SAIR radio frequency interference source sparse estimation method based on sparse bayesian learning algorithm

Abstract

The application discloses a SAIR radio frequency interference source sparse estimation method based on a sparse Bayesian learning algorithm, and mainly solves the problems that the prior art is large in calculation amount, and is greatly influenced by single snapshot, low signal-to-noise ratio and the number of RFI and the like. The technical scheme realized by the application is that: interference measurement is carried out between sparse arrays to obtain visibility data, a complex model of synthetic aperture interferometric measurement is converted into a real model, and the expression of the mean value and the covariance of the brightness temperature is calculated; under the condition that the iteration condition is met, the hyperparameter and the noise variance are updated, and finally the estimation result of the brightness temperature is obtained; and the positioning information of the radio frequency interference source is acquired by using the estimation result of the brightness temperature. The application can effectively identify the number of interferences, reduce the probability that the RFI recovery effect is poor, and effectively complete the RFI parameter estimation under the condition of single snapshot and low signal-to-noise ratio, and improve the positioning precision of the target.

Description

Technical Field

[0001] This invention belongs to the field of microwave technology, and more specifically relates to a sparse estimation method for radio frequency interference sources in a Synthetic Aperture Interferometric Radiometer (SAIR) based on a sparse Bayesian learning algorithm within the field of synthetic aperture microwave radiation measurement technology. This invention can be used to achieve super-resolution estimation of radio frequency interference sources. Background Technology

[0002] With the increasing frequency of human information activities and the rapid development of wireless communication methods, the massive amount of information exchange inevitably generates a large number of radio frequency interference (RFI) sources. In Earth remote sensing applications, the signals from the atmosphere and surface measured by microwave radiometers are inherently weak, resulting in severe RFI contamination of the observed information. This contamination is often caused by human factors, which can overwhelm the original microwave signal, making it difficult to extract accurate remote sensing information. The wide field of view and limited spatial frequency sampling of synthetic aperture radiometers lead to the Gibbs effect in imaging results, and RFI sources have a more significant impact on their performance. One approach to addressing the serious RFI problem in current synthetic aperture microwave radiometry applications is to achieve high-resolution RFI source localization, allowing national radio spectrum management authorities to forcibly shut down these illegal RFI sources. If shutting down RFI sources is not possible, then mitigation and suppression of RFI sources in the original data domain are necessary to achieve better performance than interference suppression algorithms in the visibility function domain and image domain. This relies on array synthesis technology for accurate estimation of the location and energy of RFI sources.

[0003] Huazhong University of Science and Technology proposed a method for locating radio frequency interference sources based on the reconstruction of a generalized augmented covariance matrix in its patent application "A Method for Locating Radio Frequency Interference Sources Based on the Reconstruction of a Generalized Augmented Covariance Matrix" (Application No.: 202111353176.1, Publication No.: CN 114200394 A). The implementation steps of this method are as follows: First, the original sparse array corresponding to the multi-sensor system is expanded to obtain a corresponding extended virtual array. Considering the size of the extended virtual array, the generalized extended array is obtained by relaxing the constraints of the array expansion model. Based on the positional correspondence between the differential array of the original sparse array and the differential array of the generalized extended array and the covariance matrix of the original sparse array, a generalized augmented covariance matrix is ​​constructed. Next, a reconstruction model of the generalized augmented covariance matrix is ​​established, and the generalized reweighted nuclear norm minimization algorithm is used to reconstruct the generalized augmented covariance matrix. Finally, a subspace class algorithm is used to estimate the angle of arrival of the reconstructed generalized augmented covariance matrix to obtain the radio frequency interference source location information. This method has two drawbacks. First, due to the virtual expansion of the original sparse array, the computational load is high, resulting in poor real-time performance. Furthermore, this method requires two steps, increasing its complexity. Second, while using the signal subspace method to acquire radio frequency interference source location information, it is sensitive to noise, and its imaging performance deteriorates further under low signal-to-noise ratio and single-shot conditions. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the existing technology by proposing a sparse estimation method for radio frequency interference sources (RFI) in synthetic aperture radiometers (SAIR) based on the Sparse Bayesian Learning (SBL) algorithm. This method solves the problems of high computational complexity, complex implementation steps, low signal-to-noise ratio, degraded imaging performance under single-shot conditions, and low RFI localization estimation accuracy in sparse arrays of SAIR.

[0005] The technical solution of this invention is as follows: Spatial frequency domain information of the radiation brightness temperature distribution within the field of view is obtained through correlation interferometry of an antenna array. The measured sample is called the visibility function. Since the number of RFI interferences in space is much smaller than the number of intervals in the entire spatial domain, satisfying the spatial sparsity characteristic, it can be considered as undersampling of the spatial angular intervals. The original signal is recovered from the visibility data using a sparse Bayesian learning algorithm, brightness temperature reconstruction is performed, RFI sparse estimation is completed, and RFI location information is obtained. Because this invention uses a sparse Bayesian learning algorithm and utilizes the detection data from correlation interferometry to identify interference, it relies only on visibility domain information. This overcomes the problems of cumbersome steps and high computational load caused by virtual expansion of sparse arrays in existing technologies, and avoids further processing of visibility data or sparse arrays. This greatly reduces the computational load and system complexity of the algorithm, making it more suitable for engineering applications. Because this invention uses a sparse Bayesian learning algorithm, it can process single-shot data and still has good resolution and stability even when the signal-to-noise ratio is relatively low. It overcomes the shortcomings of existing subspace-based algorithms, which can only process incoherent sources, require multiple-shot data, and suffer from underestimation or overestimation when the number of RFIs is unknown, as well as the defects of larger trailing under low signal-to-noise ratio conditions. This makes the estimation of radio frequency interference source parameters of the integrated aperture radiometer more accurate and more stable.

[0006] The implementation steps of this invention include the following:

[0007] Step 1: Convert the complex number model of the integrated aperture interferometry vector into a real number model;

[0008] Step 2: Use the sparse Bayesian learning algorithm to recover the brightness temperature data;

[0009] Step 2.1: Calculate the mean and covariance of the brightness temperature using the visibility data;

[0010] Step 2.2: Update hyperparameters and noise variance using visibility data;

[0011] Step 2.3: Determine whether the root mean square error of the current iteration meets the convergence condition or reaches the maximum number of iterations. If yes, execute step 2.1; otherwise, execute step 3 after obtaining the final recovery of the brightness temperature.

[0012] Step 3: Obtain the RFI positioning information using the recovered brightness temperature.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] First, because the present invention uses a sparse Bayesian learning algorithm to identify radio frequency interference using the detection data of related interference, it only relies on visibility domain information, avoiding the problems of cumbersome steps and large amount of computation caused by the virtual expansion of sparse arrays in the existing technology. It avoids further processing of visibility data or sparse arrays, which greatly reduces the computational load and system complexity of the algorithm, making it more suitable for engineering applications.

[0015] Secondly, because this invention uses a sparse Bayesian learning algorithm, it can process single snapshot data and still has good resolution and stability when the signal-to-noise ratio is low. This overcomes the shortcomings of existing subspace-based algorithms, which can only process incoherent sources, require multiple snapshot data, and suffer from underestimation or overestimation when the number of RFIs is unknown, resulting in greater trailing under low signal-to-noise ratio conditions. This makes the estimation of radio frequency interference source parameters of the integrated aperture radiometer more accurate and more stable. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0017] Figure 2 This is a result diagram from simulation experiment 1 of the present invention, wherein, Figure 2 (a) is the inversion image of SMOS measured data with RFI artificially added; Figure 2 (b) is a map showing the positioning estimation results obtained using existing technical methods; Figure 2 (c) is a spectrum obtained using existing technical methods; Figure 2 (d) is a map showing the positioning estimation results obtained using the method of the present invention;

[0018] Figure 3 This is a graph showing the relationship between RFI intensity and azimuth error obtained from simulation experiment 2 of this invention using both existing methods and the method of this invention.

[0019] Figure 4 This is a result diagram from simulation experiment 3 of the present invention, in which, Figure 4 (a) is the inversion image of the measured SMOS data; Figure 4 (b) is a map showing the positioning estimation results obtained using existing technical methods; Figure 4 (c) is a spectrum obtained using existing technical methods; Figure 4 (d) is a localization estimation result obtained using the method of the present invention. Detailed Implementation

[0020] The embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.

[0021] Reference Figure 1 The implementation steps of the embodiments of the present invention will be described in further detail below.

[0022] Step 1, the integrated aperture radiometer interferometric measurement model is as follows:

[0023] V = F·T + N

[0024] Where V represents the visibility data composed of snapshot data received by all sparse antenna arrays, T represents the brightness temperature value composed of sampled values ​​of all spatial frequency domain information, F is the measurement matrix, and N is the noise vector.

[0025]

[0026] Where F represents the measurement matrix, e [·] For exponential operations with the natural constant e as the base, j is the imaginary unit, π is pi, and u ij and v ij Let (ξ,η) be the baseline vectors corresponding to the i-th and j-th antennas, respectively, and let (ξ,η) be the direction cosines.

[0027] Visibility data is obtained from the following formula:

[0028]

[0029] Among them, V ij T represents the visibility data between the i-th antenna and the j-th antenna. M (ξ,η) represents the scene modify brightness temperature at the cosine of the (ξ,η) direction.

[0030] The complex model of integrated aperture interferometry is transformed into a real model as follows:

[0031]

[0032] in, Visibility data under a real number model. The brightness temperature in the real number model. Let R(·) be the measurement matrix under the real number model, where R(·) represents the operation of taking the real part and I(·) represents the operation of taking the imaginary part.

[0033] Step 2: Use the sparse Bayesian learning algorithm to recover the brightness temperature data.

[0034] Step 2.1, the formulas for calculating the covariance and mean of the estimated brightness temperature are as follows:

[0035]

[0036]

[0037] Where ∑ is the covariance of the estimated brightness temperature, α0 is the noise variance, and A is the diagonal matrix of the hyperparameter α, A=diag(α1,α2,…,α 2N ), and α i =α i+N Let i = 1, 2, ..., 2N, where N is the number of columns in the measurement matrix under the complex model. -1 This indicates the inverse operation, where μ is the mean of the estimated brightness temperature, (·). T This indicates the transpose operation.

[0038] Step 2.2, the formulas for updating hyperparameters and noise variance are as follows:

[0039]

[0040]

[0041] in, This represents the hyperparameters after the i-th iteration update. To estimate the i1th element of the mean brightness temperature, To estimate the i2th element of the brightness temperature covariance matrix; i, i1, and i2 all have the same value and each represents the current iteration number. Tr[·] represents the updated noise variance, and Tr[·] represents the trace of the matrix.

[0042] Step 2.3: Determine whether the root mean square error of the current iteration meets the convergence condition or reaches the maximum number of iterations. If yes, execute step 2.1; otherwise, execute step 3 after obtaining the final recovery of the brightness temperature.

[0043] The convergence condition is that the root mean square error between the mean vector obtained in the current iteration and the mean vector obtained in the previous iteration is less than or equal to a threshold. The value of this threshold depends on the accuracy to be achieved in the estimation. A maximum number of iterations is set to prevent entering an iterative infinite loop. In an embodiment of the invention, the threshold is set to e. -5 The maximum number of iterations is 1000.

[0044] Given the noise variance and hyperparameters, the final recovery of the brightness temperature is expressed as follows:

[0045]

[0046] in, This is for the final restoration of the brightness temperature.

[0047] Step 3: The location information of the radio frequency interference source is obtained by finding the location corresponding to the maximum brightness temperature point after the brightness temperature is recovered, and this location is used as the location of the radio frequency interference source.

[0048] The effects of this invention will be further illustrated below with simulation experiments:

[0049] 1. Simulation experimental conditions:

[0050] The software platform for the simulation experiment of this invention is: Windows 10 operating system and MATLAB R2018b.

[0051] The visibility data used in this invention is SMOS (Soil Moisture and Ocean Salinity) Level 1a data downloaded from the ESA website. Here, you can select the specific year and month to download. The format is DBL file. After downloading, use the SMOS Artificial Scene Library software downloaded from the ESA website to preview. After previewing, select the required visibility data to export. The exported format is txt.

[0052] The simulation experiment data 1 of this invention is the SMOS measured data with a snapshot number of 18-Aug-2013 00:01:58, with an artificially added radio frequency interference source with a radiation intensity of 400K at the azimuth (0.4,0.2).

[0053] The simulation data 2 of this invention is the SMOS measured data with a snapshot number of 18-Aug-2013 00:01:58. 100 Monte Carlo experiments were performed at the azimuth (0.4, 0.2), and the radio frequency interference source change range was [360K-500K].

[0054] Data 3 from the simulation experiment of this invention is the measured SMOS data with a snapshot count of 18-Aug-2013 00:28:37.

[0055] 2. Simulation content and result analysis.

[0056] The simulation experiments of this invention are three.

[0057] Simulation Experiment 1 uses the method of this invention and existing technology (MUSIC algorithm) to estimate and locate data 1, and the results are as follows. Figure 2 As shown.

[0058] In simulation experiment 1, one existing technology used is:

[0059] In their paper "Accurate geolocation of RFI sources in smosimagery based on superresolution algorithms" (IEEE 2014 Expert Conference on Microwave Radiation and Environmental Remote Sensing, pp. 29-32), Park H and Camps A first proposed a subspace method (MUSIC algorithm) based on the orthogonality of noise eigenvectors and signal steering vectors. The specific steps of this method are: First, construct a covariance matrix, where the elements of the covariance are equivalent to visibility samples, i.e., the cross-correlation of the antenna pair outputs; second, perform eigenvalue decomposition on the covariance matrix to obtain the noise subspace; third, search for spectral peaks, where the direction of the RFI is determined by local maxima; finally, georeference the direction of the RFI source.

[0060] Simulation Experiment 2 of this invention uses the method of this invention and existing technology (MUSIC algorithm) to estimate and locate data 2, respectively, and obtains the curves of RFI intensity versus azimuth mean square error after 100 Monte Carlo experiments. The results are as follows: Figure 3 As shown.

[0061] In simulation experiment 2, the same existing technology as in simulation experiment 1 is used.

[0062] Simulation Experiment 3 of this invention uses the method of this invention and existing technology (MUSIC algorithm) to estimate and locate data 3, and the results are as follows. Figure 4 As shown.

[0063] In simulation experiment 2, the same existing technology as in simulation experiment 1 is used.

[0064] The following is combined with Figure 2 , Figure 3 , Figure 4 The simulation diagrams further illustrate the effects of the present invention.

[0065] Figure 2 (a) Add the inversion image of the 400K RF interference source to the SMOS data with snapshot number 18-Aug-2013 00:01:58. Figure 2 (b) An inversion plot of the estimated data from Experiment 1 using existing techniques. Figure 2 (c) is a spectrum obtained by estimating the measured data in Experiment 1 using existing technology. Figure 2 (d) is a graph showing the result of sparse estimation of the measured data in Experiment 1 using the method of this invention. Figure 3 The diagram shows the orientation error results after 100 Monte Carlo experiments using existing technology and the technology of this invention, respectively. Figure 4(a) is the inversion image of the SMOS measured data with a snapshot number of 18-Aug-2013 00:28:37. Figure 4 (b) A graph showing the results of estimating the measured data in Experiment 3 using existing techniques. Figure 4 (c) is a spectrum obtained by estimating the measured data in Experiment 1 using existing technology. Figure 4 (d) is a graph showing the result of sparse estimation of the measured data in Experiment 2 using the method of the present invention.

[0066] Figure 2 (a) Figure 2 (b) Figure 2 In (d), the horizontal axis represents azimuth ξ, and the vertical axis represents azimuth η. The hexagons in all three images represent the field of view plane; the darker areas in the images represent the Earth's background brightness temperature, and the point sources slightly brighter than the background brightness temperature are RFI point sources. The long color plot on the right side of the images is a color scale filling the hexagonal field of view. Figure 2 (a) Figure 2 (d) indicates that the brightness temperature range is [0K-600K]. Figure 2 (d) shows the normalized peak value, ranging from [0-1], in dB; Figure 2 (c) The horizontal axis represents the composition of the field of view, and the vertical axis represents the normalized peak value.

[0067] Depend on Figure 2 (b) It can be seen that the inversion results after locating the radio frequency interference source using the existing technology show a large trailing effect, which further deteriorates the imaging performance. The azimuth of the maximum spectral peak is (0.1995, 0.3037), and the azimuth mean square error is 0.3532.

[0068] Depend on Figure 2 (c) It can be seen that the spectral peak diagram after locating the radio frequency interference source using existing technology shows patches of spectral peaks, which corresponds to... Figure 2 (b) The trailing effect in the inverted image is mainly due to the weak RFI being not much different from the Earth background scene, which reduces the accuracy of the covariance matrix and subspace estimation.

[0069] Depend on Figure 2 (d) It can be seen that in the inversion result diagram using the method of the present invention, only one obvious RFI point is seen, and the estimated azimuth is (0.3991, 0.2095), with a mean square error of 0.0095, which is better than the prior art.

[0070] Figure 3The horizontal axis represents the RFI intensity in K, and the vertical axis represents the azimuth mean square error. The pink curve, marked with a square, represents the relationship between the azimuth mean square error and the RFI intensity obtained using existing simulation techniques, while the blue curve, marked with a star, represents the relationship between the azimuth mean square error and the RFI intensity obtained using the method proposed in this invention.

[0071] from Figure 3 It can be seen that, under the same RFI intensity, the azimuth mean square error obtained by the method of the present invention is always smaller than the mean square error obtained by simulation in the prior art.

[0072] Figure 4 (a) Figure 4 (b) Figure 4 In (d), the horizontal axis represents azimuth ξ, and the vertical axis represents azimuth η. The hexagons in all three images represent the field of view plane; the darker areas in the images represent the Earth's background brightness temperature, and the point sources slightly brighter than the background brightness temperature are RFI point sources. The long color plot on the right side of the images is a color scale filling the hexagonal field of view. Figure 4 (a) Figure 4 (d) indicates that the brightness temperature range is [-250K-350K]. Figure 4 (d) shows the normalized peak value, ranging from [0-1], in dB; Figure 4 (c) The horizontal axis represents the composition of the field of view, and the vertical axis represents the normalized peak value.

[0073] Depend on Figure 4 (b) It can be seen that the inversion result map after locating the radio frequency interference source using the existing technology has a large trailing effect, and the imaging performance is further deteriorated. Figure 4 The obvious RFI source appearing in (b) and Figure 4 (a) The location of the RFI varies considerably in the inversion results, and the estimated orientation is recorded in Table 1.

[0074] Depend on Figure 4 (c) It can be seen that the spectral peak diagram after locating the radio frequency interference source using existing technology shows four obvious spectral peaks, and each peak is surrounded by multiple smaller spectral peaks, which corresponds to... Figure 4 An abnormal bright temperature point appeared in (b).

[0075] Depend on Figure 4 (d) It can be seen that in the inversion result graph using the method of this invention, there are 4 obvious RFI points, which are consistent with... Figure 4 (a) The positions of the RFIs in the inversion results are basically close, and the estimated orientations are recorded in Table 1.

[0076] Table 1 Comparison of Positioning Estimation Results of the Invention and Existing Technology in Simulation Experiment 3 Table 1 Comparison of Positioning Estimation Results of the Invention and Existing Technology in Simulation Experiment 3

[0077]

[0078] As can be seen from Table 1, the RFI location estimated by existing technologies and Figure 4 The RFI locations in (a) differ significantly, while the RFI locations estimated using this invention and Figure 4 The positions of RFI in (a) are basically the same.

[0079] The simulation experiments above show that the method of the present invention uses a sparse Bayesian learning algorithm to convert the complex model of the synthetic aperture interferometry vector into a real model, and uses visibility data to recover the brightness temperature in order to obtain the location information of radio frequency interference sources. It solves the problems of decreased estimation accuracy and deteriorated imaging performance of existing technologies under low signal-to-noise ratio and single snapshot conditions. It is a very practical sparse estimation method for SAIR radio frequency interference sources.

Claims

1. A sparse estimation method for SAIR radio frequency interference sources based on a sparse Bayesian learning algorithm, characterized in that, The complex number model of the integrated aperture interferometry vector is converted into a real number model, and the covariance, mean, hyperparameters, and noise variance in the sparse Bayesian learning algorithm are updated using visibility data. The steps of this estimation method are as follows: Step 1, convert the complex number model of the integrated aperture interferometry vector into a real number model as follows: ； ； in, Visibility data under a real number model. The brightness temperature in the real number model. The measurement matrix is ​​in the real number model. This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part. This represents visibility data composed of snapshot data received by all sparse antenna arrays. This represents the brightness temperature value composed of sampled values ​​from all spatial frequency domain information. For the measurement matrix, This is the noise vector; Step 2: Use the sparse Bayesian learning algorithm to recover the brightness temperature data; Step 2.1: Calculate the covariance and mean of the brightness temperature using the visibility data: ； ； in, To calculate the covariance of brightness temperature, For noise variance, For hyperparameters diagonal matrix, ,and N is the number of columns in the measurement matrix under the complex model. This indicates the inverse operation. To calculate the mean brightness temperature, Indicates the transpose operation; Step 2.2, update hyperparameters and noise variance using visibility data: ； ； in, Let these be the hyperparameters updated in the i-th iteration. To calculate the average brightness temperature of the first One element, To calculate the first brightness temperature covariance matrix One element; This is the updated noise variance. This is the trace operation of the matrix; Step 2.3: Determine whether the root mean square error of the current iteration meets the convergence condition or reaches the maximum number of iterations. If yes, execute step 2.1; otherwise, execute step 3 after obtaining the final recovery of the brightness temperature. Step 3: Use the recovered brightness temperature to obtain the RFI positioning information.

2. The sparse estimation method for SAMR radio frequency interference sources based on the sparse Bayesian learning algorithm according to claim 1, characterized in that, The measurement matrix is ​​as follows: ； Where F represents the measurement matrix, This is an exponential operation with the natural constant e as the base, and j is the imaginary unit. Pi and Let be the baseline vectors corresponding to the i-th antenna and the j-th antenna, respectively. Here are the direction cosine coordinates.

3. The sparse estimation method for SAIR radio frequency interference sources based on the sparse Bayesian learning algorithm according to claim 1, characterized in that, The convergence condition described in step 2.3 is that the root mean square error between the mean vector obtained in the current iteration and the mean vector obtained in the previous iteration is less than or equal to a threshold. The value of this threshold depends on the accuracy that the estimation is intended to achieve. The maximum number of iterations is set to prevent entering an infinite iteration loop.

4. The sparse estimation method for SAIR radio frequency interference sources based on the sparse Bayesian learning algorithm according to claim 1, characterized in that, The final brightness temperature recovery in step 2.3 is represented as follows: ； in, This is for the final restoration of the brightness temperature.

5. The sparse estimation method for SAIR radio frequency interference sources based on the sparse Bayesian learning algorithm according to claim 1, characterized in that, The positioning information mentioned in step 3 is the location corresponding to the maximum brightness temperature point obtained from the recovered brightness temperature, and this location is used as the location of the radio frequency interference source.

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