Time delay estimation method of multipath clutter of external radiating radar based on atomic norm

Abstract

The present invention discloses a method for estimating the time delay of multipath clutter of an external radiation source radar based on an atomic norm, which belongs to the field of digital signal processing. The implementation method of the present invention is as follows: the monitoring signal and the reference signal are sampled and time-synchronized at equal rates, and the channel frequency domain response of the monitoring signal is calculated; the sparsity of the channel frequency domain response of the monitoring signal in the atomic set is utilized, and the sparsity of the reconstructed signal is constrained by joint optimization to minimize the atomic norm as the goal, thereby reconstructing a noise-free channel frequency domain response; the dual polynomial of the channel frequency domain response is calculated, and the frequency support set of the channel frequency domain response of the monitoring signal is found. According to the obtained frequency support set, the fractional time delay estimate of the multipath clutter of the external radiation source radar is obtained, thereby realizing the time delay estimation of the multipath clutter of the external radiation source radar. The present invention can effectively estimate the fractional time delay of the multipath clutter, is more conducive to removing the interference of the clutter, and thus better realizes the detection of the external radiation source radar target.

Description

Technical Field

[0001] The invention relates to a time delay estimation method for multipath clutter of external radiation source radar based on atomic norm, and belongs to the field of digital signal processing. Background Art

[0002] Delay estimation is a key research topic in digital signal processing, with widespread applications in fields such as radar, sonar, biomedical engineering, and geophysics. For example, in exo-radio radar target detection, the monitoring channel contains not only weak target echoes but also strong multipath clutter, often distributed over non-integer delays. Existing clutter suppression methods are limited to clutter with delays that are integer multiples of the sampling period and cannot effectively suppress clutter with fractional delays, posing a significant challenge to exo-radio radar detection.

[0003] Currently, there are four main methods for delay estimation. First, the delay estimation method based on correlation theory. This method estimates the time difference of the signals by the peak position of the cross-correlation function of the received signals. This method has a simple process and is easy to implement, but it requires the signal and noise to be stationary and uncorrelated, making it significantly affected by noise. Second, the delay estimation method based on high-order cumulants. This method exploits the property that the cumulants of Gaussian processes above the second order are always zero, making it suitable for delay estimation of non-Gaussian signals in a Gaussian noise background. Third, the parameter estimation method. This method requires the known probability density function of the signal and is computationally intensive. Fourth, the delay estimation method based on spatial spectrum estimation. Its basic principle is to perform eigenvalue decomposition of the covariance matrix constructed from the received signal and calculate the delay estimate using the orthogonality of the signal and noise subspaces. Although this type of algorithm has high resolution, it is computationally intensive and performs well only when the signal spectrum is flat or nearly flat. In recent years, research has also introduced machine learning algorithms such as neural networks and genetic algorithms into delay estimation to improve the accuracy of delay estimation.

[0004] Existing delay estimation methods are limited in accuracy by the sampling frequency, and can only estimate delay values ​​that are integer multiples of the sampling period, resulting in low accuracy. To effectively estimate fractional delays, the sampling frequency can be increased or the data length can be increased, but this increases the requirements for system hardware and software, limiting their practical application. Therefore, fractional delay estimation algorithms have attracted considerable attention. A key issue is how to overcome the limitations of the sampling frequency and make fractional delay estimation methods practical. Summary of the Invention

[0005] The present invention discloses a method for estimating the time delay of multipath clutter of an external radiation source radar based on an atomic norm. The technical problem to be solved is: utilizing the sparsity of the channel frequency domain response of the monitoring signal in an atomic set, ensuring the continuity of the estimated signal in the frequency domain based on the atomic norm, and realizing fractional time delay estimation of multipath clutter of an external radiation source radar without increasing the sampling frequency or the data length, even in the case of data missing or compressed sampling.

[0006] The purpose of the present invention is achieved through the following technical solutions.

[0007] The present invention discloses a method for estimating the time delay of multipath clutter of an exo-radiation radar based on an atomic norm. The method samples a monitoring signal and a reference signal at equal rates and performs time synchronization processing, and calculates the channel frequency domain response of the monitoring signal. The method utilizes the sparsity of the channel frequency domain response of the monitoring signal in an atomic set, and constrains the sparsity of the reconstructed signal by jointly optimizing the minimum atomic norm as the goal, thereby reconstructing a noise-free channel frequency domain response. The method calculates the dual polynomial of the channel frequency domain response, finds the frequency support set of the channel frequency domain response of the monitoring signal, and obtains the fractional time delay estimate of the multipath clutter of the exo-radiation radar based on the obtained frequency support set, thereby realizing the time delay estimation of the multipath clutter of the exo-radiation radar. The method can effectively estimate the fractional time delay of the multipath clutter, is more conducive to removing the interference of the clutter, and thus better realizes the detection of the exo-radiation radar target.

[0008] The present invention discloses a method for estimating time delay of multipath clutter of external radiation source radar based on atomic norm, comprising the following steps:

[0009] Step 1: Perform equal-rate sampling and time synchronization processing on the monitoring signal and the reference signal to obtain a time-synchronized monitoring time-domain signal s(t) and a reference time-domain signal r(t).

[0010] The reference time domain signal expression is,

[0011] r(t)=a0d(t)+n ref (t) (1)

[0012] Where d(t) is the direct wave time domain signal, a0 is its complex amplitude, and n ref (t) is the reference channel noise.

[0013] The monitoring time domain signal expression is:

[0014]

[0015] Where d(t) is the direct wave time domain signal, γ0 is its complex amplitude, The delay is The complex amplitude of multipath clutter, N mis the number of multipath clutter, α0 is the target complex amplitude with a delay of τ0, f d is the target Doppler, n surv (t) is the monitoring channel noise.

[0016] Step 2: Perform fast Fourier transform (FFT) on the reference time domain signal r(t) obtained in step 1 to obtain a reference frequency domain signal R(k); perform FFT on the monitoring time domain signal s(t) obtained in step 1 to obtain a monitoring frequency domain signal S(k); compare the monitoring frequency domain signal S(k) with the reference frequency domain signal R(k) to obtain the channel frequency domain response G(k) of the monitoring signal.

[0017] Step 2.1: Perform FFT on the reference time domain signal r(t) to obtain the reference frequency domain signal expression as shown below:

[0018] R(k)=CD(k)+N ref (k), k=1,2,...,N (3)

[0019] Where D(k) is the direct wave frequency domain signal, C is its complex amplitude, and N ref (k) is the reference channel noise, and N is the number of FFT points.

[0020] Step 2.2: Perform FFT on the monitoring time domain signal s(t) to obtain the monitoring frequency domain signal expression as shown below:

[0021]

[0022] Where D(k) is the direct wave frequency domain signal, Its complex amplitude, f s is the sampling rate, is the complex amplitude of the mth clutter, k d is the target's Doppler, β0 is the target's complex amplitude, N surv (k) is the monitoring channel noise.

[0023] Step 2.3: Calculate the channel frequency domain response of the monitoring signal. The calculation formula of the channel frequency domain response G(k) of the monitoring signal is as follows:

[0024] G(k)=S(k) / R(k) (5)

[0025] Step 3: Using the sparsity of the channel frequency domain response of the monitoring signal in the atomic set, the sparsity of the reconstructed signal is constrained by joint optimization to minimize the atomic norm as the goal, and the noise-free channel frequency domain response Q(k) is reconstructed.

[0026] The channel frequency domain response expression of the monitoring signal is as follows:

[0027] G(k)=Q(k)+N G (k) (6)

[0028] Where Q(k) is the noise-free channel frequency domain response, N G (k) is noise.

[0029] Atomic norm-based denoising is achieved by solving the joint optimization problem of the following formula:

[0030]

[0031] Among them, ||·|| A is the atomic norm, τ is the regularization operator, and the relationship between it, the noise variance σ and the number of sampling points N is:

[0032] Step 4: Use the noise-free channel frequency domain response vector obtained by step 3 optimization Obtain the dual vector U of the noise-free channel frequency domain response.

[0033] Among them, the calculation formula of the dual vector U is,

[0034]

[0035] Step 5: Use the dual vector obtained in step 4 to obtain the dual polynomial through FFT calculation, then find the frequency position when the polynomial modulus is 1 as the harmonic frequency support set, and obtain the fractional delay estimate of the external radiation source radar multipath clutter based on the obtained frequency support set.

[0036] The method further includes step 6, wherein an adaptive filtering algorithm is used according to the fractional time delay of the multipath clutter of the external radiation source radar obtained in step 5, so as to be more conducive to removing the interference of the clutter and improving the detection accuracy of the external radiation source radar.

[0037] Beneficial effects:

[0038] 1. The present invention discloses a method for estimating the time delay of multipath clutter of an exo-radiation source radar based on the atomic norm. This method utilizes the sparsity of the channel frequency domain response of the monitoring signal in an atomic set and uses the minimization of the atomic norm as the goal to constrain the sparsity of the reconstructed signal. It can also ensure the continuity of the signal in the frequency domain and avoid additional errors caused by frequency domain discretization. Without increasing the sampling frequency or increasing the data length, and even in the case of data missing or compressed sampling, the fractional time delay estimation of multipath clutter of an exo-radiation source radar can be achieved based on the atomic norm.

[0039] 2. The atomic norm-based delay estimation method for exo-radiation radar multipath clutter disclosed in the present invention utilizes the fractional delay estimation results of exo-radiation radar multipath clutter, combined with an adaptive filtering algorithm, to suppress multipath clutter and improve the detection accuracy of exo-radiation radar targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a delay estimation flow chart in an embodiment of the present invention's "delay estimation method for multipath clutter of external radiation source radar based on atomic norm."

[0041] Figure 2 It is a schematic diagram of the structure of an external radiation source radar system in an embodiment of the present invention's "time delay estimation method for multipath clutter of external radiation source radar based on atomic norm".

[0042] Figure 3 It is a channel time domain response diagram of the monitoring signal in the embodiment of the "Time Delay Estimation Method for External Radar Multipath Clutter Based on Atomic Norm" of the present invention.

[0043] Figure 4 It is a channel time domain response diagram of the monitoring signal constructed by the atomic norm in the embodiment of the "Time Delay Estimation Method for External Radar Multipath Clutter Based on the Atomic Norm" of the present invention.

[0044] Figure 5 This is a diagram of the delay estimation result based on the atomic norm in the embodiment of the "delay estimation method for multipath clutter of external radiation source radar based on the atomic norm" of the present invention. DETAILED DESCRIPTION

[0045] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific examples. It should be pointed out that the described embodiments are only intended to facilitate the understanding of the present invention and do not serve any limiting role.

[0046] In the embodiment of the present invention, the signal is a digital television terrestrial broadcasting (DTTB) signal in a single-carrier mode, with a bandwidth of 7.56 MHz and a receiving end sampling rate of 9 MHz.

[0047] like Figure 1 As shown, the method for estimating time delay of multipath clutter of external radiation source radar based on atomic norm disclosed in this embodiment is specifically implemented as follows:

[0048] Step 1: Perform equal-rate sampling and time synchronization processing on the monitoring signal and the reference signal to obtain the time-synchronized monitoring time-domain signal s(t) and reference time-domain signal r(t). Figure 2 shown.

[0049] The reference time domain signal expression is,

[0050] r(t)=a0d(t)+n ref (t) (1)

[0051] Where d(t) is the direct wave time domain signal, a0 is its complex amplitude, and n ref (t) is the reference channel noise.

[0052] Step 2: Perform FFT on the reference time domain signal r(t) obtained in step 1 to obtain a reference frequency domain signal R(k); use the obtained reference frequency domain signal to simulate the monitoring frequency domain signal S(k); compare the monitoring frequency domain signal S(k) with the reference frequency domain signal R(k) to obtain the channel frequency domain response G(k) of the monitoring signal.

[0053] Perform FFT on the reference time domain signal r(t) to obtain the reference frequency domain signal R(k) as shown below:

[0054] R(k)=CD(k)+N ref (k), k=1,2,...N (3)

[0055] Where D(k) is the direct wave frequency domain signal, C is its complex amplitude, and N ref (k) is the reference channel noise, and N is the number of FFT points.

[0056] Here, four clutters are used to simulate the monitoring signal. The clutter parameters are shown in Table 1.

[0057] Table 1 Monitoring signal clutter simulation parameters

[0058]

[0059] The expression of the monitoring frequency domain signal S(k) is,

[0060]

[0061] Where D(k) is the direct wave frequency domain signal, is the delay of the mth clutter, f s is the sampling rate, is the relative amplitude of the mth clutter, N m is the number of multipath clutter, N surv (k) is the monitoring channel noise.

[0062] Calculate the channel frequency domain response of the monitoring signal. The calculation formula of the channel frequency domain response G(k) of the monitoring signal is as follows:

[0063] G(k)=S(k) / R(k) (5)

[0064] Step 3: Utilizing the sparsity of the channel frequency domain response of the monitoring signal in the atomic set, the sparsity of the reconstructed signal is constrained by joint optimization to minimize the atomic norm as the goal, and the noise-free channel frequency domain response Q(k) is reconstructed.

[0065] The channel frequency domain response expression of the monitoring signal is as follows:

[0066] G(k)=Q(k)+N G (k) (6)

[0067] Where Q(k) is the noise-free channel frequency domain response, N G (k) is noise.

[0068] Atomic norm-based denoising is achieved by solving the joint optimization problem of the following formula:

[0069]

[0070] Among them, ||·|| A is the atomic norm, τ is the regularization operator, and the relationship between it, the noise variance σ and the number of sampling points N is:

[0071] Perform fast inverse Fourier transform on G(k) and Q(k) respectively, and the transformation results are as follows Figure 3 and Figure 4 As shown in the figure, by comparing the two figures, it can be seen that the atomic norm can effectively reconstruct the noise-free signal, which illustrates the robustness of the reconstruction algorithm based on the atomic norm.

[0072] Step 4: Use the noise-free channel frequency domain response vector obtained by step 3 optimization Obtain the dual vector U of the noise-free channel frequency domain response.

[0073] Among them, the calculation formula of the dual vector U is,

[0074]

[0075] Step 5: Using the dual vector obtained in step 4, calculate the dual polynomial through FFT, and then find the frequency position when the polynomial modulus is 1 as the harmonic frequency support set. Based on the obtained frequency support set, the fractional delay estimate of the multipath clutter of the external radiation source radar is obtained. The estimation result is as follows: Figure 5 As shown in Table 1, it can be seen that this embodiment can effectively estimate the fractional delay of the multipath clutter of the external radiation source radar.

[0076] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating time delay of multipath clutter from external radiation source radar based on atomic norm, characterized by: The following steps are included: Step 1: Perform equal-rate sampling and time synchronization processing on the monitoring signal and the reference signal to obtain a time-synchronized monitoring time-domain signal s(t) and a reference time-domain signal r(t); Step 2: Perform a fast Fourier transform (FFT) on the reference time domain signal r(t) obtained in step 1 to obtain a reference frequency domain signal R(k); perform an FFT on the monitoring time domain signal s(t) obtained in step 1 to obtain a monitoring frequency domain signal S(k); compare the monitoring frequency domain signal S(k) with the reference frequency domain signal R(k) to obtain the channel frequency domain response G(k) of the monitoring signal; Step 3: Utilizing the sparsity of the channel frequency domain response of the monitoring signal in the atom set, the sparsity of the reconstructed signal is constrained by joint optimization to minimize the atomic norm as the goal, and the noise-free channel frequency domain response Q(k) is reconstructed. Step 4: Use the noise-free channel frequency domain response vector obtained by step 3 optimization Obtain the dual vector U of the noise-free channel frequency domain response; Step 5: Use the dual vector obtained in step 4 to obtain the dual polynomial through FFT calculation, then find the frequency position when the polynomial modulus is 1 as the harmonic frequency support set, and obtain the fractional delay estimate of the external radiation source radar multipath clutter based on the obtained harmonic frequency support set.

2. The method for estimating time delay of multipath clutter of external radiation source radar based on atomic norm according to claim 1, characterized in that: The method further includes step 6, wherein an adaptive filtering algorithm is used according to the fractional time delay of the multipath clutter of the external radiation source radar obtained in step 5, so as to be more conducive to removing the interference of the clutter and improving the detection accuracy of the external radiation source radar.

3. The method for estimating time delay of multipath clutter of external radiation source radar based on atomic norm according to claim 1 or 2, characterized in that: The implementation method of step one is: The reference time domain signal expression is, r(t)=a0d(t)+n ref (t) (1) Where d(t) is the direct wave time domain signal, a0 is its complex amplitude, and n ref (t) is the reference channel noise; The monitoring time domain signal expression is: Where d(t) is the direct wave time domain signal, γ0 is its complex amplitude, The delay is The complex amplitude of multipath clutter, N m is the number of multipath clutter, α0 is the target complex amplitude with a delay of τ0, f d is the target Doppler, n surv (t) is the monitoring channel noise.

4. The method for estimating time delay of multipath clutter of external radiation source radar based on atomic norm according to claim 3, characterized in that: The implementation method of step 2 is: Step 2.1: Perform FFT on the reference time domain signal r(t) to obtain the reference frequency domain signal expression as shown below: R(k)=CD(k)+N ref (k),k=1,2,...,N (3) Where D(k) is the direct wave frequency domain signal, C is its complex amplitude, and N ref (k) is the reference channel noise, N is the number of FFT points; Step 2.2: Perform FFT on the monitoring time domain signal s(t) to obtain the monitoring frequency domain signal expression as shown below: Where D(k) is the direct wave frequency domain signal, Its complex amplitude, f s is the sampling rate, is the complex amplitude of the mth clutter, k d is the target's Doppler, β0 is the target's complex amplitude, N surv (k) is the monitoring channel noise; Step 2.3: Calculate the channel frequency domain response of the monitoring signal. The calculation formula of the channel frequency domain response G(k) of the monitoring signal is as follows: G(k)=S(k) / R(k) (5).

5. The method for estimating time delay of multipath clutter of external radiation source radar based on atomic norm according to claim 4, characterized in that: The implementation method of step three is: The channel frequency domain response expression of the monitoring signal is as follows: G(k)=Q(k)+N G (k) (6) Where Q(k) is the noise-free channel frequency domain response, N G (k) is noise; Atomic norm-based denoising is achieved by solving the joint optimization problem of the following formula: Among them, ||·|| A is the atomic norm, τ is the regularization operator, and the relationship between it, the noise variance σ and the number of sampling points N is:

6. The method for estimating time delay of multipath clutter of external radiation source radar based on atomic norm according to claim 5, characterized in that: In step four, The calculation formula of the dual vector U is,

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