A radar frequency band fusion extension method based on MP and root-MUSIC algorithm

Abstract

The application belongs to the technical field of radar target recognition, and particularly relates to a radar frequency band fusion expansion method based on MP and Root-MUSIC algorithm. The method comprises the following steps: step 1: setting two adjacent radars, the observation angles of which are the same, and the working frequencies of which are different, so that a full-polarization GTD model of low-frequency and high-frequency electromagnetic echo is established for a stationary target composed of scattering centers; step 2: using echo data and conjugate data, incoherent parameters, i.e. linear phase and fixed phase, are estimated; step 3: using an improved algorithm to process coherent data, poles and amplitudes of a wideband full-polarization model are estimated, and then original data of low-frequency subband and high-frequency subband are used to calculate a fusion signal of a full frequency band. The multi-frequency band fusion method provided by the application uses original data and a conjugate form to construct a new covariance matrix, so that the modified algorithm has better parameter estimation performance under the same signal-to-noise ratio.

Description

Technical Field

[0001] This invention belongs to the field of radar target recognition technology, specifically relating to a radar band fusion and extension method based on MP and Root-MUSIC algorithms. Background Technology

[0002] High resolution plays a crucial role in applications such as non-cooperative radar target identification, space target surveillance, and ballistic missile defense. Radar resolution can be improved by designing and manufacturing ultra-wideband (UVB) radars. However, this approach is difficult to implement due to technological and cost limitations. To address this issue, a common method is to decompose the wideband signal into multiple narrowband signals in the frequency domain, and then perform narrowband processing directly on each subband.

[0003] Since subband signals are measured from radars operating at different frequencies, they are incoherent. Cuomo et al. at Lincoln Laboratory analyzed multi-band radars and found that the incoherence between different radars ultimately introduces linear and fixed phase shifts into the signal. Therefore, to improve accuracy, these parameters should be estimated and mutually compensated before subband fusion. Cuomo et al. proposed using the Root-MUSIC algorithm and least squares method to estimate incoherent parameters. However, such algorithms suffer from excessive computational complexity. Another approach proposes a linear phase shift method that utilizes the correlation of a one-dimensional image of the target to obtain a fixed phase shift with a cost function constraint. Compared to the former, this algorithm has higher estimation accuracy, but its estimation performance is unstable due to limitations in the number of signal samples. Some researchers have also proposed incoherent estimation methods based on the Root-MUSIC algorithm and the ESPRIT (Estimated Signal Parameters Via Rotational Invariance Technique) algorithm. However, this method suffers from poor parameter estimation performance under low signal-to-noise ratio conditions. In addition, the all-phase fast Fourier transform (apFFT) spectral analysis method has also been used to estimate incoherent parameters. This method avoids using prior knowledge of the scattering center, but it has the drawback of being limited by the sampling frequency. Improving radar resolution has been a key focus and challenge in the radar field for the past decade, and multi-band fusion algorithms used in this area are constantly being updated.

[0004] After parameter compensation, incoherent subband signals become coherent, requiring further model fitting. Model fitting directly determines the accuracy of multi-band fusion and is a crucial step in the process. Researchers at Lincoln Laboratory proposed an all-pole model for fitting electromagnetic scattering data. When the relative bandwidth of the operating radar is relatively small, the all-pole model approximates the Geometrical Theory of Diffraction (GTD) model. The GTD model can provide a relatively high-precision description of electromagnetic scattering of radar targets and is widely used in radar signal modeling. Parameter estimation algorithms for the GTD model are relatively mature; typical estimation algorithms such as Sparse Bayesian Learning (SBL), ESPRIT, and MUSIC can effectively estimate the parameters of the GTD model. Summary of the Invention

[0005] To address the aforementioned problem that traditional spatial algorithms such as Matrix Bundle (MP) and Root-MUSIC cannot accurately estimate parameters under low signal-to-noise ratio (SNR) conditions due to the similarity between noise and signal eigenvalues, this invention proposes an incoherent parameter estimation and multi-band fusion method based on MP and Root-MUSIC algorithms. The proposed algorithm constructs a new covariance matrix using the original data and its conjugate form, enabling the modified algorithm to achieve better parameter estimation performance at the same SNR.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A radar band fusion and extension method based on MP and Root-MUSIC algorithms includes:

[0008] Step 1: Set up two adjacent radars with the same observation angle but different operating frequencies. For a stationary target composed of scattering centers, establish an all-polar GTD model of low-frequency and high-frequency electromagnetic echoes.

[0009] Step 2: Based on Step 1, using the echo data and its conjugate data, the incoherence parameters, namely linear phase and fixed phase, are estimated;

[0010] Step 3: Based on the linear phase and fixed phase obtained in Step 2, the coherent data is processed using an improved algorithm to estimate the poles and amplitude of the broadband full polarization model. Then, the fused signal of the entire frequency band is calculated using the original data of the low-frequency subband and the high-frequency subband.

[0011] Preferably, step 1 includes:

[0012] Step 1.1: Set up two adjacent radars, both operating at the same observation angle but with different operating frequencies. Therefore, for a stationary target composed of scattering centers, the electromagnetic echoes of the two sub-bands can be represented as:

[0013]

[0014]

[0015] In the formula: S1 is the low-frequency wavelet echo, S2 is the high-frequency wavelet echo, and f m and f' m’ f0 and f 00 f represents the initial operating frequencies of the low-frequency and high-frequency subbands, respectively. m =f0+(m-1)Δf and f' m’ =f 00 +(m'-1)Δf represents the mth and m'th frequency points, respectively, and M1 and M2 represent the total number of frequency points in the low-frequency and high-frequency sub-bands, respectively; r i Indicates the location of the scattering center, α i Indicates the scattering type, A i α represents the scattering intensity. i ∈[-1,-0.5,0,0.5,1] represents different typical scattering structures, c=3×10 8 m / s is the speed of light, β represents the fixed phase, η represents the linear phase, β and η represent the incoherent relationship between the low-frequency subband and the high-frequency subband, w(m) and w(m') represent the Gaussian white noise of the low-frequency subband and the high-frequency subband, respectively, I is the number of scattering centers, j is the imaginary unit, and Δf is the frequency step.

[0016] Step 1.2: When the operating bandwidth is less than 10% of the center frequency, the following approximation is achieved:

[0017] Δf / f0 << 1 (3)

[0018]

[0019] Step 1.3: Substitute equations (3)-(4) obtained in Step 2 into equations (1)-(2) to obtain the omnipolar GTD model for low-frequency and high-frequency electromagnetic echoes:

[0020]

[0021]

[0022] Preferably, step 2 specifically includes:

[0023] Step 2.1: First, assume the low-frequency subband and high-frequency subband signal echoes are as follows:

[0024] Y1=(s1(1),s1(2),...,s1(M1)) T (7)

[0025] Y2=(s2(1),s2(2),...,s2(M2)) T (8);

[0026] Let M1 = M2 = M, then the covariance matrices of Y1 and Y2 can be expressed as:

[0027]

[0028]

[0029] In the formula: A 1p and A 2p They represent M×I and / or the zero matrix of M×I, respectively; Λ1 and Λ2 represent I×I diagonal matrices; σ 2 Let I represent the noise variance, and let I represent the M×M identity matrix. For R Y1 eigenvalues ​​of the matrix For R Y2 eigenvalues ​​of the matrix;

[0030] Step 2.2: Construct the echo data matrix of formula (11-12):

[0031]

[0032]

[0033] In the formula: L is the matrix bundle parameter, and J is an M×M permutation matrix, the expression of which is as follows:

[0034]

[0035] The cross covariance and the covariance of different subbands are combined to construct the matrix shown below:

[0036]

[0037]

[0038] Step 2.3: In the construction and Then, SVD processing is performed on it, and the same steps as the traditional MP algorithm and the traditional Root-MUSIC algorithm are repeated to obtain linear phase and fixed phase, thus completing the sub-band confusion of different frequency bands.

[0039] Preferably, the specific steps of step 2.3 are as follows:

[0040] Step 2.3.1: For the matrix and Perform eigenvalue decomposition:

[0041]

[0042]

[0043] Based on the MDL method, the signal is decomposed into a low-frequency subband signal subspace A. 11 and the noise subspace A of the high-frequency subband 22 :

[0044]

[0045]

[0046] In the formula: and These represent the signal subspace and noise subspace of the low-frequency subband, respectively. and These represent the signal subspace and noise subspace of the high-frequency subband, respectively.

[0047] Step 2.3.2: Based on A in Step 2.3.1 11 and A 22 ,calculate

[0048]

[0049]

[0050] Step 2.3.3: Place a 1i or b 1i represent or The first column, Reexpressed as:

[0051]

[0052]

[0053] Step 2.3.4: Calculation The root closest to the unit circle was selected as the pole of the fully polarized GTD model. Finally, the amplitude was calculated using the least squares method. and

[0054] Step 2.3.5: Calculate the linear phase and fixed phase, and calculate the echo data of the two sub-bands.

[0055] Preferably, step 2.4.5 specifically includes:

[0056] The amplitude coefficients estimated by the MP algorithm are:

[0057]

[0058] The phase angle is:

[0059]

[0060] Based on expressions (24) and (25), we can conclude that:

[0061]

[0062] The fixed phase is calculated as follows:

[0063]

[0064] In the formula: ΔB=f 00 -f0;

[0065] Calculate the phase of incoherent subbands in the high-frequency region

[0066]

[0067] Preferably, step 3 specifically includes:

[0068] Step 3.1: Based on the linear phase and fixed phase estimated in Step 2, calculate the high-frequency sub-band as follows:

[0069]

[0070] Step 3.2: Process the coherent data from Step 2 using the improved algorithm to estimate the poles and amplitudes of the broadband fully polarized model, expressed as follows:

[0071]

[0072] In the formula: and M represents the estimated amplitude and poles, and M' represents the number of broadband frequencies;

[0073] Therefore, subband Electromagnetic scattering data can be expressed as:

[0074]

[0075] Step 3.3: To reduce estimation errors, calculate the fused signal across the entire frequency band using the raw data from the low or high frequency sub-bands. The expression for this signal is:

[0076]

[0077] Compared with the prior art, the beneficial effects of the present invention are:

[0078] 1. This invention transforms bandwidth expansion from a hardware problem into a software implementation problem, reduces the cost of bandwidth fusion, and provides an algorithmic foundation for future super-resolution imaging and high-precision distance estimation;

[0079] 2. Compared with traditional methods, this invention improves the algorithm's noise resistance and effectively enhances its robustness while maintaining essentially the same computational complexity.

[0080] 3. It expands the application scope of existing frequency band fusion algorithms, enabling frequency band fusion to be performed even when the frequency band gap is larger. Attached Figure Description

[0081] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0082] In the attached diagram:

[0083] Figure 1 This is a flowchart of the method of the present invention;

[0084] Figure 2 The results of linear phase estimation under different signal-to-noise ratio conditions;

[0085] Figure 3 The results of fixed phase estimation under different signal-to-noise ratio conditions;

[0086] Figure 4 This is a schematic diagram of the HRRP algorithm of the present invention;

[0087] Figure 5 A schematic diagram for reconstructing the backscattering electromagnetic characteristics;

[0088] Figure 6 shows a comparison of the linear phase parameter estimation results of the three MP algorithms under different signal-to-noise ratios;

[0089] Figure 7 shows a comparison of the fixed phase parameter estimation results of the three MP algorithms under different signal-to-noise ratios;

[0090] Figure 8 shows a comparison of the linear phase parameter estimation results of the three types of MUSIC algorithms under different signal-to-noise ratios;

[0091] Figure 9 shows a comparison of the fixed phase parameter estimation results of the three types of MUSIC algorithms under different signal-to-noise ratios;

[0092] Figure 10 For missile CAD model;

[0093] Figure 11 This represents the fitting result of high-frequency subband fusion using the MP algorithm.

[0094] Figure 12 This represents the full-band fusion fitting result of the MP algorithm;

[0095] Figure 13 A comparison chart of HRRP results across different bands;

[0096] Figure 14 Comparison of computational complexity under different L conditions. Detailed Implementation

[0097] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0098] Example:

[0099] See attached document Figure 1-14 As shown, a radar band fusion and extension method based on MP and Root-MUSIC algorithms includes:

[0100] Step 1: Set up two adjacent radars with the same observation angle but different operating frequencies. Therefore, for a stationary target composed of scattering centers, establish an all-polar GTD model of low-frequency and high-frequency electromagnetic echoes. Specifically, this includes:

[0101] Step 1.1: In the high-frequency region, the backscattered electromagnetic echo of a radar target can be considered as the total response of multiple scattering center echoes. The echo characteristics of these scattering centers can be accurately described using the GTD model. In this embodiment, two adjacent radars are set up, both operating at the same observation angle but with different operating frequencies. Therefore, for a stationary target composed of scattering centers, the electromagnetic echoes of the two sub-bands can be expressed as:

[0102]

[0103]

[0104] In the formula: S1 is the low-frequency wavelet echo, S2 is the high-frequency wavelet echo, and f m and f' m’ f0 and f 00 f represents the initial operating frequencies of the low-frequency and high-frequency subbands, respectively. m =f0+(m-1)Δf and f' m’ =f 00 +(m'-1)Δf represents the mth and m'th frequency points, respectively, and M1 and M2 represent the total number of frequency points in the low-frequency and high-frequency sub-bands, respectively; r iIndicates the location of the scattering center, α i Indicates the scattering type, A i α represents the scattering intensity. i ∈[-1,-0.5,0,0.5,1] represents different typical scattering structures, c=3×10 8 m / s is the speed of light, β represents the fixed phase, η represents the linear phase, β and η represent the incoherent relationship between the low-frequency subband and the high-frequency subband, w(m) and w(m') represent the Gaussian white noise of the low-frequency subband and the high-frequency subband, respectively, I is the number of scattering centers, j is the imaginary unit, and Δf is the frequency step.

[0105] Step 1.2: When the operating bandwidth (the frequency difference of radar operation) is less than 10% of the center frequency, the following approximate value is achieved:

[0106] Δf / f0 << 1 (3)

[0107]

[0108] Step 1.3: Substitute equations (3)-(4) obtained in Step 2 into equations (1)-(2) to obtain the omnipolar GTD model for low-frequency and high-frequency electromagnetic echoes:

[0109]

[0110]

[0111] Step 2: The all-polar model is essentially a harmonic superposition problem, which can be solved using harmonic decomposition algorithms. In this embodiment, the traditional MP algorithm and Root-MUSIC algorithm are used to estimate the incoherent parameters η and β. However, the parameter performance of these two algorithms is poorly affected by the signal-to-noise ratio (SNR), resulting in low parameter estimation accuracy under low SNR conditions. To address this issue, this embodiment next designs an improved MP algorithm and an improved Root-MUSIC algorithm. The improved algorithms utilize echo data and its conjugate data, and both theoretical and simulation data verify the effectiveness of the improved algorithms. Specifically, this includes:

[0112] Based on step 1, the incoherence parameters, namely linear phase and fixed phase, are estimated using echo data and its conjugate data. Specific steps include:

[0113] Step 2.1: First, assume the low-frequency subband and high-frequency subband signal echoes are as follows:

[0114] Y1=(s1(1),s1(2),...,s1(M1)) T (7)

[0115] Y2=(s2(1),s2(2),...,s2(M2))T (8);

[0116] Let M1 = M2 = M, then the covariance matrices of Y1 and Y2 can be expressed as:

[0117]

[0118]

[0119] In the formula: A 1p and A 2p They represent M×I and / or the zero matrix of M×I, respectively; Λ1 and Λ2 represent I×I diagonal matrices; σ 2 Let I represent the noise variance, and let I represent the M×M identity matrix. For R Y1 eigenvalues ​​of the matrix For R Y2 eigenvalues ​​of the matrix;

[0120] Step 2.2: Construct the echo data matrix of equation (11-12) to fully utilize the conjugate information of echo signals from different sub-bands:

[0121]

[0122]

[0123] In the formula: L is the matrix bundle parameter, and J is an M×M permutation matrix, the expression of which is as follows:

[0124]

[0125] By combining the cross covariance and the covariance of different subbands, the following matrix is ​​constructed to fully utilize the information from the original electromagnetic scattering data and its conjugate form:

[0126]

[0127]

[0128] Step 2.3: In the construction and Then, SVD processing is performed on it, and the same steps as the traditional MP algorithm and the traditional Root-MUSIC algorithm are repeated to obtain linear phase and fixed phase, thus completing the sub-band confusion of different frequency bands. The specific steps are as follows:

[0129] Step 2.3.1: For the matrix and Perform eigenvalue decomposition:

[0130]

[0131]

[0132] Based on the MDL method, the signal is decomposed into a low-frequency subband signal subspace A. 11 and the noise subspace A of the high-frequency subband 22 :

[0133]

[0134]

[0135] In the formula: and These represent the signal subspace and noise subspace of the low-frequency subband, respectively. A2n2 and A2n2 represent the signal subspace and noise subspace of the high-frequency subband, respectively;

[0136] Step 2.3.2: Based on A in Step 2.3.1 11 and A 22 ,calculate

[0137]

[0138]

[0139] Step 2.3.3: Place a 1i or b 1i represent or The first column, Reexpressed as:

[0140]

[0141]

[0142] Step 2.3.4: Calculation The root closest to the unit circle was selected as the pole of the fully polarized GTD model. Finally, the amplitude was calculated using the least squares method. and

[0143] Step 2.3.5: Calculate the linear phase and fixed phase, and calculate the echo data for the two sub-bands. Specifically, the amplitude coefficients estimated by the MP algorithm are:

[0144]

[0145] The phase angle is:

[0146]

[0147] Based on expressions (24) and (25), we can conclude that:

[0148]

[0149] The fixed phase is calculated as follows:

[0150]

[0151] In the formula: ΔB=f 00 -f0;

[0152] Calculate the phase of incoherent subbands in the high-frequency region

[0153]

[0154] Comparison of theoretical performance between the algorithm of this invention and existing algorithms:

[0155] The Hankel constructed using the traditional MP algorithm and the Root-MUSIC algorithm can be understood as a matrix smoothing process, where the matrix can be expressed as...

[0156]

[0157] In the formula: The covariance matrix of the equivalent signal is expressed as follows:

[0158]

[0159] Compared with traditional algorithms, the improved algorithm of this invention makes fuller use of the signal subspace and can complete parameter extraction in a higher noise background. The equivalent spatial smoothing matrix of the method proposed in this invention can be expressed as:

[0160]

[0161] Calculate separately and

[0162]

[0163]

[0164]

[0165] In the formula: This represents the sum of the received power of the j-th subarray.

[0166]

[0167]

[0168] In obtaining and Based on this, the equivalent covariance matrix of the proposed algorithm can be obtained.

[0169]

[0170] To compare the signal energy and noise energy in the equivalent smoothing matrix of different algorithms, the equivalent signal-to-noise ratio is defined as... It is clear from the definition that the signal-to-noise ratio (SNR) decreases as noise increases. Therefore, when the equivalent SNR increases, the accuracy of parameter estimation also increases.

[0171] The equivalent signal-to-noise ratio of the traditional MP algorithm and the improved algorithm can be expressed as:

[0172]

[0173]

[0174] It is obvious that Therefore, it has been theoretically verified that the improved algorithm of this invention has better noise resistance than the traditional algorithm.

[0175] Step 3: Based on the linear and fixed phases obtained in Step 2, the coherent data is processed using an improved algorithm to estimate the poles and amplitudes of the broadband fully polarized model. Then, the fused signal across the entire frequency band is calculated using the original data from the low-frequency and high-frequency subbands. Specifically, this includes:

[0176] Step 3.1: Based on the linear phase and fixed phase estimated in Step 2, calculate the high-frequency sub-band as follows:

[0177]

[0178] Step 3.2: Process the coherent data from Step 2 using the improved algorithm to estimate the poles and amplitudes of the broadband fully polarized model, expressed as follows:

[0179]

[0180] In the formula: and M represents the estimated amplitude and poles, and M' represents the number of broadband frequencies;

[0181] Therefore, subband Electromagnetic scattering data can be expressed as:

[0182]

[0183] Step 3.3: To reduce estimation errors, calculate the fused signal across the entire frequency band using the raw data from the low or high frequency sub-bands. The expression for this signal is:

[0184]

[0185] Experimental simulation:

[0186] Experimental Analysis:

[0187] To compare the parameter estimation performance and multi-band fusion results of the traditional and improved algorithms, simulation experiments were conducted. The full frequency range was set to 7 GHz–10 GHz with a frequency step size of 10 MHz. The low-frequency and high-frequency ranges were 7 GHz–8 GHz and 9 GHz–10 GHz, respectively. This paper assumes the target consists of four scattering centers, and the corresponding parameters are shown in Table 1.

[0188] Table 1 Parameters of the four scattering centers

[0189]

[0190] Electromagnetic backscattering echo can be expressed as

[0191]

[0192] Based on the raw data obtained in step 3, the fused signal expression for the entire frequency band is calculated. s1(m) and s2(m) are selected as the low-frequency sub-band echo and the high-frequency sub-band echo, respectively, and can be expressed as follows:

[0193] s1(m)=s(m),m∈[1,M' / 3]

[0194] s2(m)=s(m),m∈[2M' / 3+1,M']

[0195] To simulate the incoherence between different subbands, a linear phase is added to the high-frequency subband s2(m). and a fixed phase To compare the parameter estimation performance of different algorithms, this paper analyzes the root-mean-square error (RMSE).

[0196] Defined as follows:

[0197]

[0198] In the formula: μ and K represent the estimated incoherent parameters, the preset parameters, and the Monte Carlo iteration, respectively.

[0199] Figure 2 and Figure 3The average RMSE of the incoherent parameters under different signal-to-noise ratios is given. Figure 4 Results of High Resolution Profile (HRRP) for Target. Figure 5 Figures 6-9 show the electromagnetic scattering response obtained by different methods, and the results of incoherent parameter estimation using different algorithms vary with the signal-to-noise ratio.

[0200] from Figure 2 and Figure 3 As can be seen, compared with the traditional MP algorithm and the traditional Root-MUSIC algorithm, the improved MP algorithm and Root-MUSIC algorithm of this invention have better estimation performance, especially under low signal-to-noise ratio conditions, where the performance improvement is more significant. Furthermore, the difference in the RMSE curves for fixed phase between the traditional MP (Root-MUSIC) algorithm and the improved MP (Root-MUSIC) algorithm is larger than the difference in the RMSE curves for linear phase.

[0201] from Figure 4 As can be seen, the target's HRRP plot has four poles, meaning the target can be equivalent to four scattering centers. However, due to limited resolution, the first and second peaks of the low-frequency and high-frequency subbands cannot be distinguished in the HRRP plot. The improved algorithm proposed in this paper can accurately extract these four poles, verifying the effectiveness of the proposed algorithm.

[0202] Depend on Figure 5 As can be seen, the improved algorithm achieves better fitting results for the target electromagnetic characteristics than the traditional algorithm. Figures 6-9 show that, under different signal-to-noise ratio conditions, the mean square error of the improved algorithm is consistently lower than that of the traditional algorithm.

[0203] Simulation results:

[0204] The performance of the algorithm of this invention was verified using FEKO simulation data. The simulation frequency was set to 7GHz to 10GHz, the frequency step size was 1MHz, and the incident angle was 120 degrees. A 0-degree incident angle represents the warhead orientation of the missile model. Figure 10 For missile CAD model, Figure 11 and Figure 12 The results of high-frequency subband fusion fitting and full-band fusion fitting of the improved MP method are presented respectively.

[0205] from Figure 11 As can be seen from the data, after coherent compensation, the estimation results of the high-frequency subband parameters are in good agreement with the actual situation. Figure 12 The fitting results between subband fusion and the original full band are shown. From Figure 13As can be seen, there are four poles across the entire band. From the low-frequency subband HRRP and high-frequency subband HRRP results, it can be observed that the second, third, and fourth peaks are slightly shifted to the right compared to the full-band HRRP results. Therefore, the proposed MP algorithm achieves an improvement in missile target range resolution.

[0206] Computational complexity analysis:

[0207] Table 2 details the computational complexity of constructing the covariance matrix using different algorithms. Furthermore, this paper... Figure 14 The results of computational complexity varying with latitude L are illustrated using curves. In the experiment, it is assumed that the frequency sampling points M = 101. As shown in Table 2, the improved method has higher computational complexity than the traditional method and the FB-based method. This is because the proposed method constructs a new covariance matrix, increasing the computational burden. Figure 14 This also demonstrates that the computational complexity of the proposed method is higher than the other two methods. However, the increased computational complexity of the proposed method is acceptable for multi-band fusion computation.

[0208] algorithm Complexity Traditional Algorithm (ML)(L+1) Based on FB algorithm <![CDATA[M 3 +(M-L)(L+1) 2 ]]> Improved Algorithm <![CDATA[M 3 +4(M-L) 2 (L+1) 3 ]]>

[0209] In summary, to address the poor parameter estimation performance of traditional algorithms under low signal-to-noise ratio conditions, this paper improves upon the conventional MP and MUSIC algorithms. The improved algorithms fully utilize the echo signal and its conjugate information, and enhance parameter estimation accuracy by constructing a new covariance matrix. Subsequently, theoretical analysis and experimental simulations validate the effectiveness and superiority of the proposed method. Experimental results show that the proposed algorithm achieves better parameter estimation performance and subband fusion results than the conventional MP and Root-MUSIC algorithms.

[0210] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for incoherent parameter estimation and multi-band fusion based on MP and Root-MUSIC algorithms, characterized in that: include: Step 1: Set up two adjacent radars with the same observation angle but different operating frequencies. For a stationary target composed of scattering centers, establish an all-polar GTD model of low-frequency and high-frequency electromagnetic echoes. Step 2: Based on Step 1, using the echo data and its conjugate data, the incoherence parameters, namely linear phase and fixed phase, are estimated; Step 2 specifically involves: Step 2.1: First, assume the low-frequency subband and high-frequency subband signal echoes are as follows: (7) (8)； set up ,but and The covariance matrix is ​​expressed as: (9) (10)； In the formula: Indicates the noise variance. express The identity matrix, For R Y1Y1 eigenvalues ​​of the matrix For R Y2Y2 eigenvalues ​​of the matrix; Step 2.2: Construct the echo data matrix of formula (11-12): (11) (12) In the formula: These are matrix bundle parameters. for The permutation matrix is ​​expressed as follows: (13) The cross covariance and the covariance of different subbands are combined to construct the matrix shown below: (14) (15)； Step 2.3: In the construction and Then, SVD processing is performed on it, and the same steps as the traditional MP algorithm and the traditional Root-MUSIC algorithm are repeated to obtain linear phase and fixed phase, thus completing the sub-band confusion of different frequency bands; step 2.3 specifically includes: Step 2.3.1: For the matrix and Perform eigenvalue decomposition: (16) (17)； Based on the MDL method, the signal is decomposed into a low-frequency subband signal subspace A. 11 and the noise subspace A of the high-frequency subband 22 : (18) (19) In the formula: and These represent the signal subspace and noise subspace of the low-frequency subband, respectively. and These represent the signal subspace and noise subspace of the high-frequency subband, respectively. Step 2.3.2: Based on A in Step 2.3.1 11 and A 22 ,calculate , : (20) (21)； Step 2.3.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] or represent or The first column, , Reexpressed as: (22) (23)； Step 2.3.4: Calculation , The root closest to the unit circle was selected as the pole of the fully polarized GTD model. Finally, the amplitude was calculated using the least squares method. and ; Step 2.3.5: Calculate the linear phase and fixed phase, and calculate the echo data for the two sub-bands; Step 3: Based on the linear phase and fixed phase obtained in Step 2, the coherent data is processed using an improved algorithm to estimate the poles and amplitude of the broadband full polarization model. Then, the fused signal of the entire frequency band is calculated using the original data of the low-frequency subband and the high-frequency subband.

2. The method for incoherent parameter estimation and multi-band fusion based on MP and Root-MUSIC algorithms according to claim 1, characterized in that: Step 1 includes: Step 1.1: Set up two adjacent radars, both operating at the same observation angle but with different operating frequencies. Therefore, for a stationary target composed of scattering centers, the electromagnetic echoes of the two sub-bands can be represented as: (1) (2) In the formula: S1 is the low-frequency wavelet echo, and S2 is the high-frequency wavelet echo. and , and These represent the initial operating frequencies of the low-frequency and high-frequency sub-bands, respectively. and They are the mth and There are several frequency points, where M1 and M2 represent the total number of frequency points in the low-frequency and high-frequency sub-bands, respectively; r i Indicates the location of the scattering center, α i Indicates the scattering type, A i Indicates scattering intensity. These represent different typical scattering structures. It represents the speed of light, β represents a fixed phase, η represents a linear phase, and β and η represent the incoherent relationship between the low-frequency subband and the high-frequency subband. and These represent Gaussian white noise in the low-frequency and high-frequency subbands, respectively, where I is the number of scattering centers and j is the imaginary unit. For frequency stepping; Step 1.2: When the operating bandwidth is less than 10% of the center frequency, the following approximate value is achieved: (3) (4)； Step 1.3: Substitute equations (3)-(4) obtained in Step 2 into equations (1)-(2) to obtain the omnipolar GTD model for low-frequency and high-frequency electromagnetic echoes: (5) (6)。 3. The method for incoherent parameter estimation and multi-band fusion based on MP and Root-MUSIC algorithms according to claim 2, characterized in that: The specific steps of step 2.3.5 are as follows: The amplitude coefficients estimated by the MP algorithm are: (24)； The phase angle is: (25)； Based on expressions (24) and (25), we can conclude that: (26)； The fixed phase is calculated as follows: (27) In the formula: , ; Calculate the phase of incoherent subbands in the high-frequency region : (28)。 4. The method for incoherent parameter estimation and multi-band fusion based on MP and Root-MUSIC algorithms according to claim 3, characterized in that: Step 3 specifically includes: Step 3.1: Based on the linear phase and fixed phase estimated in Step 2, calculate the high-frequency sub-band as follows: (29)； Step 3.2: Process the coherent data from Step 2 using the improved algorithm to estimate the poles and amplitudes of the broadband fully polarized model, expressed as follows: (30) In the formula: and Represents the estimated magnitude and extreme points. This represents the number of frequencies in the broadband. Therefore, subband Electromagnetic scattering data can be expressed as: (31)； Step 3.3: To reduce estimation errors, calculate the fused signal across the entire frequency band using the raw data from the low or high frequency sub-bands. The expression is: (32)。

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