CN107526064A - Adaptive LFM modulated parameter estimating methods based on two dimensional character - Google Patents
Adaptive LFM modulated parameter estimating methods based on two dimensional character Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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Abstract
The present invention proposes a kind of adaptive LFM modulated parameter estimating methods based on two dimensional character, it is characterised in that according to the different adaptively selected Power Spectral Entropy of signal to noise ratio of height or box counting dimension DBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N } chirp rate, time series signal X={ x to be measured are estimated using Power Spectral Entropy when signal to noise ratio is highi, i=1,2 ..., N } chirp rate, box counting dimension D is used when signal to noise ratio is lowBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N } chirp rate.The present invention reduces computation complexity, has more preferable application value as far as possible on the premise of the degree of accuracy of parameter Estimation is ensured.
Description
Technical field
The present invention relates to a kind of adaptive parameter estimation method of LFM signals, the frequency modulation for estimation self-adaptive LFM signals
Slope.
Background technology
Modern war has no longer been the confrontation mode for simply only having aeroamphibious weaponry, and electronic countermeasure is made at present
It has been added to for a kind of new confrontation mode among confrontation.Electronic reconnaissance using electronic information technology come detect enemy some
Can electronic equipment relevant information correctly distinguish that radar signal turns into one in electronic reconnaissance system so as to obtain information
Highly important target.Traditional " five parameter method " it has been difficult to identify that the radar signal in low signal-to-noise ratio, and its strain energy
Power is poor, it is desirable to which it has been impossible that the position of a seat is obtained in the electronic warfare in the present age, it is therefore desirable to radar signal is extracted more
New characteristic parameter.Can the key that radar signal is intercepted and captured in success be quickly and accurately analyze tune in the arteries and veins of radar signal
Feature processed.Typical radar signal has pulse signal, continuous wave signal, linear FM signal, coding FM signal, non-linear tune
Frequency signal etc., these signals are all typical non-stationary signals.Non-stationary signal is being analyzed and handled to the method for time frequency analysis
When have significant effect.At present, academia research comparative maturity Time-Frequency Analysis Method have STFT, wavelet transformation,
FRFT, Wigner-Vile conversion etc..Estimate in addition, also there are some non-Time-Frequency Analysis Methods to be used for the parameter of LFM radar signals
Meter, such as maximum likelihood estimate, delay correlation method, solution line adjust method, Matched Fourier Transform method etc., are obtained for more wide
General application.
The estimated accuracy of maximum likelihood estimate is very high, but accurately to search out the maximum of likelihood function, search
Step-length needs to set to obtain very little, if step-length is too small, amount of calculation will be caused to increase, so the algorithm is not easily accomplished real-time estimation.
The correlation method operand that is delayed is small, but estimated accuracy is not high.It is the lance between operand and estimated accuracy be present to solve the shortcomings that line adjusts method
Shield.Short Time Fourier Transform is a kind of Linear Time-Frequency Analysis method, but its estimated accuracy is relatively low and its time-frequency locality can be by window
The influence of function.FRFT estimated accuracies are high, the interference without cross term and have good time-frequency locality, but amount of calculation is larger.
Wigner-Vile conversion is a kind of typical bilinear transformation, and its time-frequency locality is good and estimated accuracy is high, but in more points of estimation
When measuring the parameter of LFM signals, cross term interference be present.
The content of the invention
The purpose of the present invention is：The computation complexity of LFM Signal parameter estimations is reduced, improves computational accuracy.
In order to achieve the above object, the technical scheme is that providing a kind of adaptive LFM based on two dimensional character
Modulated parameter estimating method, it is characterised in that according to the different adaptively selected Power Spectral Entropy of signal to noise ratio of height or box counting dimension DB
To estimate time series signal X={ x to be measuredi, i=1,2 ..., N } chirp rate, power is used when signal to noise ratio is high
Entropy is composed to estimate time series signal X={ x to be measuredi, i=1,2 ..., N } chirp rate, used when signal to noise ratio is low
Box counting dimension DBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N } chirp rate, wherein：
Time series signal X={ x to be measured are estimated according to Power Spectral Entropyi, i=1,2 ..., N chirp rate
Comprise the following steps：
(a) multiple sample time-series signals of chirp rate, calculate each sample time-series signal known to obtaining
Power spectrum
In formula, X (ω) represents the Fourier transformation of current sample time-series signal；
(b) the Power Spectral Entropy H of each sample time-series signal is calculatedp：
In formula, pkRepresent that k-th of power spectrum S (k) of current sample time-series signal exists
Shared proportion is used in whole spectrum,
(c) analysis is fitted by mathematical measure, obtains the functional relation of Power Spectral Entropy and chirp rate；
(d) time series signal X={ x to be measured are calculatedi, i=1,2 ..., N } Power Spectral Entropy, utilize step (c)
Obtained functional relation is estimated to obtain chirp rate；
Box counting dimension DBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N chirp rate include with
Lower step：
To time series signal X={ xi, i=1,2 ..., N } sampled, sampling interval ε is time series signal X
Highest differentiates RFF rates, the square cartridge cover time sequence signal X for being ε with the length of side, the minimum length of side of square cartridge is set
It is set to using interval ε identical numerical value, calculating the box that the box cover time sequence signal X that the length of side is respectively k ε needs respectively
The minimum number N (k ε) of son, then by simulation software, with mathematical method matched curve logk ε~logN (k ε), time series letter
Number X box counting dimension DBNumerically equal with this slope of a curve, slope is chirp rate.
Preferably, box counting dimension DBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N chirp rate
Comprise the following steps：
Step 1, the time series signal X square cartridges for being ε with the length of side are covered, to ensure the continuity of signal,
The box of some grey is added, when calculating the number of box, the box of grey is also charged in the lump, thus obtained square
The minimum number N (ε) of box is exactly the box number that whole signal can be all covered；
Step 2, the length of side of square cartridge is corrected as 2 ε respectively, 3 ε ..., k ε, respectively repeats steps 1, obtain the length of side
For 2 ε, 3 ε ..., k ε square cartridge covers the minimum number N (2 ε) needed for time series signal X, N (3 ε) ..., N (k
ε)；
Step 3, using log ε as X-axis, logN (ε) is Y-axis, makes functional image, time series signal X box dimension of fractals
Number DBIt is exactly the opposite number of that in functional image function curve slope, i.e.,：
The present invention is joined on the basis of traditional parameter estimation algorithm using the adaptive LFM signals based on two dimensional character
Number estimation method, according to the difference of reception signal complexity and the situation of the noises of local environment, extract the two dimension of signal
Feature, the corresponding relation established respectively between two kinds of features and the chirp rate of signal, correlation curve is fitted, establishes characteristic
Storehouse, estimating to the chirp rate of signal is adaptively realized using corresponding parameter estimation algorithm when noise compares so as to see who is superior different
Meter.
Present invention the shortcomings that existing for traditional Signal parameter estimation algorithm, it is proposed that it is a kind of newly based on two dimensional character
Adaptive LFM Signal parameter estimations algorithm, based on the algorithm of two dimensional character relative to traditional algorithm based on one-dimensional characteristic,
It is the advantages of two kinds of algorithms can be integrated, adaptive using a kind of suitable algorithm in the different signal to noise ratio of height, ensureing parameter
On the premise of the degree of accuracy of estimation, computation complexity is reduced as far as possible, and there is more preferable application value.
Brief description of the drawings
Fig. 1 is the power spectrum situation of four groups of different signals of frequency modulation rate；
Fig. 2 is Power Spectral Entropy and chirp rate relation curve under the conditions of 5dB signal to noise ratio；
Fig. 3 is Power Spectral Entropy and chirp rate relation curve under the conditions of 15dB signal to noise ratio；
Fig. 4 is 5dB signal to noise ratio condition Lower box dimensions and chirp rate relation curve；
Fig. 5 is 15dB signal to noise ratio condition Lower box dimensions and chirp rate relation curve.
Embodiment
With reference to specific embodiment, the present invention is expanded on further.It should be understood that these embodiments are merely to illustrate the present invention
Rather than limitation the scope of the present invention.In addition, it is to be understood that after the content of the invention lectured has been read, people in the art
Member can make various changes or modifications to the present invention, and these equivalent form of values equally fall within the application appended claims and limited
Scope.
Existing technical method is usually the extraction that one-dimensional characteristic is carried out to signal, and a variety of parameter estimation algorithms are all
There are respective advantage and disadvantage, often amount of calculation is larger for the good method of noiseproof feature, relatively simple algorithm is calculated, under low signal-to-noise ratio
The degree of accuracy of parameter Estimation is often poor, the adaptive LFM parameters of technical scheme proposed by the invention based on two dimensional character
Algorithm for estimating, extract two kinds of feature power spectrum entropys and box counting dimension respectively to signal, and establish Power Spectral Entropy and chirp rate respectively
Relation, the relation between box counting dimension and chirp rate, the advantages of comprehensive two kinds of algorithms, using dividing shape when signal to noise ratio is low
The algorithm of box counting dimension, using the algorithm of Power Spectral Entropy when signal to noise ratio is high, can reduce amount of calculation can ensure to estimate again
The accuracy of the parameter gone out, it is possible to achieve to the accurate estimation of LFM signal chirp rates under different signal to noise ratio.
Power Spectral Entropy general principle is：
Because the frequency structure of different LFM signals is discrepant, therefore using Power Spectral Entropy as spectrum signature, to enter
The parameter Estimation of row LFM signals.
Power Spectral Entropy is defined as：Hp
Wherein, k-th of power spectrum proportion p shared in whole spectrumkTo represent, k=1,2 ..., N, N represent individual
Number, S (j) represent j-th of signaling point to be identified.
The general type of LFM signals can be expressed as：
X (t)=Aexp [j (2 π f0t+πkt2+φ)]
In formula, A is signal amplitude,It is start-phase, f0It is initial frequency, k is frequency modulation rate, the instantaneous frequency of LFM signals
F (t) is linear change over time, i.e. f (t)=f0+kt。
For discrete signal sequence { xi, i=1,2 ..., N }, the Fourier transformation of signal is X (ω).Its power spectrum is estimated
The definition of meter is：
For the Fourier transformation of discrete signal sequence.
The LFM signals of Different Slope, its power spectrum also have very big difference, as shown in Figure 1.
According to the definition of Power Spectral Entropy, calculate under the conditions of different SNR, the different LFM signals of bandwidth, chirp rate
Power Spectral Entropy HpValue, it is possible to build one on Power Spectral Entropy HpWith the feature database of chirp rate relation.
The general principle of box counting dimension is：
If in the presence of a metric space (X, d), the race of compacting of an X non-NULL is H, and B (x, ε) is that center is x, and radius is
The spheroid of ε closing.Compacted if A is a non-NULL in X, then to each positive number ε, covering A minimum is closed the number of ball
Represented with N (A, ε), close the radius of a ball and be equal to ε, that is to say, that：
Wherein, x1,x2,…xMIt is X difference.Then defining box counting dimension is：
Wherein, ln (1/ ε) represents logeThe Logarithmic calculation of (1/ ε), lnN (A, ε) implication are same.
If discrete signal is x (i), sampling interval ε means that the highest resolution of the discrete signal, if according to definition,
Allowing ε → 0, then simulation calculation does not have feasibility, so, using a kind of approximate algorithm, allow and sampling interval ε and be used in calculating
Their minimum edge length of the box of covering signal is equal, then the grid that the box length of side is k ε on discrete signal x (i)
Grid counts NkεComputing, specific N are carried out one by onekεComputational methods it is as follows：
s1=max { xk(i-1)+1,xk(i-1)+2,…xk(i-1)+k+1}
s2=min { xk(i-1)+1,xk(i-1)+2,…xk(i-1)+k+1}
Wherein, i=1,2 ..., N0/ k, k=1,2 ... K；N0For sampling number, and K ＜ N0；Chi of the signal in longitudinal coordinate
Scope is spent, is represented with s (k ε).Then NkεIt is expressed as：
Nkε=s (k ε)/k ε+1
In lgk ε~lgNkεIn select one section of region as uncalibrated visual servo, then：
lgNkε=-dBlgkε+b
Wherein, k1≤k≤k2, k is used herein1To represent the starting point of non-scaling section, k is used2To represent the terminal of non-scaling section.
This curve is fitted using MATLAB, its slope is in DBIt is numerically consistent with this signal box counting dimension.
Based on above-mentioned principle, a kind of adaptive LFM modulated parameter estimating methods based on two dimensional character provided by the invention,
Characterized in that, according to the different adaptively selected Power Spectral Entropy of signal to noise ratio of height or box counting dimension DBTo estimate the time to be measured
Sequence signal X={ xi, i=1,2 ..., N } chirp rate, estimated when signal to noise ratio is high using Power Spectral Entropy to be measured
Time series signal X={ xi, i=1,2 ..., N } chirp rate, box counting dimension D is used when signal to noise ratio is lowBIt is to be measured to estimate
Time series signal X={ xi, i=1,2 ..., N } chirp rate, wherein：
Time series signal X={ x to be measured are estimated according to Power Spectral Entropyi, i=1,2 ..., N chirp rate
Comprise the following steps：
(a) multiple sample time-series signals of chirp rate, calculate each sample time-series signal known to obtaining
Power spectrum
In formula, X (ω) represents the Fourier transformation of current sample time-series signal；
(b) the Power Spectral Entropy H of each sample time-series signal is calculatedp：
In formula, pkRepresent that k-th of power spectrum S (k) of current sample time-series signal exists
Shared proportion is used in whole spectrum,
(c) analysis is fitted by mathematical measure, obtains the functional relation of Power Spectral Entropy and chirp rate；
(d) time series signal X={ x to be measured are calculatedi, i=1,2 ..., N } Power Spectral Entropy, utilize step (c)
Obtained functional relation is estimated to obtain chirp rate；
Box counting dimension DBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N chirp rate include with
Lower step：
To time series signal X={ xi, i=1,2 ..., N } sampled, sampling interval ε is time series signal X
Highest differentiates RFF rates, the square cartridge cover time sequence signal X for being ε with the length of side, the minimum length of side of square cartridge is set
It is set to using interval ε identical numerical value, calculating the box that the box cover time sequence signal X that the length of side is respectively k ε needs respectively
The minimum number N (k ε) of son, then by simulation software, with mathematical method matched curve logk ε~logN (k ε), time series letter
Number X box counting dimension DBNumerically equal with this slope of a curve, slope is chirp rate.Comprise the following steps：
Step 1, the time series signal X square cartridges for being ε with the length of side are covered, to ensure the continuity of signal,
The box of some grey is added, when calculating the number of box, the box of grey is also charged in the lump, thus obtained square
The minimum number N (ε) of box is exactly the box number that whole signal can be all covered；
Step 2, the length of side of square cartridge is corrected as 2 ε respectively, 3 ε ..., k ε, respectively repeats steps 1, obtain the length of side
For 2 ε, 3 ε ..., k ε square cartridge covers the minimum number N (2 ε) needed for time series signal X, N (3 ε) ..., N (k
ε)；
Step 3, using log ε as X-axis, logN (ε) is Y-axis, makes functional image, time series signal X box dimension of fractals
Number DBIt is exactly the opposite number of that in functional image function curve slope, i.e.,：
For convenience of computing, the box counting dimension formula of simplified discrete space signal point set：
Wherein, ε=1/fs, signal sampling frequencies are fs, N (ε) be the box length of side be ε all sampled point of covering most
Small box number, N (2 ε) is the minimum box number for all sampled points of covering that the box length of side is 2 ε, thus, it is possible to simply handle
The box counting dimension of signal is converted into following expression formula：
Claims (2)
1. a kind of adaptive LFM modulated parameter estimating methods based on two dimensional character, it is characterised in that according to the different letter of height
Make an uproar than adaptively selected Power Spectral Entropy or box counting dimension DBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N }
Chirp rate, time series signal X={ x to be measured are estimated using Power Spectral Entropy when signal to noise ratio is highi, i=1,
2 ..., N } chirp rate, box counting dimension D is used when signal to noise ratio is lowBTo estimate time series signal X={ x to be measuredi, i=
1,2 ..., N } chirp rate, wherein：
Time series signal X={ x to be measured are estimated according to Power Spectral Entropyi, i=1,2 ..., N chirp rate include
Following steps：
(a) multiple sample time-series signals of chirp rate known to obtaining, the power of each sample time-series signal is calculated
Spectrum
In formula, X (ω) represents the Fourier transformation of current sample time-series signal；
(b) the Power Spectral Entropy H of each sample time-series signal is calculatedp：
In formula, pkRepresent that k-th of power spectrum S (k) of current sample time-series signal is entirely being composed
In shared proportion use,
(c) analysis is fitted by mathematical measure, obtains the functional relation of Power Spectral Entropy and chirp rate；
(d) time series signal X={ x to be measured are calculatedi, i=1,2 ..., N } Power Spectral Entropy, obtained using step (c)
Functional relation is estimated to obtain chirp rate；
Box counting dimension DBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N chirp rate include following step
Suddenly：
To time series signal X={ xi, i=1,2 ..., N } sampled, sampling interval ε is time series signal X best result
Distinguish RFF rates, the square cartridge cover time sequence signal X for being ε with the length of side, the minimum length of side of square cartridge be arranged to
Using interval ε identical numerical value, the box for the box cover time sequence signal X needs that the length of side is respectively k ε is calculated respectively most
Decimal N (k ε), then by simulation software, with mathematical method matched curve logk ε~logN (k ε), time series signal X's
Box counting dimension DBNumerically equal with this slope of a curve, slope is chirp rate.
2. a kind of adaptive LFM modulated parameter estimating methods based on two dimensional character as claimed in claim 1, its feature exist
In box counting dimension DBTo estimate time series signal X={ x to be measuredi, i=1,2 ..., N chirp rate include following step
Suddenly：
Step 1, the time series signal X square cartridges for being ε with the length of side are covered, to ensure the continuity of signal, addition
The box of some grey, when calculating the number of box, the box of grey is also charged in the lump, thus obtained square cartridge
Minimum number N (ε) be exactly the box number that whole signal can be all covered；
Step 2, the length of side of square cartridge is corrected as 2 ε respectively, 3 ε ..., k ε, respectively repeats steps 1, it is 2 ε to obtain the length of side,
3 ε ..., k ε square cartridge covers the minimum number N (2 ε) needed for time series signal X, N (3 ε) ..., N (k ε)；
Step 3, using log ε as X-axis, logN (ε) is Y-axis, makes functional image, time series signal X D value of fractal boxBJust
It is the opposite number of that in functional image function curve slope, i.e.,：
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| CN109164438A (en) * | 2018-09-30 | 2019-01-08 | 厦门大学 | A kind of combined estimation method of arrival time and arrival rate based on LFM coherent pulse string |
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| CN112232321A (en) * | 2020-12-14 | 2021-01-15 | 西南交通大学 | Vibration data interference noise reduction method, device and equipment and readable storage medium |
| CN115436924A (en) * | 2022-08-26 | 2022-12-06 | 杭州电子科技大学 | Multi-component LFM signal rapid parameter estimation method and system under optimized local oscillator NYFR architecture |
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