CN106597408A - Method for estimating high-order PPS signal parameter based on time-frequency analysis and instantaneous frequency curve-fitting - Google Patents

Abstract

The invention claims protection for a method for estimating a high-order PPS signal parameter based on time-frequency analysis and instantaneous frequency curve-fitting, and belongs to the technical field of signal processing. The method includes the following steps: conducting sample processing on a received high-order PPS signal, suppressing time-frequency cross-term interferences by conducting smoothed pseudo Wigner-Ville distribution, acquiring the instantaneous frequency of the signal by extracting maximum value from the obtained time-frequency distribution, and using the least square method to conducting instantaneous frequency curve-fitting, and at the same time determining a curve-fitting order, and achieving the purpose of obtaining an accurate high-order PPS signal parameter by conducting multiple tests. The method can effectively suppress cross-term interferences to the high-order PPS signal, estimates the PPS signal phase parameter of an unknown order under low signal to noise ratio, can better estimate parameters, overcomes the effects on traditional methods by time-frequency cross-term interferences, and is significant to follow-up processing of unstable signals and characteristics analysis.

Description

Based on the high-order PPS signal parameter estimation that time frequency analysis and instantaneous frequency profile are fitted Method

Technical field

The present invention relates to a kind of nonstationary random response in communicating, is specially intended based on time frequency analysis and instantaneous frequency profile Polynomial-phase letter (PPS) number Parameter Estimation Problem of conjunction.

Background technology

Polynomial Phase Signals (Polynomial Phase Signal, PPS) are a kind of typical non-stationary signals, tool There are the properties such as frequency time-varying, low probability of intercept, obtain extensively in fields such as communication, radar, biomedicine and seismic data processings General application.In various communications and radar system, the motion feature paradoxical reaction of target in the phase function of echo-signal, once phase Bit function characterizes target and moves with uniform velocity, and QP function characterizes target and does uniformly accelerated motion, and Cubic phase function characterizes mesh Mark is variable accelerated motion state.Because transmitter can cause transmission signal phase place to change over the relative motion of receiver, The change of distance between receiving and launching necessarily causes the consecutive variations of instantaneous phase, theoretical according to Weierstrass, on closed interval Continuous function can use Polynomial approximation of functions, and receive signal and be approximately Polynomial Phase Signals, therefore PPS signal parameter is estimated Meter technique study has great importance.

High-order PPS signal parameter estimation is always the important content of field of signal processing, in recent years many Chinese scholars Substantial amounts of research and exploration are all carried out to this, based on all kinds of non-stationary signal parameter estimation of Time-Frequency Analysis Method this has been become The focus of area research.In actual information system, what people often faced is signal environment complicated and changeable, PPS signal Instantaneous frequency change over, traditional time-domain analyses and frequency-domain analysis method can not be analyzed with the non-of localized variation feature Stationary signal, and time frequency analysis emphasis signal is signal time-varying spectrum signature, description signal is with time and the Energy distribution of frequency. Time frequency analysis are carried out to signal, can intuitively reflect the characteristic information of signal, but because non-stationary signal has substantial amounts of intersection Item makes its time-frequency distributions produce serious time-frequency interference, hinders further signal processing.

Currently for the research comparative maturity of second order PPS signal parameter estimation, formed perfect signal processing method and Theory, but for the research of high-order PPS signal parameter estimation is also in developmental stage, and the method for existing proposition is present necessarily Limitation, it is difficult to realize the parameter estimation of unknown exponent number PPS signal.Document " Wang Pu. the time frequency analysis of Polynomial Phase Signals With parameter esti mation electronic letters, vol, 2005 " propose based on the adaptive time frequency distribution of product ambiguity function, by design from Adapt to kernel function can strengthen time-frequency locality while suppressing crossterms, but its amount of calculation it is larger and estimate performance designed The impact of kernel function.Document " Jin Xiang. the polynomial-phase parameter esti mation electronic technology based on Fourier Transform of Fractional Order should With 2010 " high-order PPS signal is processed using time delay correlation demodulation method, by Fourier Transform of Fractional Order (FRFT) to signal Parameter estimation is carried out, although the method improves the computational efficiency of FRFT methods, but on condition that in situation known to signal exponent number Under carry out, estimate that performance is affected by noise larger.Therefore, the present invention is proposed for the Parameter Estimation Problem of high-order PPS signal A kind of method for parameter estimation being fitted based on time frequency analysis and instantaneous frequency profile.

The content of the invention

The technical problem to be solved, for existing method process high-order PPS signal when exist by cross term Interference effect is big, poor performance is estimated under low signal-to-noise ratio and the defect such as computationally intensive, proposes a kind of based on time frequency analysis and instantaneous frequency The method for parameter estimation of rate curve matching, solves a difficult problem for high-order PPS signal parameter estimation.The method overcome traditional PPS letters The deficiency of number method for parameter estimation, can effectively suppress the cross term interference of high-order PPS signal, more accurately estimate in low signal-to-noise ratio Go out unknown exponent number PPS signal phase parameter.

The present invention solves the technical scheme of above-mentioned technical problem：One kind is fitted based on time frequency analysis and instantaneous frequency profile PPS signal method for parameter estimation, its step is to carry out sampling processing to receiving unknown exponent number PPS signal first, then Sample signal is carried out into smooth and pseudo Wigner-Ville time-frequency conversion process, the time-frequency distributions without cross term interference are obtained, and is adopted Signal transient frequency is obtained with the method for extracting extreme value, finally instantaneous frequency profile fitting is carried out using method of least square, while Judge, until meeting the decision condition for setting, to realize the parameter estimation of unknown exponent number PPS signal by being fitted exponent number.

In actual communication system, noisy observation signal model is represented by x (t)=s (t)+n (t).In formula, n T () is zero-mean, variance is σ²White Gaussian noise, s (t) is normal amplitude PPS signal, and its mathematical notation isWherein A is amplitude, generally considers A=1, For signal phase, p is phase place exponent number, a₀,a₁,a₂,…,a_pFor the phase coefficient of signal.

The present invention carries out phase with the method for parameter estimation that time frequency analysis and instantaneous frequency profile are fitted to high-order PPS signal There is cross term interference in position parameter estimation, signal Analysis, and derive the Cramér-Rao lower bound limit of signal parameter unbiased esti-mator (CRB), by signal is carried out smooth and pseudo Wigner-Ville become bring suppression its cross term interference, using least square curve Approximating method is realized to unknown exponent number PPS signal parameter estimation, the method overcomes traditional method and handed over by time-frequency in estimation performance The problems such as estimating poor performance under fork interference, low signal-to-noise ratio, while suitable for the PPS signal parameter estimation of arbitrary finite order.

Description of the drawings

Fig. 1 PPS method for parameter estimation flow charts of the present invention

Fig. 2 smooth and pseudo Wigner-Ville shift theory block diagrams of the present invention

The Wigner-Ville distribution figure of Fig. 3 quadravalence PPS of the present invention

The smoothed pseudo wigner ville disstribution figure of the noisy quadravalence PPS of Fig. 4 present invention

Root-mean-square error of Fig. 5 parameters a0 of the present invention under different signal to noise ratios

Root-mean-square error of Fig. 6 parameters a1 of the present invention under different signal to noise ratios

Root-mean-square error of Fig. 7 parameters a2 of the present invention under different signal to noise ratios

Root-mean-square error of Fig. 8 parameters a3 of the present invention under different signal to noise ratios

Root-mean-square error of Fig. 9 parameters a4 of the present invention under different signal to noise ratios

Specific embodiment

Below in conjunction with accompanying drawing and instantiation, the enforcement to the present invention is further described.

Fig. 1 show high-order PPS signal parameter estimation method of estimation flow chart of the present invention, concrete steps：First to receiving To signal carry out sampling processing, sample frequency is f_s, and the signal after sampling is carried out into smooth and pseudo Wigner-Ville time-frequency Conversion process, obtains the signal time-frequency distributions without cross term interference, the side for then time-frequency distributions for obtaining being passed through into extraction extreme value Method obtains signal transient frequency, and setting fitting judges exponent number P and threshold value δ, using the instantaneous frequency of least square fitting signal, When calculating criterion ξ of the actual fitting of instantaneous frequency profile_fDuring less than threshold value δ, then phase coefficient can be obtained by fitting and realize PPS's Parameter estimation, when calculating criterion ξ of actually fitting_fDuring more than threshold value δ, then judgement exponent number P is fitted from increase by 1, i.e. P=P+ 1, least square curve fitting process is re-started, till decision condition meets.

Fig. 2 show smooth and pseudo Wigner-Ville shift theory block diagram.First by observation signal through sampling processing, then Sample signal is made two parts to process, a portion carries out-τ/2 and postpone and take conjugation, after the delay process of another part τ/2 and One impulse function δ (s-n) is multiplied, and the signal after delay process is carried out into an Integral Processing, by the signal for obtaining and One in short-term window function h (τ) by multiplier process, and carry out second Integral Processing, the result for finally exporting is signal Smoothed pseudo wigner ville disstribution time-frequency figure.Smooth and pseudo Wigner-Ville conversion is the smooth of Wigner-Ville conversion Windowing process, can effectively suppress the cross term interference of high-order PPS signal, and keep the high time-frequency locality of signal.

Fig. 3 show the Wigner-Ville distribution figure of quadravalence PPS signal of the present invention.By analogous diagram as can be seen that signal Wigner-Ville distribution there is good time-frequency locality, signal energy is concentrated on around instantaneous frequency, but the quadravalence There is cross term interference in PPS signal, the presence of its cross term have impact on Signal parameter estimation error, therefore directly it can not be entered Row signal analysis.

The following is the Wigner-Ville distribution to signal and there is cross term interference and make a concrete analysis of.

Theoretical according to time frequency analysis, the Wigner-Ville transform definitions of signal are

In formula, f is the instantaneous frequency of signal, and symbol " * " is represented and takes conjugate operation.

Consider simple component high-order PPS signal, its discrete models can be expressed as

Wherein A is amplitude,For signal phase, p is signal exponent number (p ＞ 2), a₀,a₁,a₂,…,a_pFor phase coefficient. Because instantaneous frequency is first derivative of the phase function with regard to the time, then signal transient frequency representation is

Can obtain with reference to (1) and formula (2), the Wigner-Ville conversion of signal is launched as follows

WillWithLaunch respectively to obtain by Taylor's formula：

OrderThen formula (4) can be converted into

From formula (7), when the second order of signal phase function is zero with upper derivate, its Wigner-Ville distribution is position An impulse function in the signal transient frequency, such as simple component linear FM signal shows optimal without cross term interference Time-frequency locality.When signal phase function second order is not zero with upper derivate, the higher derivative of such as PPS signal phase place be with regard to The polynomial function of time, due to its phase place high-order term effect, the WVD of signal can produce itself cross term.

Fig. 4 show the smoothed pseudo wigner ville disstribution figure of noisy quadravalence PPS of the invention.The energy of signal more collects In, restrained effectively time-frequency cross term interference.Smoothed pseudo wigner ville disstribution has preferable suppressing crossterms to disturb, former It is to have carried out smooth windowing process on the basis of Wigner-Ville conversion that cause is smooth and pseudo Wigner-Ville conversion.It is real In the communication system of border, for the PPS signal Wigner-Ville distribution under noise background, it is not only disturbed by noise, can also By the severe jamming of its own cross term, and the instantaneous frequency of signal cannot be extracted, thus can not be directly to PPS signal Wigner-Ville distribution carries out signal analysis and processing.As seen from the figure, smooth and pseudo Wigner-Ville becomes transducing and effectively suppresses The interference of its cross term, and effect of noise is inhibited to a certain extent, there is great role for signal characteristic information is extracted.

Smooth and pseudo Wigner-Ville conversion is the smooth windowing process of Wigner-Ville conversion, is defined as

Wherein, f represents the instantaneous frequency of signal, and it is g (t)=δ (t) to take impulse function, and h (t) is smooth window function.It is smooth The purpose of pseudo- Wigner-Ville conversion is that doing for time-frequency cross term is restrained effectively while high time-frequency locality is kept Disturb.

Fitting of a polynomial, instantaneous frequency profile and actual wink are carried out to the instantaneous frequency profile of signal using method of least square When frequency curve be closer to, can relatively accurately estimate the phase parameter of PPS signal.Least square curve fitting mistake substantially Journey is briefly described as follows：

Time-frequency distributions after smooth and pseudo Wigner-Ville is converted are extracted with its maximum, the instantaneous frequency of signal is obtained Rate, i.e.,

IF (n)=maxSPW_x(n,f) (9)

Fitting of a polynomial is carried out using method of least square to the instantaneous frequency of rough estimate to approach, intend after error meets decision condition The multinomial coefficient of conjunction is the phase parameter estimated value of PPS signal.

If the m data of signals collecting is (x_i,y_i), i=0,1,2 ..., m and x₀＜ x₁＜ ... ＜ x_m, least square curve The basic thought of fitting is to seek a multinomialMeet

Try to achieve multinomial coefficientSo as to obtain PPS estimates of parameters

Because the PPS signal for receiving does not have priori, thus fitting precision can by the judgement of polynomial order, When actual the Fitting Calculation criterion ξ_fDuring less than threshold value δ, multinomial coefficient can be obtained, so as to estimate the phase parameter of signal； When actual the Fitting Calculation criterion ξ_fDuring more than threshold value δ, fitting exponent number repeats new curve matching from increasing by 1, i.e. P=P+1 Process, until meeting given fitting decision condition.Can be fixed using the difference between double instantaneous frequency as criterion is calculated Justice is

Wherein, IF_iN () is the instantaneous frequency of i ＆ lt fitting, δ is threshold value set in advance.

Carat Metro lower bound (CRB) of PPS signal derives as follows：

Order receives signal and is expressed as s_n=s_n+v_n, 0 ＜ n ＜ N-1, v_nFor zero-mean additive white Gaussian noise, and discretization Afterwards PPS signal is represented by

s_n=A₀exp[j(a₀+a₁(nΔ)+a₂(nΔ)²+a₃(nΔ)³+a_Mt^M)] (12)

In formula, Δ is the sampling interval, makes η=(a₀,a₁,…,a_M)^T, x=(x₁,x₂,…x_N)^T, then likelihood function be

The element of information matrix I (η)

The CRB of each Parameter Estimation Precisions of PPS can be obtained

In formula,Through computing, each rank phase parameter The CRB of estimation can be approximately

Validation verification is carried out to method of estimation of the present invention using emulation experiment, using quadravalence PPS signal, parameter setting For：Phase coefficient a₀=0.1, a₁=0.3, a₂=-0.000561, a₃=0.000000756, a₄=1, amplitude A=1.Noisy PPS Observation signal is x (t)=s (t)+n (t), and n (t) is zero-mean, variance is σ²White Gaussian noise, s (t) represents for PPS signal For

S (t)=exp [j (0.1+0.3t-0.000561t²+0.000000756t³+t⁴)] (17)

Sampling processing is carried out to the quadravalence PPS signal, sample frequency is f_s=1kHz, sampling number is N=768.First to sample This signal carries out smooth and pseudo Wigner-Ville conversion, while being entered to signal phase parameter using least square curve fitting method Row estimation, carries out 800 Monte Carlo experiments, threshold value δ=0.01Hz in emulation.PPS letters are obtained by Computer Simulation Number phase parameter estimated value be respectively The simulating, verifying effectiveness of context of methods, can more accurately estimate PPS phase parameters.

On the basis of above-mentioned experiment, parameter estimation is carried out under different signal to noise ratios to PPS signal using context of methods, believed It is -5dB～20dB to make an uproar than scope.

Fig. 5, Fig. 6, Fig. 7, Fig. 8 and Fig. 9 represent respectively the phase parameter a of PPS signal₀,a₁,a₂,a₃,a₄Under different signal to noise ratios Parameter estimation performance.As seen from the figure, as signal to noise ratio snr ＜ 2dB, the error that quadravalence PPS signal phase parameter is estimated is with noise The increase of ratio and reduce, algorithm estimate performance it is affected by noise larger；As signal to noise ratio snr ＞ 2dB, the phase parameter of signal is estimated Meter error gradually restrains with the increase of signal to noise ratio, and estimation difference is both less than 0.01Hz, now with estimation performance well.It is imitative True result shows, when signal to noise ratio reaches to a certain degree, even if signal to noise ratio further increases, Parameter Estimation Precision also will not be with Signal to noise ratio increases and improves, and illustrates set forth herein method has robustness.

By carrying out smooth and pseudo Wigner-Ville conversion to high-order PPS signal, the energy of signal concentrates on wink to the present invention When frequency on, effectively suppress the cross term interference of signal and obtain the time-frequency distributions of high aggregation, such that it is able to the wink to signal When frequency carry out extreme value extraction, the phase parameter of PPS signal can further be estimated using least square curve fitting method. The method effectively suppresses the cross term interference that signal high order phase place is brought, and has under low signal-to-noise ratio and preferably estimate performance, gram The problem for estimating that performance is not enough and operand is big under PPS signal parameter estimation, the low signal-to-noise ratio of unknown exponent number is taken.This paper side Method can carry out parameter estimation to other non-stationary signals, have weight to the subsequent treatment and Particular Eigen-Structure of such signal Want meaning.

Claims (4)

1. a kind of PPS signal method for parameter estimation being fitted based on time frequency analysis and instantaneous frequency profile, its step is, first To the PPS signal that receives with sample frequency as f_sSampled, and the signal after sampling is carried out into Smoothing Pseudo Wigner- The process of Ville time-frequency conversions, obtains the signal time-frequency distributions (SPWVD) without cross term interference, and the time-frequency distributions for obtaining are passed through The method for extracting extreme value obtains signal transient frequency, finally carries out instantaneous frequency profile fitting using method of least square and obtains multinomial Formula coefficient, and then realize the parameter estimation of PPS.

2. method of estimation according to claim 1, it is characterised in that the observation model for setting up PPS signal is x (t)=s (t)+n(t).In formula, n (t) is zero-mean, variance is σ²White Gaussian noise, s (t) is PPS signal, and its mathematical notation isWherein A is signal amplitude,For the phase place of signal, P for signal exponent number, a₀,a₁,a₂,…,a_pFor the phase coefficient of signal.From the Mathematical representation of PPS signal, its phase place Function isThen the instantaneous frequency of the signal can be expressed as

3. method of estimation according to claim 1, it is characterised in that the Wigner-Ville of signal is transformed toWigner-Ville distribution is good for non-stationary signal has Time-frequency locality, but there is the cross term interference of order phase in PPS signal, and smooth and pseudo Wigner-Ville conversion is Wigner- The smooth windowing process of Ville conversion, i.e.,

${\mathrm{SPW}}_x(n,f)={\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}h\left(\mathrm{\τ}\right)g(s-n)x(s+\frac{\mathrm{\τ}}{2})x^{*}(s-\frac{\mathrm{\τ}}{2})e^{-j2\mathrm{\π}f\mathrm{\τ}}dsd\mathrm{\τ}$

Wherein, f represents the instantaneous frequency of signal, and impulse function is g (t)=δ (t), and h (t) is smooth window function.By to letter Number smooth and pseudo Wigner-Ville conversion process is carried out, largely solve the interference problem of time-frequency cross term.

4. the method for estimation according to claim 1-3, enters in combination with method of least square to the instantaneous frequency profile of signal Row fitting of a polynomial, it is estimated that the phase parameter of PPS signal.To the time-frequency after smooth and pseudo Wigner-Ville is converted Its maximum is extracted in distribution, obtains the instantaneous frequency of signal, i.e.,

IF (n)=maxSPW_x(n,f)

Fitting of a polynomial is carried out using method of least square to the instantaneous frequency of rough estimate to approach, intend after error meets decision condition The multinomial coefficient of conjunction is the phase parameter estimated value of PPS signal.

If the m data of signals collecting is (x_i,y_i), i=0,1,2 ..., m and x₀＜ x₁＜ ... ＜ x_m, least square curve fitting Basic thought be to seek a multinomialMeet

$I_{\min }=\min \left\{I\left({\hat{b}}_0,{\hat{b}}_1,{\hat{b}}_2,\mathrm{...},{\hat{b}}_m\right)\right\}=\min \left\{\underset{i=0}{\overset{m}{\mathrm{\Σ}}}{\[\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\hat{b}}_k{x}_i^k-y_i\]}^2\right\}$

Try to achieve multinomial coefficientAnd then PPS estimates of parameters can be tried to achieve

Because the PPS signal for receiving does not have priori, thus fitting precision can by the judgement of polynomial order, when Actual the Fitting Calculation criterion ξ_fDuring less than threshold value δ, multinomial coefficient can be obtained, so as to estimate the phase parameter of signal；When Actual the Fitting Calculation criterion ξ_fDuring more than threshold value δ, phase place exponent number repeats new curve matching mistake from increasing by 1, i.e. P=P+1 Journey, until meeting given fitting decision condition.Can define using the difference between double instantaneous frequency as criterion is calculated For

${\mathrm{\&xi;}}_f=mean\left(\frac{|{\mathrm{IF}}_{i+1}\left(n\right)-{\mathrm{IF}}_i\left(n\right)|}{\left|{\mathrm{IF}}_i\left(n\right)\right|}\right)<\mathrm{\&delta;}$

Wherein, IF_iN () is the instantaneous frequency of i ＆ lt fitting, δ is threshold value set in advance.