Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration

Defence Technology xxx (xxxx) xxx

Contents lists available at ScienceDirect

Defence Technology journal homepage: www.elsevier.com/locate/dt

Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration Cheng Cheng a, *, Xiao-dong Zhou b, Min Gao a, Zhu-lin Zong c, Yong-xiang Ji d, Bo Yu e a

Department of Missile Engineering, Army Engineering University, No.97 Westroad Heping, Shijiazhuang, China Department of Ammunition Engineering, Army Engineering University, No.97 Westroad Heping, Shijiazhuang, China c Research Institute of Electronic Science and Technology, University of Electronic Science and Technology, No. 4, Section 2, Jianbei Road, Chengdu, China d China Huayin Weapon Test Center, No. 450 Yuemiao Street, Huayin, Shaanxi, China e North Automatic Control Technology Institute, No.351 Tiyu Road, Taiyuan, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 March 2019 Received in revised form 22 April 2019 Accepted 12 June 2019 Available online xxx

In this paper, we proposed a monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration for missile-borne detector. Through iteration, the proposed algorithm automatically selects the echo signal of isolated strong-scattering points from the receiving echo signal data to accurately estimate the actual optimal monopulse response curve (MRC) of the same distance range, and we applied optimal MRC to realize the azimuth self-focusing in the process of imaging. We use real-time echo data to perform error correction for obtaining the optimal MRC, and the azimuth angulation accuracy may reach the optimum at a certain distance dimension. We experimentally demonstrate the validity, reliability and high performance of the proposed algorithm. The azimuth angulation accuracy may reach up to ten times of the detection beam-width. The simulation experiments have verified the feasibility of this strategy, with the average height measurement error being 7.8%. In the out-field unmanned aerial vehicle (UAV) tests, the height measurement error is less than 2.5 m, and the whole response time can satisfy the requirements of a missile-borne detector. © 2019 Production and hosting by Elsevier B.V. on behalf of China Ordnance Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Monopulse imaging High-resolution Adaptive iteration Missile-borne detector

1. Introduction The forward-looking imaging has been studied for a long time. There are series of research achievements around the world. Especially in recent five years, along with the SAR (synthetic aperture radar) imaging technology has been great focused, many experts and scholars at home and abroad have shifted their research focus to achieve the high-quality imaging both in efficiency and resolution. These studies can be departed to three parts: the SAR imaging technology, real-beam scanning imaging technology and mono-pulse imaging technology. These research results have greatly improved the imaging quality, but for the missileborne detector, these algorithms seem too complex. On the other hand, the limited space in the novel optional burst height proximity fuze require the complexity of signal processing algorithm and imaging strategy, therefore, we proposed a novel monopulse

* Corresponding author. E-mail address: [email protected] (C. Cheng). Peer review under responsibility of China Ordnance Society

forward-looking high-resolution imaging algorithm based on adaptive iteration. While ensuring the imaging accuracy, the complexity of the algorithm is not increased. Forward-looking imaging technique plays a significant role in navigation, self-landing, etc. Like SAR imaging technology, monopulse imaging algorithm has become a hot research topic nowadays. Of course, the research results of monopulse imaging technology are also very rich. In the book [1], forward-looking imaging algorithms have been researched in detail, in the chapter IV, an improved monopulse forward-looking imaging algorithm is presented. Firstly, the angle of the target is estimated by monopulse angle measurement. Secondly, the radar return energy is placed to the azimuth bin indicated by the estimate angle. Then, upon completion of beam scan, a high-resolution image is gained. Finally, the mask technique is used to make the target's boundary clear. Simulation results validate the effectiveness of this algorithm. From the book, angular measurement accuracy is an important factor affecting the final imaging quality of traditional monopulse imaging algorithms, when the angular resolution is increased, the resolution of monopulse imaging can be increased naturally. To overcome the deterioration of azimuth resolution, Yang [2]

https://doi.org/10.1016/j.dt.2019.06.008 2214-9147/© 2019 Production and hosting by Elsevier B.V. on behalf of China Ordnance Society. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

2

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

proposed an auto-focusing algorithm based on monopulse imaging technique to eliminate the error of monopulse response curve (MRC) in the echo signal processing. Yang's algorithm automatically extracts the echo signals of isolated strong scatters from the received data, these steps ensure the minimum error of MRC, so that, the angular measurement accuracy can be improved through the precise MRC in the same range. Shi [3] has proposed a new scheme of monopulse technique based on beam comparison to overcome the disadvantages, such as over reliance for the ratio curve, low accuracy and poor anti-interference ability for traditional method of monopulse techniques in angular measurement. The above two methods can improve the resolution compared to traditional looking-forward monopulse imaging. Zhang [4] established the airborne forward-looking scanning imaging model and optimized the range direction equation between the target and the sensor. In addition, the authors obtained the target range profile in the detection range by inverse solution mixing matrix. Therefore, the size of the antenna array becomes an important factor, in other words, the bigger the antenna array, the higher the estimation accuracy. Shui [5] has proposed a heuristic detector to detect rangespread targets in white Gaussian noise using multiple consecutive HRRPs. Based on the fact that strong scattering cells are sparse in target HRRPs, nonlinear shrinkage maps are designed to refine received HRRPs before integration, by which most of the noise-only cells in received HRRPs are suppressed while strong scattering cells most probably relevant to target signature are preserved. Since the target's scattering geometry is almost unchanged except for range walking during integration, the refined target HRRPs from consecutive pulses are highly similar while refined noise-only HRRPs are dissimilar due to randomicity. The modified correlation matrix of multiple refined HRRPs is used to measure their similarity. To obtain the HRRPs, the frequency domain (FD) algorithms have been used commonly, however, based on investigations, processing the SFPC (stepped frequency phase coding) waveform with the FD algorithm does not lead to the performance, in terms of peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR), of the single-carrier phase coding (SCPC) waveform processed with a matched filter (MF). Mahdi [6] proposed to split the spectrum of a phase coded pulse into a predetermined number of portions, and then to successively transmit the time-domain transformed versions of these various portions. An HRRP deception method based on phase-switched screen (PSS) is proposed in Xu's paper [7], this method utilizes PSS to impose phase modulation onto the radar reflected signal so that multiple false targets with verisimilar HRRP characteristics appear symmetrically around the real-target position. In the paper by Wen [8], a real-beam scanning based forwardlooking imaging method for phased array radar was proposed. The most important contribution of the paper is that it lays the analysis of the advantages and disadvantages of de-convolution

forward-looking imaging method. In addition, the reasons for lack of effective azimuth resolution improvement were pointed out. On the basis, a forward scan imaging method for scanning radar based on com-pressed sensing theory was proposed. High radial resolution was obtained by pulse compression of large time-bandwidth product signals. Since the contribution of strong scattering centers in the scene is compressible, high azimuth resolution was obtained by compressed sensing optimization method. The azimuth resolution of forward scan imaging is totally limited by the detection beam width. To improve the resolution, the detector is often relatively complex, and it is difficult for missile borne platform to provide lager space for the detector. To reduce the complexity, monopulse imaging technology can be used. Monopulse imaging technology combines antenna scanning with monopulse angle measurement technology to improve the imaging quality using high-precision angle measurement [9]. It has been used in many forward-looking high-resolution processing processes. Chen [10] used monopulse angle measurement technology to effectively improve the imaging resolution in the detection beam range. The feasibility and effectiveness of the scheme were illustrated by simple simulation. Aiming at the missile-borne wide band phased array monopulse radar system and the strong sea clutter back-ground, He [11] proposed a new method of clutter and angle measurement based on channel-level space-time adaptive processing (STAP) and adaptive transmitting beamforming (ATBF). It was shown by experimental measurements that the proposed method effectively improved the measurement accuracy and angular resolution of the target. Wu [12] proposed a self-adaptive algorithm for monopulse imaging. The method used iterative method to select isolated strong scattering echo signals from radar data automatically and accurately estimate the actual angle discrimination curve. Simulation experiments in the paper proved the robustness and feasibility of the algorithm. The monopulse imaging has the advantages of low complexity of the system structure, strong real-time performance, and no specific requirements for the radar tracks [13]. It may be applied to

Fig. 2. Diagram of high frequency waveguides.

Fig. 1. Burst height measurement diagram of missile-borne detector.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

the missile-borne platform. Based on this, in this paper we propose an effective forward-looking imaging algorithm with high resolution for the missile-borne detector. We combine the echo data in the target regions as well as the self-focusing optimized monopulse response curve, and adopt the mono-pulse angulation technology to improve the angular resolution, featuring high-resolution imaging. 2. Working principle of missile-borne detector A novel optional burst height proximity fuze is fixed on new generation long-range box-guided ammunition. It can calculate the precise real-time height of the ammunition at descending section for meeting the requirements of modern combat. The missile-borne detector working at preset measuring area is shown in Fig. 1. As we can see in Fig. 1, the missile-borne detector is a phased array platform, it can be regarded as an antenna array detector in the deduction. It is located at the front of fuze and perpendicular to the projectile axis. And the signal processing circuit is located behind the missile-borne detector (phased array platform). The definition of high frequency waveguide port for missileborne detector is shown in Fig. 2. According to the preset combat mission, missile-borne detector starts work in the descent section of projectile. It emits detection signal along the downward velocity direction, and the target region imaging can be obtained through echo signal processing. From Fig. 1, we can see that the width of the minimum resolution unit is determined through angular resolution of the same distance dimension in a certain detection region. Meanwhile, monopulse imaging algorithm has the advantages of low complexity, high realtime performance and no special requirements for projectile. It can be used in forward-looking imaging process of missile-borne detector. The transceiver channel (radio frequency front-end) consists of one transceiver common channel, three receiving channels and one calibration channel. The transmitting channel includes upconversion module, power amplifier, circulator, etc. The

3

intermediate frequency (IF) excitation signal is amplified by frequency conversion through the transmitting channel, and then radiated by the antenna. The antenna receives the target signal and outputs the IF signal through three single-channel receiving modules. In these modules, the front part of the circulator is shared with the sum channel receiving and transmitting channels, and the receiving modules of azimuth and pitch difference channels are consistent with the channel composition. Signal processing module mainly completes signal generation, echo acquisition, signal processing, data processing, timing control, data interaction and other functions. In order to control size and power consumption, signal processing module is mainly composed of radio frequency agile transceiver (AD9361), high-speed DSP processing chip and large-scale low-power FPGA. Among them, RF agile transceiver completes signal generation and acquisition, highspeed DSP processing chip carries out signal processing and data processing of various modes, and FPGA mainly completes the functions of master control, external interface, beam agility and signal pre-processing.

3. Self-focusing high resolution azimuth angulation strategy The monopulse azimuth angulation uses the echo in the detection region, and forms the sum and difference beams, denoted by SðqÞ and DðqÞ, respectively. The ratio of difference beam to sum beam is used for angle discrimination. During the process of traditional angle discrimination, the relation between the sum and difference beams can be expressed as

DðqÞ ¼ SðqÞ,tanðkpqÞj

(1)

where q is the angle of the target deviating from the detection beam centre, and k is a constant. Therefore, tanðkpqÞ is considered as the imaginary part of the ratio of the sum and difference beams, and q can be represented by

Fig. 3. The complete process of forward-looking imaging algorithm.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

4

C. Cheng et al. / Defence Technology xxx (xxxx) xxx




q ¼ ðkpÞ1 ,arctan

be represented by



DðqÞ SðqÞ

(2) imag

where []imag is the imaginary part function. It can be seen from (2) that the vital factors to determine the angular resolution are the sum and difference beams. In the conventional sense, the monopulse angulation uses all the echo data in the detection region to form the sum and difference beams to calculate the angle. But it is hard to achieve high-resolution measurements [8]. The reason is that the ‘sharpness’ degree of the tanðkpqÞ curve directly affects the angular resolution. Hence, finding the optimal MRC is the key for the realization of the azimuth high-resolution angulation. Merely considering the azimuth direction, it is assumed that the detection beam performs an azimuthal scanning at the angular velocity of uq and the point targets in the range covered by the beams are discovered at the moment t0 . Since the echo data can be taken as the convolution of the target surface scattering coefficient with the antenna pattern, the sum and difference beams are

8 > > < Sumðr; ~tÞ ¼ Sumðr; tmax þ ~tÞ Diffðr; ~tÞ ¼ Diff ðr; tmax þ ~tÞ > > ~t2Tn :;

(6)

For n ¼ 1, the achieved sum and difference beams data are called the original data. Step 3: Solving the monopulse response curve The monopulse response curve in azimuth direction of each iteration may be formulated as

tanr ðkpqÞ ¼

Diffðr; tmax þ ~tÞ,Sum ðr; tmax þ ~tÞ Sumðr; tmax þ ~tÞ,Sum ðr; tmax þ ~tÞ

;~t 2 Tn (7)

where ‘*’ shows the conjugate operation. Eq. (7) represents the achieved monopulse response curve of the r th distance dimension after n iterations. By smoothly increasing the number of iterations,

8 <

Sumðr; tÞ ¼ A,Sðr; tÞ,Sðr; tÞ : Diffðr; tÞ ¼ A,Sðr; tÞ,Dðr; tÞ

(3)

where A is the target surface scattering coefficient, r denotes the r th distance dimension, Sum is the sum beam, and Diff is the difference beam. According to the ratio of the target echo data, the actual monopulse response curve can be given by During the detection process, we take the echo data of the strongest scattering points at the dimension of the same distance in the neighbouring range as the reference data. In addition, we set the evaluation threshold, through continuous iterative computations, and then correct and reduce the range of the neighbouring data.

tanactual ðkpqÞ ¼

Diffðr; tÞ Sumðr; tÞ

(4)

Accordingly, we achieve the monopulse response curve within the range of the strongest scattering points, where the curve is considered as the optimal MRC at the dimension of this distance. We use this optimal MRC to perform the azimuth angulation at the dimension of the same distance and the angulation accuracy is significantly improved. The complete process is shown in Fig. 3. The specific steps are as follows: Step 1: Acquisition of echo signals in the detection area Setting that the sum and difference channels of the echo after the pulse pressure are respectively Sumðr; tÞ, Diffðr; tÞ, and suppose the corresponding time of the maximum radius in the angulation results is tmax . It may be considered that the time corresponds to the largest scattering target point within r th distance dimension. The target angular information is achieved at that time and applied by the monopulse response curve through Eq. (4). Hence, there is an error between the measurement time and the actual corresponding time, expressed as Dtmax . Step 2: Setting the data range The neighbouring time range of tmax is expressed by Tn, where n denotes the number of iterations, and Tn is expressed as

Tn ¼ ftjtmax  td n  t  tmax þ td n g

(5)

where td n is the time range of the n th iteration, and the width of Tn is 2td n . In addition, the value range of td n will not exceed the time of the antenna sweeping over the main lobe width of the single beam. Then, the sum and difference echo beams in the updated area can

Fig. 4. Detection model of missile borne detector.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

the monopulse response curve will tend to its optimal value. Therefore, the curve should be evaluated to meet the default requirements. Step 4: Updating the iteration conditions The optimal monopulse response curve at the strongest scattering point of the distance dimension is close to the similar impulse response. Therefore, one may use the energy ratio to determine if it has reached the optimal value. Considering Powerðr; Tn Þ as the energy at the strongest scattering point, Powerrest ðr; Tn Þ as the energy in other regions and ThresholdðrÞ as the threshold, we find if and only if the H1 event (energy ratio being larger than or equal to the pre-set threshold) occurs, tanr ðkpqÞ represents the optimal MRC under r th distance dimension. When the H0 event occurs, the energy ratio is less than the pre-set threshold, therefore, the time range td n should be updated and the n þ 1th iteration should be performed.

H1 Powerðr; Tn Þ  ThresholdðrÞ Powerrest ðr; Tn Þ < H0

(8)

Step 5: Correcting the central location The corresponding tmax of the strongest scattering point at each distance dimension is corrected. As the solution given by Eq. (7) does not perform error correction, the error of the monopulse response curve is rather large, and the achieved tmax is erroneous. Therefore, at the same time of updating the time range, tmax should be corrected. We set the correction to be ~t max jn , and then the corrected ~t max jre can be represented by

tmax jre ¼ tmax þ ~t max jn

(9)

By entering the next iteration calculation, one should correct the echo central time of the strongest scattering point. Then, tmax is replaced by tmax jre to perform the new round of iteration calculation. Step 6: Measuring the azimuth angle After the iteration calculation, we consider tanr ðkopt pqÞ as the optimal monopulse response curve under r distance dimension. The function tanr ðkopt pqÞ performs the angular estimation for the target scattering points within the r distance dimension and performs amplitude and phase detection for them. After achieving all the target angles set qr within the distance dimension, the target position may be determined by ðr; qr Þ, which can support the subsequent imaging. Step 7: Forward-looking high-resolution imaging. According to the optimal MRC and distance information, the forward-looking high-resolution imaging with height information can be obtain through data fusion.

5

the target region, G0 denotes the gain of transmitted antenna, and gU and gL denote the pattern functions of up lobe and down lobe, respectively. The power density taken from a small region, known as the differential region in the detection region can be expressed as:

dP ¼

Pg s0 dAg 4pR2

(11)

where s0 denotes the back-scattering coefficient of differential region and dAg denotes the differential area. Fig. 4 shows the missileborne detector model: In Fig. 4(a), u denotes the included angle between the median axis and boresight of the two lobes, j denotes the angle between boresight and y-axis, q denotes the angle between boresight and zaxis, and h denotes the height of missile-borne detector. Fig. 4(b) shows the sliced model of Fig. 4(a) along the boresight direction, the model established by taking the projection of z-axis and boresight on the surface of XOY as the coordinate axes. In Eq. (11), the differential area can be expressed as

dAg ¼ R2 ,cot qdqdj

(12)

By using Eq. (10) and Eq. (12), the differential expressions of the sum echo power and difference echo power can be obtained as follows:

P lG0 s0 cot q ðgL þ gU Þ2 ðgU Þ2 dqdj 64p3 R2 P lG0 s0 cot q dPL ¼ ðgL þ gU Þ2 ðgL Þ2 dqdj 64p3 R2 dPU ¼

(13)

where l denotes the wave length of emission signal and P denotes the radiant power. The radiant power during the pulse duration is given as P ¼ P0 , otherwise it is 0. This is expressed as follows:

PðtÞ ¼

8 > > > > > < P0 > > > 0 > > :

1 jtj  Tp 2 1 jtj > Tp 2

(14)

where Tp denotes the pulse duration, and c denotes the transmission speed of electromagnetic wave. As shown in Fig. 4(b), the

4. Monopulse ranging strategy In section IV, a missile-borne monopulse height measurement strategy (MBM-HMS) is proposed. In missile-borne monopulse detector, radiation antenna pattern consists of separate up lobe and down lobe [10]. The field intensity of lobes to transmit signals is added on the transmission, because they are intersecting with each other. The power density of the detection region located at a distance R from the missile-borne detector can be expressed as:

Pg ¼

Pt G0 ½gL þ gU 2 8pR2

(10)

where Pg denotes power density from target region, Pt denotes the transmitted power, R denotes the distance of detector antenna from

Fig. 5. Simulation results for the patterns of the sum and difference beams.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

6

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

PL ¼

 ðd qð2  P lG0 s0 cot q 2 2 ðg Þ ðg Þ dqdj þ g L U L 64p3 R2

d q1

 ðd qð2  P lG0 s0 cot q 2 2 dqdj PU ¼ ðg þ g Þ ðg Þ L U U 64p3 R2 d q1

9 8 > > > > > > > P lG0 s0 cot q > > 2> > > q d ðg þ g Þ 2 > ð ð> L U = < 3 2 64p R Pd ¼ dqdj > > h i > > > > 2 2 > d q1 > > > ðg Þ  ðg Þ L U > > > > ; :

Fig. 6. Comparison of the monopulse response curve for different k value conditions with the optimal monopulse response curve.

(16)

9 8 > > > > > > > > P l G s cot q > > 0 0 2 > ðg þ g Þ > > ðd qð2 > L U = < 3 2 64p R Ps ¼ dqdj > >h i > > > > 2 2 > > d q1 > ðg Þ þ ðg Þ > L U > > > > ; : where d denotes the upper or lower limit of j, determined by the missile platform itself. As shown in Fig. 4(b), d denotes the largest angle between the detection beam boresight with the flight direction, and ± only represents the direction. Generally, the monopulse signals of up lobe and down lobe can be expressed as [14‒16].

eU ðtÞ ¼ VUc cosðuc tÞ þ VUs sinðuc tÞ eL ðtÞ ¼ VLc cosðuc tÞ þ VLs sinðuc tÞ

(17)

where coefficients VUc and VUs are both determined by the radar parameters and the scattering properties of echo signal region. However, in the actual process of engineering practice, monopulse transmission signal is constructed by bessel function of the second kind [17]. Then, sum signal and difference signals can be expressed as

    sðtÞ ¼ eL ðtÞ þ eU ðtÞ ¼ VLc þ VUc cosðuc tÞ þ VLs þ VUs sinðuc tÞ dðtÞ ¼ eL ðtÞ  eU ðtÞ ¼ VLc  VUc cosðuc tÞ þ VLs  VUs sinðuc tÞ (18) Fig. 7. Angle discrimination results for different k value conditions.

angle between up lobe or down lobe and the ground is the upper limit or lower limit of q, given by q1 and q2 respectively, and they can be expressed as

After echo signal data both in sum channel and difference channel passing the phase detector, the output of phase detector is 0 if and only if the phases of the two signals are quadrature. For example, when the difference of the phase between sum signal and difference signal is 90 , we get the following:

tan1



VLs þ VUs VLc þ VUc



¼ tan1



VLs  VUs VLc  VUc

þ

p

(19)

2

By taking tangent function for the left and right side of (19), we get

Tp c sin q tan q 4h T c q2 zq þ p sin q tan q 4h

q1 zq 

(15)

By using the above expressions in Eq. (13), the total powers of the echo sum channel and the echo difference channel in the detection area can be expressed as follows:

Table 1 Simulation parameters. Parameter

Value

Target setting Main lobe width/( ) Scanning range/( ) Beam inclination angle

9 2 3:0.01:3 -p/180

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

VLs þ VUs VL  VUc ¼  c VLc þ VUc VLs  VUs

(20)

from which the following expression is obtained:

V 2Ls þ V 2Lc ¼ V 2Uc þ V 2Us

(21)

By inspecting Eq. (17), the left side of Eq. (21) is the pulse power of down lobe, while the right side is the pulse power of up lobe. When the up-detection pulse echo signal power is the same as the down detection pulse echo signal power, the output of phase detector is 0. Currently, the corresponding slope distance is the boresight

7

distance between the missile-borne detector and the target region. That means when the following expression is solved for R, when the corresponding value of R is the slope distance between the desired missile-borne detector and the target region. Scanning at the same distance dimension, the slope distance vector of this region can be calculated according to different orientation resolution and the vector scale, to realize effective measurement of missile-borne detector for foresight area.

ðd qð2  h i P lG0 s0 cot q 2 2 2 ðg dqdj ¼ 0; Pd ¼ ðg þ g Þ Þ  ðg Þ L U L U 64p3 R2  d q1

5. Experimental verification 5.1. Experiment 1: the monopulse response curve error affects the imaging of the single target The monopulse response curve tanðkpqÞ greatly affects the azimuth angulation. Fig. 5 shows the simulation results for the patterns of the sum and difference beams. In the simulation process, the half-wave width of the antenna pattern is set to 1 rad, the target offsetting is 0.3 rad away from the axis, and the ground scattering coefficient is equal to 1. To explore the relationship between the accuracy degree of the monopulse response curve and the final target azimuth angle resolution, the detection premises are simplified. We assume that the detection beam is static, i.e., without azimuthal movement, and some static target within the beam range deviates 0.3 rad away from the beam axis. Then, we use the mono-pulse angulation technology. Fig. 6 plots the target azimuth results achieved under different monopulse response curve conditions. The imaging result of a single target is shown in Fig. 7. As it can be observed in the figure, different monopulse response curves affect the final azimuth angle discrimination results. The effect is mainly on the aspect of the ‘focus’ degree of the angle discrimination. The representation by the superior monopulse response curve is closer to the angulation results of the impulse response, which conforms to the theoretical derivation in the last section. Hence, during the actual imaging process, the accuracy degree of

Fig. 8. Imaging results for two imaging algorithms.

Fig. 9. Profiles of the central points of the mono-pulse and real-beam scanning imaging.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

8

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

Fig. 10. Test environment and process.

the monopulse response curve will affect the eventual imaging results. 5.2. Experiment 2: high resolution azimuthal imaging We next perform simulation experiments for the highresolution imaging. We also compare the proposed imaging strategy with the traditional real-beam scanning imaging algorithm. Hence, we show the advantages of this imaging strategy. Fig. 7 plots the achieved imaging results, where two different imaging strategies are used to image the forward-looking targets. Compared to the theoretical derivation, Eq. (7) and Eq. (8) are generalized as follows to meet the requirements of imaging accuracy of missile borne radar (2.5 m) in the actual imaging process:

tanr;rþn ðkpqÞjopt ¼

curve from r to r þ n distance dimension. The optimal whole angle select curve can be obtained through averaging optimal angle select curve of each distance dimension. Eq. (23) provides a more universal verdict condition of tanr;rþn ðkpqÞ opt to confirm the number of iterations. The simulation parameters are shown in Table 1. The results for forward-looking imaging simulation using realbeam scanning imaging and the proposed algorithm are shown in Fig. 8. In Fig. 8, the parts of the imaging results highlighted by rectangles show that the two imaging algorithms have a large resolution difference. The mono-pulse forward-looking imaging strategy proposed in this paper exhibits better angular resolution. Fig. 9 plots the orientation profile of the imaging centre. As

P tanrþn1 ðkpqÞ n

n ðn ¼ 1; 2; 3…Þ∩ðr þ n  rangeÞ

H1 Powerr;rþn ½ðr; r þ nÞ; Tn   Thresholdðr; r þ nÞjmin Powerr;rþnj rest ½ðr; r þ nÞ; Tn  < H0

(22)

(23)

where Eq. (22) provides the solution method of optimal angle select

Fig. 11. Actual test results of sum and difference channels in different test angles.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

9

shown in the figure, mono-pulse forward-looking imaging strategy is capable of greatly improving the azimuthal resolution, nearly ten times of the real-beam scanning imaging resolution. Moreover, the quality of the imaging is better, which can meet the requirements of the missile-borne detector's high-resolution imaging. 5.3. Experiment 3: high resolution imaging accuracy analysis through actual directional diagram The dark room environment of the test is shown in Fig. 10(a). The azimuth and pitch patterns are tested in a compact anechoic chamber. The test scene for the azimuth and pitch patterns is shown in Fig. 10(b) and the transceiver antenna test site is shown in Fig. 10(c).

Fig. 12. Angle resolution results with different number of iterations in the same detection range.

Fig. 13. Results of inclined distance measurement on the condition of the same height of missile-borne detector and different drop angles.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

10

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

The directional diagram results of the sum channel, azimuth difference channel and pitch difference channel obtained from the dark room are shown in Fig. 11. By continuously narrowing the data range using increasing number of iterations, the final change of angular resolution in the same distance dimension is shown in Fig. 12. Fig. 12 shows that the angle resolution in the same range dimension is improved effectively with the increase of iterations, which reflects the effectiveness of the proposed high-resolution imaging algorithm. The angle resolution can be changed using different iterations according to the needs of different combat tasks, so that the fuze can use the echo signal data to improve the azimuth angle measurement accuracy adaptively. Once the angle measurement accuracy is improved, the high-resolution imaging of the detection area can be realized. The improved azimuth resolution is about ten times that of the traditional forward-looking scanning imaging algorithm. In addition, the complexity of the algorithm is low, so it can reach the preset resolution requirement at the eighth iteration. The main problem is the control of the number of iterations. Future work will focus on the optimization of the threshold function given by Eq. (8) to ensure that redundant iterative computation will not occur in the iterative process. 5.4. Simulation experiment 4: verification of the feasibility of MSMHMS for a single scattering point target region In this set of experiments, the involved working height range of the optical proximity fuze task for height of burst is between 30 m and 100 m, and the range of drop angle is between 45 and 65 . The detector is located at the front end of fuze, it is perpendicular to the missile axis, and the detection antenna is parallel to the missile axis. The following two conditions are considered: 1) The same drop angle (45 ) and different heights (ranging from 20 m to 100 m and taking a measurement every 20 m); 2) The same height (100 m) and different drop angles (ranging from 45 to 65 and taking a measurement every 5 ). With these conditions, the echo sum channel power and echo difference channel power obtained through simulation and the measurement errors with respect to the actual

Fig. 15. Height data of an actual terrain. Fig. 14. Results of inclined distance measurement on the condition of the same drop angle and different heights of missile-borne detector.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

11

Fig. 17. Height measurement error under different conditions.

Fig. 16. Height measurement results of different angles when the height of missileborne detector is 100 m.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

12

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

measurements are shown in Fig. 13 and Fig. 14. As shown in Fig. 13, without considering any clutter or interference, when the drop angle is 45 , under the condition of different measuring heights, the measuring accuracy of MBM-HMS reaches up to 0.65%. It indicates that when the drop angle is the same, the effect of height on measurement is small. As shown in Fig. 14(a), under the condition of different drop angles, the error of the inclined distance is different. When the drop angle increases, the error of measurement tends to the minimum value. Through these simulation experiments, we have shown that MBM-TMS can measure the inclined distance between the detector and the target region with a high accuracy, which is consistent with theoretical derivation. This indicates the feasibility of the proposed height measurement strategy. 5.5. Simulation experiment 5: performance verification of MBSHMS with actual altitude data and increasing ground clutter and receiver noise Digital elevation model (DEM) terrain height data are used to extract the terrain altitude in one region of China [11] with an area of 300 m  300 m. This terrain altitude is used to perform simulation experiments for the proposed height measurement strategy and to increase ground clutter interference as well as receiver noise. The histogram of the terrain altitude data is shown in Fig. 15 in Fig. 15, the histogram is used to represent the terrain altitude data of the smallest resolution element. It sets that the bornemissile detector enters the slope midair of this region from the middle point of azimuth at a specific time, and moves forward along the distance orientation; and the region above is the final target region. The echo frequency spectrum of the pulse signal with increasing receiver noise can be expressed as [18‒19].

S0 ¼

16T 2g f 20

p2 Bs


 Bs kTF Pd þ 2Tg f0

(24)

where, Tg denotes the receiver threshold length, f0 denotes the pulse repetition frequency, Bs denotes the Doppler Frequency Shift of echo signal, Pd denotes the difference channel input power, calculated by Eq. (16), k denotes the Boltzmann constant, T denotes the temperature of receiver and F denotes noise. Keeping the height of the missile as constant and changing the angle between the detector frontage and ground, the obtained results of the detection region measurement heights are shown in Fig. 16. Fig. 16 shows the results of the proposed height measurement strategy for the extracted terrain altitude when the height of the missile-borne detector is 100 m and beam angles are 50 , 65 and 70 . The obtained covering layer is the simulation measurement results, and the simulation errors are shown in Fig. 17. Fig. 17 shows the errors of height measurement under different measurement angles. The errors are mainly distributed in the region with largely rugged terrain. The measurement errors in flat regions are the minimum in the whole measurement region. The average error of simulation height measurement is 7.8%, and the maximum error value is 4.3 m. 5.6. Suspension flight experiment: selecting different types of earth's surface and using unmanned suspension flight detector to conduct actual measurement A six-rotor unmanned aerial vehicle (UAV) is used to perform suspension flight experiment for the actual monopulse detector. Relevant devices used in this set of experiments are shown in Fig. 18. As shown in Fig. 18(a), the suspension flight holder (i.e., taking six-rotor UAV as carrier) contains monopulse detector, wireless transmission antenna for data transmission, and power supply module. It is used to emulate a missile-borne detector. A six-rotor UAV shown in Fig. 18(b) and (c) are used to simulate missile test conditions with the suspension flight equipment attached to the UAV. Separately, a small-sized four-rotor UAV (Fig. 18(d)) is used to record the experimental process. The actual test results under different test heights of missileborne detector are shown in Fig. 19.

Fig. 18. Related equipment and module of suspension flight test.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

13

Fig. 19. The results of some different test heights.

In Fig. 19, there are series of test scenes show the results of actual tests in different heights, and the results prove the feasibility of proposed height measurement algorithm. The monopulse height measurement experiments are carried out for three types of earth

Table 2 Height measurement results under different test scenes. Scene

Platform Height/m

Measured Height/m

Flat ground

20.1 51.3 101.8 130.7 20.1 50.6 100.2 140.0 30.9 51.1 101.6 154.0

21.420 49.963 99.931 127.412 18.678 49.962 99.686 142.401 29.968 49.865 99.975 153.212

Grassland

Still-water surface

surface conditions and the obtained experimental results are shown in Table 2. The real-time platform height is measured using the six-rotor UAV itself as the reference value of measurement. The reference value is denoted by Platform Height in Table 2. The measurement data of monopulse detector are transmitted to the earth's surface terminal using the wireless transmission antenna. These data are denoted by Measured Height in Table 2. The measurement error of the pulse detector is less than 2.5 m. This small value of measurement error validates our theoretical derivations. The measurement process with the still-water surface has sharper echo signals, and as a result the measurement error for this surface is the minimum among all the three surfaces considered. The whole computation time is mainly taken up by the process of data transmission from the UAV to the ground terminal. The signal processing operation does not involve any complicated operations, so the requirements of a missile-borne detector can be satisfied.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008

14

C. Cheng et al. / Defence Technology xxx (xxxx) xxx

6. Conclusion In this paper, real-time echo data is used to put forward a selffocusing high resolution forward-looking monopulse imaging strategy. We have demonstrated the feasibility and superiority of this strategy by theoretical derivation and simulation experiments. Moreover, the quality of the imaging can be improved by about ten times of the traditional real-beam scanning imaging resolution. In addition, by establishing a height measurement model, the height measurement principles in a target region are shown. The coordinate corresponding to the zero value of the difference channel echo signal is estimated to obtain the inclined distance of strong scattering points in target region. The drop angle data are combined to calculate the height information of all strong scattering points in the detection region. This allows foresight measurement with a high accuracy. The simulation experiments have verified the feasibility of this strategy, with the average height measurement error being 7.8%. In the out-field suspension flight tests, the height measurement error is less than 2.5 m, and the whole response time can satisfy the requirements of a missile-borne detector. Such an imaging strategy is expected to find various military applications. Furthermore, the azimuth resolution can be further improved by ground clutter elimination technique and more accurate MRC acquisition technique. The main impartments are: 1. echo signal data extraction with more efficiency; 2. precise division of echo data for MRC; 3. high-resolution signal process method both in range direction and azimuth direction. Acknowledgement The name of the project that funded this article is 13th Five-Year Plan" equipment pre-research project, the number of this project is 30107030803. References [1] Jiang XM, Huang YL, Yang JY, Li WC. ‘An improved monopulse forwardlooking imaging algorithm’, Communications, signal processing, and Systems. New York: Springer; 2012.

[2] Yang CJ, Wu D, Zhu DY, Shen MW. An auto-focusing algorithm for monopulse imaging technique. In: 2016 9th international congress on image and signal processing. Biomedical Engineering and Informatics; 2016. p. 1163e7. [3] Shi JY, Liu HW, Ma PJ. A monopulse scheme in radar angle-measurement based on beam-comparison. In: 2016 9th international congress on image and signal processing. Biomedical Engineering and Informatics; 2016. p. 1263e7. [4] Zhang Y, Zhang YC, Huang YL, Yang JM. A sparse Bayesian approach for forward-looking super resolution radar imaging. Sensors 2017;17:1353. [5] Shui PL, Xu SW, Liu HW. Range-spread target detection using consecutive HRRPs. IEEE Trans Aerosp Electron Syst 2011;47:647e65. [6] Mahdi S, Samir MO, Eric G, Oussama B. A modified stepped frequency phase coding radar waveform designed for the frequency domain algorithm. Digit Signal Process 2019;88:101e15. [7] Xu LT, Feng DJ, Zhang R. High-resolution range profile deception method based on phase-switched screen. IEEE Antennas Wirel Propag Lett 2016;15: 1665e8. [8] Wen XY, Kuang GY, Hu JM, Zhan RH. Forward-looking imaging based on real beam scanning phased array radars. Acta Aeronautica Astronautica Sinica 2014;35(7):1977e91. [9] Ojowu O, Xu LZ, Li J, Anderson J. High resolution imaging for impulse-based forward-looking ground penetrating radar. Int J Rem Sens Appl 2015;5: 11e24. [10] Chen HM, Lu YB, Mu HQ, Yi XL. Knowledge-aided mono-pulse forwardlooking for airborne radar by exploiting the antenna pattern information. Electron Lett 2017;53(8):566e8. [11] He SH, Jiang ZS, Zhang J. Channel-level STAP and ATBF for missile-borne wideband phased-array mono-pulse radar. J Signal Process 2016;32(9): 1108e16. [12] Wu D, Yang CJ, Zhu DY, Shen MW. An auto focusing algorithm for monopulse imaging. Acta Electron Sin 2016;44(8):1962e8. [13] Huang GL, Zhou SG, Chio TH, Sim CYD. Wideband dual-polarized and dualmonopulse compact array for SAR system integration applications. IEEE Geosci Remote Sens Lett 2016;13(8):1203e7. [14] Diao GJ, Xu XJ. Three-dimensional monopulse radar imaging simulation of ships on sea surfaces. SAR Image Anal Model Tech 2012;8536:85360V. [15] Wang W, Cui W. Angular glint modeling algorithm of phase-comparison sumdifference monopulse radar based on deterministic model. Acta Armamentarii 2013;34(10):1258e65. [16] Manisha K, Harish P, Malay RT. Mathematical analysis of RF imaging techniques and signal processing using wavelets. Int J Signal Imaging Syst Eng 2017;10(6):286e300. [17] Wang LSB, Xu ZH, Liu XH, Wang GY. Detection for unresolved targets by using complex monopulse ratio on planar array radar. J Natl Univ Def Technol 2018;40(3):76e81. [18] Liu GM, Han HY. Design and implement on monopulse radar signal preprocessing system based on FPGA. Trans Beijing Inst Technol 2018;38(7): 752e8. [19] Guo KY, Niu TY, Sheng XQ. Location reconstructions of attributed SCs by monopulse radar. IET Radar, Sonar Navig 2018;12(9):1005e11.

Please cite this article as: Cheng C et al., Research on monopulse forward-looking high-resolution imaging algorithm based on adaptive iteration, Defence Technology, https://doi.org/10.1016/j.dt.2019.06.008