CN103412188B - Based on the SFM signal parameter estimation of Bessel's function and Toeplitz algorithm - Google Patents

Abstract

A kind of method that request of the present invention protects Bessel's function to combine with Toeplitz algorithm, belongs to signal processing technology field.The method is by Bessel's function character and Jacobi's transformation treatment S FM signal, and then associated matrix column signal Processing Algorithm detects and estimates the parameter of SFM signal.The signal covariance matrix this method solved after the conversion of SFM signal keeps off the problem of actual value.The method accurately, more comprehensively can not only estimate the parameters of this signal, and can estimate multicomponent SFM signal parameter.

Description

Based on the SFM signal parameter estimation of Bessel's function and Toeplitz algorithm

Technical field

The present invention relates to signal processing technology, particularly relate to multiple sine FM (SFM) modulated parameter estimating method.

Background technology

Multiple sine FM (SFM) signal is the one in non-stationary signal, and its instantaneous frequency is a sine function along with time nonlinearities change.The non-linear of phase function result in the non-stationary of signal, so the frequency of multiple sine FM (SFM) signal has a greater change in time, and presents stronger time local characteristics.The analytic approach of conventional Time-domain and frequency domain all can not picture analysis stationary signal applicable like that, therefore need effective research method to process this type of signal.

Time frequency analysis is the effective means of process non-stationary signal, the most frequently used method is combined with Array Signal Processing by Wigner-Ville distribution (WVD), but WVD calculates quite complicated when multi signal, require very high to sampling rate, and being easily subject to the interference of cross term, these all reduce the practicality of these class methods.For this reason, the people such as Li Liping (Li Liping, Huang Keji etc. based on the Coherent Wideband FM signal 2-D angle-of-arrival estimation [J] of STFT. electronics and information journal, 2005.27 (11): 1760-1764.) Short Time Fourier Transform (STFT) is adopted to set up Spatial time-frequency distribution, avoid the interference of WVD cross term, calculate simple.But the method limits length of window when computer memory time-frequency distributions, be similar to constant hypothesis to meet signal transient frequency.(the PELEGS such as Peleg, FRIEDLANDERB.Thediscretepoly-nomial-phasetransform [J] .IEEETrans.onSignalProcessing, 1995,43 (8): 1901-1904.) utilize discrete polynomial-phase to convert the Waveform Reconstructing realizing sine FM signal, but do not provide parameter estimation algorithm.The people such as Lv Yuan (Lv Yuan, Zhu Jun, Tang Bin. based on the NLFM signal parameter estimation [J] of DPT. electronic surveying and instrument journal, 2009,23 (6): 63-67.) realized the parameter estimation of multiple sine FM signal by discrete polynomial transformation, but in depth modulation situation, algorithm performance is poor.

In sum, less to the research of the method for parameter estimation of multiple sine FM signal, or by parameter restriction or can only estimating part parameter, therefore, be not also generally suitable for the Processing Algorithm of answering sine FM signal at present.

Summary of the invention

Technical matters to be solved by this invention is, in multiple sine FM (SFM) Signal parameter estimation process, answers sine FM (SFM) signal and there is the problem that non-stationary and after decomposing covariance matrix keeps off actual value.The SFM signal parameter estimation that Bessel's function combines with Teoplitz (Toeplitz) algorithm is proposed, in signal processing, can effectively decompose SFM signal, namely its resolve into one group of arrowband sinusoidal signal with harmonic amplitude harmonic frequency and form.Thus in conjunction with Toeplitz algorithm reconstruct covariance matrix, then utilize the method for signal subspace to estimate the parameter of SFM.The method not only frequency-measurement accuracy is high, and estimated performance is good.

The technical scheme that the present invention solves the problems of the technologies described above is, a kind of method for parameter estimation of SFM signal, a kind of method for parameter estimation of SFM signal, it is characterized in that, adopt Bessel's function treatment S FM signal, obtain arrowband sinusoidal signal, set up the covariance matrix of Received signal strength according to arrowband sinusoidal signal by Toeplitz algorithm to covariance matrix carry out pre-service, obtain the covariance matrix R of reconstruction signal _t, to covariance matrix R _tcarry out Eigenvalues Decomposition, obtain signal subspace and the noise subspace of data, utilize MUSIC algorithm to try to achieve humorous angular frequency, thus obtain carrier frequency and modulating frequency and estimate, then according to the recurrence relation J of Bessel function of the first kind _v+1(m _f)=2vJ _v(m _f)/m _f-J _v-1(m _f), estimate the index of modulation and harmonic amplitude.

Described Bessel's function treatment S FM signal is specially: arrowband sinusoidal signal SFM signal decomposition being become a group to have a harmonic amplitude harmonic frequency and form, its harmonic amplitude is: C=[AJ _-V(m _f) ... AJ ₀(m _f) ... AJ _v(m _f)], each harmonic frequency is: f ₁=f _c-Vf _m..., f _v+1=f _c+ 0f _m..., f _2V+1=f _c+ Vf _m, wherein, A is the amplitude of signal, f _cfor signal(-) carrier frequency, f _mfor signal madulation frequency, m _ffor coefficient of frequency modulation, J _vk () is first kind v rank Bessel's functions, v=1 ..., V is Bessel function of the first kind exponent number.

Be specially by Toeplitz pre-service: call formula: make matrix close to real data covariance matrix R, the element in the clinodiagonal of data covariance matrix is averaged, wherein, S _tit is Toeplitz matrix stack.

Call formula the data covariance matrix of 0≤n < M pair array carry out evaluation computing, obtain a new vector $\hat{r}=\left({\hat{r}}_T\right(-(M-1)),...,{\hat{r}}_T(-1),{\hat{r}}_T\left(0\right),{\hat{r}}_T\left(1\right),...,{\hat{r}}_T(M-1)),$ By this vector reconstruction data covariance matrix R _t, wherein, M is array number, for in element, for in clinodiagonal, element is average.To covariance matrix R _tcarry out Eigenvalues Decomposition to be specially, to R _tcarry out Eigenvalues Decomposition, obtain the diagonal matrix D=diag [λ be made up of large eigenwert and little eigenwert ₁λ ₂λ _m], wherein, eigenwert meets relation: λ ₁>=λ ₂>=...>=λ _q> λ _q+1=...=λ _m=σ ², according to formula R _n=σ ²i tries to achieve noise power, calls formula: R _t=BR _sb ^h+ R _ntry to achieve its signal covariance matrix R _s, get its real part evolution and namely obtain its harmonic amplitude.Described acquisition arrowband sinusoidal signal specifically comprises: to given SFM signal s (t), carries out discretize in t=n Δ t to it, obtains discrete sampling sequence for { s (n) }; Call formula: signal after discretize is converted, obtains the infinite multinomial sinusoidal signal sum with harmonic amplitude harmonic frequency, according to formula: J _v(m _f)=(-1) ^vj _-v(m _f) obtain the arrowband sinusoidal signal that a group has harmonic amplitude harmonic frequency.Recurrence relation according to Bessel's function: J _v+1(m _f)=2vJ _v(m _f)/m _f-J _v-1(m _f), from the top step number of Bessel function of the first kind successively down, set up all recurrence Relation composition over-determined systems, the least square solution of group of equations, is the index of modulation

The present invention, on the basis of Bessel's function treatment S FM signal, adopts the method (Toeplitz algorithm, MUSIC algorithm) of Array Signal Processing to detect and estimate the parameter of SFM signal.The method can not only good treatment S FM signal, and Frequency Estimation effect is very good, and does not limit by parameter, and calculated amount is little, more comprehensively can estimate the parameter of SFM signal.

Accompanying drawing explanation

Fig. 1 SFM Signal parameter estimation of the present invention process flow diagram;

The time domain beamformer of Fig. 2 SFM signal;

The frequency-domain waveform figure of Fig. 3 SFM signal;

Fig. 4 SFM signal transient frequency and the variation relation of time;

Fig. 5 m _fharmonic amplitude when=1;

Fig. 6 m _fharmonic amplitude when=2;

Narrow band signal real part after Fig. 7 the present invention conversion;

The spectrum of each harmonic component after Fig. 8 converts;

Each humorous angular frequency that Fig. 9 Bessel's function of the present invention combines with Toeplitz algorithm is estimated.

Embodiment

The present invention carries out frequency detecting and estimation the arrowband sinusoidal signal after decomposition according to the method for Mutual coupling on the basis of Bessel's function treatment S FM signal, solves the process of SFM poor signal and the problem by the restriction of other parameter estimation.

Below directly adopt the method for the derivation of equation, derive carrier frequency fc, the modulating frequency f of multiple sine FM signal _m, index of modulation m _fand harmonic amplitude parameter.

The parameter estimation of SFM signal is specially, and multiple sine FM signal is expressed as:

s(t)＝Aexp(j(2πf _ct+m _fsin(2πf _mt))),0≤t≤T(1)

Wherein, A is the amplitude of signal, f _cfor signal(-) carrier frequency, f _mfor signal madulation frequency, m _ffor coefficient of frequency modulation.In t=n Δ t, discrete sampling sequence is obtained for { s (n) } to Setting signal s (t) discretize:

s(n)＝Aexp(j(2πf _c(nΔt)+m _fsin(2πf _m(nΔt)))),0≤n≤N-1(2)

Wherein, N is sampling length, and Δ t is sampling interval.

Received signal strength can be expressed as:

x(n)＝s(n)+W(n)

＝Aexp(j(2πf _c(nΔt)+m _fsin(2πf _m(nΔt))))+W(nΔt),0≤n≤N-1(3)

Wherein, W is the white Gaussian noise of zero-mean.

To the signal after discretize according to Jacobi expansion identical relation:

$\exp \left(jksin\mathrm{\&beta;}\right)=\underset{v=-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{J}_v\left(k\right)\exp \left(j\mathrm{\&nu;}\mathrm{\&beta;}\right)---\left(4\right)$

Wherein, J _vk () is first kind v rank Bessel's functions.Wushu (4) substitutes into formula (3) can obtain infinite multiple form with the sinusoidal signal sum of harmonic amplitude harmonic frequency, generally desirable Δ t=1, that is:

$\begin{array}{c}x\left(n\right)=s\left(n\right)+W\left(n\right)\\ =A\exp \left(j\left(2{\mathrm{\&pi;f}}_{c}n+m_f\sin \left(2{\mathrm{\&pi;f}}_{m}n\right)\right)\right)+W\left(n\right)\\ \begin{array}{cc}=\underset{v=-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{\mathrm{AJ}}_v\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c+{\mathrm{vf}}_m\right)n\right)+W\left(n\right),& 0\&le;n\&le;N-1\end{array}\end{array}---\left(5\right)$

As can be seen from formula (5), nonlinear multiple sine FM signal by become infinite multinomial linear sinusoidal signal and form.Wherein, symmetric property by Bessel's function: J _v(m _f)=(-1) ^vj _-v(m _f), and when | v| > | during V|, J _v(m _f) ≈ 0, s (n) part component is little disregards to being left in the basket.Therefore formula (5) can be write as:

$\begin{array}{c}\begin{array}{cc}x\left(n\right)\&ap;\underset{v=-V}{\overset{V}{\mathrm{\&Sigma;}}}{\mathrm{AJ}}_v\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c+{\mathrm{vf}}_m\right)n\right)+W\left(n\right),& 0\&le;n\&le;N-1\end{array}\\ ={\mathrm{AJ}}_{-V}\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c-{\mathrm{Vf}}_m\right)n\right)+\mathrm{...}+{\mathrm{AJ}}_0\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c+0f_m\right)n\right)\\ +\mathrm{...}+{\mathrm{AJ}}_V\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c+{\mathrm{Vf}}_m\right)n\right)+W\left(n\right)\end{array}---\left(6\right)$

Wherein, V is that component of signal cannot the top step number of uncared-for Bessel function of the first kind.Namely m is worked as _fduring > 1, V ≈ m _f+ 1, but work as m _ftime ∈ [0.14,1], V=1 or 2; Work as m _f∈ [0,0.14) time, V=0.

As can be seen from formula (6), after Bessel's function decomposes, SFM signal be broken down into one group of arrowband sinusoidal signal with harmonic amplitude harmonic frequency and form, its harmonic amplitude is: C=[AJ _-V(m _f) ... AJ ₀(m _f) ... AJ _v(m _f)], each harmonic frequency is: f ₁=f _c-Vf _m..., f _v+1=f _c+ 0f _m..., f _2V+1=f _c+ Vf _m.Here it is, and Bessel's function decomposes the process of SFM signal, and the method can be good at the narrow band signal form that SFM signal transacting is become to estimate with conventional algorithm.

Known by formula (6), SFM signal through Bessel's function character and Jacobi's transformation be transformed into one group of arrowband sinusoidal signal and form.Then its real data auto-covariance matrix R is obtained according to its narrowband model.In the ideal case, the covariance matrix of array received data there is Toeplitz character, and in actual conditions, due to the impact by error, the covariance matrix of array received data general just diagonally dominant matrix.Therefore make matrix close to real data covariance matrix R at this by Toeplitz pre-service.

Namely

$\underset{R_T\&Element;S_T}{\min }\left|R_T-R\right|---\left(7\right)$

Here S _tit is Toeplitz matrix stack.Toeplitz algorithm is exactly be averaged to the element in the clinodiagonal of data covariance matrix.Equivalence can be carried out, that is: by following two formulas

$\begin{array}{cc}{\hat{r}}_T(-n)=\frac{1}{M-n}\underset{i=1}{\overset{M-n}{\&Sigma;}}{\hat{r}}_{i(i+n)}& 0\&le;n<M\end{array}---\left(8\right)$

${\hat{r}}_T\left(n\right)={\hat{r}}_T^{*}\left(-n\right)---\left(9\right)$

Wherein, M is array number, for in element, for in clinodiagonal, element is average.

Utilize the data covariance matrix of formula (8) pair array carry out evaluation computing, obtain a new vector $\hat{r}=\left({\hat{r}}_T\right(-\left(M-1\right)),...,{\hat{r}}_T(-1),{\hat{r}}_T\left(0\right),{\hat{r}}_T\left(1\right),...,{\hat{r}}_T\left(M-1\right)),$ By this vector reconstruction data covariance matrix R _t, thus to R _teigenvalues Decomposition, obtains signal subspace and noise subspace, then utilizes MUSIC algorithm to carry out the estimation of humorous angular frequency, thus estimates its carrier frequency and modulating frequency.

More than the carrier frequency of signal, the estimation of modulating frequency.

In order to solve by parameter restriction or can only the problem of estimating part parameter, the present invention gives the index of modulation and harmonic amplitude is estimated.

By Bessel function of the first kind, following recurrence relation can be obtained:

J _v+1(m _f)＝2vJ _v(m _f)/m _f-J _v-1(m _f)(10)

By formula (10) recurrence relation we do following derivation, suppose that the top step number that Bessel's function decomposes is V, then each exponent number of Bessel's function is respectively-V-V+1 ... V.Following formula is then had to set up:

And formula (11) can resolve into following form:

$J=\left[\begin{array}{cc}2\left(V-1\right)J_{V-1}\left(m_f\right)& -J_{V-2}\left(m_f\right)\\ 2\left(V-2\right)J_{V-2}\left(m_f\right)& -J_{V-3}\left(m_f\right)\\ .& .\\ .& .\\ .& .\\ .& .\\ .& .\\ .& .\\ 2\left(-V+1\right)J_{-V+1}\left(m_f\right)& -J_{-V}\left(m_f\right)\end{array}\right]\&CenterDot;\left[\begin{array}{c}\frac{1}{m_f}\\ 1\end{array}\right]=Zb---\left(12\right)$

According to the definition of over-determined systems, formula (12) is over-determined systems, and so-called over-determined systems refers to that equation number is greater than the system of equations of unknown quantity number.

Work as Z ^tz can the inverse time, and over-determined systems (12) exists least square solution, and is system of equations Z ^tzb=Z ^tthe solution of J, i.e. b=(Z ^tz) ^-1z ^tj.So have: $\left[\begin{array}{c}1/m_f\\ 1\end{array}\right]={\left(Z^{T}Z\right)}^{-1}{Z}^{T}J.$ Thus can the index of modulation be calculated, least square solution is the index of modulation.

To reconstructing the data covariance matrix R obtained _tcarry out Eigenvalues Decomposition, thus obtain the diagonal matrix D=diag [λ that is made up of large eigenwert and little eigenwert ₁λ ₂λ _m], and the eigenwert in above formula meets following relation: λ ₁>=λ ₂>=...>=λ _q> λ _q+1=...=λ _m=σ ², thus try to achieve noise power R _n=σ ²i; Utilize formula: R _t=E [XX]=BR _sb ^h+ R _n, try to achieve its signal covariance matrix R _s, get its real part evolution and namely obtain its harmonic amplitude.

Below in conjunction with concrete accompanying drawing and simulation example, enforcement of the present invention is further described in detail, but embodiments of the present invention are not limited in this.

Be illustrated in figure 1 the method for parameter estimation process flow diagram that Bessel's function of the present invention and Toeplitz algorithm combine, as follows to SFM Signal parameter estimation concrete steps, suppose the broadband SFM signal having two identical time-frequency distributions:

s ₁(t)＝A ₁exp{j[2π*f _ct+m _f*sin(2π*f _mt)]}

s ₂(t)＝A ₂exp{j[2π*f _ct+m _f*sin(2π*f _mt)]}

Signal parameter is set to: m _f=1, f _c=0.35, f _m=0.03, signal amplitude is A ₁=1, A ₂=2A ₁, SNR=20dB, fast umber of beats N=256.

Step 1: in t=n Δ t to Setting signal s ₁(t), s ₂t () discretize obtains discrete sampling sequence for { s ₁(n), s ₂(n) }.

Step 2: utilize Jacobi expansion formula: $\exp \left(jksin\mathrm{\&beta;}\right)=\underset{v=-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{J}_v\left(k\right)\exp \left(j\mathrm{\&nu;}\mathrm{\&beta;}\right),$ And rear narrow band signal x (n) can be converted according to the symmetric property of Bessel's function and can be expressed as:

$x\left(n\right)\&ap;\underset{v=-2}{\overset{2}{\mathrm{\&Sigma;}}}{\mathrm{AJ}}_v\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\right(f_c+{\mathrm{vf}}_m\left)n\right)+W\left(n\right),0\&le;n\&le;N-1---\left(13\right)$

Through decomposing, formula (13) can be write as expression-form below:

$\begin{array}{c}\begin{array}{cc}x\left(n\right)\&ap;\underset{v=-2}{\overset{2}{\mathrm{\&Sigma;}}}{\mathrm{AJ}}_v\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\right(f_c+{\mathrm{vf}}_m\left)n\right)+W\left(n\right),& 0\&le;n\&le;N-1\end{array}\\ ={\mathrm{AJ}}_{-2}\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c-2f_m\right)n\right)+{\mathrm{AJ}}_{-1}\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c-1f_m\right)n\right)\\ +{\mathrm{AJ}}_0\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c+0f_m\right)n\right)+{\mathrm{AJ}}_1\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c+1f_m\right)n\right)\\ +{\mathrm{AJ}}_2\left(m_f\right)\exp \left(j2\mathrm{\&pi;}\left(f_c+2f_m\right)n\right)+W\left(n\right)\end{array}---\left(14\right)$

Step 3: the data covariance matrix of being tried to achieve Array Model reception by formula (14), adopts Toeplitz algorithm to carry out pre-service to it, obtains the data covariance matrix reconstructed.

Step 4: to the data covariance matrix Eigenvalues Decomposition of reconstruct, thus obtain signal subspace and noise subspace and its eigenwert space.

Step 5: utilize the Power estimation formula of MUSIC algorithm to try to achieve each humorous angular frequency.

Step 6: estimate carrier frequency and modulating frequency according to the symmetry of Bessel's function and each humorous angular frequency of estimating.

Step 7: from formula (10), formula (11), work as m _fwhen=1, when namely the top step number of Bessel function of the first kind is 2, this recurrence relation can be expressed as:

$\left\{\begin{array}{cc}v=1,& J_2\left(m_f\right)=2J_1\left(m_f\right)/m_f-J_0\left(m_f\right)\\ v=0,& J_1\left(m_f\right)=2\&CenterDot;0\&CenterDot;J_0\left(m_f\right)/m_f-J_{-1}\left(m_f\right)\\ v=-1,& J_0\left(m_f\right)=2\&CenterDot;(-1)\&CenterDot;J_{-1}\left(m_f\right)/m_f-J_{-2}\left(m_f\right)\end{array}\right.---\left(15\right)$

So following relation can be obtained by formula (15):

$J=\left[\begin{array}{cc}2J_1\left(m_f\right)& -J_0\left(m_f\right)\\ 2\&CenterDot;0\&CenterDot;J_0\left(m_f\right)& -J_{-1}\left(m_f\right)\\ 2\&CenterDot;\left(-1\right)\&CenterDot;J_{-1}\left(m_f\right)& -J_{-2}\left(m_f\right)\end{array}\right]\&CenterDot;\left[\begin{array}{c}\frac{1}{m_f}\\ 1\end{array}\right]=J_Z\left[\begin{array}{c}\frac{1}{m_f}\\ 1\end{array}\right]---\left(16\right)$

Therefore by $\left[\begin{array}{c}1/m_f\\ 1\end{array}\right]={\left({J_Z}^T{J}_Z\right)}^{-1}{J_Z}^{T}J$ Thus estimate the index of modulation

Step 8: the feature equal with noise power according to little eigenwert, thus to try to achieve its noise power be R _n=σ ²the little eigenwert of I=, then utilizes formula: R _t-R _n=BR _sb ^h, try to achieve its signal covariance matrix R _s, get its real part evolution and namely obtain harmonic amplitude.

In order to better understand the non-stationary property of SFM signal, analyze this signal from time domain, frequency domain, time-frequency domain respectively below, its oscillogram is shown in shown in Fig. 2, Fig. 3, Fig. 4 respectively.

By the time-domain expression of the multiple sine FM signal shown in formula (1), can obtain its instantaneous frequency expression formula is:

$f_{SFM}\left(t\right)=f_c+m_f\frac{{\mathrm{\&omega;}}_m}{2\mathrm{\&pi;}}cos\left({\mathrm{\&omega;}}_{m}t\right)---\left(17\right)$

As shown in Figure 2, as can be seen from the figure this signal is a complicated signal to the time domain waveform of signal, and can find out its duration and signal amplitude relation over time; I.e. Fig. 3 viewed from frequency domain, we only know its frequency content, but can't see its temporal information; But the instantaneous frequency of signal as shown in Figure 4, the information of signal time and frequency can not only be found out, and the frequency of signal and the variation relation of time can be indicated, give the directviewing description of a two-dimentional T/F.

Fig. 5, Fig. 6 are the harmonic amplitude figure of different modulating frequency of the present invention, and this picture group demonstrates symmetric property and the v ≈ m of Bessel function of the first kind _f+ 1, when | v| > | m _f| time, J _v(m _f) ≈ 0, namely s (n) part component is little disregards to being left in the basket.Fig. 5 gets m _f=1, when V>=3, obviously J can be found out ₃(1) ≈ 0; Fig. 6 gets m _f=2, when V>=4, obviously J can be found out ₄(2) ≈ 0.

From formula (6), (14), become one group of arrowband sinusoidal signal by Bessel's function and Jacobi's transformation signal.Its simulation result as shown in Figure 7, Figure 8.Narrow band signal after Fig. 7 gives conversion respectively when there is no noise and SNR=20dB, the real part amplitude characteristic figure of signal.As can be seen from the figure, after conversion, when not having noise, signal has been transformed into the signal of arrowband; As SNR=20dB, the signal of reception has been transformed into narrow band signal and noise.Thus the signal in broadband is become the signal of arrowband, be conducive to carrying out parameter estimation by the method for comparative maturity.Fig. 8 gives the spectrum of conversion each harmonic component rear.Namely corresponding with the harmonic frequency of each non-zero in Fig. 5.

From analyzing above, SFM signal, after Bessel's function conversion, in conjunction with Toeplitz algorithm reconstruct data covariance matrix, thus adopts MUSIC algorithm to carry out parameter estimation.As shown in Figure 9, when signal parameter is above known, the theoretical value of each harmonic frequency should be its simulation result: $\begin{array}{c}{f}_1=(f_c-2f_m)=029,f_2=(f_c-1f_m)=0.32,f_3=(f_c+0f_m)=0.35\\ f_4=\left(f_c+1f_m\right)=0.38,f_5=\left(f_c+2f_m\right)=0.41\end{array}.$ Then these 5 humorous angular frequency theoretical values of composing peak corresponding are respectively:

ω ₁＝2πf ₁＝(f _c-2f _m)*2π＝0.58π,ω ₂＝2πf ₂＝(f _c-f _m)*2π＝0.64π

ω ₃＝2πf ₃＝(f _c)*2π＝0.7π,ω ₄＝2πf ₄＝(f _c+f _m)*2π＝0.76π

ω ₅＝2πf ₅＝(f _c+2f _m)*2π＝0.82π

By Fig. 9 and above Data Comparison, the frequency estimating methods clearly combined with Toeplitz algorithm can be good at estimating each humorous angular frequency, thus utilize formula ω=2 π f to estimate each harmonic frequency, and then according to the symmetry of these harmonic frequencies, namely all harmonic frequency sums are the integral multiples of carrier frequency, obtain the difference of any two adjacent harmonic frequencies is modulating frequencies, obtains or wherein the actual value of carrier frequency is f _c=0.35, what simulation result obtained is and modulating frequency actual value is f _m=0.03, what simulation result obtained is therefore carrier frequency and modulating frequency can be estimated accurately in error allowed band.

Then utilize the recursive nature of Bessel's function, composition over-determined systems, estimates the coefficient of frequency modulation of SFM signal according to the theorem of over-determined systems.In order to the validity of sufficient proof the method, the index of modulation is allowed to be respectively m _f=1 and m _f=2.

According to the theorem of over-determined systems, what estimate should be the inverse of modulating frequency, and the result therefore estimated is: with from simulation result, the coefficient of frequency modulation estimated and actual value are identical substantially, and therefore coefficient of frequency modulation obtains good estimation.

Due to the method for parameter estimation also unsound imperfection of SFM signal, the parameter estimation of a lot of SFM signal is all subject to the restriction of partial parameters, or can not be complete estimate its whole parameter, in order to the integrality of parameter estimation, here is the estimation of its harmonic amplitude.Be respectively according to each harmonic amplitude of theory calculate: (A ₁+ A ₂) J ₂, (A ₁+ A ₂) (-J ₁), (A ₁+ A ₂) J ₀, (A ₁+ A ₂) J ₁, (A ₁+ A ₂) J _2,a is known by hypothesis above ₁=1, A ₂=2, the actual value of harmonic amplitude can be obtained by actual emulation and the Bessel's function table found.Each rank Bessel's function is respectively: J ₂=0.1149, J ₁=0.4401, J ₀=0.7652.What then each harmonic amplitude was estimated the results are shown in Table shown in 1.

Table 1: each harmonic amplitude estimated result

Harmonic amplitude	(A 1+A 2)J 2	(A 1+A 2)(-J 1)	(A 1+A 2)J 0	(A 1+A 2)J 1	(A 1+A 2)J 2
						Actual value	0.3447	-1.3203	2.2956	1.3203	0.3447
Emulation 1	0.3486	-1.3063	2.2544	1.3075	0.3079
						Emulation 2	0.3320	-1.2868	2.2624	1.2954	0.3319
Emulation 3	0.3365	-1.3040	2.2777	1.2878	0.3317
						Emulation 4	0.3451	-1.3107	2.2223	1.2870	0.3185
Emulation 5	0.3523	-1.3045	2.2607	1.3209	0.3600

As can be seen from Table 1, the method can not only estimate each harmonic frequency, but also can easier estimate each harmonic amplitude.And each harmonic amplitude differs seldom with actual theoretical value, therefore has higher estimated accuracy.

What the present invention adopted is the SFM signal of 2 components with identical time-frequency distributions, and the method is easy to the situation of the SFM signal being generalized to multiple component.And the method can not only estimate parameters accurately, and does not limit by partial parameters, and more completely can estimate the parameters etc. of SFM signal.

Claims (5)

1. a method for parameter estimation for SFM signal, is characterized in that, adopts Bessel's function treatment S FM signal, obtains arrowband sinusoidal signal, set up the covariance matrix of Received signal strength according to arrowband sinusoidal signal by Toeplitz algorithm to covariance matrix carry out pre-service, obtain the covariance matrix R of reconstruction signal _t, to the covariance matrix R of reconstruction signal _tcarry out Eigenvalues Decomposition, obtain signal subspace and the noise subspace of data, thus try to achieve humorous angular frequency, obtain carrier frequency and modulating frequency estimation, according to the recurrence relation J of Bessel function of the first kind _v+1(m _f)=2vJ _v(m _f)/m _f-J _v-1(m _f), estimate the index of modulation and harmonic amplitude, wherein, v=1 ..., V is Bessel function of the first kind exponent number, m _ffor the index of modulation, J _vk () is first kind v rank Bessel's functions.

2. method according to claim 1, is characterized in that, described Bessel's function treatment S FM signal is specially: arrowband sinusoidal signal SFM signal decomposition being become a group to have a harmonic amplitude harmonic frequency and form, its harmonic amplitude is: C=[AJ _-V(m _f) ... AJ ₀(m _f) ... AJ _v(m _f)], each harmonic frequency is: f ₁=f _c-Vf _m..., f _v+1=f _c+ 0f _m..., f _2V+1=f _c+ Vf _m, wherein, A is the amplitude of signal, f _cfor signal(-) carrier frequency, f _mfor signal madulation frequency, m _ffor the index of modulation, J _vk () is first kind v rank Bessel's functions, v=1 ..., V is Bessel function of the first kind exponent number, and the top step number that Bessel's function decomposes is V.

3. method according to claim 1, is characterized in that, by Toeplitz algorithm to covariance matrix pre-service is specially: call formula: make matrix close to real data covariance matrix R, to covariance matrix clinodiagonal on element be averaged, wherein, S _tit is Toeplitz matrix stack.

4. method according to claim 1, is characterized in that, calls formula ${\hat{r}}_T(-n)=\frac{1}{M-n}\underset{i=1}{\overset{M-n}{\&Sigma;}}{\hat{r}}_{i(i+n)},0\&le;n<M,$ To covariance matrix carry out evaluation computing, obtain a new vector $\hat{r}=\left({\hat{r}}_T\right(-\left(M-1\right)),...,{\hat{r}}_T(-1),{\hat{r}}_T(0),{\hat{r}}_T(1),...,{\hat{r}}_T(M-1\left)\right),$ By the covariance matrix R of this vector reconstruction signal _t, wherein, M is array number, for in element, for in clinodiagonal, element is average.

5. method according to claim 1, is characterized in that, the estimation of the described index of modulation specifically comprises, the recurrence relation according to Bessel function of the first kind: J _v+1(m _f)=2vJ _v(m _f)/m _f-J _v-1(m _f), from the top step number of Bessel function of the first kind successively down, set up all recurrence Relation composition over-determined systems, calculate the least square solution of over-determined systems, be the index of modulation.