CN104880697B - Chirp signal parameter estimating method based on sparse constraint - Google Patents

Abstract

The invention discloses a chirp signal parameter estimating method based on sparse constraint. The invention mainly solves problems of low resolution rate and large calculating amount of a prior method. The technical scheme includes that (1) obtaining a projection spectrum by utilizing the sparsity of an object and according to a Radon-Ambiguity converter technique; (2) performing angle division on an angle measurement range and designing a sparse matrix of two-dimension projection; (3) constructing a relational expression by utilizing the projection spectrum and sparse matrix; (4) obtaining a high resolution angle spectrum by solving the relational expression; (5) performing peak value detection of the angle spectrum by using a threshold value comparing method and obtaining angle values corresponding to signals; (6) acquiring frequency modulating value through calculation based on the angle values. The method provided by the invention has advantages of being small in calculating amount and high resolution rate and can be applied to communication and information processing systems.

Description

Linear frequency-modulated parameter estimating method based on sparse constraint

Technical field

The invention belongs to communication technical field, further relates to the method for estimation of linear frequency-modulated parameter, can be used for To the parameter estimation of linear FM signal in signal processing.

Background technology

Linear FM signal is extensively used as a kind of typical non-stationary signal and with big when m- frequency band product In various information systeies.From from the point of view of electronic warfare and electronic interferences, be solve the contradiction of operating distance and range resolution ratio with And the disguise of raising signal, generally using linear FM signal.Therefore the detection for linear FM signal and parameter estimation, Become the emphasis for electronics research.

At present, the method that linear frequency-modulated parameter is estimated has Radon-Ambiguity converter techniques and fractional order Fu Ye to become Change FRFT methods.

The first Radon-Ambiguity converter technique, is the ambiguity function for first seeking linear FM signal, and then it is carried out Radon is converted, final to obtain frequency modulation rate.For example, the paper of Zhao Xinghao, happy and carefree, Zhou Siyong, Wang Yue " is based on Radon- Ambiguity converts the chirp signal detections and multi-parameter inversion with fraction Fourier conversion " (《Beijing Institute of Technology is learned Report》The 3rd phase of volume 23 in June, 2003) it is exactly the method for parameter estimation to linear FM signal, the deficiency of this method is anti-noise Acoustic performance is not high, and in multiple signals, the frequency modulation rate for estimating is not very accurate.

Second fractional order Fu's leaf transformation FRFT method, is scanned by variable of rotation angle α, obtains linear FM signal FRFT conversion, so as to form signal energy, in parameter plane, (α, the u) Two dimensional Distribution of plane, is carried out in this plane according to threshold value Plane search detection obtains the parameter estimation of linear FM signal.For example, paper " the LPI radar signals based on FRFT of Tang Jiang Method for parameter estimation is studied ", information engineering university of PLA navigates and Kong Tian targets engineering college, and 2013, be exactly a kind of right The method for parameter estimation of linear FM signal, but the shortcoming of this method is to estimate that degree of accuracy is not high.

The content of the invention

The invention reside in for the deficiency of above-mentioned prior art, proposing that a kind of linear FM signal based on sparse constraint is joined Number estimation method, to reduce error, improves the degree of accuracy for estimating parameter.

The technical thought for realizing the present invention is that, by setting up sparse reconstruction model, iterative optimization problem obtains high-resolution Rate angular spectrum, by carrying out peakvalue's checking to angular spectrum the angle information of target is obtained, then obtains its corresponding frequency modulation rate.Its tool Body step includes as follows：

(1) radar emission linear FM signal s (t), obtains echo-signal x (t), and echo-signal x (t) is carried out from Sampling is dissipated, discrete signal x (n) is obtained, 0≤n≤M-1, M is sampling number；

(2) according to discrete signal x (n), ambiguity function is obtained；

Wherein τ express times, f_dRepresent frequency deviation, t_sFor the sampling interval, M is number of samples, x^*Represent the conjugation of x；

(3) to ambiguity function AF (τ, f_d) Radon conversion is carried out, obtain projecting spectral line R (α)；

(4) according to the following formula by angular range, theta_max~θ_minP angle is divided at equal intervals, and i-th angle is：

Wherein, i=1,2 ..., P, θ_minFor the minima of measurable angle range, θ_maxFor the maximum of measurable angle range；

(5) angle according to obtained by dividing in (4), using formula k=tan θ, obtains i-th angle, θ_iCorresponding tune Frequency slope k_i；

(6) under noise-free case, by chirp rate k₁,k₂,…,k_i,…,k_P, it is calculated projection spectral line R₁(α),R₂ (α),…,R_i(α),…R_P(α), and sparse matrix is constructed

(7) sparse matrix is utilizedWith middle projection spectral line R (α), following relational expression is built：

Wherein, min { } represents the operative symbol for asking minimum, and λ is regularization parameter, | | | |₁Represent 1 model of vector Number, | | | |₂2 norms of vector are represented, β represents sparse angular spectrum vector；

(8) relational expression in (7) is solved using sedumi functions in the SeDuMi tool kits of MATLAB, obtains sparse angle Spectrum vector β；

(9) threshold value comparison method is adopted, peakvalue's checking is carried out to angular spectrum vector β, obtain angular spectrum vector peak value element rope Draw value l, angle value θ is determined by peak value element index value l：

(10) according to angle, θ, frequency modulation rate k=tan θ is obtained.

The present invention has the advantage that compared with prior art：

First, because the present invention is scanned on one-dimensional, rather than the face battle array of two dimension, so reducing amount of calculation, carry High operation efficiency.

Second, because the present invention is by setting up sparse base, there is certain anti-noise effect, thus exchange the angle corresponding to frequency Degree Detection results are more projected.

Description of the drawings

Fig. 1 is the flowchart of the present invention；

Fig. 2 is the simulation result figure of the angular spectrum vector obtained with existing Radon-Ambiguity converter techniques；

Fig. 3 is the simulation result figure that the inventive method obtains angular spectrum vector.

Specific embodiment

The present invention is described in further detail below in conjunction with the accompanying drawings.

With reference to Fig. 1, the specific implementation step of the present invention is as follows：

Step 1, obtains echo-signal.

Radar emission linear FM signal：Obtain echo-signal：X (t)=s (t-t₀)+ω (t), wherein, t₀It is that the signal that distance causes propagates relative time-delay, ω (t) is that average is 0, and variance is δ²'s White Gaussian noise, A for linear FM signal amplitude, f₀For the initial frequency of linear FM signal, k is chirp rate.

Step 2, obtains discrete signal.

Echo-signal x (t) to receiving carries out discrete sampling, obtains discrete signal x (n)：

Wherein, t₀It is that the signal that distance causes propagates relative time-delay, ω (n) is that average is 0, and variance is δ²Gauss White noise, A for linear FM signal amplitude, f₀For the initial frequency of linear FM signal, k is chirp rate, t_sRepresent sampling Interval.

Step 3, according to discrete signal x (n), obtains ambiguity function AF (τ, f_d)：

Wherein, τ express times, f_dRepresent frequency deviation, t_sFor the sampling interval, M is number of samples.

Step 4, to ambiguity function AF (τ, f_d) Radon conversion is carried out, obtain projecting spectral line R (α)：

Wherein AF (τ, f_d) it is ambiguity function, δ () is impulse function, and M is number of samples, τ_kRepresent k-th time sampling Point, f_dnN-th stepped-frequency signal is represented, m represents frequency modulation rate m=tan (α), and α represents the tangent angle corresponding to frequency modulation rate.

Step 5, constructs sparse matrix.

(5a) angular range is divided at equal intervals according to the following formula P angle, i-th angle is：

Wherein, i=1,2 ..., P, θ_minFor the minima of measurable angle range, θ_maxFor the maximum of measurable angle range；

(5b) angle according to obtained by division, using formula k=tan θ, obtains i-th angle, θ_iCorresponding frequency modulation is oblique Rate k_i；

(5c) under noise-free case, by chirp rate k₁,k₂,…,k_i,…,k_P, it is calculated projection spectral line R₁(α),R₂ (α),…,R_i(α),…R_P(α)；

(5d) by projection spectral line R₁(α),R₂(α),…,R_i(α),…R_P(α) sparse matrix is constructed：

Step 6, obtains angular spectrum vector.

(6a) sparse matrix is utilizedWith middle projection spectral line R (α), following relational expression is built：

Wherein, min { } represents the operative symbol for asking minimum, and λ is regularization parameter, | | | |₁Represent 1 model of vector Number, | | | |₂2 norms of vector are represented, β represents sparse angular spectrum vector；

(6.b) relational expression in (6a) is solved using sedumi functions in the SeDuMi tool kits of MATLAB, is obtained sparse Angular spectrum vector β.

Step 7, determines target angle angle value

(7a) angular spectrum vector β is normalized, obtains normalization angular spectrum vector

(7b) threshold epsilon=0.2 is set, and peak value index value l is obtained as the following formula is：

Wherein,For normalization angular spectrum vectorI-th element, P represented angular range, theta_max~θ_minAt equal intervals The number of division；

(7.c) determine that the angle value θ of target is as the following formula by peak value index value l：

Step 8, according to angle, θ, obtains frequency modulation rate k=tan θ.

The effect of the present invention can be illustrated by following l-G simulation tests:

1. simulated conditions

Runtime be Intel (R) Core (TM) i7-3770CPU@3.40GHz, 64 bit manipulation systems, simulation software is adopted MATLAB R2011b, simulation parameter is used to arrange as shown in table 1.

The parameter setting of table 1

Parameter	Parameter value
		Original frequency (signal 1)	0.1
Cut-off frequency (signal 1)	0.3
		Original frequency (signal 2)	0.1
Cut-off frequency (signal 2)	0.31
		Sampling number	120
Target number	2
		Signal to noise ratio	10dB

2. emulation content

Emulation 1, with the parameter estimation of existing Radon-Ambiguity converter techniques simulated linear FM signal, acquisition The simulation result of the corresponding angular spectrum vector of frequency modulation rate, as shown in Figure 2.

Emulation 2, with the parameter estimation of the inventive method simulated linear FM signal, obtain the corresponding angular spectrum of frequency modulation rate to Amount simulation result, as shown in Figure 3.

From Figure 2 it can be seen that Radon-Ambiguity converter techniques cannot be differentiated, angle interval is less, i.e. tune frequency phase-difference is less Two linear FM signals.

As seen from Figure 3, the inventive method, it is little successfully to tell angle interval, that is, adjust frequency phase-difference it is less two it is linear FM signal, so the degree of accuracy of the frequency modulation rate of corresponding two targets is improved.

Radon-Ambiguity converter techniques are contrasted with simulation result of the present invention, such as table 2：

The Radon-Ambiguity converter techniques of table 2 and present invention contrast

Signal	Signal 1	Signal 2
			Radon-Ambiguity methods obtain angle (degree)	21.68	21.68
This method obtains angle (degree)	21.64	23.08
			Radon-Ambiguity methods obtain frequency modulation rate	0.3974	0.3974
This method obtains frequency modulation rate	0.3967	0.4262

From table 2, Radon-Ambiguity converter techniques cannot distinguish the less two linear frequency modulations letter of tune frequency phase-difference Number, the present invention can effectively tell less two linear FM signals of tune frequency phase-difference, it is seen that the present invention is effectively improved The degree of accuracy that linear frequency-modulated parameter is estimated.

Claims (4)

1. a kind of linear frequency-modulated parameter estimating method based on sparse constraint, comprises the steps：

(1) radar emission linear FM signal s (t), obtains echo-signal x (t), and carries out discrete adopting to echo-signal x (t) Sample, obtains discrete signal x (n), and 0≤n≤M-1, M is sampling number；

(2) according to discrete signal x (n), ambiguity function is obtained；

$AF(\mathrm{\τ},f_d)=\underset{n=0}{\overset{M-1}{\Σ}}x(n+\frac{\mathrm{\τ}}{2})x^{*}(n-\frac{\mathrm{\τ}}{2})e^{j2\mathrm{\π}\left({\mathrm{nt}}_s\right)f_d},$

Wherein τ express times, f_dRepresent frequency deviation, t_sFor the sampling interval, M is number of samples, x^*Represent the conjugation of x；

(3) to ambiguity function AF (τ, f_d) Radon conversion is carried out, obtain projecting spectral line R (α)：

$R\left(\mathrm{\α}\right)=\frac{1}{M^2}\underset{k=0}{\overset{M-1}{\Σ}}\underset{n=0}{\overset{M-1}{\Σ}}\left|A(\mathrm{\τ},f_d)\right|\mathrm{\δ}(f_{dn}-{\mathrm{m\τ}}_k)$

Wherein AF (τ, f_d) it is ambiguity function, δ () is impulse function, and M is number of samples, τ_kK-th time sampling point is represented, f_dnN-th stepped-frequency signal is represented, m represents frequency modulation rate m=tan (α), and α represents the tangent angle corresponding to frequency modulation rate；

(4) according to the following formula by angular range, theta_max~θ_minP angle is divided at equal intervals, and i-th angle is：

${\mathrm{\θ}}_i={\mathrm{\θ}}_{min}+\frac{i-1}{P-1}({\mathrm{\θ}}_{max}-{\mathrm{\θ}}_{min}),$

Wherein, i=1,2 ..., P, θ_minFor the minima of measurable angle range, θ_maxFor the maximum of measurable angle range；

(5) angle according to obtained by dividing in (4), using formula k=tan θ, obtains i-th angle, θ_iCorresponding chirp rate k_i；

(6) under noise-free case, by chirp rate k₁,k₂,…,k_i,…,k_P, it is calculated projection spectral line R₁(α),R₂ (α),…,R_i(α),…R_P(α), and sparse matrix is constructed

(7) sparse matrix is utilizedWith middle projection spectral line R (α), following relational expression is built：

Wherein, min { } represents the operative symbol for asking minimum, and λ is regularization parameter, | | | |₁1 norm of vector is represented, | | ||₂2 norms of vector are represented, β represents sparse angular spectrum vector；

(8) solve relational expression in (7) using sedumi functions in the SeDuMi tool kits of MATLAB, obtain sparse angular spectrum to Amount β；

(9) threshold value comparison method is adopted, peakvalue's checking is carried out to angular spectrum vector β, obtain angular spectrum vector peak value element index value L, by the peak value element index value l angle value θ is determined：

$\mathrm{\θ}={\mathrm{\θ}}_{min}+\frac{l-1}{P-1}({\mathrm{\θ}}_{max}-{\mathrm{\θ}}_{min});$

(10) according to angle, θ, frequency modulation rate k=tan θ is obtained.

2. the linear frequency-modulated parameter estimating method based on sparse constraint according to claim 1, wherein the step (1) linear FM signal s (t) in, is expressed as：

$s\left(t\right)=A\exp \left(j2\mathrm{\π}\right(f_{0}t+\frac{1}{2}{\mathrm{kt}}^2\left)\right)$

Wherein A for linear FM signal amplitude, f₀For the initial frequency of linear FM signal, k is chirp rate, when t is represented Between.

3. the linear frequency-modulated parameter estimating method based on sparse constraint according to claim 1, wherein the step (1) echo-signal x (t) in, is expressed as：

X (t)=s (t-t₀)+ω(t)

Wherein, t₀It is that the signal that distance causes propagates relative time-delay, it is δ for 0, variance that ω (t) is average²Gauss white noise Sound.

4. the linear frequency-modulated parameter estimating method based on sparse constraint according to claim 1, wherein the step (9) by threshold value comparison method in, peakvalue's checking is carried out to angular spectrum vector β, obtains angular spectrum vector peak value element index value l, Carry out according to the following steps：

(9a) angular spectrum vector β is normalized, obtains normalization angular spectrum vector

(9b) threshold epsilon=0.2 is set, according to equation below peak value index value is obtained：

$l=\left\{i\right|{\stackrel{\‾}{\mathrm{\β}}}_i>\mathrm{\ϵ},i=1,2,...,P\},$

Wherein,For normalization angular spectrum vectorI-th element, P represented angular range, theta_max~θ_minDivide at equal intervals Number.