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

Chng Chng ,Xio-ong Zhou ,Min Go ,Zhu-lin Zong ,Yong-xing Ji ,Bo Yu

a Department of Missile Engineering,Army Engineering University,No.97 Westroad Heping,Shijiazhuang,China

b 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

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

ABSTRACT 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 MRCto 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.?2020 China Ordnance Society.Production and hosting by Elsevier B.V.on behalf of KeAi Communications Co.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

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 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]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,how ever,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 PSSto 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 forward looking 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.

Fig.2.Diagram of high frequency waveguides.

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

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 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 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 Σ（θ）and Δ（θ）,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

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

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

where[]imagis 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 tan（kπθ）curve directly affects the angular resolution.Hence,finding the optimal MRCis 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 ωθand 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

where A is the target surface scattering coefficient,r denotesthe rthdistance 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.

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 Sum（r，t）,Diff（r，t）,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 rthdistance 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 Δtmax.

Step 2:Setting the data range

The neighbouring time range of tmaxis expressed by Tn,where n denotes the number of iterations,and Tnis expressed as

where tδnis the time range of the nthiteration,and the width of Tnis 2tδn.In addition,the value range of tδnwill 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 be represented by

For n=1,the achieved sum and difference beams data are called the original data.

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Step 3:Solving the monopulse response curve

The monopulse response curve in azimuth direction of each iteration may be formulated as

where‘*’shows the conjugate operation.Eq.(7)represents the achieved monopulse response curve of the rthdistance dimension after n iterations.By smoothly increasing the number of iterations,the monopulse response curve will tend to its optimal value.Therefore,the curve should be evaluated to meet the default requirements.

Fig.4.Detection model of missile borne detector.

Step 4:Up dating 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 Power（r，Tn）as the energy at the strongest scattering point,Powerrest（r，Tn）as the energy in other regions and Threshold（r）as the threshold,we find if and only if the H1event(energy ratio being larger than or equal to the pre-set threshold)occurs,tanr（kπθ）represents the optimal MRC under rthdistance dimension.When the H0event occurs,the energy ratio is less than the pre-set threshold,therefore,the time range tδnshould be updated and the n+1thiteration should be performed.

Step 5:Correcting the central location

The corresponding tmaxof 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 tmaxis erroneous.Therefore,at the same time of updating the time range,tmaxshould be corrected.We set the correction to beand then the correctedcan be represented by

By entering the next iteration calculation,one should correct the echo central time of the strongest scattering point.Then,tmaxis replaced by tmax|reto perform the new round of iteration calculation.

Step 6:Measuring the azimuth angle

After the iteration calculation,we consider tanr（koptπθ）as the optimal monopulse response curve under r distance dimension.The function tanr（koptπθ）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 setθrwithin the distance dimension,the target position may be determined by（r，θr）,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.

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:

where Pgdenotes power density from target region,Ptdenotes the transmitted power,R denotes the distance of detector antenna from the target region,G0denotes the gain of transmitted antenna,and gUand gLdenote 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:

where σ0denotes the back-scattering coefficient of differential region and d Agdenotes the differential area.Fig.4 shows the missileborne detector model:

In Fig.4(a),ω denotes the included angle between the median axis and boresight of the two lobes,ψ denotes the angle between boresight and y-axis,θ 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

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

where λ denotes the wave length of emission signal and P denotes the radiant pow er.The radiant pow er during the pulse duration is given as P=P0,otherwise it is 0.This is expressed as follow s:

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

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

Fig.7.Angle discrimination results for different k value conditions.

where Tpdenotes the pulse duration,and c denotes the transmission speed of electromagnetic wave.As shown in Fig.4(b),the angle between up lobe or down lobe and the ground is the upper limit or lower limit of θ,given by θ1and θ2respectively,and they can be expressed as

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:

where δ denotes the upper or lower limit of ψ,determined by the missile platform itself.As shown in Fig.4(b),δ 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].

where coefficients VUcand VUsare both determined by the radar parameters and the scattering properties of echo signal region.How ever,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

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:

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

Table 1 Simulation parameters.

from which the following expression is obtained:

Fig.8.Imaging results for two imaging algorithms.

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 is0.Currently,the corresponding slope distance is the boresight 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.

5.Experimental verification

5.1.Experiment 1:the monopulse response curve error affects the imaging of the single target

The monopulse response curve tan（kπθ）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 the monopulse response curve will affect the eventual imaging results.

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

Fig.10.Test environment and process.

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:

where Eq.(22)provides the solution method of optimal angle select curve from r to r+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，r+n（kπθ）optto con f i rm the number of iterations.The simulation parameters are shown in Table 1.

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

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 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.

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.

Fig.14.Results of inclined distance measurement on the condition of the same drop angle and different heights of missile-borne detector.

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).

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.

Fig.15.Height data of an actual terrain.

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

Fig.17.Height measurement error under different conditions.

The follow ing 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 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].

where,Tgdenotes the receiver threshold length,f0denotes the pulse repetition frequency,Bsdenotes the Doppler Frequency Shift of echo signal,Pddenotes 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.

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

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

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 theUAV.Separately,a small-sized four-rotor UAV(Fig.18(d))is used to record the experimental process.

Table 2 Height measurement results under different test scenes.

The actual test results under different test heights of missileborne detector are shown in Fig.19.

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 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.

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 allow s 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.