A bistatic radar cooperative imaging method based on complementary random waveforms

Abstract

The present application belongs to the technical field of radar imaging, and relates to a kind of dual-base radar cooperative imaging method based on complementary random waveform, it is characterized in that, including the following steps: step 1: establish dual radar cooperative detection echo model, radar 1 and radar 2 all adopt random frequency hopping waveform;Step 2: carry out distance difference compensation, eliminate the phase modulation term of the phase difference of the echo signal received by radar 1 and radar 2, realize distance difference compensation;Step 3: carry out echo motion compensation, eliminate the component related to velocity component in echo, realize echo motion compensation;Step 4: carry out band fusion imaging, rearrange different frequency band random frequency hopping, carry out zero filling processing to echo data on the missing frequency point, and through setting tight constraint condition, make the echo signal of two radar through FFT transformation to realize phase correlation fusion imaging.The imaging method of the present application designs new frequency hopping waveform, realizes efficient motion compensation, and realizes band fusion by using phase correlation processing algorithm.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of ISAR imaging, and particularly relates to a dual-base radar cooperative imaging method based on complementary random waveforms. BACKGROUND

[0002] ISAR (Inverse Synthetic Aperture Radar) is a radar that analyzes the distance delay and Doppler resolution of echo signals, and can obtain the scattering intensity of each part of a target, that is, the image of the target. In any plane perpendicular to the radar line-of-sight direction, the distance to the radar is equal, which is called an equal distance plane. In any plane parallel to the rotation axis and the radar line-of-sight direction, the Doppler velocity is equal, which is called a Doppler plane. Through distance resolution and Doppler resolution of the target, the scattering intensity distribution of the target with position can be obtained, and thus the image of the target can be obtained. The ISAR radar has all-weather, all-day, and long-distance detection capabilities, and is an important sensor for imaging detection of a missile-borne platform target, and plays an important role in precision guidance tasks. However, with the progress of target stealth technology and the rapid development of jamming countermeasure technology, such as the reduction of the RCS (Radar Cross Section) of a target, a radar needs to adopt a large antenna aperture and a large bandwidth signal system, which brings great challenges to single-radar detection. Compared with single-radar detection, multi-radar cooperative detection can not only obtain more observation times, but also obtain different dimensional features of a target in the frequency domain, the polarization domain, and the spatial domain, and is an important development direction for detection of a stealth target in a complex electromagnetic environment.

[0003] Existing multi-radar cooperative detection technology can be divided into spatial cooperation and frequency cooperation according to the detection angle and radar operating frequency band, thus obtaining spatial diversity and frequency diversity benefits. The former realizes target detection and identification by joint processing of multiple detection angle information, thereby reducing the probability of single-angle detection error. The latter performs coherent processing on the frequencies of different radars to obtain higher range resolution and pulse compression gain. For the application scenario of missile-borne radar, multiple missile-borne radars fly together, and the difference in detection angle is small, so the frequency fusion method is usually used for target detection. Due to the high-speed motion of different radars and the distribution of echo data on multiple non-continuous frequency bands, it is necessary to first eliminate the phase error introduced by platform motion and compensate for the system error between different radar echoes, and then realize effective fusion of different frequency band data. The processing process involves key technologies such as motion compensation, coherent registration, and data fusion. In the aspect of motion compensation, the literature (see Liao Z K, Hu J M, Lu D W, et al. Motion analysis and compensation method for random stepped frequency radar using the Pseudorandom code[J]. IEEE Access. 2018, 6(1): 57643-57654) uses the cross-correlation of adjacent distance vectors to estimate the velocity, and the compensation accuracy is determined by the bandwidth, which cannot be applied to radar waveforms sensitive to motion such as random frequency hopping. The literature (see Li X, Li G S, et al. Autofocusing of ISAR images based on entropy minimization[J]. IEEE Trans. on Aerospace and Electronic Systems. 1999, 35(4): 1240-1252) searches for the extreme value of the cost function to determine the target velocity, and the algorithm performance is sensitive to the step size and range of the search. The literature (see Liao Z K, Lu D W, Hu J M, et al. Waveform design for random stepped frequency radar to estimate object velocity[J]. Electronics letters, 2018, 54(14): 894-896) proposes a velocity estimation method based on complementary code modulation, which realizes high-precision velocity estimation by transmitting adjacent pulse trains with complementary relationship, but it needs two pulse trains to complete the velocity estimation, which reduces the radar data rate.In the aspect of phase correlation, the literature (see TIAN Biao, CHEN Zengping, and XU Shiyou. Sparse sub-band fusion imaging based on parameter estimation of geometrical theory of diffraction model[J]. IET Radar Sonar & Navigation, 2014, 8(4): 318-326) divides the phase to be compensated between sub-bands into two parts, linear phase and fixed phase, and solves them by using the all-pole model, the shortcoming of which is that the order of the pole is difficult to determine. The literature (see TIAN Jihua, SUN Jinping, WANG Guohua, et al. Multiband radar signal coherent fusion processing with IAA and apFFT[J]. IEEE Signal Processing Letters, 2013, 20(5): 463-466) solves the linear phase term by using the cross-correlation method and the fixed phase term by using the FFT (Fast Fourier Transform), which avoids the problem of determining the order of the pole. In the aspect of frequency band data fusion, the literature (see BAI Xueru, ZHOU Feng, WANG Qi, et al. Sparse sub-band imaging of space targets in high-speed motion[J]. IEEE Transactions on Geoscience and Remote Sensing, 2013, 51(7): 4144-4154 and HU Pengjiang, XU Shiyou, WU Wenzhen, et al. Sparse sub-band ISAR imaging based on autoregressive model and smoothed l 0 algorithm[J]. IEEE Sensors Journal, 2018, 18(22): 9315-9323) fills the missing frequency band into a wide-band signal and then performs imaging, however, the frequency band estimation is based on the existing frequency band information and does not increase the amount of additional information.The document (see ZHOU Feng and BAI Xueru.High-resolution sparse sub-band imaging based on Bayesian learning with hierarchical priors[J].IEEE Transactions on Geoscience and Remote Sensing, 2018, 56 (8): 4568-4580) establishes a probability model for sparse frequency band echo signals, and after azimuth dimension imaging of the target, distance fusion imaging is carried out by using the Bayesian learning algorithm, which avoids the error introduced by the frequency band filling algorithm, however, the azimuth dimension imaging needs accurate target motion compensation, and the compensation accuracy of the sub-band data needs further analysis.

[0004] The main defects of the existing missile-borne ISAR radar system detection are: 1) based on the target track information extracted by each radar respectively, data level fusion is carried out, and the gain brought by radar target echo signal cooperative processing is not considered; 2) the frequency band fusion algorithm is mainly based on two kinds of ideas, one is to fill the missing frequency band after imaging by using frequency band extrapolation, this method is based on the existing frequency band information, and does not increase the amount of additional information. The other idea is to extract the scattering center parameters by using modern spectrum, sparse representation or Bayesian method for super-resolution distance imaging, since the parameter extraction process loses the original information of the radar data, it is difficult to perform two-dimensional imaging. SUMMARY

[0005] The purpose of the application is to provide a kind of based on complementary random waveform's bistatic radar cooperative imaging method, new frequency hopping waveform is designed for bistatic radar cooperative detection scene, efficient motion compensation is realized, the phase coherent processing algorithm of bistatic echo signal is designed, frequency band fusion is realized, and the echo signal-to-noise ratio and distance resolution capability of radar are improved.

[0006] The specific technical scheme of the application is a kind of based on complementary random waveform's bistatic radar cooperative imaging method, characterized in that, comprising the following steps:

[0007] Step 1: establish a bistatic radar cooperative detection echo model, radar 1 and radar 2 use random frequency hopping waveform, then the transmit signal model of the two radars is represented as the following formula (I) and (II):

[0008]

[0009] Wherein, the phase coherent processing pulse train contains N sub-pulses and has the same frequency hopping rule, and the pulse repetition period is T r, the pulse width is T, the random modulation frequency is distributed in a given bandwidth B, the minimum frequency hopping step is Δf=B / N, the frequency hopping coefficients of radar 1 and radar 2 are c1(n) and c2(n) respectively, and f1 and f2 are the carrier frequencies of radar 1 and radar 2 respectively,

[0010] When radar 1 transmits and radar 1 receives, the nth sub-pulse echo after mixing can be represented by the following formula (III):

[0011]

[0012] Wherein, it is assumed that the target contains K scattering centers, at the initial moment, the distance of the kth scattering center relative to radar 1 is r 1k , the radial motion speed of the target is v, and at the nth sub-pulse transmission moment, the distance of the scattering center relative to radar 1 can be represented as r 1k 1k +vnT r ,σ k represents the intensity of the kth scattering center,

[0013] When radar 2 transmits and radar 2 receives, the nth sub-pulse echo after mixing can be represented by the following formula (V):

[0014]

[0015] Wherein, Δr=r 2k -r 1k , the distance of the kth scattering center relative to radar 2 is r 2k ,

[0016] The echo s 21 (n) received by radar 2 when radar 1 transmits and the echo s 12 (n) received by radar 2 when radar 1 transmits, are represented by the following formula (VI) and (VII) respectively:

[0017]

[0018] Step 2: Perform distance difference compensation to eliminate the phase modulation term of the phase difference between the echo signals received by radar 1 and radar 2, realize distance difference compensation, and the echo after distance difference compensation can be represented by the following formula (IX) and (X) respectively:

[0019]

[0020] Step 3: Perform echo motion compensation to eliminate the component related to the velocity component in the echo, realize echo motion compensation, and the echo after echo motion compensation can be represented by the following formula (XVI) and (XVII) respectively,

[0021] ​

[0022]

[0023] wherein, wherein f0=(f1+f2) / 2, c(n)=c1(n)+(f1-f2) / 2Δf, c2(n)=-c1(n);

[0024] Step 4: Band fusion imaging is performed, echo data on the missing frequency points are zero-filled, and tight constraints are set to enable the echo signals of the two radars to be in-phase fused and imaged through FFT transformation.

[0025] Further, the echo motion compensation in step 3 is that the frequency hopping coefficient c1(n) of the radar 1 transmitting pulse is equal in size and opposite in direction to the frequency hopping coefficient of the radar 2 transmitting pulse, wherein f0=(f1+f2) / 2, c(n)=c1(n)+(f1-f2) / 2Δf, c2(n)=-c1(n), and substitution into formula (IX) and formula (X) can obtain:

[0026]

[0027] The echo components are multiplied to obtain the following results:

[0028]

[0029] The target velocity after FFT transformation of the sequence peak position is as follows formula (XIV):

[0030]

[0031] wherein k0 is the peak position, after obtaining the target velocity, the component related to the velocity component in the echo is eliminated, and echo motion compensation is performed on formula (XI) and formula (XII).

[0032] Further, the specific method of performing band fusion imaging in step 4 is that the echo sequences of formula (XVI) and formula (XVII) are arranged from small to large according to the minimum frequency hopping step, and the obtained echo sequence is represented as:

[0033] s all (n)=[s all (0), s all (1), s all (2),..., s all (L-1)]......(XVIII)

[0034] wherein, L=M+2N is the length of the zero-filled echo sequence, s all (n) is the first N components of s 21(n) the result of rearrangement, the last N components are s 11 (n) the result of rearrangement, all valid observations, the missing band is [f1, f2], the missing bandwidth f1-f2 is an integer multiple of the frequency hopping step Δf, and the corresponding zero-padding point number is M=(f1-f2) / Δf-1, for s all (n) the high-resolution range profile obtained by FFT transformation can be expressed as:

[0035] hrrp(k)=FFT[s all (n)]......(XIX).

[0036] The beneficial effects of the present application are 1) the complementary random waveform-based bistatic radar cooperative imaging method of the present application adopts a complementary random frequency hopping waveform to detect the target, which can effectively eliminate the phase term introduced by the platform distance difference. 2) The range image after fusion provides more detailed target information, and the estimated speed accuracy can meet the focusing requirements of high-resolution range imaging; 3) the use of fusion imaging mode makes the resolution improved, the distribution area of the target scattering center is larger, and the target detail information provided is more abundant, and the ISAR imaging result under ideal speed compensation is also given, and the focusing performance of the image is measured by contrast. The actual use results show that the method of the present application can effectively realize the motion compensation of the bistatic radar and the fusion detection of the target. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 It is a flow chart of the complementary random waveform-based bistatic radar cooperative imaging method of the present application;

[0038] Figure 2 It is a bistatic radar cooperative detection schematic diagram of the complementary random waveform-based bistatic radar cooperative imaging method of the present application;

[0039] Figure 3 It is a bistatic radar random frequency hopping complementary modulation schematic diagram of the complementary random waveform-based bistatic radar cooperative imaging method of the present application;

[0040] Figure 4 It is a random frequency hopping echo rearrangement and zero padding schematic diagram of the complementary random waveform-based bistatic radar cooperative imaging method of the present application;

[0041] Figure 5 It is a target point scattering model schematic diagram;

[0042] Figure 6 It is a bistatic cooperative detection geometric scene schematic diagram of the complementary random waveform-based bistatic radar cooperative imaging method of the present application;

[0043] Fig. 7(a) is a distance difference introduced phase estimation result diagram for comparing the fusion range imaging effect of the method of the present application;

[0044] Fig. 7(b) is a target speed estimation result diagram for fusion range imaging effect comparison using the method of the present application (v tLOS = 3 m / s);

[0045] Fig. 7(c) is a radar 1 range high resolution imaging result diagram for fusion range imaging effect comparison using the method of the present application;

[0046] Fig. 7(d) is a radar 2 range high resolution imaging result diagram for fusion range imaging effect comparison using the method of the present application;

[0047] Fig. 7(e) is an actual fusion detection range high resolution imaging result diagram for fusion range imaging effect comparison using the method of the present application;

[0048] Fig. 7(f) is an ideal fusion detection range high resolution imaging result diagram for fusion range imaging effect comparison using the method of the present application;

[0049] Fig. 8(a) is a radar 1-ISAR high resolution imaging result diagram for radar imaging result comparison using the method of the present application;

[0050] Fig. 8(b) is a radar 2-ISAR high resolution imaging result diagram for radar imaging result comparison using the method of the present application;

[0051] Fig. 8(c) is an actual fusion ISAR imaging result diagram for radar imaging result comparison using the method of the present application;

[0052] Fig. 8(d) is an ideal fusion ISAR imaging result diagram for radar imaging result comparison using the method of the present application. DETAILED DESCRIPTION

[0053] The technical solutions of the present application are described further below in conjunction with the accompanying drawings of the specification.

[0054] As shown in the accompanying Figure 1 Fig. 1 is a flow chart of the method of the present application for bi-static radar cooperative imaging based on complementary random waveforms. The principle of bi-static radar cooperative detection is shown in the accompanying Figure 2 Fig. 2, using a 2-transmit 2-receive cooperative detection system, the separated echo sets are denoted as {s 11 (t), s 12 (t), s 21 (t), s 22 (t)}. Wherein S pq represents the echo representation under the mode of radar p (p = 1, 2) transmitting pulses and radar q (q = 1, 2) receiving.

[0055] Firstly, two radar echo signals satisfying the complementary characteristics of tight constraint conditions are designed, and then different band-pass filters are set according to the carrier frequency difference to obtain the separated target echo sequence. After obtaining the echo components of 4 paths, the modulation phase term introduced by the distance time delay difference in different paths is calculated and used to compensate the additional phase introduced by the distance difference in different paths, so that the distance difference correction of different paths is completed, and the 4-path echo signals with the same distance time delay are obtained. On this basis, a pair of double-base random frequency hopping signal waveforms with complementary characteristics are proposed. By simultaneously transmitting random frequency hopping signals with equal frequency hopping coefficient size and opposite direction by two radars, the 4-path echo signals with the same distance time delay are obtained, and then after simple multiplication processing, the effective estimation of target velocity can be realized by combining FFT transformation. Based on the estimated velocity, the target echo is compensated to obtain the random frequency hopping echo sequence in different frequency bands. Then, the high-resolution range imaging of the random frequency hopping echo in different frequency bands is realized by rearranging and zero padding. Finally, combined with the envelope alignment and initial phase correction method in the ISAR imaging process, the high-resolution two-dimensional imaging of the double-base cooperative detection is completed.

[0056] The method of the present application specifically implements the following steps:

[0057] Step 1: Establishing a double-radar cooperative detection echo model:

[0058] Radar 1 and radar 2 both use random frequency hopping waveforms, the coherent processing pulse train contains N sub-pulses and has the same frequency hopping rule, and the pulse repetition period is T r , and the pulse width is T. The random modulation frequency is distributed in a given bandwidth B, and the minimum frequency hopping step is Δf=B / N. The frequency hopping coefficient is a random integer sequence with a length of N in the interval

[0059] [0, N-1], in order to ensure sufficient utilization of the frequency band, the frequency hopping coefficient usually traverses the interval and is not repeated. Let the frequency hopping coefficients of radar 1 and radar 2 be c1(n) and c2(n) respectively, and the transmission signal models of the two radars are represented as follows:

[0060]

[0061] Where f1 and f2 are the carrier frequencies of radar 1 and radar 2 respectively.

[0062] Taking double-radar cooperative detection as an example, in order to separate the signal components of different radars, the difference between the carrier frequencies f1 and f2 of the two radars needs to be greater than the radar signal modulation bandwidth, and then it is realized through the corresponding band-pass filter. Let the target contain K scattering centers, and at the initial moment, the distance of the kth scattering center relative to radar 1 is r 1k . The target radial motion velocity is v, and at the n th sub-pulse transmission moment, the distance of the scattering center to radar 1 can be represented as r 1k (n)=r 1k+ vnT r The echo of the nth sub-pulse after mixing can be expressed as:

[0063]

[0064] where K is the number of scattering centers contained in the target, σ k represents the intensity of the kth scattering center. For the scene of cooperative detection by multiple missile-borne radars, the detection angles of the radars are very small, and the intensity of any scattering center on the target and the speed are basically consistent for the two radars. Let the distance of the kth scattering center relative to radar 2 at the initial time be r 2k The echo of the nth sub-pulse after mixing can be expressed as:

[0065]

[0066] Let Δr = r 2k -r 1k represents the electromagnetic wave transmission time corresponding to the distance difference of the two radars, then the above formula can be rewritten as:

[0067]

[0068] Similarly, the echo s 21 (n) received by radar 1 when radar 2 transmits and the echo s 12 (n) received by radar 2 when radar 1 transmits can be expressed as:

[0069]

[0070] Step 2: Distance difference compensation:

[0071] Comparing formula (III) and formula (VII), it can be seen that the phase modulation term introduced by the different distance delays of the echo signals received by the same radar but different radars is processed, and the phase modulation term is eliminated, so as to realize the distance difference compensation. s 12 (n) can be expressed as: 11 (n):

[0072]

[0073] where φ(n) = 2πΔr(f1 + c1(n)Δf) / c, φ(n) can be calculated by the echo signal received by the radar and used for distance difference compensation of s 12 (n), the compensation process of s 22 (n) and s 21 (n) is similar, and the echoes after distance compensation can be expressed as:

[0074]

[0075] It is evident that after the radar range differences are compensated, the echoes emitted by different radars exhibit the same variation pattern. Therefore, subsequent analysis based on echo s... 11 (n) and s 21 (n) Conduct collaborative detection.

[0076] Step 3: Echo Motion Compensation:

[0077] As can be seen from the above echo model, the frequency change and range change of the random frequency hopping waveform are coupled, which will introduce a higher-order phase term into the echo. This results in severe defocusing in the high-resolution range image obtained by direct FFT, thus requiring compensation for target motion. By comparing equations and , it can be seen that s 11 (n) and s 21 (n) Having the same range delay and different signal frequencies, if the random frequency hopping mode of the two radars is reasonably designed, the influence of frequency modulation can be eliminated, thereby realizing the rapid estimation of target motion parameters.

[0078] The random frequency hopping modulation patterns of the two radars are shown in the attached figure. Figure 3 As shown in the figure, where f0=(f1+f2) / 2, c(n)=c1(n)+(f1-f2) / 2Δf, c2(n)=-c1(n), it can be seen from the figure that the random frequency hopping signals transmitted by the two radars have complementary frequency variation patterns, that is, the frequency hopping coefficient c1(n) of the pulse transmitted by radar 1 is equal in magnitude and opposite in direction to the frequency hopping coefficient of the pulse transmitted by radar 2. Substituting into equations (IX) and (X), we can obtain:

[0079]

[0080] Multiplying the echo components yields the following result:

[0081]

[0082] In the formula, It contains no variables related to n, so it is a constant. This includes the variable c(n), where s'(n) varies with the number of sub-pulses n. Therefore, s(n) consists of a single-frequency signal component S0 and a varying component s'(n). After the FFT transformation, the energy of the single-frequency signal components is coherently accumulated to form a peak, while s'(n) remains in a defocused state. Therefore, the target velocity can be determined by the peak position of the sequence after the FFT transformation, as follows:

[0083]

[0084] where k0 is the peak position. After obtaining the target velocity, the echo motion compensation can be performed on the echo sequences of equation (XI) and equation (XII) by eliminating the component related to the velocity component in the echo.

[0085]

[0086] It can be seen that equation (XVI) and equation (XVII) describe the detection results of the target in the different frequency bands of the random frequency hopping signal. Subsequently, the coherent fusion of the random frequency hopping echoes of different frequency bands is performed to obtain high-resolution imaging.

[0087] Step 4: Frequency band fusion imaging:

[0088] The random frequency hopping of different frequency bands is rearranged, the echo data on the missing frequency points are zero-padded, and the echo signals of the two radars can be coherently fused and imaged by FFT transformation by setting a tight constraint condition. The missing bandwidth is an integer multiple of the frequency hopping step, which is a tight constraint. The rearrangement and zero-padding process is shown in FIG. 2. Figure 4 The echo sequences of equation (XVI) and equation (XVII) are arranged from small to large according to the minimum frequency hopping step, and the obtained echo sequence is represented as:

[0089] s all (n) = [s all (0), s all (1), s all (2),..., s all (L-1)]... (XVIII)

[0090] where L = M + 2N is the length of the zero-padded echo sequence, s all (n) is the result of rearrangement of s 21 (n), and the last N components are the results of rearrangement of s 11 (n) are all valid observations, and the missing frequency band is [f1, f2]. In order to ensure the coherence of the frequency hopping signals of the two radars, a tight constraint condition is set: the missing bandwidth f1-f2 is an integer multiple of the frequency hopping step Δf, and the corresponding zero-padded frequency point number is M = (f1-f2) / Δf-1.

[0091] It can be seen that the zero-padded position of s all (n) is located in the middle missing frequency band, and the distance resolution of s all (n) is consistent with the performance of the echo sequence with a continuous bandwidth of 2B. The specific derivation process H is as follows:

[0092] Let s Δ (n) be a valid observation sequence with a sampling step of Δf in the frequency band [f1-B, f2+B], and s H(n) is the effective observation sequence with sampling step Δf for frequency band [f1-B, f1+B], where n = 0, 1,..., L-1. Then

[0093] s H (n) = h1(n)s Δ (n)

[0094] s all (n) = h2(n)s Δ (n)

[0095] where is a window function. The corresponding FFT results are:

[0096]

[0097] s H (n) and s all (n) are respectively:

[0098]

[0099] where, denotes circular convolution, S Δ (k) denotes the FFT imaging result of the full-band effective observation sequence s Δ (n). The FFT transform result of the rectangular window function is a sinc envelope H1(k) and H2(k) with the same shape. Therefore, the spread modulation performance of the distance image peak is consistent after the circular convolution.

[0100] The high-resolution range profile obtained by performing FFT transform on s all (n) can be expressed as:

[0101] hrrp(k) = FFT[s all (n)] (XIX)

[0102] Thus, the high-resolution range imaging result under the dual-base cooperative detection can be obtained, and further combined with the envelope alignment and initial phase correction algorithm, the two-dimensional high-resolution range image of the target can be obtained.

[0103] In one specific embodiment of the present application, the simulation target ship point scattering model is as shown in the attached figure 1. Figure 5As shown, the ship is composed of 367 scattering points, the ship length l=120m, b=30m. Radar 1 transmits signal with carrier frequency f1=15GHz, radar 2 transmits signal with carrier frequency f2=15.255GHz, and the signal bandwidth is B=128MHz, Δf=1MHz. The signal modulation rule c1(n) of radar 1 is a non-repeated random integer sequence with length N in the interval [0, N-1]. The signal modulation rule c2(n) of radar 2 is -c1(n). The geometry scene of the bistatic cooperative detection is shown in Fig. 1. Figure 6 As shown, the ship is located at the origin of the coordinate system OXYZ, and the two detection platforms fly along the positive direction of the Y axis with the same flight speed v r =225m / s. At the initial moment, the distance between radar 1 and the center of the ship is 10km, and the distance between radar 2 and the center of the ship is 10.017km. The target is in a mobile state, and the projection component of the moving speed on the radar line of sight is v tLOS =3m / s. At the initial moment, the azimuth angle θ and the elevation angle β of the radar line of sight in the target coordinate system are θ=80 degrees and β=10 degrees, respectively.

[0104] The target is detected by using the complementary random frequency hopping waveform of the method, and the target echo sequence separated by the band-pass filter is represented as {s 11 (t), s 12 (t), s 21 (t), s 22 (t)}. The phase introduced by the radar distance difference is shown in Fig. 7(a), and the theoretical calculation result of the phase is also given in the figure. It can be seen that the method can effectively eliminate the phase term introduced by the platform distance difference. The FFT transform result of s(n) is given in Fig. 7(b), and the target speed estimated according to the peak position is 3.099m / s. Fig. 7(c) and Fig. 7(d) respectively give the distance imaging results of the two radars respectively. Due to the limitation of the bandwidth, the scattering centers are distributed in a small number of distance units, and the target detail information that can be obtained is less. The high-resolution range image fused by using the method is shown in Fig. 7(e), and the high-resolution range image after ideal compensation of the target speed is also given. It can be seen by comparison that the fused range image provides more abundant target detail information, and the estimated speed accuracy can meet the focusing requirements of high-resolution range imaging.

[0105] The radar two-dimensional imaging results obtained by using the envelope cross-correlation method and the PGA (Phase Gradient Autofocus) phase gradient autofocusing method for envelope alignment and initial phase correction are shown in Figs. 8(a)-8(d), wherein Figs. 8(a) and 8(b) respectively show the imaging results of radar 1 and radar 2 independent imaging, due to the limitation of the distance resolution, the target is distributed in about 15 distance units in the distance direction, the scattering center distribution is relatively fuzzy, and the target contour is not clear. The result obtained by using the fusion imaging mode is shown in Fig. 8(c), due to the improvement of the resolution, the target scattering center distribution area is larger, about 50 distance units, and the target detail information is richer, and the ISAR imaging result under the ideal velocity compensation is given, and the contrast (see M. Martorella., B. Haywood., F. Berizzi., and E. Dalle Mese. Performance Analysis of an ISAR Contrast-Based Autofocusing Algorithm Using Real Data [J]. IEEE Radar conference. pp. 30-35, 2003) is used to measure the focusing performance of the image, wherein the actual fused ISAR image contrast is 16.38, and the ideal compensation ISAR image contrast is 17.26. The experimental results show that the method can effectively realize the motion compensation of the bi-static radar and the fusion detection of the target.

[0106] Although the present application has been disclosed in the preferred embodiments as above, the embodiments are not intended to limit the present application. Any equivalent change or modification made without departing from the spirit and scope of the present application shall also fall within the protection scope of the present application. Therefore, the protection scope of the present application shall be defined by the content of the claims of the present application.

Claims

1. A bistatic radar cooperative imaging method based on complementary random waveforms, characterized in that, Includes the following steps: Step 1: Establish a dual-radar cooperative detection echo model. Both radar 1 and radar 2 use random frequency hopping waveforms. The transmission signal models of the two radars are expressed as equations (I) and (II) respectively: The coherent processing pulse trains each contain N sub-pulses with the same frequency hopping pattern, and the pulse repetition period is T. r The pulse width is T, the random modulation frequency is distributed within a given bandwidth B, and the minimum frequency hopping step size is Δf = B / N. Let the frequency hopping coefficients of radar 1 and radar 2 be c1(n) and c2(n) respectively, and f1 and f2 be the carrier frequencies of radar 1 and radar 2 respectively. When radar 1 transmits and radar 1 receives, the echo of the nth sub-pulse, after mixing, can be expressed as the following equation (III): Here, we assume the target contains K scattering centers, and at the initial moment, the distance between the k-th scattering center and radar 1 is r. 1k The target's radial velocity is v. At the moment of the nth sub-pulse transmission, the distance between the scattering center and radar 1 can be expressed as r. 1k (n)=r 1k +vnT r , σ k This represents the intensity of the k-th scattering center. When radar 2 transmits and radar 2 receives, the echo of the nth sub-pulse, after mixing, can be expressed as the following equation (V): Where, Δr=r 2k -r 1k The distance between the k-th scattering center and radar 2 is r. 2k , Radar 2 transmits the echo s received by Radar 1 21 (n) and the echo s transmitted by radar 1 and received by radar 2 12 (n), respectively, are expressed as equations (VI) and (VII): Step 2: Perform range difference compensation to eliminate the phase modulation term of the phase difference between the echo signals received by radar 1 and radar 2, thereby achieving range difference compensation. The range-compensated echoes can be expressed as equations (IX) and (X) respectively: Step 3: Perform echo motion compensation to eliminate the velocity-related components in the echo, thus achieving echo motion compensation. The echo after echo motion compensation can be expressed as equations (XVI) and (XVII) respectively. Where f0 = (f1 + f2) / 2, c(n) = c1(n) + (f1 - f2) / 2Δf, c2(n) = -c1(n); Step 4: Perform frequency band fusion imaging, rearrange the random frequency hopping of different frequency bands, zero-fill the echo data on the missing frequency points, and perform coherent fusion imaging of the echo signals of the two radars through FFT transformation by setting tight constraints.

2. The bistatic radar cooperative imaging method based on complementary random waveforms according to claim 1, characterized in that, The echo motion compensation in step 3 is as follows: Assume the frequency hopping coefficient c1(n) of the pulse transmitted by radar 1 is equal in magnitude and opposite in direction to the frequency hopping coefficient of the pulse transmitted by radar 2, where f0 = (f1 + f2) / 2, c(n) = c1(n) + (f1 - f2) / 2Δf, c2(n) = -c1(n). Substituting these values ​​into equations (IX) and (X), we obtain: Multiplying the echo components yields the following result: The target velocity at the peak position of the sequence after FFT transformation is as follows (XIV): Where k0 is the peak position, after obtaining the target velocity, the components related to the velocity component in the echo are eliminated, and echo motion compensation is performed on equations (XI) and (XII).

3. The bistatic radar cooperative imaging method based on complementary random waveforms according to claim 1, characterized in that, The specific method for performing frequency band fusion imaging in step 4 is to arrange the echo sequences of equations (XVI) and (XVII) in ascending order according to the minimum frequency hopping step size, and the resulting echo sequence is expressed as: s all (n)=[S all (0),S all (1),S all (2),...,S all (L-1)]......(XVIII) Where L=M+2N is the length of the zero-padded echo sequence, s all The first N components of (n) are s 21 (n) The result of the rearrangement is that the last N components are s. 11 (n) The rearranged results are all valid observations, with a missing frequency band of [f1, f2]. The missing bandwidth f1-f2 is an integer multiple of the frequency hopping step size Δf, and the corresponding number of zero-filled frequency points is M = (f1-f2) / Δf-1. For s all The high-resolution range image obtained by performing FFT transformation on (n) can be represented as: hrrp(k)=FFT[S all (n)]……(XIX)。

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