An improved parallel factor target parameter joint estimation method based on hybrid complex correlation entropy

Abstract

The application discloses an improved parallel factor target parameter joint estimation method based on a hybrid complex correlation entropy, and relates to the technical field of radars. Mainly comprising: performing PARAFAC decomposition on a transmission angle equivalent estimation matrix, a receiving angle equivalent estimation matrix and a Doppler frequency equivalent estimation matrix based on a dynamic weight adaptive mechanism, and constructing a cost function of the PARAFAC decomposition based on a hybrid complex correlation entropy; converting the constructed cost function into a weighted least square problem based on a semi-quadratic optimization theory, and solving a factor matrix closed-form analytical solution of a target parameter; and obtaining an estimated target parameter based on the factor matrix closed-form analytical solution of the target parameter. The application can be applied to joint estimation of a Doppler frequency shift, a transmission angle and a receiving angle parameter of a low-altitude environment target, and can realize automatic pairing, thereby providing a more reliable and efficient technical solution for a low-altitude security field.

Description

Technical Field

[0001] This invention belongs to the field of radar data processing technology, specifically, it relates to an improved method for joint estimation of parallel factor target parameters based on hybrid complex correlation entropy. Background Technology

[0002] Bistatic MIMO (Multiple-Input Multiple-Output) radar, as a new type of radar combining MIMO technology with the advantages of bistatic radar, has shown broad application prospects in military reconnaissance, environmental monitoring, and air traffic control in recent years. Bistatic coherent MIMO radar, as an important branch of this system, achieves joint estimation of transmit and receive angles by carefully designing the orthogonal waveforms between the elements of the transmit array and fully utilizing the coherent characteristics between the received signals. This also effectively improves the system's target resolution and parameter estimation accuracy.

[0003] Detecting low-small-slow (LSS) targets in low-altitude environments presents a significant challenge in radar signal processing. With the increasing penetration of drones and other low-small-slow-slow-slow-slow targets in civilian and commercial applications, the resulting security threats are becoming increasingly severe. Incidents such as drone incursions over airport runways causing flight delays and balloons carrying equipment for illegal monitoring in sensitive areas are commonplace, posing a major challenge to low-altitude security systems. Due to their low flight altitude, small radar cross-section (RCS), and slow speed, low-small-slow-slow-slow-slow targets are easily masked by strong ground clutter during detection. Furthermore, their weak echo signals result in a low signal-to-noise ratio (SNR), leading to non-stationary signal characteristics. This further complicates target detection and parameter estimation, severely hindering technological development in the low-altitude security field.

[0004] Tensor decomposition, as a powerful tool for processing multidimensional information, has been increasingly widely used in MIMO radar signal processing in recent years. Parallel Factor Analysis (PARAFAC) decomposition has attracted much attention because it can extract multidimensional structural information from complex-valued tensor models, thereby improving estimation performance in low signal-to-noise ratio (SNR) scenarios. Existing literature has applied PARAFAC decomposition to estimate the angle of departure (DOD) and angle of arrival (DOA) of bistatic MIMO radar systems. Although these methods exhibit robust performance in Gaussian noise environments, their effectiveness decreases significantly under impulse noise conditions. Impulse noise phenomena are very common in natural environments. For example, radar clutter and electromagnetic noise in mobile radio channels exhibit short-term impulse characteristics in the time domain. These noises are usually characterized by suddenness and high amplitude, posing a significant challenge to signal processing. In low-altitude environments, the impulse characteristics of noise are particularly pronounced, with larger pulse amplitudes and shorter durations, making low-altitude target detection even more challenging, especially under low SNR and strong ground clutter interference. In such practical scenarios, traditional parameter estimation methods based on second-order statistics experience severe performance degradation or even complete failure. This problem is particularly prominent in complex electromagnetic environments such as near-shore surveillance and urban environmental sensing, which severely restricts the application effectiveness of bistatic MIMO radar in practical engineering. Summary of the Invention

[0005] To address the shortcomings of existing target parameter estimation methods in low-altitude complex noise environments, this invention provides an improved method for joint estimation of target parameters based on a hybrid complex correlation entropy (MCCGL) with parallel factors. A mixed complex correlation entropy function based on a complex Gaussian kernel and a Laplacian kernel (MCCGL) with adaptive parameter selection is proposed. The objective function of the PARAFAC algorithm based on the TALS criterion is modified using the maximum MMCCGL criterion to make it applicable to impulse noise environments. A PARAFAC algorithm based on the MMCCGL criterion (MMCCGL-PARAFAC algorithm) is derived, which can be applied to the joint estimation of target Doppler shift, transmission angle, and reception angle parameters in low-altitude environments. It also enables automatic pairing, providing a more reliable and efficient technical solution for low-altitude security.

[0006] The technical means employed in this invention are as follows:

[0007] An improved method for joint estimation of parallel factor target parameters based on hybrid complex correlation entropy is applied to a bistatic MIMO radar system, wherein the bistatic MIMO radar system comprises M transmitter elements with a transmitter element spacing of . The transmitting array and the receiving array having N elements with a spacing between the receiving elements are The receiving array, in In the case of one target, The filter output for each echo is:

[0008]

[0009] in, Represents the equivalent matrix of the emission angle. Indicates the launch angle. Represents the equivalent matrix of the receiving angle. Indicates the receiving angle. Represents the Doppler frequency equivalent matrix. Indicates the Doppler frequency. Represents the noise matrix;

[0010] The method includes the following steps:

[0011] S1. Obtain the output signal of the matched filter, and obtain slices of the output signal along the receiving direction, the transmitting direction and the snapshot direction;

[0012] S2. Randomly initialize the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency;

[0013] S3. Perform PARAFAC decomposition based on dynamic weight adaptive mechanism on the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency, and construct the cost function of PARAFAC decomposition based on the hybrid complex correlation entropy.

[0014] S4. Based on the semi-quadratic optimization theory, the constructed cost function is transformed into a weighted least squares problem. The closed-form analytical solution of the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency is obtained by using the weighted least squares method.

[0015] S5. Obtain the receiver angle estimate based on the closed-form analytical solution of the receiver angle equivalent estimation matrix; obtain the transmission angle estimate based on the closed-form analytical solution of the transmission angle equivalent estimation matrix; obtain the Doppler frequency estimate based on the closed-form analytical solution of the Doppler frequency equivalent estimation matrix.

[0016] Furthermore, the constructed cost function includes:

[0017] The cost function of the equivalent estimation matrix of the receiving angle is:

[0018]

[0019] in, This represents the equivalent estimation matrix of the receiving angle at the k-th step. This represents the equivalent estimation matrix of the Doppler frequency at step k-1. Let represent the equivalent estimation matrix of the emission angle at step k-1, with parameters... and These are the weighting coefficients of the mixed complex correlation entropy. By combining kurtosis and skewness, a comprehensive noise index is constructed and mapped to the weighting coefficients. This allows for a reduction in the Gaussian kernel weight when noise impulsivity increases, and a balanced weight distribution when the noise approximates a Gaussian distribution, thus preserving the smoothness advantage of the complex correlation entropy. It is a complex Gaussian kernel function. It is the Laplace kernel function. This represents a slice of the output signal of the matched filter in the receiving direction. yes The estimated value,

[0020] The cost function for constructing the equivalent estimation matrix of the emission angle is:

[0021]

[0022] in, Let represent the equivalent estimation matrix of the emission angle at the k-th step. This represents the equivalent estimation matrix of the receiving angle at the k-th step. This represents the equivalent estimation matrix of the Doppler frequency at step k-1. This represents a slice of the output signal of the matched filter in the transmission direction.

[0023] The cost function for constructing the equivalent Doppler frequency estimation matrix is:

[0024]

[0025] in, Let represent the equivalent estimation matrix of the Doppler frequency at the k-th step. Let represent the equivalent estimation matrix of the emission angle at the k-th step. This represents the equivalent estimation matrix of the receiving angle at the k-th step. This represents a slice of the output signal of the matched filter in the snap direction. express The estimated value.

[0026] Furthermore, the dynamic weight adaptive mechanism is configured to automatically adjust the weight ratio of the Gaussian kernel and the Laplace kernel in the mixed complex correlation entropy according to the noise environment, so that the weight of the Laplace kernel increases under impulse noise and outlier environments. Furthermore, based on semi-quadratic optimization theory, the constructed cost function is transformed into the following weighted least squares problem:

[0027]

[0028] in, , Indicates the Gaussian kernel width. Indicates the width of the Laplace core. Represents the residual of the cost function. The cost function is represented by the first... The residual generated in the next iteration.

[0029] Furthermore, the closed-form analytical solutions for the equivalent estimation matrices of the transmission angle, reception angle, and Doppler frequency, obtained using the weighted least squares method, are as follows:

[0030]

[0031]

[0032]

[0033] in, Let represent the equivalent estimation matrix of the emission angle in the k-th iteration. Let represent the equivalent estimation matrix of the receiving angle in the k-th iteration. Let represent the equivalent estimation matrix of the Doppler frequency in the k-th iteration. This represents a slice of the output signal of the matched filter in the receiving direction. This represents a slice of the output signal of the matched filter in the transmission direction. This represents a slice of the output signal of the matched filter in the snap direction. , , The first In each iteration, the diagonal weight matrix corresponds to the slice data of the receiving direction, transmitting direction, and snapshot direction.

[0034] Furthermore, the current receiver angle estimate is obtained using the following formula:

[0035]

[0036] in, Represents the equivalent estimation matrix of the receiving angle. No. Line number Column elements, Indicates the transmitted wavelength signal;

[0037] The current estimated emission angle is obtained using the following formula:

[0038] in, Represents the equivalent estimation matrix of the emission angle. No. Line number Column elements;

[0039] The estimated Plé frequency is obtained using the following formula:

[0040] in, Represents the Doppler frequency equivalent estimation matrix No. Line number Column elements, This represents the pulse repetition period, where L is the number of pulses. This represents the scattering coefficient of the j-th pulse on the i-th target.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] 1. This invention uses Hybrid Complex Correlation Entropy (MCCGL) as a novel cost function for PARAFAC decomposition and applies it to target parameter estimation in bistatic MIMO radar. The MCCGL is not merely used for noise control but serves as the objective function, driving the joint estimation of multiple target parameters. By combining the PARAFAC algorithm with the MCCGL, complex multi-parameter estimation tasks can be handled, achieving accurate estimation even in complex noise environments.

[0043] 2. This invention adopts an adaptive mechanism of dynamic weights and dynamic kernel width, which can automatically adjust the kernel width and weights according to the noise characteristics of each iteration. This enables the algorithm to adaptively optimize under various noise environments, especially in complex impulse noise environments, thereby improving estimation accuracy and robustness.

[0044] 3. This invention combines hybrid correlation entropy with bistatic MIMO radar target parameter estimation, solving the problem of joint estimation of multiple parameters of the target such as DOD, DOA, and Doppler. Especially under low signal-to-noise ratio and complex noise conditions, this invention significantly improves the accuracy and stability of target parameter estimation.

[0045] 4. This invention introduces semi-quadratic optimization techniques to transform the traditional least squares problem into a weighted least squares problem, further improving computational efficiency and stability. Compared to the fixed kernel width and least squares method in existing technologies, this invention avoids local minima through semi-quadratic optimization, accelerates convergence speed, and ensures estimation accuracy.

[0046] In summary, this application derives a novel joint estimation algorithm for bistatic MIMO radar target parameters suitable for impulse noise environments. This algorithm is based on a hybrid complex correlation entropy function with adaptive kernel width selection and improves the cost function based on the TALS criterion in the PARAFAC algorithm using the MMCCGL criterion. The algorithm not only effectively suppresses impulse noise interference and has good estimation accuracy, but also enables automatic pairing.

[0047] Simulation results show that, under impulse noise and Gaussian noise environments, the MMCCGL-PARAFAC algorithm has better parameter estimation performance than the other two algorithms, especially showing better adaptability to abrupt signal environments. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a schematic diagram of the bistatic MIMO radar system structure in an embodiment of the present invention.

[0050] Figure 2a For the parameter estimation RMSE of the method in this embodiment of the invention, the following applies: Change curve.

[0051] Figure 2b For comparison of the parameter estimation RMSE of method 1 in this embodiment of the invention, Change curve.

[0052] Figure 2c For comparison method 2 parameter estimation RMSE in the embodiments of the present invention, Change curve.

[0053] Figure 3a The parameter estimation accuracy of the method in this application varies with the embodiments of the present invention. Change curve.

[0054] Figure 3b For comparison, the parameter estimation accuracy of method 1 in this embodiment of the invention varies. Change curve.

[0055] Figure 3c For comparison, the parameter estimation accuracy of method 2 in this embodiment of the invention varies. Change curve.

[0056] Figure 4a The RMSE of the parameter estimation method in this embodiment of the invention varies with the noise characteristic index. Change curve.

[0057] Figure 4b For comparison with the noise characteristic index of method 1 in this embodiment of the invention, the RMSE of parameter estimation is compared. Change curve.

[0058] Figure 4c For comparison with the noise characteristic index of method 2 in this embodiment of the invention, the RMSE of parameter estimation is compared. Change curve.

[0059] Figure 5a The parameter estimation accuracy of the method in this application varies with the noise characteristic index in the embodiments of the present invention. Change curve.

[0060] Figure 5b As a comparison of the parameter estimation accuracy of method 1 with the noise characteristic index in the embodiments of the present invention Change curve.

[0061] Figure 5c As a comparison of the parameter estimation accuracy of method 2 with the noise characteristic index in this embodiment of the invention Change curve. Detailed Implementation

[0062] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0063] This invention provides an improved method for joint estimation of target parameters based on hybrid complex correlation entropy, which is applied to bistatic MIMO radar systems.

[0064] 1. Signal Model

[0065] The structure of the bistatic MIMO radar system used in this application is as follows: Figure 1As shown. Within one transmit pulse cycle, the target's cross-sectional area (RCS) remains constant, while the fluctuations between pulses are statistically independent, and the RCS fluctuations of different targets are uncorrelated. The number of transmitting and receiving elements are respectively... and The spacing between array elements are respectively and Existing at the same range resolution unit One goal, Indicates the first The radar transmit and receive angles corresponding to each target. Each transmit element simultaneously transmits mutually orthogonal phase-coded signals. If the first target... The first element launched Each pulse is

[0066] (1)

[0067] In the formula, and These correspond to slow time and fast time, respectively. This indicates the pulse repetition period. For the first The baseband waveform of the first transmitting element. Then, for single-target observation, the... The receiving array element receives the first... Each echo pulse is

[0068]

[0069] (2)

[0070] In the formula , , Echo delay for the target As a standard Stable distribution noise. For the first The first transmission pulse in the... The scattering coefficient on each target. and These are the spatial frequencies of the receiving guide vector and the transmitting guide vector, respectively. For the first The Doppler frequency of the target.

[0071] Since the signals emitted by each transmitting element are orthogonal to each other, that is, they satisfy: ,in and They represent the first The and the first The transmitted signal of each transmitting element This is a conjugate operation. Utilizing... The transmitted signals of each transmitting element are matched and filtered against the echo signals received by each receiving element to separate the signals, thus obtaining the signal at the same time. In the case of the first objective, the... The filter output for the second echo is shown below.

[0072] (3)

[0073] in, , ,

[0074] , ,

[0075] , It is the Khatri-Rao product.

[0076] From equation (3), we can obtain that In the case of one target, The filter output of each echo is

[0077] (4)

[0078] in for A dimensional output matrix. for A 3D matrix vector that is a function of the Doppler frequency (assuming the target's scattering coefficient is known). Let be the noise matrix. From equation (4), it can be seen that estimating the transmit angle, receive angle, and Doppler frequency of the MIMO radar can be transformed into estimating the noise matrix. , and Estimation of three matrices.

[0079] This application improves the cost function of the iterative algorithm using the MMCCGL criterion, proposes the PARAFAC algorithm based on the MMCCGL criterion, and applies this algorithm to target parameter estimation in bistatic MIMO radar. Specifically, it includes the following steps.

[0080] S1. Obtain the output signal of the matched filter, and obtain slices of the output signal along the receiving direction, the transmitting direction and the snapshot direction.

[0081] Specifically, the output of the matched filter It possesses the characteristics of a three-sided array model, therefore it can be used Slice set along the receiving direction, transmitting direction, and snapshot direction The specific calculation method is shown below.

[0082] (5)

[0083] (6)

[0084] (7)

[0085] S2. Randomly initialize the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency.

[0086] Specifically, initialization with any random matrix. , and The iteration number is .

[0087] S3. Perform PARAFAC decomposition based on dynamic weight adaptive mechanism on the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency, and construct the cost function of PARAFAC decomposition based on the mixed complex correlation entropy.

[0088] Parallel factor analysis (PARAFAC) was first proposed as a data analysis tool in physiology, primarily used in chemometrics, spectroscopy, and chromatography, and is a method for multidimensional data analysis. In recent years, parallel factor analysis has received widespread attention in signal processing and communication. PARAFAC is a three-dimensional matrix processing method. Under Kruskal conditions, parallel factor models possess unique identifiability and can yield a matrix containing target parameter information in a single matrix factorization, enabling automatic parameter pairing.

[0089] Parallel factor analysis models are typically performed using the Trilnear Alternating Least Squares Regression (TALS) method. The specific idea is as follows: based on the partial matrix estimates obtained in the previous iteration, other matrices are estimated. This alternating mapping least squares regression process is repeated until convergence.

[0090] Impulse noise is characterized by its short duration and high amplitude, while the tail decay of a Gaussian kernel function is relatively slow, resulting in limited suppression of impulse noise. This makes the cost function constructed based on the correlation entropy of a single Gaussian kernel susceptible to noise interference in impulse noise environments, thus affecting the accuracy of parameter estimation. The correlation entropy cost function of a single Gaussian kernel is extremely sensitive to the kernel width parameter. An inappropriate kernel width can significantly degrade the algorithm's performance. To improve robustness in non-Gaussian / impulse noise environments, a mixture of multiple Gaussian kernel functions can be used. Although the mixed correlation entropy weighted by two Gaussian kernels improves robustness to noise to some extent, due to the inherent characteristics of the Gaussian kernel, its suppression capability in strong impulse noise environments is still not ideal. The cost function constructed by the mixed correlation entropy weighted by two Gaussian kernels may not accurately reflect the true characteristics of the signal, leading to significant deviations in parameter estimation.

[0091] The Laplace distribution (double exponential distribution) has a thicker tail than the Gaussian distribution, making it more suitable for describing noise with sudden and impulsive characteristics (such as impulse noise). It decays faster when the error is large, which can more effectively suppress the influence of outliers and improve the robustness of parameter estimation.

[0092] Existing hybrid methods are based on Gaussian kernels in the real domain, which cannot fully utilize the phase information of complex signals. In practical systems (especially radar and wireless communication), received signals are usually in complex form (including amplitude and phase), and traditional correlation entropy methods are mostly limited to the real domain, ignoring the structural characteristics of complex signals. Complex correlation entropy extends correlation entropy theory to the complex domain. This extension maintains its applicability to real signals while also enabling the processing of complex signals.

[0093] Therefore, to better adapt to different noise environments and effectively utilize all the information of complex signals, this application proposes a hybrid correlation entropy function combining a complex Gaussian kernel and a Laplace kernel. This method not only enhances the suppression of impulse noise but also improves the robustness and accuracy of the overall estimation by combining the advantages of the two kernels. The expression for the hybrid complex correlation entropy MCCGL based on the complex Gaussian kernel and the Laplace kernel is as follows:

[0094] (8)

[0095] in and It is a complex random variable. It is a complex Gaussian kernel function. It is the Laplace kernel function. and For kernel width, parameters and These are the weighting coefficients of the mixed complex correlation entropy. , .when When the mixed entropy function degenerates into the traditional Gaussian kernel correlation entropy function; when When the mixture entropy function is equal to the Laplace kernel correlation entropy function, the mixture entropy function is the same as the Laplace kernel correlation entropy function.

[0096] Hybrid complex correlation entropy is a novel form of correlation entropy obtained by weighted combination of complex Gaussian and Laplace kernels. Its cost function combines the characteristics of both kernels, and by adjusting their weights, optimal signal estimation can be achieved under various noise environments. In impulse noise environments, this hybrid complex correlation entropy cost function can more accurately describe the similarity between signals, reduce impulse noise interference, and thus improve the accuracy and robustness of parameter estimation.

[0097] In practical applications, the joint distribution function of two random variables is usually unknown and needs to be estimated using a finite number of samples. In this case, the discrete expression is:

[0098] (9)

[0099] in .

[0100] From the definition of mixed complex correlation entropy, we know that if and only if hour, It has a maximum value of .

[0101] To improve the robustness of the mixed complex correlation entropy to non-Gaussian noise (especially impulse noise), this application also proposes a strategy for real-time automatic weight updates, which adjusts the contribution ratio of the Gaussian kernel and the Laplace kernel by dynamically evaluating the statistical properties (kurtosis and skewness) of the data.

[0102] Kurtosis is typically used to measure the thickness of the tails in a data distribution. The kurtosis of a Gaussian distribution is 3; a higher kurtosis value indicates stronger impulse characteristics of the noise (e.g., a thicker tail in an alpha-stable distribution). Skewness measures the asymmetry of the data distribution. Non-zero skewness indicates a directional bias in the noise, requiring further suppression of outliers.

[0103] By combining kurtosis and skewness, a comprehensive noise index is constructed and mapped to weight parameters. This allows for a reduction in the Gaussian kernel weight (enhancing the robustness of the Laplace kernel) when noise impulsivity increases (peak or high skewness); and a balanced weight distribution when noise approaches a Gaussian distribution to preserve the smoothness advantage of the complex correlation entropy.

[0104] Define the comprehensive noise index Weighted sum of kurtosis and skewness:

[0105] (10)

[0106] in: For kurtosis, ; For skewness, , This is the skewness adjustment coefficient (experimental setting, usually). . It is the standard deviation of the centralized signal. It is a signal The mean, It is the number of signal samples.

[0107] By using the Sigmoid function Mapping to weights ,

[0108] (11)

[0109] In the formula For slope parameter (usually) ), controlling the sensitivity of weights to changes in noise.

[0110] Through this nonlinear mapping, It can dynamically adjust according to the kurtosis of the signal, thereby achieving adaptive noise suppression.

[0111] In the mixed complex correlation entropy, the complex Gaussian kernel width is selected based on the Silverman criterion. and the width of the Laplace core The Silverman criterion adaptively determines the kernel width based on the local variance of the data and the sample size, aiming to balance bias and variance: too small a kernel width leads to overfitting noise and large estimation variance; too large a kernel width leads to underfitting data and large estimation bias.

[0112] For centralized complex data ( (where the mean is used), calculate its element-wise standard deviation:

[0113] (12)

[0114] For the complex field (d=2), the complex Gaussian kernel width is: To avoid excessively small kernel width, an adjustment coefficient can be introduced. (generally Therefore, the complex Gaussian kernel width The adaptive selection formula is

[0115] (13)

[0116] The Laplace nucleus decays faster than the Gaussian nucleus, is more sensitive to nucleus width, and requires a smaller size. To capture local features, but it is necessary to ensure The value cannot be too small, otherwise it will lead to unstable values. This article The adaptive selection formula is

[0117] (14)

[0118] in .

[0119] To improve the performance of the joint estimation algorithm for target parameters in low-altitude complex noise environments, this application adopts the maximum mixture complex correntropy criterion (MMCCGL based on a complex Gaussian kernel and a Laplacian kernel) to improve the objective function in the PARAFAC algorithm. The cost function based on the MMCCGL criterion is thus obtained as follows:

[0120] (15)

[0121] (16)

[0122] (17)

[0123] This patent improves the objective function in the PARAFAC algorithm by employing the maximum mixed complex correlation entropy criterion, resulting in the following cost function: [Insert cost function here].

[0124] (18)

[0125] (19)

[0126] (20)

[0127] S4. Based on semi-quadratic optimization theory, the constructed cost function is transformed into a weighted least squares problem. The closed-form analytical solution of the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency is obtained by weighted least squares method.

[0128] According to the three-sided array Estimated matrix , and The Trilinear Alternating Least Squares (TALS) method is typically used. TALS is a commonly used method for testing three-sided matrix model data. Its basic idea is as follows: after obtaining a set of initial estimates, one estimation matrix is ​​updated in each step. The update method is as follows: the matrix to be updated in this step is used as the variable, and the other matrices are updated using the previous estimation result as constants, using the least squares method. After updating all estimation matrices, the next iteration is performed, until the algorithm converges.

[0129] As is well known, the least squares algorithm is based on second-order statistics, but impulse noise does not have second-order moments. Therefore, the performance of parameter estimation methods based on least squares will degrade or even fail in the context of impulse noise.

[0130] The cost function of the maximum mixture correlation entropy criterion is non-convex and non-Gaussian. In practical applications, the optimization process faces non-convexity issues, leading to slow convergence, local minima, and direct optimization difficulties in traditional optimization methods (such as alternating least squares). To effectively solve the above optimization problem, this application introduces semi-quadratic optimization theory. This theory, by introducing auxiliary variables, performs a quadratic approximation of the complex cost function, transforming the complex kernel function non-convex optimization problem into a series of easier-to-solve quadratic optimization problems.

[0131] Semi-quadratic optimization theory states that for the kernel function used in this invention... There exists an auxiliary function This makes the following equation true:

[0132] (twenty one)

[0133] in It is an auxiliary variable The relevant function. The meaning of this expression is to maximize the kernel function. Equivalent to about auxiliary variables Maximize the quadratic term within the parentheses. This naturally leads to a class of alternating optimization algorithms: fixed optimization Then fix optimization Until it converges.

[0134] In the context of the hybrid kernel function of this invention, the above derivation needs to be performed separately for the complex Gaussian kernel and the Laplace kernel. For the complex Gaussian kernel... Its corresponding semi-quadratic optimization form is:

[0135] (twenty two)

[0136] The optimal auxiliary variable can be obtained by solving the problem:

[0137] (twenty three)

[0138] To ensure the stability and efficiency of the algorithm in actual iterations, this invention adopts its normalized simplified form. That is, in the... In this iteration, the contribution of the complex Gaussian kernel is represented by a constant weight term, the value of which is... .

[0139] For the Laplace nucleus Its corresponding semi-quadratic optimization form is:

[0140] (twenty four)

[0141] The optimal auxiliary variable can be obtained by solving the problem:

[0142] (25)

[0143] Similarly, the present invention adopts its simplified form. In the first... In this iteration, the contribution of the Laplace kernel is represented by a weighted term related to the residual from the previous round, with a value of ,in It is the first The residual generated in the next iteration.

[0144] Based on the above derivation, in the first... In this iteration, maximizing the mixed complex correlation entropy cost function is equivalent to solving the following weighted least squares problem:

[0145] (26)

[0146] Among them, the The total weight of each residual It is the superposition of the weights of the Gaussian kernel and the Laplace kernel:

[0147] (27)

[0148] This weighting formula is key to achieving robust estimation: the constant weight term ensures performance under Gaussian noise, while the weight term, which is inversely proportional to the residual, can automatically suppress the influence of outliers such as impulse noise.

[0149] Based on the derived weighted least squares problem, this invention, within the framework of alternating least squares, addresses the three factor matrices. , , The algorithm is iteratively updated. Each subproblem has a closed-form analytical solution, thus ensuring the efficiency and stability of the algorithm.

[0150] Definition: Note , , The first In this iteration, the diagonal weight matrix corresponding to the slice data of the receiving direction, transmitting direction, and snapshot direction is given by the formula... , , Calculated.

[0151] S4.1 Estimating the matrix Specifically, the update will , Substituting into equation (18) to find its maximum correlation entropy solution, we obtain... The The estimated value of the next iteration As shown in equation (28).

[0152] (28)

[0153] To solve equation (18), the maximization problem can be solved. Equivalent to a minimization problem, the cost function is:

[0154] (29)

[0155] Based on the weighted least squares problem,

[0156] (30)

[0157] in Let denote the weighted Frobenius norm. The problem has the following closed-form analytical solution:

[0158] (31)

[0159] S4.2 Estimating the matrix Update

[0160] Based on the previous Doppler frequency equivalent estimation matrix, the current reception angle equivalent estimation matrix, and the slice of the output signal of the matched filter in the transmission direction, the current transmission angle equivalent estimation matrix is ​​obtained.

[0161] Will , Substituting into equation (19), we find its maximum correlation entropy solution and obtain the first... The estimated value of the next iteration As shown in equation (19).

[0162] (32)

[0163] Similarly, based on updates The cost function optimization problem is the weighted least squares problem as follows:

[0164] (33)

[0165] Its closed-form analytical solution is:

[0166] (34)

[0167] S4.3, Estimating the matrix Update

[0168] Based on the current equivalent estimation matrix of the receiving angle, the current equivalent estimation matrix of the transmitting angle, and the slice of the output signal of the matched filter in the snap direction, the current equivalent estimation matrix of the Doppler frequency is obtained.

[0169] Will , Substituting into the weighted least squares framework based on semi-quadratic optimization theory,

[0170] (35)

[0171] Available The The estimated value of the next iteration Its closed-form analytical solution is:

[0172] (36)

[0173] Convergence criterion:

[0174] In obtaining , , Next, check if the algorithm converges. This invention uses the update amount of the factor matrix as the convergence criterion. Calculate the relative change norm of the factor matrix between the current iteration and the previous iteration:

[0175] (37)

[0176] like ( If the error threshold is preset, then return to step S3 to continue iteration; if If the algorithm converges, proceed to step S5.

[0177] S5. Obtain the receiver angle estimate based on the closed-form analytical solution of the receiver angle equivalent estimation matrix; obtain the transmission angle estimate based on the closed-form analytical solution of the transmission angle equivalent estimation matrix; obtain the Doppler frequency estimate based on the closed-form analytical solution of the Doppler frequency equivalent estimation matrix.

[0178] After the above iterative calculations, we obtain , and final estimate , and and order , , The three estimated matrices are respectively the first one. Line number The column elements are obtained by averaging the column vectors using equations (38)-(40). , , , . This represents the phase angle operation for retrieving elements.

[0179] (38)

[0180] (39)

[0181] (40)

[0182] The effects of the present invention will be further illustrated below through specific simulation experiments.

[0183] Assume the number of transmitting elements and receiving elements are respectively and The bistatic MIMO radar has two targets in the far field, namely... The transmit angle and receive angle relative to the transmit element and receive element are respectively , Doppler frequency parameters , Number of echoes Each transmitting element emits mutually orthogonal Hadamard-coded signals, and the number of phase codes within each repetition period is... This section uses the Generalized Signal-to-Noise Ratio (GSNR) as a measure of signal and impulse noise. The definition of GSNR is: ,in, Indicates the power of the signal. yes The dispersion coefficient of the distribution. Estimation accuracy. Defined as Where D is the actual value, It is an estimate, when there are multiple targets. This paper presents the average accuracy of estimating multiple target parameters, specifically the average accuracy of two targets. Under the same conditions, the results are compared with the MCC-PARAFAC and TALS-PARAFAC algorithms. All simulation results are derived from 500 Monte Carlo experiments.

[0184] Experiment 1: In this section, we assume the characteristic index of the impulse noise is... The range of generalized signal-to-noise ratio (GSNR) is . Figures 2a-2c The root mean square error of the target parameter estimation for three algorithms is given as follows: Change curve. Figures 3a-3c The comparison of parameter estimation accuracy is shown.

[0185] As shown in the figure, the TALS-PARAFAC algorithm based on second-order statistics deteriorates under impulse noise conditions. This is because second-order statistics are extremely sensitive to heavy-tailed impulse noise, leading to severe biases in parameter estimation. Both the MCC-PARAFAC and MCCC-PARAFAC algorithms demonstrate good resistance to impulse noise. MCC-PARAFAC suppresses real-part impulse noise through real correlation entropy, maintaining a stable RMSE. MCCC-PARAFAC further utilizes the complex correlation entropy criterion; the complex Gaussian kernel function acts on both the real and imaginary parts of the signal, achieving joint suppression of complex-domain impulse noise. The maximum complex correlation entropy criterion strengthens local similarity through exponential weighting, effectively reducing the impact of outliers on tensor decomposition, and its RMSE curve is consistently lower than the other two algorithms. Experimental data demonstrate the necessity of complex-domain processing. Furthermore, the proposed algorithm incorporates the Laplace kernel function, which has a thicker tail than the Gaussian distribution, making it more suitable for describing noise with sudden and impulsive characteristics (such as impulse noise). It decays faster when the error is large, effectively suppressing the influence of outliers and improving the robustness of parameter estimation. Therefore, the MCCGL-PARAFAC algorithm has better estimation performance.

[0186] Experiment 2: The performance of parameter estimation and the characteristic index of impulse noise were investigated. The relationship. In this section, the parameter is set as the generalized signal-to-noise ratio. Characteristic index of impulse noise The range of variation is . Figures 4a-4c and Figures 5a-5c The RMSE and estimation accuracy versus noise characteristic index of the three algorithms are shown respectively. The relationship.

[0187] As shown in the figure, with the characteristic index As α decreases (α→0), the impulse characteristics of the noise are significantly enhanced. Under this condition, the traditional TALS-PARAFAC algorithm, relying on second-order statistics, completely lacks the ability to suppress impulse noise, leading to 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 recovers its good estimation performance. This phenomenon verifies the sensitivity of second-order statistical methods to the characteristics of noise distribution. In contrast, the information theory-based MCC-PARAFAC and MMCCGL-PARAFAC algorithms both exhibit stable anti-interference capabilities within the α∈(0,2] range. MCC-PARAFAC effectively suppresses impulse interference from the real part of noise through real correlation entropy, while the proposed MMCCGL-PARAFAC algorithm innovatively employs a weighted hybrid of complex Gaussian and Laplace kernel functions. Its dual-channel suppression mechanism can simultaneously process the real and imaginary noise components of the signal, and the Laplace kernel function effectively suppresses the influence of impulse noise. This not only enhances the suppression capability against impulse noise but also improves the robustness and accuracy of the overall estimation by combining the advantages of both kernels. Experimental data demonstrate the necessity of joint optimization in the complex domain for non-Gaussian noise processing, providing a theoretical basis and engineering implementation scheme for parameter estimation under impulse noise environments.

[0188] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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. An improved method for joint estimation of parallel factor target parameters based on hybrid complex correlation entropy, applied to a bistatic MIMO radar system, wherein the bistatic MIMO radar system comprises M transmitting elements with an element spacing of . The transmitting array and the receiving array having N elements with a spacing between the receiving elements are The receiving array, in In the case of one target, The filter output for each echo is: in, Represents the equivalent matrix of the emission angle. Indicates the launch angle. Represents the equivalent matrix of the receiving angle. Indicates the receiving angle. Represents the Doppler frequency equivalent matrix. Indicates the Doppler frequency. Represents the noise matrix; The method is characterized by comprising the following steps: S1. Obtain the output signal of the matched filter, and obtain slices of the output signal along the receiving direction, the transmitting direction and the snapshot direction; S2. Randomly initialize the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency; S3. Perform PARAFAC decomposition based on a dynamic weight adaptive mechanism on the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency, and construct a cost function for the PARAFAC decomposition based on the mixed complex correlation entropy; the cost function includes: The cost function of the equivalent estimation matrix of the receiving angle is: in, This represents the equivalent estimation matrix of the receiving angle at the k-th step. This represents the equivalent estimation matrix of the Doppler frequency at step k-1. Let represent the equivalent estimation matrix of the emission angle at step k-1, with parameters... and These are the weighting coefficients of the mixed complex correlation entropy. By combining kurtosis and skewness, a comprehensive noise index is constructed and mapped to the weighting coefficients. This allows for a reduction in the Gaussian kernel weight when noise impulsivity increases, and a balanced weight distribution when the noise approximates a Gaussian distribution, thus preserving the smoothness advantage of the complex correlation entropy. It is a complex Gaussian kernel function. It is the Laplace kernel function. This represents a slice of the matched filter's output signal in the receiving direction. The maximum value of the discrete expression of the mixed complex correlation entropy (MCCGL) of the complex Gaussian kernel and the Laplace kernel; The cost function for constructing the equivalent estimation matrix of the emission angle is: in, Let represent the equivalent estimation matrix of the emission angle at the k-th step. This represents the equivalent estimation matrix of the receiving angle at the k-th step. This represents the equivalent estimation matrix of the Doppler frequency at step k-1. This represents a slice of the output signal of the matched filter in the transmission direction. The cost function for constructing the equivalent Doppler frequency estimation matrix is: in, Let represent the equivalent estimation matrix of the Doppler frequency at the k-th step. Let represent the equivalent estimation matrix of the emission angle at the k-th step. This represents the equivalent estimation matrix of the receiving angle at the k-th step. This represents a slice of the output signal of the matched filter in the snap direction. S4. Based on the semi-quadratic optimization theory, the constructed cost function is transformed into a weighted least squares problem. The closed-form analytical solution of the equivalent estimation matrix of the transmission angle, the equivalent estimation matrix of the reception angle, and the equivalent estimation matrix of the Doppler frequency is obtained by using the weighted least squares method. S5. Obtain the receiver angle estimate based on the closed-form analytical solution of the receiver angle equivalent estimation matrix; obtain the transmission angle estimate based on the closed-form analytical solution of the transmission angle equivalent estimation matrix; obtain the Doppler frequency estimate based on the closed-form analytical solution of the Doppler frequency equivalent estimation matrix.

2. The improved method for joint estimation of parallel factor objective parameters based on mixed complex correlation entropy according to claim 1, characterized in that, The dynamic weight adaptive mechanism is set to automatically adjust the weight ratio of the Gaussian kernel and the Laplace kernel in the mixed complex correlation entropy according to the noise environment, so that the weight of the Laplace kernel increases in the environment of impulse noise and outliers.

3. The improved method for joint estimation of parallel factor objective parameters based on mixed complex correlation entropy according to claim 1, characterized in that, Based on semi-quadratic optimization theory, the constructed cost function is transformed into the following weighted least squares problem: in, Indicates the first The total weight of each residual , Indicates the Gaussian kernel width. Indicates the width of the Laplace core. Represents the residual of the cost function. The cost function is represented by the first... The residual generated in the next iteration.

4. The improved method for joint estimation of parallel factor target parameters based on mixed complex correlation entropy according to claim 1, characterized in that, The closed-form analytical solutions for the equivalent estimation matrices of the transmission angle, reception angle, and Doppler frequency, obtained using the weighted least squares method, are as follows: in, Let represent the equivalent estimation matrix of the emission angle in the k-th iteration. Let represent the equivalent estimation matrix of the receiving angle in the k-th iteration. Let represent the equivalent estimation matrix of the Doppler frequency in the k-th iteration. This represents a slice of the matched filter's output signal in the receiving direction. This represents a slice of the output signal of the matched filter in the transmission direction. This represents a slice of the output signal of the matched filter in the snap direction. , , The first In each iteration, the diagonal weight matrix corresponds to the slice data of the receiving direction, transmitting direction, and snapshot direction.

5. An improved method for joint estimation of parallel factor target parameters based on mixed complex correlation entropy according to claim 4, characterized in that, The current estimated receiving angle is obtained using the following formula: in, Represents the equivalent estimation matrix of the receiving angle. No. Line number Column elements, Indicates the transmitted wavelength signal; The current estimated emission angle is obtained using the following formula: in, Represents the equivalent estimation matrix of the emission angle. No. Line number Column elements; The estimated Plé frequency is obtained using the following formula: in, Represents the Doppler frequency equivalent estimation matrix No. Line number Column elements, This represents the pulse repetition period, where L is the number of pulses. This represents the scattering coefficient of the j-th pulse on the i-th target.

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