CN108037494B - Radar target parameter estimation method under impulse noise environment - Google Patents

Radar target parameter estimation method under impulse noise environment Download PDF

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CN108037494B
CN108037494B CN201711265954.5A CN201711265954A CN108037494B CN 108037494 B CN108037494 B CN 108037494B CN 201711265954 A CN201711265954 A CN 201711265954A CN 108037494 B CN108037494 B CN 108037494B
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李丽
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Abstract

The invention relates to a radar target parameter estimation method under an impulse noise environment. The invention defines a new broadband fuzzy function, namely the broadband fuzzy function based on Sigmoid transformation, can realize the joint estimation of Doppler scale expansion and time delay in the impulse noise environment, then defines the Correlation function based on Sigmoid transformation, further provides the MUSIC algorithm based on Sigmoid Correlation, and realizes the joint estimation of DOD and DOA. The invention provides a radar target parameter estimation method under an impulse noise environment, which can resist the influence of Alpha stable distributed noise, effectively solve the problems of Doppler scale expansion and time delay existing in a broadband signal echo signal and improve the accuracy of parameter estimation and positioning of a moving target in a broadband bistatic MIMO radar system.

Description

Radar target parameter estimation method under impulse noise environment
Technical Field
The invention belongs to the field of communication and information systems, and particularly relates to a novel broadband bistatic MIMO radar target parameter estimation method based on Sigmoid transformation in an impulse noise environment.
Background
In recent years, Multiple Input Multiple Output (MIMO) radars have attracted more and more scholars' attention and have emerged a lot of research on target parameter estimation. At present, the target parameter estimation algorithm is mainly applied to two aspects of a narrow-band MIMO radar and a broadband MIMO radar system.
In the wideband radar system, the echo signal of the wideband signal not only contains Doppler shift, but also contains Doppler shift scale expansion factor (DS), so that the difficulty of parameter estimation is increased. In this case, the use of a narrow-band signal model is obviously not suitable. The current research on the problem comprises two DOA estimation methods of broadband chirp signals, a DOA estimation method based on a coherent signal subspace, a DOA estimation method proposed by utilizing the orthogonality of a projection subspace and the like. However, these methods cannot achieve joint estimation of Doppler frequency shift scale expansion factor and Time Delay (TD), but these two parameters are very critical for parameter estimation and positioning of moving objects in the wideband bistatic MIMO radar system. Currently, there are relatively few studies on joint estimation of doppler shift scale-spreading factor, time delay, and transmit-receive angle.
Currently, most parameter estimation methods for array signal processing assume that the noise is gaussian noise. However, it has been found that the actual noise of radar, sonar and wireless communication systems often contains a large amount of impulse components. In this case, a signal model using gaussian noise is not suitable, and such noise is more suitably described by an Alpha stable distribution model. However, for a stable distribution of 0 < α < 2, only the statistics below the α -th order are present, and the high order statistics, both second and above, are absent. The estimation performance of conventional second-order statistics-based algorithms in impulse noise environments will be severely degraded.
In order to reduce the interference of Alpha stable distributed noise and improve the performance of the algorithm, researchers propose a plurality of parameter estimation algorithms based on a fractional low-order statistic theory. Although the method obtains a good estimation effect, the method has certain limitations: (1) the fractional low-order moment p must satisfy 1 ≦ p < alpha or 0 < p < alpha/2; (2) if the prior knowledge of the noise characteristic index alpha is not available or the estimation value cannot be correctly estimated, the improper value of the order can cause the performance of the algorithm to be seriously reduced or even fail, so the estimation result of the characteristic index alpha and the value of the fractional low-order moment p can influence the performance of the algorithm.
Disclosure of Invention
The invention provides a radar target parameter estimation method under an impulse noise environment, which aims to reduce the interference of Alpha stable distributed noise and solve the problems of Doppler frequency shift scale expansion factor (DS) and Time Delay (TD) existing in a broadband signal echo signal.
The technical scheme adopted by the invention for solving the technical problem is to provide a radar target parameter estimation method under an impulse noise environment, and the method comprises the following steps:
step 1: establishing a signal model
Assuming that the numbers of the transmitting array elements and the receiving array elements are Q and N respectively, and the distances between the transmitting array elements and the receiving array elements are d respectivelytAnd drThe spacing between the transmitting array elements and the spacing between the receiving array elements are equal intervals dt＝drLet the radar work in a wide-band far-field condition, with the transmit and receive arrays at the same phase center, with L targets on the same range resolution unit,
Figure GDA0002863736480000021
representing the radar transmitting angle and receiving angle corresponding to the ith target, the echo signal received by the nth receiving array element can be represented as:
Figure GDA0002863736480000022
wherein x isq(t) is the transmission signal of the qth transmission array element:
xq(t)＝Aqexp[j2π(fq0t+μq0t2/2)] (2)
βlamplitude attenuation factor, σ, representing the ith targetlAnd τlA doppler shift scale spread factor and time delay generated for the ith target;
Figure GDA0002863736480000023
to transmit steering vectors, An(θl)＝exp(j2π(n-1)sinθl) For receiving steering vectors, noise wn(t) is the standard S α S stationary distribution noise;
extracting the echo signal in a fractional domain through a band-pass filter, performing fractional order Fourier inversion to return to a time domain, and extracting the echo signal yqn(t)：
Figure GDA0002863736480000031
Wherein y isqn(t) represents the single echo signal of the qth transmitting array element transmitting LFM signal reaching the nth receiving array element after being reflected by the L targets;
step 2: broadband fuzzy function and correlation function based on Sigmoid transformation
1) Broad band fuzzy function
The expression for the wideband blur function (WBAF) is:
Figure GDA0002863736480000032
wherein
Figure GDA0002863736480000033
σ0And τ0Is a doppler shift scale expansion factor and time delay;
according to the Schwarz inequality, the following inequality is obtained:
Figure GDA0002863736480000034
wherein
Figure GDA0002863736480000035
Is the energy of signal s (t), when τ ═ τ0And σ ═ σ0When the inequality (5) is equal, that is, when τ is τ0And σ ═ σ0When the temperature of the water is higher than the set temperature,
Figure GDA0002863736480000036
Figure GDA0002863736480000037
with the maximum value, i.e.:
Figure GDA0002863736480000038
according to equation (5), a signal x is obtainedq(t) and xr(t) broadband blur function
Figure GDA0002863736480000039
Figure GDA0002863736480000041
Wherein
Figure GDA0002863736480000042
According to the Schwarz inequality, the following inequality is obtained:
Figure GDA0002863736480000043
when formula (8) satisfies τ ═ τlAnd σ ═ σlWhen the temperature of the molten steel is higher than the set temperature,
Figure GDA0002863736480000044
with the maximum, TD and DS can be estimated by:
Figure GDA0002863736480000045
2) broadband fuzzy function based on Sigmoid (Sigmoid-WBAF)
The expression of Sigmoid transformation is:
Figure GDA0002863736480000046
the expression of the wideband fuzzy function (Sigmoid-WBAF) based on Sigmoid is as follows:
Figure GDA0002863736480000047
Figure GDA0002863736480000048
denotes s for different values of τ and σr(t) and
Figure GDA0002863736480000049
sigmoid correlation of (2);
in formula (11), signal sr(T) at time intervals of interest [ -T/2, T/2]Above based on Sigmoid broadband fuzzy function (Sigmoid-WBAF)
Figure GDA00028637364800000410
The estimation can be done using equation (12), i.e. for a finite time-width signal,
Figure GDA00028637364800000411
the estimation is performed using the following equation:
Figure GDA00028637364800000412
in the same way, by searching
Figure GDA0002863736480000051
The abscissa and ordinate, which are the maximum, can enable joint estimation of TD and DS:
Figure GDA0002863736480000052
3) sigmoid correlation function
In order to inhibit the influence of impulse noise and improve the performance of the MUSIC algorithm, a Correlation function is defined and is based on the Correlation function (Sigmoid Correlation) of Sigmoid transformation
Figure GDA0002863736480000053
The expression of (a) is:
Figure GDA0002863736480000054
wherein (a)tRepresents a statistical time average;
and step 3: parameter joint estimation based on Sigmoid-WBAF and Sigmoid-MUSIC algorithms
1) Sigmoid-WBAF based TD and DS estimation
Substituting formulae (2) and (3) into formula (12) to obtain yqnl(t) and xq(t) expression of Sigmoid-WBAF:
Figure GDA0002863736480000055
wherein
Figure GDA0002863736480000056
Representing noise and transmitted signal xqThe Sigmoid-WBAF of (t) can be considered as an interference signal;
by obtaining the position coordinates of the peak point of equation (15), joint estimation of TD and DS is achieved:
Figure GDA0002863736480000057
2) DOD and DOA joint estimation based on Sigmoid-MUSIC algorithm
Writing signals received by a receiving array into a matrix form:
Figure GDA0002863736480000058
wherein A ═ a1,...,aL]And B ═ B1,...,bL]Respectively a receive direction vector and a transmit direction vector,
Figure GDA0002863736480000061
which represents the product of the Kronecker reaction,
Figure GDA0002863736480000062
S＝[s1,...,sL],
Figure GDA0002863736480000063
n (t) is Alpha stable distribution noise; .
According to the formula (17), two subarrays Y are obtained1And Y2：
Y1＝AS+N1 q＝1 (18)
Y2＝BS+N2 n＝1 (19)
According to equation (14), a reception matrix Y is obtained1Sigmoid correlation function of (t)
Figure GDA0002863736480000064
The expression of (a) is:
Figure GDA0002863736480000065
wherein
Figure GDA0002863736480000066
A Sigmoid correlation function representing the matrix S;
since the signal and noise are independent of each other, equation (20) is written as:
Figure GDA0002863736480000067
singular value decomposition is performed on equation (21):
Figure GDA0002863736480000068
wherein U isSAnd UNRespectively are eigenvectors corresponding to eigenvalues of the signal subspace and the noise subspace; sigmaSSum ΣNThe diagonal matrix formed by the characteristic values respectively representing the signal subspace and the noise subspace is formed because the signal and the noise are independent and orthogonal to each other
Figure GDA0002863736480000069
aH(θ)UN＝0 (24)
Obtaining the spatial spectrum of Sigmoid-MUSIC algorithm
Figure GDA00028637364800000610
Figure GDA00028637364800000611
By pairs
Figure GDA00028637364800000612
Searching spectral peaks to obtain an estimated value theta of DOAl；
Similarly, the Sigmoid-MUSIC algorithm is applied to Y2To obtain a matrix Y2Sigmoid-MUSIC spatial spectrum of
Figure GDA0002863736480000071
Figure GDA0002863736480000072
Wherein
Figure GDA0002863736480000073
Representation matrix Y2Singular value decomposition is carried out to obtain a feature vector corresponding to the feature value of the noise subspace; by pairs
Figure GDA0002863736480000074
Searching spectral peaks to obtain an estimated value of DOD
Figure GDA0002863736480000075
The invention provides a radar target parameter estimation method under an impulse noise environment, which can resist the influence of Alpha stable distribution noise, effectively solve the problems of Doppler frequency shift scale expansion factor (DS) and Time Delay (TD) existing in a broadband signal echo signal, and improve the accuracy of parameter estimation and positioning of a moving target in a broadband bistatic MIMO radar system.
Drawings
Figure 1 bistatic MIMO radar array model.
Fig. 2 shows comparison of single estimation results of WBAF, flo-WBAF and Sigmoid-WBAF under impulse noise environment (τ is 300/f)s,σ＝1.2,GSNR＝0dB,α＝1.2,p＝1.1)。
Fig. 3 shows comparison of single estimation results of WBAF, flo-WBAF and Sigmoid-WBAF under impulse noise environment (τ 300/f)s,σ＝1.2,GSNR＝-5dB,α＝1.2,p＝1.5)。
Figure 4 MUSIC spatial spectrum of four algorithms.
FIG. 5 shows the RMSE versus GSNR for the parametric estimation.
FIG. 6 is a plot of RMSE for parameter estimation as a function of noise figure index α.
Detailed Description
The invention is further described with reference to the following drawings and detailed description.
A radar target parameter estimation method under an impulse noise environment comprises the following steps:
step 1: establishing a signal model
Fig. 1 shows a bistatic MIMO radar array model used in the present invention. The numbers of the transmitting array elements and the receiving array elements are respectively Q and N, and the distances between the transmitting array elements and the receiving array elements are respectively dtAnd drThe spacing between the transmitting array elements and the spacing between the receiving array elements are equal intervals dt＝drLet the radar work in a wide-band far-field condition, with the transmit and receive arrays at the same phase center, with L targets on the same range resolution unit,
Figure GDA0002863736480000081
and indicating the transmitting angle and the receiving angle of the radar corresponding to the ith target. In order to improve the anti-interference performance, the transmitting signals of the transmitting array elements are considered to be chirp signals, and under the broadband condition, the echo signals received by the radar can generate the scale transformation of the signals besides the Doppler frequency shift due to the movement of the target, namely, the Doppler frequency shift scale expansion factor (DS) is generated. The echo signal received by the nth receiving array element can be expressed as:
Figure GDA0002863736480000082
wherein x isq(t) is the transmission signal of the qth transmission array element:
xq(t)＝Aqexp[j2π(fq0t+μq0t2/2)] (2)
βlamplitude attenuation factor, σ, representing the ith targetlAnd τlA doppler shift scale spread factor and time delay generated for the ith target;
Figure GDA0002863736480000083
to transmit steering vectors, An(θl)＝exp(j2π(n-1)sinθl) For receiving steering vectors, noise wn(t) is the standard S.alpha.S stationary distribution noise.
Since the Wigner distribution of the LFM signal with finite length appears as a dorsal fin distribution of an oblique line on a time-frequency plane, if the fractional fourier transform of the signal is calculated on a fractional domain perpendicular to the oblique line, an obvious peak appears at a certain position of the domain. The invention selects proper bandwidth according to the band-pass filter in the Fractional domain proposed in the documents' X.J Kang, etc., Multiple-Parameter Discrete Fractional transformation and Its Applications, IEEE Transactions on Signal Processing,2016,64(13):3402-qn(t)：
Figure GDA0002863736480000084
Wherein y isqn(t) represents the single echo signal of the qth transmitting array element transmitting LFM signal reaching the nth receiving array element after being reflected by the L targets;
step 2: broadband fuzzy function and correlation function based on Sigmoid transformation
1) Broad band fuzzy function
The expression for the wideband blur function (WBAF) is:
Figure GDA0002863736480000091
wherein
Figure GDA0002863736480000092
σ0And τ0Is the Doppler shift scale expansion factor and time delay;
according to the Schwarz inequality, the following inequality is obtained:
Figure GDA0002863736480000093
wherein
Figure GDA0002863736480000094
Is the energy of signal s (t), when τ ═ τ0And σ ═ σ0When the inequality (5) is equal, that is, when τ is τ0And σ ═ σ0When the temperature of the water is higher than the set temperature,
Figure GDA0002863736480000095
Figure GDA0002863736480000096
with the maximum value, i.e.:
Figure GDA0002863736480000097
according to equation (5), a signal x is obtainedq(t) and xr(t) broadband blur function
Figure GDA0002863736480000098
Figure GDA0002863736480000099
Wherein
Figure GDA00028637364800000910
According to the Schwarz inequality, the following inequality is obtained:
Figure GDA0002863736480000101
when formula (8) satisfies τ ═ τlAnd σ ═ σlWhen the temperature of the molten steel is higher than the set temperature,
Figure GDA0002863736480000102
with a maximum value. Therefore, the estimation problem of TD and DS is converted into a solution
Figure GDA0002863736480000103
The location of the maximum. According to equation (8), TD and DS can be estimated by the following equation:
Figure GDA0002863736480000104
the localization of the peak of the broadband ambiguity function may fail when Alpha stationary distributed noise is mixed in the signal. This is because Alpha stationary distributed noise does not have finite second and higher order moments, whereas the broadband blur function is based on second order moments. Therefore, if the signal contains impulse noise with alpha < 2, the broadband ambiguity function will be dispersed, and the estimation performance will be deteriorated. Therefore, the invention adopts a nonlinear transformation, namely Sigmoid transformation, to inhibit the interference of Alpha stable distribution noise.
2) Broadband fuzzy function based on Sigmoid (Sigmoid-WBAF)
Sigmoid transformation is a common non-linear transformation, and the expression is:
Figure GDA0002863736480000105
in order to solve the problem of signal parameter estimation in an impulse noise environment, the invention combines Sigmoid transformation and broadband fuzzy function, and provides a broadband fuzzy function (Sigmoid-WBAF) based on Sigmoid transformation, wherein the expression of the broadband fuzzy function (Sigmoid-WBAF) based on Sigmoid is as follows:
Figure GDA0002863736480000106
Figure GDA0002863736480000107
denotes s for different values of τ and σr(t) and
Figure GDA0002863736480000108
sigmoid correlation of (2);
for a signal of a finite time width,
Figure GDA0002863736480000111
the estimation can be made using the following equation:
Figure GDA0002863736480000112
in the same way, by searching
Figure GDA0002863736480000113
The abscissa and ordinate, which are the maximum, can enable joint estimation of TD and DS:
Figure GDA0002863736480000114
3) sigmoid correlation function
Because the traditional MUSIC algorithm is based on second-order statistics, the performance of the traditional MUSIC algorithm is seriously reduced or even fails under an Alpha stable distributed noise environment. In order to inhibit the influence of impulse noise and improve the performance of the MUSIC algorithm, a Correlation function is defined and is based on the Correlation function (Sigmoid Correlation) of Sigmoid transformation
Figure GDA0002863736480000115
The expression of (a) is:
Figure GDA0002863736480000116
wherein<·>tRepresents a statistical time average;
and step 3: parameter joint estimation based on Sigmoid-WBAF and Sigmoid-MUSIC algorithms
1) Sigmoid-WBAF based TD and DS estimation
Substituting formulae (2) and (3) into formula (12) to obtain yqnl(t) and xq(t) expression of Sigmoid-WBAF:
Figure GDA0002863736480000117
wherein
Figure GDA0002863736480000118
Representing noise and transmitted signal xqThe Sigmoid-WBAF of (t) can be considered as an interference signal;
by obtaining the position coordinates of the peak point of equation (15), joint estimation of TD and DS is achieved:
Figure GDA0002863736480000121
in the above, the Sigmoid-WBAF algorithm provided by the invention is adopted to realize the joint estimation of the target parameters TD and DS in the broadband bistatic MIMO radar system.
2) DOD and DOA joint estimation based on Sigmoid-MUSIC algorithm
Writing signals received by a receiving array into a matrix form:
Figure GDA0002863736480000122
wherein A ═ a1,...,aL]And B ═ B1,...,bL]Respectively a receive direction vector and a transmit direction vector,
Figure GDA0002863736480000123
which represents the product of the Kronecker reaction,
Figure GDA0002863736480000124
S＝[s1,...,sL],
Figure GDA0002863736480000125
tau is already obtained by the formula (16)lAnd σlSo that the matrix S is known and n (t) is Alpha stationary distributed noise; .
According to the formula (17), two subarrays Y are obtained1And Y2：
Y1＝AS+N1 q＝1 (18)
Y2＝BS+N2 n＝1 (19)
According to equation (14), a reception matrix Y is obtained1Sigmoid correlation function of (t)
Figure GDA0002863736480000126
The expression of (a) is:
Figure GDA0002863736480000127
wherein
Figure GDA0002863736480000128
A Sigmoid correlation function representing the matrix S;
in the Sigmoid-MUSIC subspace algorithm provided by the invention, the Sigmoid correlation function is used for replacing the traditional correlation function, so that the interference of impulse noise can be well inhibited. Since the signal and noise are independent of each other, equation (20) is written as:
Figure GDA0002863736480000129
singular value decomposition is performed on equation (21):
Figure GDA0002863736480000131
wherein U isSAnd UNRespectively are eigenvectors corresponding to eigenvalues of the signal subspace and the noise subspace; sigmaSSum ΣNThe diagonal matrix formed by the characteristic values respectively representing the signal subspace and the noise subspace is formed because the signal and the noise are independent and orthogonal to each other
Figure GDA0002863736480000132
aH(θ)UN＝0 (24)
Obtaining the spatial spectrum of Sigmoid-MUSIC algorithm
Figure GDA0002863736480000133
Figure GDA0002863736480000134
By pairs
Figure GDA0002863736480000135
Searching spectral peaks to obtain an estimated value theta of DOAl；
Similarly, the Sigmoid-MUSIC algorithm is applied to Y2To obtain a matrix Y2Sigmoid-MUSIC spatial spectrum of
Figure GDA0002863736480000136
Figure GDA0002863736480000137
Wherein
Figure GDA0002863736480000138
Representation matrix Y2Singular value decomposition is carried out to obtain a feature vector corresponding to the feature value of the noise subspace; by pairs
Figure GDA0002863736480000139
Searching spectral peaks to obtain an estimated value of DOD
Figure GDA00028637364800001310
The beneficial effects of the invention can be further illustrated by the following simulations:
in order to verify the performance of the algorithm, the two algorithms provided by the invention are compared with other algorithms: comparing the estimated performances of the DS and the TD of a WBAF algorithm, a FLOS-WBAF algorithm and the Sigmoid-WBAF algorithm in the same environment; the MUSIC algorithm, FLOM-MUSIC algorithm, lpThe MUSIC algorithm is compared with the Sigmoid-MUSIC algorithm proposed by the present invention for the estimated performance of DOD and DOA.
Since the S α S random process has no finite second moment, the generalized signal-to-noise ratio (GSNR) is used to measure the strength of the signal and noise:
Figure GDA0002863736480000141
wherein the content of the first and second substances,
Figure GDA0002863736480000142
γ is the dispersion coefficient of the random process of S α S, which is the variance of the signal.
Simulation conditions are as follows:
the number of the transmitting array elements and the receiving array elements is Q-6 and N-8 respectively, the number of the targets is L-2, and the transmitting angles and the receiving angles relative to the transmitting array elements and the receiving array elements are respectively
Figure GDA0002863736480000143
Doppler shift scale expansion factor parameter sigma1＝1.2，σ20.9, the multipath delays are τ respectively1＝300/fs，τ2＝100/fs. Sampling frequency of fsThe number of sampling points is 1000 and the number of Monte-Carlo experiments is 300 under 1 KHz. RMSE is defined as
Figure GDA0002863736480000144
Wherein
Figure GDA0002863736480000145
And
Figure GDA0002863736480000146
is x1And x2The estimated value of (1) is K is the number of sampling points and L is the Monte-Carlo times.
Simulation content:
simulation experiment 1: comparing the single estimation results of different algorithms under S alpha S distributed noise (sigma)1,τ1)。
From fig. 2 and fig. 3, it can be seen that the WBAF algorithm fails in an impulse noise environment, the broadband ambiguity function of the signal is completely drowned by the noise, and the peak point of the broadband ambiguity function cannot be found. Under the conditions that the generalized signal-to-noise ratio GSNR is 0dB, the noise characteristic index alpha is 1.2, and the fractional low-order moment p is 1.1, the broadband fuzzy function (FLOS-WBAF) based on the fractional low-order statistic can inhibit the interference of impulse noise, and the peak point of the FLOS-WBAF of the signal can be obtained. However, when the generalized signal-to-noise ratio GSNR is-5 dB, the noise figure α is 1.2, and the fractional low-order moment p is 1.5, the flo-WBAF algorithm fails to obtain the peak point of the signal, which is caused by improper values of the fractional low-order moment p. According to the theory of fractional low-order statistics, 1-p < alpha or 0-p < alpha/2 is required to be satisfied between the noise characteristic index alpha and the fractional low-order moment p, if the priori knowledge of the noise characteristic index alpha is not available, the FLOS-based algorithm cannot obtain better estimation performance, and if the value of the fractional low-order moment p is not appropriate, the performance of the algorithm is seriously reduced or even fails. The algorithm Sigmoid-WBAF parameter estimation performance of the invention is not affected by the fractional low-order moment p value, and the algorithm provided by the invention can obtain a more accurate peak point under the impulse noise environment, thereby obtaining better estimation performance, which is obtained from the graph 2(c) and the graph 3 (c).
Simulation experiment 2: MUSIC spectral performance of four algorithms
At this time, the simulation is carried outIn the experiment, the generalized signal-to-noise ratio GSNR is 0dB, and the noise figure α is 1.2. FIG. 4 shows four algorithms MUSIC, FLOM-MUSIC, lp-spatial spectrum of MUSIC and Sigmoid-MUSIC. From fig. 4, it can be seen that the performance of the classical MUSIC algorithm is severely degraded under the impulse noise environment. Despite FLOM-MUSIC and lpThe MUSIC algorithm has two spectral peaks, but the spectral peaks are off the correct position and lpThe MUSIC algorithm does not have two very distinct peaks. The Sigmoid transformation can inhibit the interference of impulse noise, especially can inhibit the influence of noise under the conditions of low generalized signal-to-noise ratio and strong impulse noise, and the figure shows that the Sigmoid-MUSIC spatial spectrum has two obvious peaks, and the algorithm has better estimation performance.
Simulation experiment 3 generalized Signal-to-noise ratio GSNR
In the simulation experiment, the noise characteristic index α is 1.2, and in order to illustrate the influence of fractional low-order moments on the flo-WBAF algorithm, the fractional low-order moments in the flo-WNAF algorithm are respectively set to be p 1.0 and p 1.6. The fractional low order moment is set to p-1.0 in the FLOM-MUSIC algorithm to estimate the performance of DOD and DOA. Fig. 5 shows the performance of different algorithm parameter estimation in relation to the change in GSNR.
From fig. 5(a) - (b) we can find that the WBAF algorithm has a weak estimation performance. When the fractional low-order moment p takes different values, the FLOS-WBAF algorithm has different estimation performances, and it can be seen that the estimation performance of the FLOS-WBAF algorithm can be influenced by the fractional low-order moment. When p > α, the FLOS-WBAF algorithm has poor estimation performance. Through simulation experiments, the estimated performance of the Sigmoid-WBAF algorithm is obviously superior to that of the WBAF algorithm and the FLOS-WBAF algorithm when GSNR is less than 5. When GSNR is larger than or equal to 5, the estimated performance of the Sigmoid-WBAF algorithm is equivalent to the performance of the other two algorithms. As can be seen from fig. 5(c) - (d), the estimation performance of the conventional MUSIC algorithm is weaker than that of other algorithms under the impulse noise environment. Sigmoid-MUSIC and l when generalized signal-to-noise ratio is lowpThe performance of the-MUSIC algorithm is superior to that of the FLOM-MUSIC algorithm and the MUSIC algorithm, but the Sigmoid-MUSIC algorithm has lower RMSE and can obtain more accurate estimation results. Therefore, under the impulse noise environment, the estimation performance of the Sigmoid-MUSIC algorithm is obviously superior to that of other algorithmsA method.
Simulation experiment 4 noise characteristic index alpha
In the simulation experiment, the generalized signal-to-noise ratio is set to GSNR equal to 5dB, and when discussing the estimated performance of TD and DS, the fractional low-order moment p in the flo-WBAF algorithm is set to p equal to α -0.2 and p equal to 1.6, respectively. In discussing the estimated performance of DOD and DOA, the fractional low-order moment in the flo-MUSIC algorithm is set to p ═ 1.4. Fig. 6 shows the estimated performance of different algorithms as a function of the noise figure a variation.
As can be seen from fig. 6(a) - (b), both the WBAF algorithm and the flo-WBAF algorithm with p ═ 1.6 have poor estimation performance. The estimated performance of the FLOS-WBAF algorithm is significantly improved when p < alpha. For the FLOS-WBAF algorithm with p ═ alpha-0.2, the Sigmoid-WBAF algorithm performs significantly better than the FLOS-WBAF algorithm when 0.5 < alpha < 1.5. This is because, although both Sigmoid transformation and fractional low order statistics theory have the ability to suppress impulse noise, flo has a weaker ability to suppress impulse noise than Sigmoid transformation. FLOS noise suppression increases with decreasing order p, but when | x2(t)|＞|x1If t > 1, x is still present2(t)|p＞|x1(t)|pAnd 1, the reason is that when the impulse is strong, the outliers far away from the mean value of the signal are not sufficiently suppressed, and the estimation is easy to generate errors. Compared with FLOS, Sigmoid transform performs approximately linear transformation on x (t) in the part where the modulus of x (t) is smaller, and suppresses x (t) in the part where the modulus is far larger than zero. The signal can be considered to be zero-mean in general, that is, the Sigmoid transform can be considered to perform approximately linear transformation on the signal, and suppress outliers. And when | x (t) | > 1, there are
|x2(t)|p＞|x1(t)|p＞1＞|Sigmoid[x(t)]|
Namely, the Sigmoid transformation has stronger inhibition effect on outliers than FLOS. Therefore, under the strong impulse noise environment, the estimation accuracy of the WBAF algorithm based on Sigmoid transformation is higher than that of the WBAF algorithm based on the flo theory. It can be seen from fig. 6(c) - (d) that the conventional MUSIC algorithm performs weaker than the other methods. In a strong impulse noise environment, the Sigmoid-MUSIC algorithm is relatively different from other algorithmsHas better estimation performance. Sigmoid-MUSIC and l when alpha is more than or equal to 1pThe MUSIC methods all have smaller RMSE and comparable performance.
The invention introduces Sigmoid transformation for suppressing Alpha stable distribution noise. A new broadband fuzzy function is defined, namely the broadband fuzzy function based on Sigmoid transformation, and the joint estimation of DS and TD under the impulse noise environment can be realized. Next, a Correlation function (Sigmoid Correlation) based on Sigmoid transformation is defined. Further, a MUSIC algorithm (Sigmoid-MUSIC) based on Sigmoid Correlation is provided to realize joint estimation of DOD and DOA.

Claims (1)

1. A radar target parameter estimation method under an impulse noise environment is characterized by comprising the following steps:
step 1: establishing a signal model
Assuming that the numbers of the transmitting array elements and the receiving array elements are Q and N respectively, and the distances between the transmitting array elements and the receiving array elements are d respectivelytAnd drThe spacing between the transmitting array elements and the spacing between the receiving array elements are equal intervals dt＝drLet the radar work in a wide-band far-field condition, with the transmit and receive arrays at the same phase center, with L targets on the same range resolution unit,
Figure FDA0002863736470000011
and representing the radar transmitting angle and receiving angle corresponding to the ith target, and then representing the echo signal received by the nth receiving array element as follows:
Figure FDA0002863736470000012
wherein x isq(t) is the transmission signal of the qth transmission array element:
xq(t)＝Aqexp[j2π(fq0t+μq0t2/2)] (2)
βlamplitude attenuation factor, σ, representing the ith targetlAnd τlDoppler shift scale spread factor (DS) and Time Delay (TD) generated for the ith target;
Figure FDA0002863736470000015
to transmit steering vectors, An(θl)＝exp(j2π(n-1)sinθl) For receiving steering vectors, noise wn(t) is the standard S α S stationary distribution noise;
extracting the echo signal in a fractional domain through a band-pass filter, performing fractional order Fourier inversion to return to a time domain, and extracting the echo signal yqn(t)：
Figure FDA0002863736470000013
Wherein y isqn(t) represents the single echo signal of the qth transmitting array element transmitting LFM signal reaching the nth receiving array element after being reflected by the L targets;
step 2: broadband fuzzy function and correlation function based on Sigmoid transformation
1) Broad band fuzzy function
The expression for the wideband blur function (WBAF) is:
Figure FDA0002863736470000014
wherein
Figure FDA0002863736470000021
σ0And τ0Is a doppler shift scale expansion factor and time delay;
according to the Schwarz inequality, the following inequality is obtained:
Figure FDA0002863736470000022
wherein
Figure FDA0002863736470000023
Is the energy of signal s (t), when τ ═ τ0And σ ═ σ0When the inequality (5) is equal, that is, when τ is τ0And σ ═ σ0When the temperature of the water is higher than the set temperature,
Figure FDA0002863736470000024
Figure FDA0002863736470000025
with the maximum value, i.e.:
Figure FDA0002863736470000026
according to equation (5), a signal x is obtainedq(t) and xr(t) broadband blur function
Figure FDA0002863736470000027
Figure FDA0002863736470000028
Wherein
Figure FDA0002863736470000029
According to the Schwarz inequality, the following inequality is obtained:
Figure FDA00028637364700000210
when formula (8) satisfies τ ═ τlAnd σ ═ σlWhen the temperature of the molten steel is higher than the set temperature,
Figure FDA00028637364700000211
with the maximum value, TD and DS are given byThe formula estimates to yield:
Figure FDA00028637364700000212
2) broadband fuzzy function based on Sigmoid (Sigmoid-WBAF)
The expression of Sigmoid transformation is:
Figure FDA0002863736470000031
the expression of the wideband fuzzy function (Sigmoid-WBAF) based on Sigmoid is as follows:
Figure FDA0002863736470000032
Figure FDA0002863736470000033
denotes s for different values of τ and σr(t) and
Figure FDA0002863736470000034
sigmoid correlation of (2);
signal sr(T) at time intervals of interest [ -T/2, T/2]Above based on Sigmoid broadband fuzzy function (Sigmoid-WBAF)
Figure FDA0002863736470000035
The estimation can be done using equation (12), i.e. for a finite time-width signal,
Figure FDA0002863736470000036
the estimation is performed using the following equation:
Figure FDA0002863736470000037
in the same way, by searching
Figure FDA0002863736470000038
Abscissa and ordinate at maximum to achieve joint estimation of TD and DS:
Figure FDA0002863736470000039
3) sigmoid correlation function
In order to inhibit the influence of impulse noise and improve the performance of the MUSIC algorithm, a Correlation function is defined and is based on the Correlation function (Sigmoid Correlation) of Sigmoid transformation
Figure FDA00028637364700000310
The expression of (a) is:
Figure FDA00028637364700000311
wherein (a)tRepresents a statistical time average;
and step 3: parameter joint estimation based on Sigmoid-WBAF and Sigmoid-MUSIC algorithms
1) Sigmoid-WBAF based TD and DS estimation
Substituting formulae (2) and (3) into formula (12) to obtain yqnl(t) and xq(t) expression of Sigmoid-WBAF:
Figure FDA0002863736470000041
wherein
Figure FDA0002863736470000042
Representing noise and transmitted signal xq(t) Sigmoid-WBAF as interference signal;
by obtaining the position coordinates of the peak point of equation (15), joint estimation of TD and DS is achieved:
Figure FDA0002863736470000043
2) DOD and DOA joint estimation based on Sigmoid-MUSIC algorithm
Writing signals received by a receiving array into a matrix form:
Figure FDA0002863736470000044
wherein A ═ a1,...,aL]And B ═ B1,...,bL]Respectively a receive direction vector and a transmit direction vector,
Figure FDA0002863736470000045
which represents the product of the Kronecker reaction,
Figure FDA0002863736470000046
S＝[s1,...,sL],
Figure FDA0002863736470000047
n (t) is Alpha stable distribution noise; .
According to the formula (17), two subarrays Y are obtained1And Y2：
Y1＝AS+N1 q＝1 (18)
Y2＝BS+N2 n＝1 (19)
According to equation (14), a reception matrix Y is obtained1Sigmoid correlation function of (t)
Figure FDA0002863736470000048
The expression of (a) is:
Figure FDA0002863736470000049
wherein
Figure FDA00028637364700000410
A Sigmoid correlation function representing the matrix S;
since the signal and noise are independent of each other, equation (20) is written as:
Figure FDA0002863736470000051
singular value decomposition is performed on equation (21):
Figure FDA0002863736470000052
wherein U isSAnd UNRespectively are eigenvectors corresponding to eigenvalues of the signal subspace and the noise subspace; sigmaSSum ΣNThe diagonal matrix formed by the characteristic values respectively representing the signal subspace and the noise subspace is formed because the signal and the noise are independent and orthogonal to each other
Figure FDA0002863736470000053
aH(θ)UN＝0 (24)
Obtaining the spatial spectrum of Sigmoid-MUSIC algorithm
Figure FDA0002863736470000054
Figure FDA0002863736470000055
By pairs
Figure FDA0002863736470000056
Searching spectral peaks to obtain an estimated value theta of DOAl；
Similarly, the Sigmoid-MUSIC algorithm is applied to Y2To obtain a matrix Y2Sigmoid-MUSIC spatial spectrum of
Figure FDA0002863736470000057
Figure FDA0002863736470000058
Wherein
Figure FDA0002863736470000059
Representation matrix Y2Singular value decomposition is carried out to obtain a feature vector corresponding to the feature value of the noise subspace;
by pairs
Figure FDA00028637364700000510
Searching spectral peaks to obtain an estimated value of DOD
Figure FDA00028637364700000511
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