A distributed array multi-drfm jamming signal range-difference positioning method

Abstract

The application provides a distributed array multi-DRFM interference signal level time difference positioning method, and the technical scheme comprises the following steps: firstly, for the received multiple DRFM interference signals, a DBI-K-means clustering algorithm is proposed for interference source number estimation and multi-interference signal division according to the differences of different interference signals in the time domain feature space; then, high-precision time delay difference estimation is realized by combining signal level correlation processing; finally, multi-DRFM interference positioning is realized through multi-parameter simultaneous solution. The application can realize accurate positioning of multi-DRFM interference.

Description

Technical Field

[0001] This invention belongs to the field of interference source localization technology, specifically relating to a distributed array multi-DRFM interference signal level time difference localization method. Background Technology

[0002] Digital Radio Frequency Memory (DRFM) jamming, particularly on the main lobe, is a major threat to radar, and no mature and stable countermeasures exist. Existing radar anti-DRFM jamming algorithms often require precise jammer location information. Accurate localization of the jamming source provides reliable data support for subsequent anti-jamming strategy selection. Furthermore, considering the characteristics of main lobe jamming—that the jamming source and the protected target are spatially close—locating the jamming source can also provide a rough understanding of the target information.

[0003] Radar positioning algorithms can be divided into two types: direct positioning and indirect positioning. Direct positioning achieves positioning by performing a one-step joint processing of the raw data received by each sub-radar, which can improve positioning accuracy at low signal-to-noise ratios, but its computational complexity is high and it is not easy to implement in engineering. Indirect positioning methods consist of two steps. The first step is to estimate different types of measurement parameters, typically including echo angle of arrival, frequency difference of arrival, and time difference of arrival. The second step is to perform data fusion, constructing and solving a set of positioning equations based on prior information such as radar structure. However, existing indirect positioning methods perform the measurement of intermediate parameters and the positioning solution process independently, without considering the spatial geometric constraints between the target and the radar station during parameter measurement. Simultaneously, when multiple DRFM interferences coexist, the time difference estimation accuracy decreases due to the correlation between the interfering signals, thus affecting the positioning accuracy of the interference source. Summary of the Invention

[0004] In view of this, the present invention provides a distributed radar multi-DRFM interference signal level time difference localization method, which can realize the accurate localization of multiple DRFM interference sources, without involving complex optimization algorithms, with low computational complexity and strong real-time performance.

[0005] A flowchart of a distributed radar multi-DRFM interference signal level time difference localization method is shown below. Figure 1 As shown, the specific steps include the following:

[0006] Step 1: Receive multiple DRFM interference signals

[0007] A distributed system is constructed, consisting of a main radar and two auxiliary arrays. The main radar both transmits signals and receives echoes, while the auxiliary arrays only receive echoes. A schematic diagram of the distributed array interference source localization system is shown below. Figure 2As shown, the main radar is located at the central point, and the two auxiliary arrays are deployed at points 5km to 10km away from the main radar.

[0008] Assuming the signals from the K interference sources propagate to the radar via a line-of-sight, the received echo from the distributed array can be expressed as:

[0009]

[0010] Where: s0(t) and s i (t), i = 1, 2 represent the interference signals arriving at the main radar and the auxiliary array, respectively; η k,i j represents the signal amplitude coefficient; k (t) represents the signal from the k-th interference source; τ k,0 and τ k,i , i = 1, 2 represent the time delays of the jamming signal arriving at the main radar and the auxiliary array, respectively; n i (t) represents mutually independent zero-mean complex Gaussian white noise.

[0011] Step 2: Dataset Construction

[0012] For distributed array echo s i (t) Perform pulse compression processing:

[0013]

[0014] Where: h(t) = s * (-t) represents the impulse response function of the matched filter, and s(t) is the radar transmitted signal.

[0015] r i (t) The result after passing through the square-law detector and the threshold V T The judgment criteria for comparison with routine testing are as follows:

[0016]

[0017] Where: V T When only noise exists, |r i (t)| 2 The probability density function and the false alarm probability P of conventional radar fa A decision can be expressed as

[0018]

[0019] in: This represents the noise variance.

[0020] Assume the vector representations of the distributed array echo and pulse compression results are as follows: and Where L is the number of range cells, and the amplitude corresponding to the i-th radar node and the l-th range cell is denoted as a. l,i If s i (l) in the l n,i n = 1, 2, ..., N i Each distance unit satisfies

[0021] m i (l n,i )=1 (5)

[0022] This indicates that s i (l) in the l n,i Each distance cell may have DRFM interference, where N i s i The number of range cells identified as interference in (l).

[0023] A corresponding dataset is constructed for the echo signals received by each radar node. Where, N i x represents the number of data samples. n =[l n,i ,a l,i ] T These are the eigenvectors.

[0024] Step 3: Time Domain Division of Multiple DRFM Interference Signals

[0025] Based on the differences in the time-domain feature space of different DRFM interference signals, a DBI-K-means clustering algorithm is proposed for the sample dataset X. i Clustering is performed to estimate the number of interference sources and segment the interference signals. The time-domain segmentation method for interference signals based on the DBI-K-means clustering algorithm is implemented as follows:

[0026] 1. Assume the maximum number of interference sources is N. max Then the optimal number of cluster centers K i The range of values ​​is in Indicates rounding down;

[0027] 2. For For each value, K-means clustering based on Euclidean distance is performed to obtain the corresponding clustering results, and the cluster centers are... The K-means clustering algorithm based on Euclidean distance is as follows:

[0028]

[0029] 3. Define the DBI (Davies-Bouldin Index, DBI) as follows:

[0030]

[0031] Where: R k =max(R) kj ), k,j∈[2,K] and k≠j, R kj The definition is as follows:

[0032]

[0033] in

[0034]

[0035] Used to describe the degree of dispersion of samples in cluster k, where ||·|| p T represents the p-norm. k This represents the number of samples in cluster k.

[0036] M kj =||c k -c j || q (9)

[0037] This represents the distance between the cluster centers of cluster k and cluster j.

[0038] 4. Calculate the DBI index for each clustering result to select the optimal K value. opt,i And based on this, X is obtained. i The corresponding K opt,i for:

[0039] K opt,i ={K|min k [DBI(K i (10)

[0040] The estimated number of interference sources N gr It can be represented as:

[0041]

[0042] 5. N can be obtained using the K-means algorithm. gr The corresponding clustering results show that the time-domain partitioning unit of the interference signal can be represented as follows:

[0043]

[0044] Assume the observation range of the distributed array is [R] min ,R max ], where: R min R represents the minimum observation distance. max This indicates the maximum observation distance. Correspondingly, the windowing start unit L... min and window termination unit Lmax Set them to:

[0045]

[0046] Where: L min <min(l ds (nn))≤max(l ds (nn))<L max f s This indicates the sampling rate.

[0047] According to equations (12) and (13), the echo data s can be... i Divided into N gr There are data fragments, defined as s. k,i For the i-th radar node to receive the k-th data segment of the echo, ideally, each s k,i It contains only one interference signal. The time-domain partitioning process for multiple DRFM interference signals is as follows: Figure 3 As shown, where: M k ,1≤k≤N gr This represents the number of times the sampling slice of the k-th interference source is forwarded.

[0048] Step 4: High-precision time delay difference estimation

[0049] Assume the coordinates of each radar node in the distributed radar system are l i =(x i ,y i ,z i ) T The coordinates of the interference source are u k =(x k ,y k ,z k ) T k = 1, ..., N gr , where N gr This indicates the number of interference sources located within the intersection area of ​​the main radar and the auxiliary small array beams.

[0050] Taking the main radar l0 as the reference radar, and the interference source u k Arrival Auxiliary Radar i The difference in propagation distance for i = 1 and 2 is

[0051] Δr k,i =r k,i -r k,0 =c·Δτ k,i (14)

[0052] in

[0053]

[0054] Indicates the interference source u k To radar l i The distance, c is the speed of light, τ i,k Indicates the interference source u k To each radar node i The propagation delay.

[0055] Assuming the interference source signal propagates along a line of sight to the radar, the preprocessed echo of the distributed array can be expressed as:

[0056]

[0057] The value of s can be calculated using the Fast Fourier Transform (FFT) and the Inverse Fast Fourier Transform (IFFT). k,i (t) and s k,0 cross-correlation function of (t)

[0058]

[0059] in: For the interference source signal j k The autocorrelation function of (t).

[0060] According to equation (17), the cross-correlation function R k,i (τ) at τ=Δτ k,i R reaches its maximum value at this time. k,i The maximum value of (τ) corresponds to the τ value, which is the time delay difference between the arrival of the k-th interference source at the main radar and the auxiliary array.

[0061] Figure 4 A schematic diagram of the spatial geometric positional relationship of the distributed array is given. According to the triangle relationship, the maximum time delay difference satisfies the following spatial geometric constraints:

[0062]

[0063] Considering the constraints imposed by the geometric relationship between the interference source and the receiving station on the peak distribution area of ​​the time delay difference, windowing is applied to the time delay difference to reduce the impact of spurious peaks. Furthermore, considering that the time delay estimation accuracy of traditional cross-correlation algorithms is limited by the sampling rate, Chirp-Z transform is used to locally upsample the cross-correlation function near the peak, obtaining high-precision time delay difference estimation results.

[0064] Step 5: Calculation of Interference Source Location

[0065] In 3D passive time-difference positioning, the distributed array can only obtain two sets of time difference information (one less than the number of nodes), leading to an underdetermined positioning equation set. Therefore, it is necessary to introduce pitch information from the interference source to eliminate ambiguity. Geometrically speaking, solving for the spatial target position is equivalent to solving for the intersection of three surfaces: two hyperboloids determined by the distance difference and a conical surface determined by the pitch angle.

[0066] The interference source localization model is represented as follows:

[0067]

[0068] in: This represents the pitch estimation result of the interference source.

[0069] Since equation (19) is a nonlinear system of equations, it is quite complex to solve directly. Therefore, we first linearize it to obtain the following system of equations:

[0070]

[0071] in

[0072]

[0073] In equation (20) x k y k and z k Let z be the unknowns. To solve this system of linear equations, we first set z to... k Treating them as known variables, the first two equations of equation (20) can be rearranged as follows:

[0074]

[0075] in

[0076]

[0077] According to equation (22), we can obtain

[0078]

[0079] in

[0080]

[0081] Substituting equation (24) into the third equation in equation (20), we get:

[0082]

[0083] in

[0084]

[0085] By solving equation (26), we can obtain z. k By selecting the root that is greater than zero and substituting it into equation (24), the location of the interference source can be estimated.

[0086] Beneficial effects:

[0087] This invention provides a distributed radar multi-DRFM interference signal level time difference localization method. For scenarios with multiple DRFM interference sources coexisting, this method, based on a long-baseline distributed array configuration, proposes a DBI-K-means clustering method to estimate the number of interference sources while simultaneously partitioning the time domain of the multiple DRFM interference signals. Then, high-precision time difference estimation is achieved by combining signal-level correlation processing. Finally, accurate localization of multiple interference sources is achieved through multi-parameter simultaneous solution. This invention can achieve precise localization of multiple DRFM interference sources, with no false localization points, and does not involve complex optimization algorithms, exhibiting low computational complexity and strong real-time performance. Attached Figure Description

[0088] Figure 1 Flowchart of a distributed array multi-DRFM interference signal level time difference localization method;

[0089] Figure 2 Schematic diagram of a distributed array interference source localization system;

[0090] Figure 3 Time-domain partitioning process for multiple DRFM interference signals;

[0091] Figure 4 This is a schematic diagram of the spatial geometry of a distributed array.

[0092] Figure 5 This is a schematic diagram of the interference scenario in the simulation example;

[0093] Figure 6 The process of building the dataset in the simulation instance;

[0094] Figure 7 The results of clustering based on the DBI-K-means algorithm in the simulation example;

[0095] Figure 8 The results show the estimated time delay difference of the interference source in the simulation example;

[0096] Figure 9 This is the result of locating the interference source in the simulation example. Detailed Implementation

[0097] The following is a simulation example of applying the present invention, and its specific process is explained.

[0098] The simulation was implemented using MATLAB R2019a software. The distributed array parameters and waveform parameters are set as follows:

[0099] Distributed array parameters and waveform parameters

[0100]

[0101] Consider the simulation scenario: all three jammers are located within the main radar beam, characterized by the presence of three jammers with indistinguishable angles. The jammer positions at time t are shown below, and the beam coverage is as follows. Figure 5 As shown.

[0102] Jammer location (polar coordinates in the Northeast Celestial Coordinate System)

[0103] jammer number Distance (km) Azimuth (°) Pitch angle (°) 1 172 19.38 2 2 270 19.35 1.90 3 339 19.31 1.93

[0104] Assuming all jammers transmit DRFM jamming, and considering the different receiving gains of the main radar and the auxiliary array, the JNR of the jamming echo received by the auxiliary array is 15dB lower than that of the main radar at the same time. The three sets of jamming parameters are shown below.

[0105] Interference parameters

[0106] jammer number Slice width (μs) Number of reposts Main radar echo interference-to-noise ratio (dB) 1 12 15 40 2 15 10 30 3 20 15 20

[0107] Step 1: Receive multiple DRFM interference signals

[0108] Assuming the normalized radar baseband transmitted signal is

[0109]

[0110] in: T is a rectangular gate function; p The pulse width; Let be the phase modulation function. DRFM jamming involves sampling, storing, modulating, and forwarding intercepted radar transmitted signals. Taking typical intermittent sampling and repetitive forwarding jamming as an example, the jamming signal transmitted by the k-th jammer can be expressed as:

[0111]

[0112] Wherein: T c,k T represents the slice width. s,k =(M k +1)T c,k M is the sampling repetition period. k Indicates the number of times the interference slice is forwarded; This indicates the number of sampled slices.

[0113] Step 2: Dataset Construction

[0114] First, pulse compression processing is performed on the distributed array echo; then, the false alarm rate P is set. fa =1e -9 According to equation (4), the fixed thresholds for the received echoes of each radar node are calculated as 5.70, 5.69, and 5.68, respectively. The distributed array echo pulse compression results are then routinely tested, and range cells exceeding the thresholds are identified as interference cells. Finally, interference feature vectors are extracted, and an interference dataset X is constructed. i The dataset construction process is as follows: Figure 6 As shown.

[0115] Step 3: Time Domain Division of Multiple DRFM Interference Signals

[0116] First, assume the maximum number of interference sources is N. max =10.

[0117] Next, for the interference dataset X i For each value of i = 1, 2, 3 Perform K-means clustering and calculate the DBI index for each cluster result, where the K value corresponding to the minimum DBI index is... i The value is the optimal K value. Figure 6 (a), (c), and (e) respectively give X i The clustering metric plot based on the DBI index shows that K... opt,1 =K opt,2 =K opt,3 =3, then N can be calculated according to equation (11). gr =3.

[0118] Finally, K can be obtained using the K-means algorithm. opt,i The corresponding clustering results, such as Figure 6 As shown in (b), (d), and (f), the corresponding time-domain partitioning units are 15728 and 21568, respectively, i.e., l ds =[15728,21568].

[0119] Assuming minimum observation distance R min =100km, maximum observation distance R max =400km; The starting unit L of the window opening can be calculated according to equation (13). min =6671, Window opening termination unit L max =26685, satisfying L min <min(l ds (nn))≤max(l ds (nn))<L max .

[0120] Based on this, the distributed array echo data s iThe i = 1, 2, 3 data segments are divided into three groups of interference data segments, named s respectively. 1,i s 2,i and s 3,i .

[0121] Step 4: High-precision time delay difference estimation

[0122] The three sets of interference array echoes obtained in step three are subjected to signal-level correlation processing, and the time delay difference estimation results are as follows: Figure 8 As shown in the figure, the purple-red dashed line represents the actual time delay difference, and the red triangle represents the estimated time delay difference. The simulation results show that the estimated time delay difference errors for the two channels of the auxiliary array and the main radar for interference source 1, interference source 2, and interference source 3 are as follows.

[0123] Delay difference estimation results

[0124] Interference source 1 Interference source 2 Interference source 3 Auxiliary 1 formation 0.50ns 1.46ns 7.80ns Auxiliary 2 formation 1.14ns 0.63ns 4.52ns

[0125] Step 5: Calculation of Interference Source Location

[0126] Interference source localization results are as follows Figure 9 As shown, the localization errors of the three interference sources are 0.42 km, 0.93 km, and 5.05 km, respectively. Therefore, in the current scenario, the proposed method can achieve accurate localization of multiple DRFM interferences.

[0127] In summary, the above are merely implementation examples of the present invention and are 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 within the scope of protection of the present invention.

Claims

1. A distributed array multi-DRFM interference signal level time difference localization method, characterized in that, Includes the following steps: Step 1: Receive multiple DRFM interference signals; Step 2: Perform pulse compression processing on the distributed array echo, and extract feature vectors based on the detection results after pulse compression to construct a sample dataset to characterize the distribution characteristics of DRFM interference signals in the time domain feature space. Step 3: Without prior information on the number of interference sources, the DBI-K mean clustering algorithm is used to adaptively estimate the number of interference sources based on the differences in the time-domain feature space of different DRFM interference signals, and the time-domain division of the interference signals is realized. Step 4: Perform signal-level cross-correlation processing on the echo data segments obtained in Step 3; based on the spatial geometric relationship between the interference source and the receiving station, determine the physically feasible distribution range of the time delay difference peak based on the triangle relationship, and suppress spurious peaks that do not satisfy the spatial geometric relationship through time delay difference windowing processing; perform local upsampling using Chirp-Z transform in the neighborhood of the cross-correlation peak that satisfies the spatial geometric relationship to obtain high-precision time delay difference estimation results; Step 5: Based on the high-precision time delay difference estimation results and pitch angle estimation results, construct an interference source localization model containing two distance difference constraints and one pitch angle constraint; linearize the two distance difference constraints to obtain a linear relationship between the horizontal coordinates and the altitude coordinates of the interference source; substitute the linear relationship into the pitch angle constraint to obtain a quadratic equation in one variable about the altitude coordinates of the interference source; solve the quadratic equation and substitute it back to obtain the three-dimensional coordinates of multiple DRFM interference sources.

2. The distributed array multi-DRFM interference signal level time difference localization method as described in claim 1, characterized in that, In step two, the feature vector consists of the range cells that are determined to have DRFM interference and their corresponding amplitudes.

3. The distributed array multi-DRFM interference signal level time difference localization method as described in claim 1, characterized in that, In step four, the spatial geometric relationship is as follows: based on the triangle relationship between the main radar, auxiliary radar and interference source, the physical constraint range that the maximum time delay difference satisfies is determined, and the peak value of the cross-correlation function is searched within the physical constraint range to suppress spurious peaks outside the range.

4. The distributed array multi-DRFM interference signal level time difference localization method as described in claim 1, characterized in that, In step four, the local upsampling of the Chirp-Z transform is performed only within the neighborhood of the cross-correlation peak that satisfies the spatial geometric relationship after the time delay difference windowing process, rather than upsampling over the entire time delay range.

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