series resolution ratio is k

Now frequency resolution is Δ f_m=1/2 π kNt_s；With the increase of LFB series resolution ratio k, frequency resolution also can Increase；Now estimate that frequency is

Wherein maximal term LFB coefficients are

Now, the frequency resolution of adjacent two LFB series is

3rd step：The errors of centration frequency in interval where adjacent two LFB series is calculated, carries out estimating frequency amendment, obtained To the estimation frequency of each component；

By maximal term () the LFB series estimation frequency that calculates SFM signals isNormal conditions Under, maximum estimated error frequency is the half of frequency resolution, is

Now actual frequency is adjacent two LFB coefficient theory of correspondences frequencies J_0,m/ 2 π T and J_0,m+1The average value of/2 π T；So And such case is only applicable to a frequency content and is only projected on a single spectral line or single series (such as FT).In LFB series, One frequency content is projected on some rank Bessel series, that is to say, that f_mPeak value is obtained simultaneously neighbouring in m series Some class numbers on projection be not zero；If m of LFB series is equal with m+1 amplitude, then estimate that frequency is located at area Between f ∈ (J_0,m/2πT,J_0,m+1/ 2 π T) on；If signal duration T=1s, k=1, then

Consider

Approx, above equation can be converted into

Consider that basic inequality can be obtained

Wherein J_0,m+1≠J_0,m.So when m LFB series is equal with m+1 LFB series amplitude, estimating that frequency will More than the average value of two theoretic frequencies；That is, actual frequency is slightly less than estimation frequency.Therefore, maximum estimated error meets

Therefore, we seek a kind of reduction evaluated error by calculating the errors of centration frequency of adjacent two LFB series Method；The frequency separation f that adjacent two LFB series theory of correspondences frequency is constituted_i∈[f_m-1,f_m+1) on, Frequency Estimation Error frequency f centered on the mean value definition of maximum difference and minimal difference_cen, by calculating the errors of centration on the interval frequently Rate come carry out estimate frequency amendment.

The calculating of errors of centration frequency is divided into three steps, and the first step calculates the corresponding LFB coefficients of signal, by LFB coefficients Amplitude maximum item obtains estimating frequencySecond step, selects adjacent two, m-1 and m+1 LFB series, and calculates Their corresponding theoretic frequency f_m-1And f_m+1；3rd step, selects suitable step-length, calculates f on frequency separation_i∈[f_m-1,f_m+1) The corresponding estimation frequency of respective LFB coefficient amplitudes maximal termAnd be calculated as below

As errors of centration frequency f_cen；Therefore, the evaluated error frequency of amendment is

After amendment, evaluated error frequency meets f_bias≤Δf_m/2。

Finally, the maximum that LFB series is calculated successively is gone forward side by side line parameter estimation, until maximum without obvious LFB series Untill value.

Example：Multi -components SFM signal parameter estimation

Emulation experiment：If multi -components SFM signal models are

Wherein R_i、a_i、f_iThe respectively amplitude of signal, the index of modulation and modulating frequency.W (n) is additive white Gaussian noise. Component of signal parameter is respectively：Component one：R₁=2, a₁=1, f₁=4.98Hz；Component two：R₂=2, a₂=1.5, f₂= 19.47Hz；Component three：R₃=3, a₃=2, f₃=34.19Hz.The time frequency analysis result of multi -components SFM signals is as shown in Figure 2.From Fig. 2 can be seen that multi -components SFM signals and be overlapped in time-frequency domain, it is impossible to differentiate the letter such as its component number and signal modulation frequency Breath.

In LFB series calculating process, resolution takes k=10.LFB series calculates as shown in Figure 3.From figure 3, it can be seen that LFB series obtains peak value at the 104th, the 392nd and the 688th respectively.It is computed, three SFM signals of component estimate frequency Rate is respectively 4.9845Hz, 19.4845Hz and 34.1845Hz, and evaluated error is 0.0045Hz, 0.0145Hz and 0.0055Hz.

Decomposition result such as Fig. 4 (a) of multi -components SFM signals, Fig. 4 (b), Fig. 4 (c) are respectively component one, component two and divide The time frequency analysis result of amount three.As can be seen that time frequency analysis result clearly reflects the time-frequency characteristics of each component from figure.

Fig. 5 (a)-Fig. 5 (d) be different signal to noise ratios and different LFB series resolution conditions under, using 200 Monte Carol experiment obtained by estimation frequency normalization mean square error (Normalized Root Mean Square Error, NRMSE) simulation result.Result shows, under the conditions of identical signal to noise ratio, LFB series resolution ratio is higher, estimates the NRMSE of frequency Smaller, estimated accuracy is higher；In SNR>Under the conditions of -4dB, when resolution ratio is identical, signal to noise ratio estimation effect higher is better.

The present invention proposes a kind of conversion on the basis of the relevant nature analysis of Bessel function --- LFBT, Jin Erji The parameter Estimation of multi -components SFM signals is completed in LFBT, the separation of each component SFM signals is carried out exactly.

Claims (5)

1. a kind of multi -components SFM signal parameter estimation based on LFBT, comprises the following steps：

The first step：Multi -components SFM signals are judged with the presence or absence of phase ambiguity, if carrying out Used for Unwrapping Phase Ambiguity treatment in the presence of if；

Second step：Suitable LFB series resolution ratio k is selected, LFBT is carried out to the multi -components SFM signals after ambiguity solution；

3rd step：The errors of centration frequency in interval where adjacent two LFB series is calculated, carries out estimating frequency amendment, obtain each The estimation frequency of component.

2. a kind of multi -components SFM signal parameter estimation based on LFBT according to claim 1, the wherein first step tool Body is：

If the total phase offset of discrete sample signals is excessive, phase ambiguity can be produced；Because the phase measurement of signal is located at area Between on (- π, π), therefore phase ambiguity phenomenon is produced when total phase offset is more than 2 π；Total phase offset reaches the integer K times of 2 π When, K is phase ambiguity number；Phase ambiguity can be modified by the phase difference value between neighbouring sample point, work as neighbouring sample When phase difference value between point is no more than π, can be modified by the following method

$phar\left(n\right)=\left\{\begin{array}{cc}pha\left(n\right)-2\mathrm{\&pi;},& pha\left(n\right)-pha(n-1)>\mathrm{\&pi;}\\ pha\left(n\right)+2\mathrm{\&pi;},& pha(n-1)-pha\left(n\right)>\mathrm{\&pi;}\\ pha\left(n\right),& |pha\left(n\right)-pha(n-1)|<\mathrm{\&pi;}\end{array}\right.$

Wherein pha (n)=Im [lns (n)], phar (n) are the difference of revised phase shift and measured value；Therefore, when signal is adjacent When the phase difference value of sampled point is no more than π, Used for Unwrapping Phase Ambiguity treatment can be carried out.

3. a kind of multi -components SFM signal parameter estimation based on LFBT according to claim 1, wherein second step tool Body is：

Suitable LFB series resolution ratio k is selected, LFBT is carried out to the multi -components SFM signals after ambiguity solution；

Known sine FM signal model is

S (t)=Rexp { j [asin (ω t)+bcos (ω t)] }

Wherein R is signal amplitude, and a, b are respectively the modulation index of SFM signals, and ω is modulating frequency；

The LFBT of definition signal s (t) is

$S_{\mathrm{\&alpha;}}\left(\mathrm{\&omega;}\right)={\&Integral;}_0^{\mathrm{\&infin;}}jtln\&lsqb;s\left(t\right)\&rsqb;J_{\mathrm{\&alpha;}}\left(\mathrm{\&omega;}t\right)dt$

Wherein J_αT () is first kind α rank Bessel functions, ω is conversion domain variable；Corresponding logarithm Fourier-Bezier inversion Changing (Inverse Logarithmic Fourier-Bessel Transform, ILFBT) is

$s\left(t\right)=\exp \&lsqb;j{\&Integral;}_0^{\mathrm{\&infin;}}{\mathrm{\&omega;S}}_{\mathrm{\&alpha;}}\left(\mathrm{\&omega;}\right)J_{\mathrm{\&alpha;}}\left(\mathrm{\&omega;}t\right)d\mathrm{\&omega;}\&rsqb;$

Fourier transform (Fourier Transform, FT) shows as fourier series in finite interval, with Fourier transform Similar, LFBT is represented in finite interval with LFB series (LFB Series)；In actual signal treatment, actual signal is usual By discrete sampling, the LFB series of discrete signal shows as the finite term sum on signal phase

$s\left(n\right)=\exp \&lsqb;j\underset{m=1}{\overset{M}{\&Sigma;}}{C}_m{J}_{\mathrm{\&alpha;}}\left(\frac{J_{\mathrm{\&alpha;},m}{t}_s}{N}n\right)\&rsqb;$

Wherein n=1 ..., N, N count for signal sampling, t_sFor signal sampling is spaced and N=T/t_s；M LFB coefficient is calculated as

$L_m=K_1{K}_{2,m}j\underset{m=1}{\overset{M}{\&Sigma;}}nln\&lsqb;s\left(n\right)\&rsqb;J_{\mathrm{\&alpha;}}\left(\frac{J_{\mathrm{\&alpha;},m}{t}_s}{N}n\right)$

Wherein COEFFICIENT K₁=2/ (N²t_s) it is an imaginary constant, coefficientChange with LFB number of term in series m；By Constant row { J is constituted in the positive root of α rank Bessel functions_α,m, therefore { K_2,mAlso for one does not arrange with the constant of signal intensity, lead to Often take α=0；

LFB number of term in series is corresponded with the frequency modulated component of SFM signals, and m LFB series is f in frequency content_mPlace takes Obtain maximum

$f_m=\frac{J_{0,m}}{2\mathrm{\&pi;}T}$

Therefore, after carrying out LFBT conversion to SFM signals, using maximum amplitude LFB series estimating as SFM signal modulation frequencies Meter；

$\hat{f}=\frac{J_{0,m_{peak}}}{2\mathrm{\&pi;}T}$

Wherein

$\begin{array}{cc}{m}_{peak}=\underset{m}{\max }\left\{L_m\right\}& s.t.f>\frac{J_{0,m}}{2{\mathrm{\&pi;Nt}}_s}\end{array}$

The corresponding frequency-splitting of adjacent two LFB series, i.e. frequency resolution is calculated as

${\mathrm{\&Delta;f}}_m=\frac{J_{0,m+1}}{2\mathrm{\&pi;}T}-\frac{J_{0,m}}{2\mathrm{\&pi;}T}<\frac{1}{2T}$

If frequency resolution Δ f_mSmaller, then the corresponding theoretic frequency value difference value of adjacent two LFB series reduces, then evaluated error Also can reduce；

LFB series resolution ratio k values are introduced, when LFB series resolution ratio is k

$L_m^k=K_1{K}_{2,m}j\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}n\ln \&lsqb;s\left(n\right)\&rsqb;J_0\left(\frac{J_{0,m}{t}_s}{kN}n\right)$

Now frequency resolution is Δ f_m=1/2 π kNt_s, with the increase of LFB series resolution ratio k, frequency resolution can also increase Plus；Now estimate that frequency is

${\hat{f}}^k=\frac{J_{0,m_{peak}^k}}{2\mathrm{\&pi;}T}$

Wherein maximal term LFB coefficients are

$\begin{array}{cc}{m}_{peak}^k=\underset{m}{max}\left\{L_m^k\right\}& s.t.f>\frac{J_{0,m}}{2{\mathrm{\&pi;kNt}}_s},k\&GreaterEqual;1\end{array}$

Now, the frequency resolution of adjacent two LFB series is

${\mathrm{\&Delta;f}}_m^k=\frac{J_{0,m+1}}{2\mathrm{\&pi;}kT}-\frac{J_{0,m}}{2\mathrm{\&pi;}kT}<\frac{1}{2kT}.$

4. a kind of multi -components SFM signal parameter estimation based on LFBT according to claim 1, wherein the 3rd step has Body is：

The errors of centration frequency in interval where adjacent two LFB series is calculated, carries out estimating frequency amendment, obtain estimating for each component Meter frequency；

By maximal term () the LFB series estimation frequency that calculates SFM signals isUnder normal circumstances, frequency Rate evaluated error f_biasNo more than the half of frequency resolution

$f_{bias}\&le;\frac{1}{2}{\mathrm{\&Delta;f}}_m=\frac{J_{0,m}+J_{0,m+1}}{4\mathrm{\&pi;}T}$

Now actual frequency is adjacent m and m+1 LFB coefficient theory of correspondences frequencies J_0,m/ 2 π T and J_0,m+1/ 2 π T's is flat Average；But such case is only applicable to a frequency content and is only projected on a single spectral line or single series (such as FT)；In LFB In series, a frequency content is projected on some rank Bessel series, that is to say, that f_mIt is same peak value to be obtained in m series When projection amplitude in neighbouring some class numbers be not zero；

The frequency separation f that adjacent two LFB series theory of correspondences frequency is constituted_i∈[f_m-1,f_m+1) on, the maximum of Frequency Estimation Error frequency f centered on the mean value definition of difference and minimal difference_cen, by calculate the errors of centration frequency on the interval come Carry out estimate frequency amendment, successively calculate LFB series maximum go forward side by side line parameter estimation, until without obvious LFB series Untill maximum.

5. a kind of multi -components SFM signal parameter estimation based on LFBT according to claim 4, the errors of centration The calculating of frequency is divided into three steps：The first step, calculates the corresponding maximal term LFB coefficients of signal, by the amplitude maximum of LFB coefficients Calculate and estimate frequencySecond step, selection m-1 and m+1 LFB series, and calculate their corresponding theoretic frequencies f_m-1And f_m+1；3rd step, selects suitable step-length, calculates f on frequency separation_i∈[f_m-1,f_m+1) respective LFB coefficient amplitudes are most The corresponding estimation frequency of sportAnd be calculated as below

$f_{cen}=\frac{1}{2}\&lsqb;max\left\{\right|{\hat{f}}_i-f_i\left|\right\}+min\left\{\right|{\hat{f}}_i-f_i\left|\right\}\&rsqb;$

f_cenAs errors of centration frequency；Therefore, the evaluated error frequency of amendment is

${\hat{f}}_r={\hat{f}}_m^k-f_{cen}$

After amendment, evaluated error frequency meets f_bias≤Δf_m/2。