Target parameter joint estimation method based on MCC criterion in pulse noise environment

Abstract

The application discloses a target parameter joint estimation method based on an MCC criterion in a pulse noise environment and belongs to the technical field of radars. The application adopts a maximum complex correlation entropy (MCC) criterion to correct a target function based on a TALS criterion in a PARAFAC algorithm so as to make the target function applicable to an impulse noise environment, deduces a PARAFAC algorithm based on the MCC criterion, and applies the algorithm to target parameter estimation of a bistatic MIMO radar, breaks through the dependence of a FLOS method on prior knowledge of characteristic indexes, and realizes joint estimation of target parameters.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of radar technology, in particular to a target parameter joint estimation method based on MCC criterion in a pulse noise environment. BACKGROUND

[0002] As a new system radar combining the advantages of MIMO technology and bistatic radar, bistatic MIMO radar has shown broad application prospects in the fields of military reconnaissance, environmental monitoring, air traffic control, etc. This radar system can effectively overcome the inherent defects of monostatic radar by separating the transmitting array and the receiving array, and combining the characteristics of multiple-input multiple-output of MIMO technology, the system's degree of freedom and parameter estimation accuracy are significantly improved. Among them, the bistatic coherent MIMO radar as an important branch of this system, through careful design of the orthogonal waveforms between each array element of the transmitting array, and full use of the coherence characteristics between the received signals, not only can realize the joint estimation of the transmitting-receiving angle, but also can effectively improve the target resolution ability and parameter estimation accuracy of the system.

[0003] However, it should be pointed out that most of the existing researches on parameter estimation of bistatic MIMO radar are based on the ideal Gaussian white noise assumption. These researches use classical algorithms based on second-order statistics, such as MUSIC (Multiple Signal Classification), ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques), and reduced-dimension Capon methods, which indeed show good estimation performance in Gaussian noise environment. However, a large number of theoretical researches and actual measurement data show that in radar, sonar and modern wireless communication systems, the estimation noise often shows obvious pulse characteristics. This non-Gaussian characteristic makes the statistical distribution of noise have significant "heavy-tailed" characteristics. In this actual scenario, the traditional parameter estimation method based on second-order statistics will have serious performance degradation, and even completely fail. This problem is particularly prominent in complex electromagnetic environments such as near-shore monitoring and urban environment perception, which seriously restricts the application effect of bistatic MIMO radar in actual engineering.

[0004] For the modeling of pulse noise, the Alpha-stable distribution is an ideal choice due to its accurate description of heavy-tailed characteristics. At present, the method based on fractional lower-order statistics is widely used, but its order selection is seriously dependent on the prior knowledge of the signal characteristic exponent. However, in actual application, the characteristic exponent may be time-varying and difficult to accurately estimate, which limits the applicability of FLOS method. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides a target parameter joint estimation method based on the MCC criterion in a pulse noise environment. The present application adopts the maximum complex correlation entropy (MCC) criterion to modify the target function based on the TALS criterion in the PARAFAC algorithm to make it applicable to the impulse noise environment, and applies the modified algorithm to the target parameter estimation of the bistatic MIMO radar, breaks through the dependence of the FLOS method on the characteristic index prior knowledge, realizes the joint estimation of the target parameters, and can realize automatic pairing.

[0006] The technical means adopted by the present application are as follows:

[0007] A target parameter joint estimation method based on the MCC criterion in a pulse noise environment is applied to a bistatic MIMO radar system, and the method comprises the following steps:

[0008] S1, randomly initializing the estimated value of the MIMO radar transmitting angle equivalent matrix, the estimated value of the MIMO radar receiving angle equivalent matrix, and the estimated value of the MIMO radar Doppler frequency equivalent matrix;

[0009] S2, based on the estimated value of the MIMO radar transmitting angle equivalent matrix of the previous step and the estimated value of the MIMO radar Doppler frequency equivalent matrix of the previous step, calculating the correlation entropy by using the cost function improved based on the MCC criterion, and then solving the estimated value of the current MIMO radar receiving angle equivalent matrix;

[0010] S3, based on the estimated value of the MIMO radar Doppler frequency equivalent matrix of the previous step and the estimated value of the current MIMO radar receiving angle equivalent matrix, calculating the correlation entropy by using the cost function improved based on the MCC criterion, and then solving the estimated value of the current MIMO radar transmitting angle equivalent matrix;

[0011] S4, based on the estimated value of the current MIMO radar receiving angle equivalent matrix and the estimated value of the current MIMO radar transmitting angle equivalent matrix, calculating the correlation entropy by using the cost function improved based on the MCC criterion, and then solving the estimated value of the current MIMO radar Doppler frequency equivalent matrix;

[0012] S5, iteratively performing S2-S4 until the iteration termination condition is met, to obtain the final estimated value of the MIMO radar transmitting angle equivalent matrix, the final estimated value of the MIMO radar receiving angle equivalent matrix, and the final estimated value of the MIMO radar Doppler frequency equivalent matrix.

[0013] Further, the method further comprises:

[0014] S6, obtaining the final MIMO radar transmitting angle estimation value based on the final estimated value of the MIMO radar transmitting angle equivalent matrix;

[0015] The final MIMO radar receiving angle estimation value is calculated based on the final MIMO radar receiving angle equivalent matrix estimation value;

[0016] The final MIMO radar Doppler frequency estimation value is calculated based on the final MIMO radar Doppler frequency equivalent matrix estimation value.

[0017] Further, the bistatic MIMO radar system comprises:

[0018] a transmitting array with M transmitting elements, and the distance between adjacent transmitting elements is d t , and each transmitting element transmits a signal orthogonal to each other;

[0019] a receiving array with N receiving elements, and the distance between adjacent receiving elements is d r ;

[0020] The echo signals received by each receiving element are matched filtered by the transmitting signals of the M transmitting elements, and the filter outputs of L echoes in the case of P targets are

[0021]

[0022] where Y=[η1,η2,…,η L ] is an MN×L-dimensional filter output matrix, is the equivalent matrix of the MIMO radar transmitting angle , Bθ is the equivalent matrix of the MIMO radar receiving angle θ, C f d is the equivalent matrix of the MIMO radar Doppler frequency f d , and W is a stable distribution noise matrix.

[0023] Further, the current MIMO radar receiving angle equivalent matrix estimation value is calculated based on the previous MIMO radar transmitting angle equivalent matrix estimation value and the previous MIMO radar Doppler frequency equivalent matrix estimation value, and the correlation entropy is calculated by using a cost function improved based on the MCC criterion, and then the current MIMO radar receiving angle equivalent matrix estimation value is solved, wherein the cost function is:

[0024]

[0025] wherein, is the kth iteration estimation value of the MIMO radar receiving angle equivalent matrix, k=1,2,3,..., σ>0 is a core length parameter, Y1 is a slice set of the filter output matrix along the receiving direction, is the k-1th iteration estimation value of the MIMO radar Doppler frequency equivalent matrix, is the k-1th iteration estimation value of the MIMO radar transmitting angle equivalent matrix, is the kth iteration estimate of the MIMO radar receive angle equivalent matrix.

[0026] Further, based on the previous step MIMO radar Doppler frequency equivalent matrix estimate and the current MIMO radar receive angle equivalent matrix estimate, the correlation entropy is calculated by using a cost function improved based on the MCC criterion, and then the current MIMO radar transmit angle equivalent matrix estimate is solved, wherein the cost function is:

[0027]

[0028] wherein, is the kth iteration estimate of the MIMO radar transmit angle equivalent matrix, k=1, 2, 3, …, σ>0 is a core length parameter, Y2 is a slice set of the filter output matrix along the transmit direction, is the k-1th iteration estimate of the MIMO radar Doppler frequency equivalent matrix, is the kth iteration estimate of the MIMO radar receive angle equivalent matrix, is the transpose of the k-1th iteration estimate of the MIMO radar transmit angle equivalent matrix.

[0029] Further, based on the current MIMO radar receive angle equivalent matrix estimate and the current MIMO radar transmit angle equivalent matrix estimate, the correlation entropy is calculated by using a cost function improved based on the MCC criterion, and then the current MIMO radar Doppler frequency equivalent matrix estimate is solved, wherein the cost function is:

[0030]

[0031] wherein, is the kth iteration estimate of the MIMO radar Doppler frequency equivalent matrix, k=1, 2, 3, …, σ>0 is a core length parameter, Y3 is a slice set of the filter output matrix along the snap direction, is the kth iteration estimate of the MIMO radar receive angle equivalent matrix, is the transpose of the k-1th iteration estimate of the MIMO radar Doppler frequency equivalent matrix.

[0032] Compared with the prior art, the present application has the following advantages:

[0033] The application adopts the MCC criterion to improve the cost function based on the TALS criterion in the PARAFAC algorithm, and deduces a new algorithm suitable for bistatic MIMO radar target parameter joint estimation in the impulsive noise environment. The algorithm can not only effectively suppress the interference of impulsive noise, has good estimation accuracy, but also can realize automatic pairing. Simulation experiments show that, compared with other two algorithms, the MCCC_PARAFAC algorithm has good parameter estimation performance in the impulsive noise and Gaussian noise environment, and especially has better adaptability to the sudden signal environment. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0035] Figure 1 It is a schematic diagram of the bistatic MIMO radar array model in the embodiment of the present application.

[0036] Figure 2 It is a schematic diagram of the comparison of the ability of MCCC and MCC to suppress impulse noise, wherein (a) is a schematic diagram of the comparison of the real and imaginary parts of the signal, and (b) is a schematic diagram of the comparison of the weights of the two correlation entropies to suppress impulse noise.

[0037] Figure 3 It is a curve of the RMSE of parameter estimation of different algorithms varying with GSNR in the embodiment of the present application, wherein (a) is the RMSE of Doppler shift estimation, (b) is the RMSE of DOD estimation, and (c) is the RMSE of DOA estimation.

[0038] Figure 4 It is a curve of the RMSE of parameter estimation of different algorithms varying with the noise characteristic index in the embodiment of the present application, wherein (a) is the RMSE of Doppler shift estimation, (b) is the RMSE of DOD estimation, and (c) is the RMSE of DOA estimation. DETAILED DESCRIPTION

[0039] In order to make the person skilled in the art better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should belong to the protection scope of the present application.

[0040] The application provides a target parameter joint estimation method based on an MCC criterion in a pulse noise environment, which is applied to a bistatic MIMO radar system. Figure 1 As shown in the figure. In one transmission pulse period, the radar cross section (RCS) of the target remains unchanged, the fluctuation between pulses is statistically independent, and the RCS fluctuation of different targets is irrelevant. The number of transmission and receiving elements is M and N respectively, and the element spacing is d t and d r There are P targets in the same range resolution unit, The radar transmission angle and receiving angle corresponding to the ith target are represented. Each transmission element simultaneously transmits mutually orthogonal phase-coded signals. If the mth element transmits the lth pulse, it is

[0041] s m.l t=s m t′+lT (1)

[0042] In the formula, t and t' correspond to slow time and fast time respectively, and T represents the pulse repetition period. s m t is the baseband waveform of the mth transmission element. Then, when a single target is observed, the lth echo pulse received by the nth receiving element is

[0043]

[0044] In the formula, n=1,...,N, l=1,...,L, τ is the echo delay of the target, w n,l t is a standard SαS stable distribution noise. ρ li is the scattering coefficient of the lth transmission pulse on the ith target. α ni =2πn-1 d r sinθ i / λ and are the spatial frequencies of the receiving steering vector and the transmission steering vector respectively. f di is the Doppler frequency of the ith target. Since the signals transmitted by each transmission element are mutually orthogonal, that is, it satisfies: where s q (t) and s k (t) represent the transmission signals of the qth and kth transmission elements respectively, and * is the conjugate operation. The transmission signals of the M transmission elements are used to respectively match filter the echo signals received by each receiving element, and the signals are separated, so that in the case of P targets, the filter output of the lth echo is

[0045]

[0046] where, Bθ=[a r θ1,…,a r θ P ] c l f d =[ρ l1 exp j2πf d1 Tl,...,ρ P exp j2πf dP Tl], ⊙ is the Khatri-Rao product.

[0047] From equation (3), we can obtain the filter output for L echoes when there are P targets:

[0048]

[0049] Where Y = [η1, η2, ..., η L ] is the MN×L dimensional output matrix. Let be a P×L dimensional matrix vector, which is a function of the Doppler frequency (assuming the target's scattering coefficient is known). From equation (4), it can be seen that estimating the transmit angle, receive angle, and Doppler frequency of a MIMO radar can be transformed into estimating... Bθ and Cf d Estimation of three matrices.

[0050] Based on the above, the method of this application includes the following steps:

[0051] S1. Randomly initialize the estimated values ​​of the MIMO radar transmit angle equivalent matrix, the MIMO radar receive angle equivalent matrix, and the MIMO radar Doppler frequency equivalent matrix.

[0052] In this application, an arbitrary random matrix is ​​used to initialize the estimated value of the MIMO radar transmit angle equivalent matrix. Estimated value of the equivalent matrix of the MIMO radar receiver angle Estimated values ​​of the Doppler frequency equivalent matrix of MIMO radar The iteration numbers are k = 1, 2, 3, ...

[0053] S2. Based on the estimated values ​​of the previous step MIMO radar transmit angle equivalent matrix and the previous step MIMO radar Doppler frequency equivalent matrix, the relevant entropy is calculated using the cost function improved based on the MCC criterion, and then the estimated value of the current MIMO radar receive angle equivalent matrix is ​​solved.

[0054] It should be noted that, since a stable distribution process with a characteristic exponent of α (α≤2) only has a finite number of moments less than the characteristic exponent α, many traditional parameter estimation algorithms perform significantly worse under the condition of stable distribution impulsive noise. Alpha-stable distribution (often referred to as “stable distribution” for short) is one of the most promising and attractive models for describing the above random process.

[0055] If a random variable X exists parameters 0 < α ≤ 2, γ ≥ 0, -1 ≤ β ≤ 1 and a real number a such that its characteristic function has the form of equation (5)

[0056]

[0057] In the equation

[0058] The random variable X obeys a stable distribution. Wherein α is called the characteristic exponent, which determines the degree of impulsive characteristics of the distribution. The smaller the value of α, the thicker the tail of the corresponding distribution, and the more significant the impulsive characteristics. Conversely, as the value of α increases, the tail of the corresponding distribution becomes thinner, and the impulsive characteristics weaken. When α = 2, it is a Gaussian distribution, which is a special case of alpha-stable distribution. γ > 0 is the dispersion coefficient, -1 < β < 1 is called the symmetry parameter, and a is called the location parameter.

[0059] It should be further noted that the correlation entropy, like the correlation function, is a similarity measurement concept, and its characteristic is that it can effectively suppress impulsive noise. The complex correlation entropy extends the definition domain of the correlation entropy from the real number domain to the complex number domain, and can be applied to both real-valued signals and complex-valued signals. In fact, in the field of communication technology, complex signals often exist.

[0060] In order to solve the problem of using correlation entropy to analyze and process signals under the condition of complex-valued signals, Guimaraes et al. proposed the concept of complex correlation entropy (CC), which extends the concept and theoretical method of correlation entropy from the real number domain to the complex number domain.

[0061] Let X and Y be complex-valued random variables obeying independent and identically distributed symmetric alpha-stable distribution (SαS), and the characteristic exponent satisfies 1 < α ≤ 2. For two random variables X and Y, the complex correlation entropy is defined as:

[0062]

[0063] In the equation, is the complex kernel function, σ > 0 is the kernel length parameter, and E[·] is the mathematical expectation. Literature proves that the complex correlation entropy R is bounded. In this application, the complex Gaussian kernel is selected:

[0064]

[0065] where ε = X - Y is the complex error variable.

[0066] From the definition of complex correlation entropy, it can be seen that the complex correlation entropy contains the complex Gaussian kernel, so it has a good inhibitory effect on non-Gaussian noise with large amplitude impulse. C X, Y have the following two properties:

[0067]

[0068]

[0069] If and only if X = Y, the maximum value of is obtained.

[0070] The discrete form of the complex correlation entropy is:

[0071]

[0072] In order to verify the ability of the complex correlation entropy MCCC algorithm to suppress impulse noise, the error weights of the complex correlation entropy and the correlation entropy for impulse noise suppression are compared, as shown in Figure 2 The correlation entropy only suppresses the real part of the impulse, ignoring the imaginary part of the noise. The complex correlation entropy optimizes the amplitude and phase of the complex error at the same time, and suppresses the real and imaginary parts of the impulse, while preserving the phase information of the coherent signal.

[0073] Figure 2 The signal containing complex impulse noise is shown in (a). As can be seen from the figure, the noise signal presents impulsiveness in both the real and imaginary parts. Figure 2 In (b), the error weight distribution of the two algorithms is shown. The red curve in the figure is the correlation entropy, and the blue curve is the complex correlation entropy. Figure 2 In (a), the real part of the marked point presents impulsiveness, and in (b), the error weight of the real part of the MCC algorithm is close to 0, playing a suppression role. Figure 2 In (a), the imaginary part of the marked point presents impulsiveness, but the imaginary part of the impulse is not suppressed by the MCC algorithm, that is, even if the real part weight is 0, the imaginary part of the noise will still pollute the result. However, the error weights of the real and imaginary parts of the marked points are close to 0 for the MCCC algorithm, which well suppresses the interference of the impulse noise. Figure 2

[0074] ​It should be further noted that the parallel factor analysis (PARAFAC) is first proposed as a data analysis tool in physiology, mainly used in chemometrics, spectroscopy and chromatography, and is a method of multi-dimensional data analysis. In recent years, the parallel factor technology has been widely concerned in the field of signal processing and communication. PARAFAC is a three-dimensional matrix processing method. Under the Kruskal condition, the parallel factor model has unique identifiability, and the matrix containing the target parameter information can be obtained in one matrix decomposition, so that the parameters can be automatically paired.

[0075] The parallel factor analysis model is usually completed by using a trilinear alternating least squares regression (TALS) method. The specific idea is as follows: based on the partial matrix estimation values obtained in the last iteration, other matrices are estimated. The least squares regression process in the form of the interlaced mapping is looped until convergence.

[0076] Output of the matched filter Has a three-surface array model characteristic, so it can be represented by Y along the receiving direction, the transmitting direction and the slice set Y1, Y2, Y3 in the snap direction, wherein

[0077] Estimating matrix according to three-surface array Y1, Y2, Y3 Bθ and C f d Usually completed by using a trilinear alternating least squares method (TALS). TALS is a commonly used method for data detection of a three-surface array model. The basic idea is as follows: when a set of initial estimation values are obtained, an estimation matrix is updated at each step. The updating method is as follows: taking the matrix to be updated in this step as a variable, and other matrices are taken as constants according to the estimation results in the last time, the least squares method is used for updating. After all the estimation matrices are updated, the next iteration is performed until the algorithm converges.

[0078] It is known that the least squares algorithm is based on the second-order statistics, and the impulse noise does not exist the second moment, so the performance of the parameter estimation method based on the least squares method in the impulse noise environment will be degraded or even invalid.

[0079] In order to improve the parameter estimation performance of the TALS-PARAFAC algorithm in the impulse noise environment, the MCCC (Maximum Complex Correntropy Criterion, MCCC) criterion is used to improve the cost function of the iteration in the algorithm, the PARAFAC algorithm based on the MCC criterion is proposed, and the algorithm is applied to the target parameter estimation of the bistatic MIMO radar.

[0080] In S2, put into equation (10) to obtain the kth iteration estimate of B0 As shown in equation (13).

[0081]

[0082] To solve equation (10), the maximization problem can be equivalent to the minimization problem, and the cost function is

[0083]

[0084] where

[0085]

[0086] where, [·] # denotes the inverse operation, and [·] T denotes the transpose operation.

[0087] S3, based on the estimate of the MIMO radar Doppler frequency equivalent matrix of the previous step and the estimate of the current MIMO radar receiving angle equivalent matrix, the correlation entropy is calculated by using the cost function improved based on the MCC criterion, and then the estimate of the current MIMO radar transmitting angle equivalent matrix is solved.

[0088] In S3, put into equation (14) to obtain the kth iteration estimate of B0 As shown in equation (14).

[0089]

[0090] S4, based on the estimate of the current MIMO radar receiving angle equivalent matrix and the estimate of the current MIMO radar transmitting angle equivalent matrix, the correlation entropy is calculated by using the cost function improved based on the MCC criterion, and then the estimate of the current MIMO radar Doppler frequency equivalent matrix is solved.

[0091] In S4, put into equation (16) to obtain the kth iteration estimate of C f d As shown in equation (17).

[0092]

[0093] ​S5, iteratively performing S2-S4 until an iteration termination condition is met to obtain a final estimated value of the MIMO radar transmit angle equivalent matrix, a final estimated value of the MIMO radar receive angle equivalent matrix and a final estimated value of the MIMO radar Doppler frequency equivalent matrix.

[0094] In S5, the following is calculated where D l [·] represents a diagonal matrix formed by the lth row elements of the matrix, If |δ k -δ k1 |>ε (ε is an error threshold), steps S2-S4 are repeated. If |δ k -δ k1 |<ε, the final estimated values of Bθ and C f Bθ and C f d and W ..l is a SαS stable distribution noise matrix.

[0095] Further, the method of the present application further comprises:

[0096] S6, obtaining a final MIMO radar transmit angle estimated value based on the final estimated value of the MIMO radar transmit angle equivalent matrix, obtaining a final MIMO radar receive angle estimated value based on the final estimated value of the MIMO radar receive angle equivalent matrix, and obtaining a final MIMO radar Doppler frequency estimated value based on the final estimated value of the MIMO radar Doppler frequency equivalent matrix.

[0097] Specifically, according to the final estimated values of Bθ and C f Bθ and C f d and and letting are the jth row ith column elements of the three estimated matrices respectively, the following is obtained by averaging each column vector by using equations (18)-(20) i=1,...,P. angle· represents a phase angle operation of elements.

[0098]

[0099] The scheme and effects of the present application are further illustrated below through specific simulation experiments.

[0100] It is assumed that the number of transmit array elements and receive array elements are M=6 and N=8 respectively, that there are two targets in the far field of the bistatic MIMO radar, i.e. P=2, and that the transmit angle and receive angle relative to the transmit array elements and receive array elements are respectively The Doppler frequency parameter f d1 ​​= 800 Hz, f d2 = 1600 Hz, number of echoes L = 50. Each transmit array element transmits mutually orthogonal Hadamard coded signals, and the number of phase encodings Q = 256 in each repetition period. The generalized signal-to-noise ratio (GSNR) is used as a measure of signal and impulse noise in this section. The definition of GSNR is

[0101]

[0102] where, denotes the power of the signal, and γ is the dispersion coefficient of the SαS distribution. All simulation results are obtained by 500 times of Monte-Carlo experiments, compared with the MCC-PARAFAC and TALS-PARAFAC algorithms under the same conditions.

[0103] Experiment 1: In this subsection, the characteristic exponent of the impulse noise is assumed to be α = 1.3, and the range of the generalized signal-to-noise ratio GSNR is 0 ≤ GSNR ≤ 30. Figure 3 The curves of the root mean square error of the target parameter estimation with respect to GSNR are given for the three algorithms. It can be seen from the figure that the TALS-PARAFAC algorithm is based on the second-order statistics, and the algorithm performance deteriorates in the impulse noise environment. The MCC and MCCC algorithms have good performance in the impulse noise environment, and the complex Gaussian kernel function in the algorithm based on the maximum complex correlation entropy criterion can suppress the real and imaginary parts of the impulse noise, and the suppression of the impulse noise is better, so the parameter estimation performance of the MCCC-PARAFAC algorithm proposed in this paper is better than that of other algorithms.

[0104] The analysis of the experimental results of the target parameter estimation performance is as follows Figure 3The root mean square error (RMSE) of TALS-PARAFAC, MCC-PARAFAC and MCCC-PARAFAC algorithms with respect to the signal-to-noise ratio (SNR) is compared in the figure. The experimental results show that the RMSE of TALS-PARAFAC algorithm based on second-order statistics increases significantly and the performance degrades rapidly in the presence of impulse noise. This is because the second-order statistics is extremely sensitive to the heavy-tailed distributed impulse noise, resulting in a serious bias in parameter estimation. Both MCC-PARAFAC and MCCC-PARAFAC algorithms show good anti-impulse noise ability. MCC-PARAFAC suppresses the real part of the impulse noise through real correlation entropy, and the RMSE remains stable. MCCC-PARAFAC further utilizes the complex correlation entropy criterion, and the complex Gaussian kernel function acts on the real and imaginary parts of the signal simultaneously to achieve joint suppression of complex domain impulse noise. The maximum complex correlation entropy criterion effectively reduces the influence of outliers on tensor decomposition by exponentially weighting the local similarity, and its RMSE curve is always lower than that of the other two algorithms. Experimental data show the necessity of complex domain processing.

[0105] Experiment 2: The relationship between parameter estimation performance and characteristic index of impulse noise α is studied. In this subsection, the parameter is set to be, and the generalized signal-to-noise ratio GSNR is 15 dB. The characteristic index of impulse noise α ranges from 1 to 2. Figure 3 The relationship between the RMSE of parameter estimation of the three algorithms and the noise characteristic index α is given.

[0106] The experimental results are analyzed as shown in Figure 4 With the decrease of the characteristic index α (α→0), the impulse characteristics of the noise are significantly enhanced. Under this condition, the traditional TALS-PARAFAC algorithm completely lacks the ability to suppress impulse noise due to its dependence on second-order statistics, resulting in a sharp increase in the root mean square error (RMSE) of parameter estimation. When α tends to 2, the noise degenerates to Gaussian distribution, and the TALS-PARAFAC algorithm restores good estimation performance, which verifies the sensitivity of the second-order statistical method to the noise distribution characteristics. In contrast, the information theory-based MCC-PARAFAC and MCCC-PARAFAC algorithms show stable anti-interference ability in the range of α∈(0,2]: MCC-PARAFAC effectively suppresses the real part of the impulse noise through real correlation entropy, while the MCCC-PARAFAC algorithm proposed in this paper further innovatively uses a complex Gaussian kernel function, and its dual-channel suppression mechanism can simultaneously process the real and imaginary part of the signal noise components. Experimental data show the necessity of complex domain joint optimization in non-Gaussian noise processing, providing a theoretical basis and engineering implementation scheme for parameter estimation in the presence of impulse noise.

[0107] The application adopts a maximum complex correlation entropy (MCC) criterion to modify a target function based on a TALS criterion in a PARAFAC algorithm to make it applicable to an impulsive noise environment, deduces a PARAFAC algorithm based on the MCC criterion (MCCC-PARAFAC algorithm), and applies the algorithm to target parameter estimation of a bistatic MIMO radar, breaks through the dependence of a FLOS method on prior knowledge of a characteristic index, realizes joint estimation of target parameters, and can realize automatic pairing. Simulation experiments show that the new algorithm proposed in the application has good robustness in the impulsive noise environment. The research results can provide theoretical support and technical reference for radar target detection in a complex electromagnetic environment.

[0108] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for joint estimation of target parameters based on the MCC criterion under impulse noise environment, characterized in that, Applied to a bistatic MIMO radar system, the method includes the following steps: S1. Randomly initialize the estimated values ​​of the MIMO radar transmit angle equivalent matrix, the MIMO radar receive angle equivalent matrix, and the MIMO radar Doppler frequency equivalent matrix. S2. Based on the estimated values ​​of the previous step MIMO radar transmit angle equivalent matrix and the previous step MIMO radar Doppler frequency equivalent matrix, the relevant entropy is calculated using the cost function improved based on the MCC criterion, and then the estimated value of the current MIMO radar receive angle equivalent matrix is ​​solved. S3. Based on the estimated value of the Doppler frequency equivalent matrix of the MIMO radar in the previous step and the estimated value of the current MIMO radar receiver angle equivalent matrix, the relevant entropy is calculated using the cost function improved based on the MCC criterion, and then the estimated value of the current MIMO radar transmit angle equivalent matrix is ​​solved. S4. Based on the estimated values ​​of the current MIMO radar receiver angle equivalent matrix and the current MIMO radar transmit angle equivalent matrix, the relevant entropy is calculated using the cost function improved based on the MCC criterion, and then the estimated value of the current MIMO radar Doppler frequency equivalent matrix is ​​solved. S5. Iterate through S2-S4 until the iteration termination condition is met to obtain the final estimated values ​​of the MIMO radar transmit angle equivalent matrix, the final estimated value of the MIMO radar receive angle equivalent matrix, and the final estimated value of the MIMO radar Doppler frequency equivalent matrix.

2. The method for joint estimation of target parameters based on the MCC criterion under impulse noise environment according to claim 1, characterized in that, The method further includes: S6. Obtain the final estimated value of the MIMO radar emission angle based on the estimated value of the final MIMO radar emission angle equivalent matrix. The final estimated value of the MIMO radar receiver angle is obtained based on the estimated value of the final MIMO radar receiver angle equivalent matrix. The final MIMO radar Doppler frequency estimate is obtained based on the estimate of the equivalent matrix of the final MIMO radar Doppler frequency.

3. The method for joint estimation of target parameters based on the MCC criterion under impulse noise environment according to claim 1, characterized in that, The bistatic MIMO radar system includes: It has M transmitting elements, and the distance between adjacent transmitting elements is d. t The transmitting array, wherein the signals emitted by each transmitting element in the transmitting array are mutually orthogonal; It has N receiving array elements, and the distance between adjacent receiving array elements is d. r The receiving array; By performing matched filtering on the echo signals received by each receiving element using the transmitted signals of M transmitting elements, the filter output for L echoes in the case of P targets is obtained as follows: Where Y = [η1, η2, ..., η] L [ ] represents the MN×L dimensional filter output matrix. For MIMO radar transmission angle The equivalent matrix, Bθ is the equivalent matrix of the MIMO radar receiving angle θ, C f d For the MIMO radar Doppler frequency f d The equivalent matrix is ​​W, where W is the noise matrix.

4. The method for joint estimation of target parameters based on the MCC criterion under impulse noise environment according to claim 3, characterized in that, The estimated values ​​of the MIMO radar transmit angle equivalent matrix and the Doppler frequency equivalent matrix from the previous step are used to calculate the correlation entropy using a cost function improved based on the MCC criterion, and then the estimated value of the current MIMO radar receive angle equivalent matrix is ​​obtained. The cost function is: in, This is the k-th iteration estimate of the equivalent matrix of the MIMO radar receiver angle, where k = 1, 2, 3, ... Y1 is the set of slices of the filter output matrix along the receiving direction, where Y is the kernel length parameter. This is the (k-1)th iteration estimate of the Doppler frequency equivalent matrix of the MIMO radar. This is the estimated value of the (k-1)th iteration of the MIMO radar transmit angle equivalent matrix. This is the transpose of the k-th iteration estimate of the MIMO radar receiver angle equivalent matrix.

5. The method for joint estimation of target parameters based on the MCC criterion under impulse noise environment according to claim 3, characterized in that, Based on the previous estimate of the MIMO radar Doppler frequency equivalent matrix and the current estimate of the MIMO radar receiver angle equivalent matrix, the correlation entropy is calculated using a cost function improved based on the MCC criterion, and then the estimate of the current MIMO radar transmit angle equivalent matrix is ​​obtained. The cost function is: in, This is the k-th iteration estimate of the equivalent matrix of the MIMO radar transmit angle, where k = 1, 2, 3, ... Y is the kernel length parameter, and Y2 is the set of slices of the filter output matrix along the emission direction. This is the (k-1)th iteration estimate of the Doppler frequency equivalent matrix of the MIMO radar. This is the estimated value of the k-th iteration of the MIMO radar receiver angle equivalent matrix. This is the transpose of the estimated value of the k-th iteration of the MIMO radar transmit angle equivalent matrix.

6. The method for joint estimation of target parameters based on the MCC criterion under impulse noise environment according to claim 3, characterized in that, Based on the estimated values ​​of the current MIMO radar receive angle equivalent matrix and transmit angle equivalent matrix, the correlation entropy is calculated using a cost function improved based on the MCC criterion, and then the estimated value of the current MIMO radar Doppler frequency equivalent matrix is ​​obtained. The cost function is: in, This is the k-th iteration estimate of the Doppler frequency equivalent matrix of the MIMO radar, where k = 1, 2, 3, ... Y is the kernel length parameter, and Y3 is the set of slices of the filter output matrix along the snapshot direction. This is the k-th iteration estimate of the equivalent matrix of the MIMO radar transmit angle. Let be the estimated value of the equivalent matrix of the MIMO radar receiver angle in the k-th iteration. This is the transpose of the estimated value of the MIMO radar Doppler frequency equivalent matrix in the kth iteration.

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