Target parameter joint estimation method based on MCCC criterion in impulse noise environment

Abstract

The invention discloses a target parameter joint estimation method based on an MCCC criterion in an impulse noise environment, and belongs to the technical field of radars. According to the method, the target function based on the TALS criterion in the PARAFAC algorithm is corrected by adopting the maximum multiple correlation entropy MCCC criterion to enable the target function to be suitable for the impulse noise environment, the PARAFAC algorithm based on the MCCC criterion is derived, the algorithm is applied to bistatic MIMO radar target parameter estimation, dependence of the FLOS method on feature index priori knowledge is broken through, and joint estimation of target parameters is achieved.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to a target parameter joint estimation method based on the MCCC criterion in an impulse noise environment. Background Art

[0002] Bistatic MIMO (Multiple-Input Multiple-Output) radar, a new radar system that combines the advantages of MIMO technology with bistatic radar, has recently shown broad application prospects in military reconnaissance, environmental monitoring, air traffic control, and other fields. By separating the transmit and receive arrays, this radar system effectively overcomes the inherent shortcomings of monostatic radar. Furthermore, by combining the multiple-input, multiple-output characteristics of MIMO technology, it significantly improves the system's degrees of freedom and parameter estimation accuracy. Bistatic coherent MIMO radar, a key component of this system, achieves joint estimation of transmit and receive angles through the careful design of orthogonal waveforms between the transmit array elements and the full utilization of the coherence between the received signals. This effectively improves the system's target resolution and parameter estimation accuracy.

[0003] However, it should be noted that most existing research on bistatic MIMO radar parameter estimation is based on the assumption of ideal Gaussian white noise. These studies employ classic algorithms based on second-order statistics, such as MUSIC (Multiple Signal Classification), ESPRIT (Signal Parameter Estimation Based on Rotational Invariance), and the reduced-dimensional Capon method, which indeed demonstrate good estimation performance in Gaussian noise environments. However, extensive theoretical research and practical measurement data have shown that in radar, sonar, and modern wireless communication systems, the estimated noise often exhibits a pronounced impulse characteristic. This non-Gaussian nature results in a significant "heavy-tail" characteristic in the statistical distribution of the noise. In such practical scenarios, traditional parameter estimation methods based on second-order statistics suffer from severe performance degradation or even complete failure. This problem is particularly prominent in complex electromagnetic environments such as offshore surveillance and urban environmental perception, severely restricting the practical application of bistatic MIMO radars.

[0004] For modeling impulse noise, the alpha-stable distribution is an ideal choice due to its accurate description of heavy-tailed characteristics. Currently, methods based on fractional low-order statistics are widely used, but the selection of their order relies heavily on prior knowledge of the signal's characteristic exponent. However, in practical applications, the characteristic exponent can be time-varying and difficult to accurately estimate, limiting the applicability of the FLOS method. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the present invention provides a joint target parameter estimation method based on the MCCC criterion in an impulse noise environment. This method uses the Maximum Complex Correlation Entropy (MCCC) criterion to modify the TALS criterion-based objective function in the PARAFAC algorithm, making it suitable for impulse noise environments. The modified algorithm is then applied to target parameter estimation in a bistatic MIMO radar, overcoming the FLOS method's reliance on prior knowledge of characteristic exponents. This method achieves joint target parameter estimation and automatic pairing.

[0006] The technical means adopted in the present invention are as follows:

[0007] A target parameter joint estimation method based on the MCCC criterion in an impulse noise environment is applied to a bistatic MIMO radar system. The method comprises the following steps:

[0008] S1, randomly initialize the estimated value of the MIMO radar transmission angle equivalent matrix, the estimated value of the MIMO radar reception 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 transmission angle equivalent matrix and the estimated value of the MIMO radar Doppler frequency equivalent matrix in the previous step, the correlation entropy is calculated using the cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar reception angle equivalent matrix is ​​solved;

[0010] S3, based on the estimated value of the MIMO radar Doppler frequency equivalent matrix in the previous step and the estimated value of the current MIMO radar reception angle equivalent matrix, the correlation entropy is calculated using the cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar transmission angle equivalent matrix is ​​solved;

[0011] S4, based on the estimated value of the current MIMO radar reception angle equivalent matrix and the estimated value of the current MIMO radar transmission angle equivalent matrix, calculate the correlation entropy using a cost function improved based on the MCCC criterion, and then solve the estimated value of the current MIMO radar Doppler frequency equivalent matrix;

[0012] S5. Iteratively execute S2-S4 until the iteration termination condition is met, and obtain the estimated value of the final MIMO radar transmission angle equivalent matrix, the estimated value of the final MIMO radar reception angle equivalent matrix, and the estimated value of the final MIMO radar Doppler frequency equivalent matrix.

[0013] Furthermore, the method further comprises:

[0014] S6. Obtaining a final MIMO radar emission angle estimate based on the final MIMO radar emission angle equivalent matrix estimate;

[0015] Obtaining a final MIMO radar reception angle estimation value based on an estimation value of a final MIMO radar reception angle equivalent matrix;

[0016] A final MIMO radar Doppler frequency estimation value is obtained based on an estimation value of the final MIMO radar Doppler frequency equivalent matrix.

[0017] Furthermore, the bistatic MIMO radar system includes:

[0018] There are M transmitting array elements, and the distance between adjacent transmitting array elements is d t A transmitting array, wherein the signals transmitted by the transmitting elements in the transmitting array are orthogonal to each other;

[0019] There are N receiving array elements, and the distance between adjacent receiving array elements is d r The receiving array;

[0020] The echo signals received by each receiving element are matched filtered using the transmission signals of the M transmitting elements. In the case of P targets, the filter output of L echoes is:

[0021]

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

[0023] Furthermore, based on the estimated value of the previous step MIMO radar transmission angle equivalent matrix and the estimated value of the previous step MIMO radar Doppler frequency equivalent matrix, the correlation entropy is calculated using a cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar reception angle equivalent matrix is ​​solved, wherein the cost function is:

[0024]

[0025] in, is the kth iteration estimate of the MIMO radar receiving angle equivalent matrix, k=1,2,3,..., σ>0 is the kernel length parameter, Y1 is the slice set of the filter output matrix along the receiving direction, is the k-1th iteration estimate of the MIMO radar Doppler frequency equivalent matrix, is the estimated value of the k-1th iteration of the MIMO radar transmission angle equivalent matrix, is the transpose of the k-th iteration estimate of the MIMO radar reception angle equivalent matrix.

[0026] Furthermore, the estimated value of the MIMO radar Doppler frequency equivalent matrix in the previous step and the estimated value of the current MIMO radar reception angle equivalent matrix are used to calculate the correlation entropy using a cost function improved based on the MCCC criterion, thereby solving the estimated value of the current MIMO radar transmission angle equivalent matrix, wherein the cost function is:

[0027]

[0028] in, is the kth iteration estimate of the MIMO radar transmission angle equivalent matrix, k=1,2,3,..., σ>0 is the kernel length parameter, Y2 is the slice set of the filter output matrix along the emission direction, is the k-1th iteration estimate of the MIMO radar Doppler frequency equivalent matrix, is the estimated value of the k-th iteration of the MIMO radar reception angle equivalent matrix, is the transpose of the estimated value of the MIMO radar transmission angle equivalent matrix at the k-1th iteration.

[0029] Furthermore, based on the estimated values ​​of the current MIMO radar receiving angle equivalent matrix and the estimated values ​​of the current MIMO radar transmitting angle equivalent matrix, the correlation entropy is calculated using the cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar Doppler frequency equivalent matrix is ​​solved. The cost function is:

[0030]

[0031] in, is the k-th iteration estimate of the MIMO radar Doppler frequency equivalent matrix, k=1,2,3,…, σ>0 is the kernel length parameter, Y3 is the slice set of the filter output matrix along the snapshot direction, is the estimated value of the k-th iteration of the MIMO radar reception angle equivalent matrix, is the transpose of the estimated value of the k-1th iteration of the MIMO radar Doppler frequency equivalent matrix.

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

[0033] This application uses the MCCC criterion to improve the TALS-based cost function in the PARAFAC algorithm, deriving a new joint target parameter estimation algorithm for bistatic MIMO radars in impulse noise environments. This algorithm not only effectively suppresses impulse noise interference, achieving good estimation accuracy, but also enables automatic pairing. Simulation experiments demonstrate that the MCCC_PARAFAC algorithm exhibits superior parameter estimation performance compared to the other two algorithms in both impulse and Gaussian noise environments, demonstrating particularly improved adaptability to abrupt signal changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0035] Figure 1 Schematic diagram of a bistatic MIMO radar array model in an embodiment of the present invention.

[0036] Figure 2 Schematic diagram comparing the impulse noise suppression capabilities of MCCC and MCC in an embodiment of the present invention, where (a) is a schematic diagram showing the comparison results of the real and imaginary parts of the signal, and (b) is a schematic diagram showing the comparison results of the weights of the two correlation entropies for suppressing impulse noise.

[0037] Figure 3 1 is a curve showing the RMSE of different algorithm parameter estimates versus GSNR in an embodiment of the present invention, where (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 1 is a curve showing the RMSE of different algorithm parameter estimates versus noise characteristic index in an embodiment of the present invention, where (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 enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0040] The present invention provides a target parameter joint estimation method based on the MCCC criterion in an impulse noise environment, which is applied to a bistatic MIMO radar system. The bistatic MIMO radar system structure used in this application is as follows: Figure 1 As shown. Within a transmission pulse cycle, the target's scattering cross-section (RCS) remains unchanged, while the fluctuations between pulses are statistically independent, and the RCS fluctuations of different targets are unrelated. The number of transmitting and receiving array elements is M and N respectively, and the array element spacing is d t and d r , there are P targets on the same distance resolution unit, Represents the radar transmission angle and reception angle corresponding to the i-th target. Each transmitting array element simultaneously transmits mutually orthogonal phase coded signals. If the l-th pulse transmitted by the m-th array element is

[0041] s m.l t=s m t′+lT (1)

[0042] Where t and t′ correspond to slow time and fast time respectively, and T represents the pulse repetition period. m t is the baseband waveform of the mth transmitting array element. When observing a single target, the lth echo pulse received by the nth receiving array element is

[0043]

[0044] Where n=1,...,N,l=1,...,L,τ is the echo delay of the target, w n,l t is the standard SαS stable distribution noise. ρ li is the scattering coefficient of the lth transmitted pulse on the i-th target. ni =2πn-1 d r sinθ i / λ and are the spatial frequencies of the receiving and transmitting steering vectors, respectively. di is the Doppler frequency of the i-th target. Since the signals transmitted by each transmitting array element are orthogonal to each other, it satisfies: where s q (t) and s k (t) represents the transmission signals of the qth and kth transmitting elements respectively, and * is the conjugate operation. The transmission signals of the M transmitting elements are used to perform matched filtering on the echo signals received by each receiving element, and the signals are separated. In the case of P targets, the filter output of the lth echo can be obtained as

[0045]

[0046] in, 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 formula (3), we can get that in the case of P targets, the filter output of L echoes is

[0048]

[0049] where Y=[η1,η2,…,η L ] is the output matrix of MN×L dimensions. is a P×L dimensional matrix vector, which is a function of the Doppler frequency (assuming the scattering coefficient of the target is known). From formula (4), we can see that the estimation of the transmission angle, receiving angle and Doppler frequency of the MIMO radar can be converted into Bθ and C f d Estimation of 3 matrices.

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

[0051] S1, randomly initialize the estimated value of the MIMO radar transmission angle equivalent matrix, the estimated value of the MIMO radar reception angle equivalent matrix, and the estimated value of the MIMO radar Doppler frequency equivalent matrix.

[0052] In this application, the estimated value of the MIMO radar transmission angle equivalent matrix is ​​initialized by an optional random matrix Estimation of the equivalent matrix of MIMO radar reception angle and the estimated value of the Doppler frequency equivalent matrix of MIMO radar The iteration sequence is k=1,2,3,...

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

[0054] It's important to note that because a stable distribution with a characteristic exponent α (α ≤ 2) has only a finite number of moments smaller than the characteristic exponent α, many traditional parameter estimation algorithms severely degrade under stable distribution impulse noise. The alpha-stable distribution (often referred to as the "stable distribution") is one of the most promising and attractive models for describing such random processes.

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

[0056]

[0057] In the formula

[0058] Then the random variable X follows a stable distribution. α is called the characteristic exponent, which determines the degree of impulse characteristics of the distribution. Smaller α values ​​correspond to thicker tails and, therefore, more pronounced impulse characteristics. Conversely, as α increases, the tails become thinner and the impulse characteristics weaken. When α = 2, the distribution is Gaussian, a special case of the α-stable distribution. γ > 0 is the dispersion coefficient, -1 < β < 1 is the symmetry parameter, and a is the location parameter.

[0059] It's important to note that correlation entropy, like the correlation function, is a similarity measure that effectively suppresses impulse noise. Complex correlation entropy extends the domain of correlation entropy from the real to the complex domain, making it applicable to both real-valued and complex-valued signals. Complex signals are often present in fields like communications.

[0060] In order to solve the problem of using correlation entropy for signal analysis and processing under complex-valued signal conditions, Guimaraes et al. proposed the concept of complex correlation entropy (CC), extending 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 that obey independent and identically distributed symmetric alpha stable distribution (SαS), and their characteristic exponents satisfy 1<α≤2. For two random variables X and Y, the complex correlation entropy is defined as:

[0062]

[0063] Where, 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. This application chooses the complex Gaussian kernel:

[0064]

[0065] where ε=XY 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 function, so it has a good suppression effect on non-Gaussian noise with large amplitude impulses. C X and Y have the following two properties:

[0067]

[0068]

[0069] If and only if X=Y, then Get the maximum value.

[0070] The discrete form of 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 the following example: Figure 2 As shown in Figure 2, correlation entropy only suppresses real pulses and ignores imaginary noise. Complex correlation entropy jointly optimizes the amplitude and phase of the complex error, suppressing both real and imaginary pulses while preserving the phase information of the coherent signal.

[0073] Figure 2 (a) shows that the signal contains a complex impulse noise signal. It can be seen from the figure that the noise signal is impulsive in both the real and imaginary parts. Figure 2 (b) shows the error weight distribution of the two algorithms. The red curve in the figure is the correlation entropy. Figure 2 The real part of (a) shows pulse characteristics. Figure 2 In (b), the MCC algorithm has a suppressive effect on the real part error weight of the noise, which is close to 0. Figure 2 In (a), the imaginary part of the labeled points exhibits impulses, but the MCC algorithm fails to suppress these impulses. Even with a real weight of 0, the imaginary noise still contaminates the result. However, the MCCC algorithm applies close to 0 error weights to both the real and imaginary parts of the labeled points, effectively suppressing the interference of impulse noise.

[0074] It is also worth noting that parallel factor analysis (PARAFAC) was first proposed as a data analysis tool in physiology, primarily used in chemometrics, spectroscopy, and chromatography. It is a method for multidimensional data analysis. In recent years, parallel factor technology has garnered widespread attention in the fields of signal processing and communications. PARAFAC is a three-dimensional matrix processing method. Parallel factor models are uniquely identifiable when the Kruskal condition is satisfied. A matrix containing target parameter information can be obtained in a single matrix decomposition, enabling automatic parameter pairing.

[0075] The parallel factor analysis model is usually completed using the Trilnear Alternating Least Squares Regression (TALS) method. The specific idea is: based on the fixed matrix estimation values ​​obtained in the previous iteration, other matrices are estimated, and the least squares regression process in the form of an alternating mapping is repeated until convergence.

[0076] Matched filter output It has the characteristics of a three-sided array model, so it can be represented by a set of slices Y1, Y2, Y3 along the receiving direction, transmitting direction and snapshot direction, where

[0077] Estimate the matrix based on the three-dimensional matrix Y1, Y2, Y3 Bθ and C f d This is typically accomplished using the trilinear alternating least squares method (TALS). TALS is a common method for data testing of three-sided array models. Its basic concept is that after obtaining a set of initial estimates, an estimated matrix is ​​updated at each step. The update method uses the matrix to be updated in that step as a variable, and the other matrices are updated using the least squares method based on the previous estimate as constants. After all estimated matrices are updated, the next iteration is performed until the algorithm converges.

[0078] As we all know, the least squares algorithm is based on second-order statistics, but impulse noise does not have second-order moments. Therefore, the performance of the parameter estimation method based on the least squares method will degrade or even fail in the impulse noise environment.

[0079] In order to improve the parameter estimation performance of the TALS-PARAFAC algorithm in impulse noise environments, this paper adopts the MCCC (Maximum Complex Correntropy Criterion, MCCC) criterion to improve the iterative cost function in the algorithm, proposes a PARAFAC algorithm based on the MCCC criterion, and applies the algorithm to bistatic MIMO radar target parameter estimation.

[0080] In S2, Substitute into formula (10) to find the maximum correlation entropy solution and obtain the kth iteration estimate of Bθ As shown in formula (13).

[0081]

[0082] In order to solve Equation (10), the maximization problem can be Equivalent to the minimization problem, the cost function is

[0083]

[0084] in

[0085]

[0086] in,[·] # Indicates a violation operation, [·] T Represents a transpose operation.

[0087] S3. Based on the estimated value of the MIMO radar Doppler frequency equivalent matrix in the previous step and the estimated value of the current MIMO radar reception angle equivalent matrix, the correlation entropy is calculated using the cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar transmission angle equivalent matrix is ​​solved.

[0088] In S3, Substitute into formula (14) and find the maximum correlation entropy solution, and obtain the k-th iteration estimate As shown in formula (14).

[0089]

[0090] 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, the correlation entropy is calculated using the cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar Doppler frequency equivalent matrix is ​​solved.

[0091] In S4, Substitute into formula (16) and find the maximum correlation entropy solution to obtain C f d The k-th iteration estimate of As shown in formula (17).

[0092]

[0093] S5. Iteratively execute S2-S4 until the iteration termination condition is met, and obtain the estimated value of the final MIMO radar transmission angle equivalent matrix, the estimated value of the final MIMO radar reception angle equivalent matrix, and the estimated value of the final MIMO radar Doppler frequency equivalent matrix.

[0094] In S5, calculation Among them D l [·] represents a diagonal matrix formed by the l-th row elements of the matrix, If |δ k -δ k1 |>ε (ε is the error threshold), then repeat steps S2-S4. k -δ k1 |<ε, then we get Bθ and C f d The final estimate of and W ..l is the SαS stable distribution noise matrix.

[0095] Furthermore, the present application method also includes:

[0096] S6. Obtain a final MIMO radar transmission angle estimate based on an estimate of the final MIMO radar transmission angle equivalent matrix; obtain a final MIMO radar reception angle estimate based on an estimate of the final MIMO radar reception angle equivalent matrix; and obtain a final MIMO radar Doppler frequency estimate based on an estimate of the final MIMO radar Doppler frequency equivalent matrix.

[0097] Specifically, according to Bθ and C f d The final estimate of and And order are the j-th row and i-th column elements of the three estimation matrices respectively, and the average of each column vector is obtained by equations (18)-(20). i=1,…,P. angle· represents the phase angle operation of the elements.

[0098]

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

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

[0101]

[0102] Where, represents the power of the signal, and γ is the dispersion coefficient of the SαS distribution. Under the same conditions, the algorithm is compared with the MCC-PARAFAC and TALS-PARAFAC algorithms. All simulation results are obtained by statistically analyzing 500 Monte-Carlo experiments.

[0103] Experiment 1: In the experiments in this section, it is assumed that the characteristic exponent α of the impulse noise is 1.3 and the range of the generalized signal-to-noise ratio GSNR is 0≤GSNR≤30. Figure 3 Curves showing the root mean square error (RMS) of target parameter estimation for the three algorithms as a function of GSNR are presented. The figure shows that the TALS-PARAFAC algorithm, based on second-order statistics, performs poorly in environments with impulsive noise. However, the MCC and MCCC algorithms perform better in environments with impulsive noise. Furthermore, the complex Gaussian kernel function in the algorithm based on the maximum complex correlation entropy criterion can suppress both the real and imaginary parts of impulse noise, providing better suppression of impulse noise. Therefore, the proposed MCCC-PARAFAC algorithm outperforms other algorithms in parameter estimation.

[0104] The experimental results analysis of the target parameter estimation performance is as follows Figure 3Figure 2 compares the root mean square error (RMSE) curves of the TALS-PARAFAC, MCC-PARAFAC, and MCCC-PARAFAC algorithms as they vary with the signal-to-noise ratio. Experimental results show that the TALS-PARAFAC algorithm, based on second-order statistics, significantly increases its RMSE in an impulsive noise environment, leading to a sharp performance degradation. This is because second-order statistics are extremely sensitive to heavy-tailed impulsive noise, leading to severe bias in parameter estimation. Both the MCC-PARAFAC and MCCC-PARAFAC algorithms demonstrate good robustness against impulsive noise. MCC-PARAFAC suppresses real impulsive noise using real correlation entropy, maintaining a stable RMSE. MCCC-PARAFAC further utilizes the complex correlation entropy criterion, with a complex Gaussian kernel function acting on both the real and imaginary parts of the signal, achieving joint suppression of complex-domain impulsive noise. The maximum complex correlation entropy criterion enforces local similarity through exponential weighting, effectively reducing the impact of outliers on tensor decomposition. Its RMSE curves are consistently lower than those of the other two algorithms. Experimental data demonstrate the necessity of complex-domain processing.

[0105] Experiment 2: We studied the relationship between parameter estimation performance and the impulse noise characteristic exponent α. In this section, we set the parameters to GSNR = 15dB and the impulse noise characteristic exponent α to 1≤α≤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 follows Figure 4 As shown, as the characteristic exponent α decreases (α→0), the impulse characteristics of the noise significantly increase. Under these conditions, the traditional TALS-PARAFAC algorithm, relying on second-order statistics, is completely unable to suppress impulse noise, resulting in a sharp increase in the root mean square error (RMSE) of parameter estimation. When α approaches 2, the noise degenerates into a Gaussian distribution, at which point the TALS-PARAFAC algorithm regains good estimation performance. This phenomenon demonstrates the sensitivity of second-order statistical methods to the characteristics of noise distribution. In contrast, the information-theoretic MCC-PARAFAC and MCCC-PARAFAC algorithms both exhibit stable interference rejection within the range α∈(0,2]. MCC-PARAFAC effectively suppresses the impulse interference of the real part of the noise through real correlation entropy, while the proposed MCCC-PARAFAC algorithm further innovatively employs a complex Gaussian kernel function. Its dual-channel suppression mechanism can simultaneously process both the real and imaginary noise components of the signal. Experimental data demonstrate the necessity of complex-domain joint optimization for non-Gaussian noise processing, providing a theoretical basis and an engineering implementation solution for parameter estimation in impulse noise environments.

[0107] This application uses the Maximum Complex Correlation Entropy (MCCC) criterion to modify the TALS-based objective function in the PARAFAC algorithm, making it suitable for impulse noise environments. This application derives the MCCC-PARAFAC algorithm based on the MCCC criterion and applies it to target parameter estimation in a bistatic MIMO radar. This algorithm overcomes the FLOS method's reliance on prior knowledge of characteristic exponents, enabling joint estimation of target parameters and automatic pairing. Simulation experiments demonstrate that the proposed algorithm exhibits excellent robustness in impulse noise environments. This research result can provide theoretical support and technical reference for radar target detection in complex electromagnetic environments.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A target parameter joint estimation method based on MCCC criterion in an impulse noise environment, characterized by: Applied to a bistatic MIMO radar system, the method comprises the following steps: S1, randomly initialize the estimated value of the MIMO radar transmission angle equivalent matrix, the estimated value of the MIMO radar reception angle equivalent matrix, and the estimated value of the MIMO radar Doppler frequency equivalent matrix; S2, based on the estimated value of the MIMO radar transmission angle equivalent matrix and the estimated value of the MIMO radar Doppler frequency equivalent matrix in the previous step, the correlation entropy is calculated using the cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar reception angle equivalent matrix is ​​solved; S3, based on the estimated value of the MIMO radar Doppler frequency equivalent matrix in the previous step and the estimated value of the current MIMO radar reception angle equivalent matrix, the correlation entropy is calculated using the cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar transmission angle equivalent matrix is ​​solved; S4, based on the estimated value of the current MIMO radar reception angle equivalent matrix and the estimated value of the current MIMO radar transmission angle equivalent matrix, calculate the correlation entropy using a cost function improved based on the MCCC criterion, and then solve the estimated value of the current MIMO radar Doppler frequency equivalent matrix; S5. Iteratively execute S2-S4 until the iteration termination condition is met, and obtain the estimated value of the final MIMO radar transmission angle equivalent matrix, the estimated value of the final MIMO radar reception angle equivalent matrix, and the estimated value of the final MIMO radar Doppler frequency equivalent matrix.

2. The target parameter joint estimation method based on the MCCC criterion in an impulse noise environment according to claim 1 is characterized in that: The method further comprises: S6. Obtaining a final MIMO radar emission angle estimate based on the final MIMO radar emission angle equivalent matrix estimate; Obtaining a final MIMO radar reception angle estimation value based on an estimation value of a final MIMO radar reception angle equivalent matrix; A final MIMO radar Doppler frequency estimation value is obtained based on an estimation value of the equivalent matrix of the final MIMO radar Doppler frequency.

3. The target parameter joint estimation method based on the MCCC criterion in an impulse noise environment according to claim 1, characterized in that: The bistatic MIMO radar system comprises: There are M transmitting array elements, and the distance between adjacent transmitting array elements is d t A transmitting array, wherein the signals transmitted by the transmitting elements in the transmitting array are orthogonal to each other; There are N receiving array elements, and the distance between adjacent receiving array elements is d r The receiving array; The echo signals received by each receiving element are matched filtered using the transmission signals of the M transmitting elements. In the case of P targets, the filter output of L echoes is: where Y = [η1, η2, ..., η L ] is the filter output matrix of MN×L dimensions, is the MIMO radar transmission angle The equivalent matrix of , Bθ is the equivalent matrix of MIMO radar receiving angle θ, C f d is the MIMO radar Doppler frequency f d The equivalent matrix of , W is the noise matrix.

4. The target parameter joint estimation method based on the MCCC criterion in an impulse noise environment according to claim 3 is characterized in that: Based on the estimated value of the MIMO radar transmission angle equivalent matrix and the estimated value of the MIMO radar Doppler frequency equivalent matrix in the previous step, the correlation entropy is calculated using a cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar reception angle equivalent matrix is ​​solved, wherein the cost function is: in, is the kth iteration estimate of the MIMO radar receiving angle equivalent matrix, k=1,2,3,…, is the kernel length parameter, Y1 is the slice set of the filter output matrix along the receiving direction, is the k-1th iteration estimate of the MIMO radar Doppler frequency equivalent matrix, is the estimated value of the k-1th iteration of the MIMO radar transmission angle equivalent matrix, is the transpose of the k-th iteration estimate of the MIMO radar reception angle equivalent matrix.

5. The target parameter joint estimation method based on MCCC criterion in an impulse noise environment according to claim 3 is characterized in that: The estimated value of the MIMO radar Doppler frequency equivalent matrix based on the previous step and the estimated value of the current MIMO radar reception angle equivalent matrix are used to calculate the correlation entropy using a cost function improved based on the MCCC criterion, and then solve the estimated value of the current MIMO radar transmission angle equivalent matrix, wherein the cost function is: in, is the kth iteration estimate of the MIMO radar transmission angle equivalent matrix, k=1,2,3,…, is the kernel length parameter, Y2 is the slice set of the filter output matrix along the emission direction, is the k-1th iteration estimate of the MIMO radar Doppler frequency equivalent matrix, is the estimated value of the k-th iteration of the MIMO radar reception angle equivalent matrix, is the transpose of the estimated value of the k-th iteration of the MIMO radar transmission angle equivalent matrix.

6. The target parameter joint estimation method based on MCCC criterion in an impulse noise environment according to claim 3, characterized in that: Based on the estimated values ​​of the current MIMO radar receiving angle equivalent matrix and the estimated values ​​of the current MIMO radar transmitting angle equivalent matrix, the correlation entropy is calculated using the cost function improved based on the MCCC criterion, and then the estimated value of the current MIMO radar Doppler frequency equivalent matrix is ​​solved. The cost function is: in, is the k-th iteration estimate of the MIMO radar Doppler frequency equivalent matrix, k=1,2,3,…, is the kernel length parameter, Y3 is the slice set of the filter output matrix along the snapshot direction, is the kth iteration estimate of the MIMO radar emission angle equivalent matrix, is the estimated value of the k-th iteration of the MIMO radar reception angle equivalent matrix, is the transpose of the estimated value of the k-th iteration of the MIMO radar Doppler frequency equivalent matrix.

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