ZHANG Yuan,ZHANG Qiming,WANG Yanping,*,LIN Yun,LI Yang,BAI Zechao,and LI Fang

1.School of Information Science and Technology,North China University of Technology,Beijing 100144,China;2.Quanzhou Institute of Equipment Manufacturing,Haixi Institutes,Chinese Academy of Sciences,Jinjiang 362200,China

Abstract:Ground-based synthetic aperture radar(GB-SAR)has been successfully applied to the ground deformation monitoring.However,due to the short length of the GB-SAR platform,the scope of observation is largely limited.The practical applications drive us to make improvements on the conventional linear rail GB-SAR system in order to achieve larger field imaging.First,a turntable is utilized to support the rotational movement of the radar.Next,a series of high-squint scanning is performed with multiple squint angles.Further,the high squint modulation phase of the echo data is eliminated.Then,a new multi-angle imaging method is performed in the wave number domain to expand the field of view.Simulation and real experiments verify the effectiveness of this method.

Key words:ground-based synthetic aperture radar(GB-SAR),high squint,multi-angle.

1.Introduction

Synthetic aperture radar(SAR)has been widely applied in many aspects of earth observation by spaceborne or airborne platforms.Usually spaceborne platforms are used to perform monitoring periodically,while in an emergency the airborne platform is dispatched to do local surveillance.Although this traditional operation mode has greatly improved our observation ability,in practical experience,considering factors such as scheduling and revisit times,it is still insufficient for repeat observations that are often needed for local small-scale areas,e.g.,for landslide or infrastructure monitoring,where both spaceborne and airborne SAR come to their limitations due to the lack of flexibility.Under these circumstances,a SAR platform with rapid response and repeated local observation becomes a desired tool.

As an important complement,ground based-SAR(GBSAR)can achieve more accurate and efficient results than satellites or airborne SAR systems in local environments,and is increasingly concerned by civilian applications.The currently disclosed linear rail GB-SAR system includes Tohoku University’s ground-based interferometric system at Ku band,which successfully monitored the landslide of Aratozawa[1].University of Florence’s continuous-wave step frequency radar at C-band monitored the slow movement of Glacier with the scan time of36 min[2].The Polytechnic University of Catalonia used the X-band system to make long-term observations of the slow movement of the mountain and obtained the corresponding moving speed[3].Researchers from the European Commission used the multiple input multiple output(MIMO)mode to replace the way the radar moves along the rail,and compared it with previous systems at 13.85 GHz[4].Temesgen et al.developed the X-band Tomographic mode GB-SAR for near-range measurement of ice thickness[5].The systems listed here are some of the outstanding representative results,but GB-SAR systems are not limited to these.

Compared with the conventional SAR,the significant difference in imaging of the GB-SAR system is that the synthetic aperture is limited by the platform length,so it cannot form a complete aperture,also called suboptimal aperture[6].However,since the radar platform is completely stationary,the main advantage of GB-SAR imaging is that the platform motion speed is more stable during data acquisition.Therefore,the accuracy of deformation monitoring is much higher,which is generally considered to be millimeter-level.Moreover,it can be used for long-term monitoring of local areas,such as bridge monitoring[7],discontinuous monitoring of slow deformation[8],iron open pit monitoring[9],post-earthquake damage inspection[10],evaluation of snow-mass characteris-tic[11],post-landslide monitoring[12],subsidence phenomenon in urban environment[13],atmospheric correction[14],height-dependent atmospheric artifacts compensation[15],soil surface roughness characterization[16],and castle cliff monitoring[17].

Since GB-SAR has the above characteristics,the research community has carried out research on related imaging algorithms from the beginning.Joaquim et al.proposed a fast pseudo-polar format imaging algorithm for far- field scenarios[18],which is improved further for nearfield imaging[19].ZENG et al.proposed keystone formatting technique to solve the problem of space-variant range cell migration correction(RCMC)[20].Reale et al.addressed the use of multi-baseline ground-based data for the reconstruction of the three-dimentional backscattering properties[21].The above-mentioned methods make approximations of the slant-range.Thus,Monti Guarnieri et al.introduced the wave number domain focusing algorithm into the GB-SAR system[22].Guo et al.proposed a similar method for GB-SAR imaging in the frequency modulated continuous wave(FMCW)mode[23].Most GB-SAR systems have been used in the step-frequency mode in the past[24].In this mode,the radar is almost perfectly stationary when receiving the echo signal,which helps to improve the coherence,but in actual use,this mode costs too much acquisition time,usually in about tens of minutes.In the FMCW mode,the radar collects data while moving,thereby improving the efficiency of data acquisition.Therefore,this paper uses the FMCW mode that can complete scanning within one minute.

Actual systems are typically deployed within 5 km from the observation scene.For the system in this paper,it has an azimuth beam angle ofβand a moving speedvas shown in Fig.1.Here,the azimuth beam angle is defined as the angle of the antenna azimuth pattern at–3 dB.Since the platform limits the synthetic aperture length,the system also has a limited imaging field of view.One solution to the expansion of the field of view is to use the Arc-SAR system[25,26].However,this kind of system requires additional long rotating arm(usually 1 m to 2 m)for the antenna to form the synthetic aperture in the circular scanning mode.Moreover,the Arc-SAR system uses the circular imaging methods,which makes the system processing more complex.Without considering the development of a new Arc-SAR system,for users who have already deployed the linear rail GB-SAR,can they continue to use the original system and expand the scope of monitoring?This is not only meaningful from a research perspective,but also very useful for actual users to control their costs.

This paper proposes a high squint multi-angle imaging approach of linear rail GB-SAR for larger fields of view.First,a turntable is installed on the bracket to support the radar.After that,the scanning with various squint angles of the observed area is performed.Then,we make joint imaging of the multi-angle echo data in the wave number domain.Finally,after expanding the field of view,the corresponding imaging results can be further used for the differential interferometry.

Fig.1Imaging scope of conventional GB-SAR

2.High squint multi-angle scanning in improved GB-SAR system

In this section,the radar is mounted on a rotatable bracket that can point at any angle controlled by the computer.The scanning process is shown in Fig.2.It scansMtimes in squint angles ofθ1,θ2,...,θM,respectively.We define the angle between the direction of motion and the direction of the LOS of the radar as squint angleθi.The subscript number,i.e.,i=1,2,...,Min respectiveθ1,θ2,...,θM,represents the different squint angles in a scanning group.Within a single scanning pass,the squint angle keeps unchanged.When the radar is in the return trip after scanning,the system will quickly change the squint angle,so that in the next scanning it can adopt the new squint angle.Then,theseMtimes echo data are formed as Group1 to generate Image 1 by the multi-angle joint imaging method.Then,the above process will be repeated to generate Image 2,Image 3,...,ImageM.

Fig.2Scanning process of the improved GB-SAR system

In the interferometry processing,we use the image pairs with the same squint angle,as shown in Fig.3.For example,the data of the squint angleθ1in each group are used for the interferometric process to generate a deformation map at the directionθ1.The data of the squint angleθ2in each group are used for the interferometric process to generate a deformation map at the directionθ2,and so on.The interferogram is formed by fan-shaped regions according to the number of squint angles.

Fig.3Interferometry processing flow

The deformation map is composed of multiple data with different squint angles by stitching,so the field of view will be much larger than that in the conventional linear mode system.And the difference between each adjacent squint angles is usually less than the system azimuth beam angleβ,so there is no blind zone between the boundarie sof each sector data.Finally,we can get a larger deformation map than the original system.

Through the above processing,the system will have the ability of a significant expansion of the observation area by making minor changes to the original linear rail GB-SAR system.Compared with the original system,since the improved one makes scanning with severals quint angles,we need further study the imaging method for multi-angle echo data.It should be noted that the enlargement of the field of view is due to the fact that the radar can be pointed in different squint directions with the help of the rotating bracket.On this basis,the problem of joint imaging of multiple echo data with different squint angles is the focus of this paper.

3.High squint multi-angle imaging algorithm

Fig.4 shows a data acquisition geometry diagram with the squint angle.Here we define the angle between the direction of motion and the direction of the line of sight(LOS)of the radar as squint angleθ.The radar speed isv,and the scanning time along the platform isTa.The current azimuth sampling time ist.rcis the distance between the scene center and the radar position att=0.The coordinate of the scene center is(rccosθ,rcsinθ),the point target locates at(x,y)=(rccosθ+x0,rcsinθ+y0),and the radar is at(vt,0).Therefore,the slant-range can be expressed as

Fig.4High squint data acquisition geometry

The transmitted signal is

whereτis the range time,Tpis the time width of the transmitted signal,f0is the carrier frequency,andKris the chirp rate.The slant-range represented by(1)induces a time delay in the range shown below:

where c is the velocity of light.τpcontains the squint angleθ.

Thus,the echo signal can be written as

wheretis the time in the azimuth,Tais the scanning time along the azimuth.Assume that the scattering coefficient is a unit value.The relationship between the transmitted signal and the received signal is displayed in a time-frequency manner as shown in Fig.5.

Fig.5Relationship between the transmitted signal and the received signal

We use the‘Dechirp-on-receive’technique to reduce the sampling requirements by mixing the received and transmitted signals[27].And the output of the mixer is then low-pass filtered before being sampled.Echoed signals from the scene of interest usually have high frequencies resulting from the characteristics of the FMCW system.In order to demodulate the frequency spectrum of echo signals to the baseband,the reference signal with delay time ofτcis given by

whereτc=2rc/c is the time delay of the reference signal.The dechirped signal can be expressed as

whereτd=τ?τcandτΔ=τp?τc.?represents the complex conjugate.

In the actual system,the dechirped signal is acquired as a digital signal by the A/D converter.For ease of derivation,the continuous signal form is still used later.In(6),the last exponential term is well-known as the residual video phase(RVP).It could be eliminated by a method named‘Deskew’,which comprises Fourier transform(FT),phase multiplication,and inverse FT[27,28].After the RVP removal,we obtain

Performing the time-frequency substitution offr=Krτdyields

whereBris the bandwidth of the transmitted signal.The above process is a common pre-processing step of FMCWSAR.In order to ensure the integrity,we still write it out.Note thatτΔcontains the squint angleθ.The phase in(8)can be written as

Next,we perform the FT of(9)along the azimuth direction.Note that for the suboptimal aperture data,it requires a zero padding for echoes to satisfy the azimuth size of the scene[22].After that,according to the principle of the stationary phase,the phase in the wave number domain can be expressed by

where

To understand(10),we refer to Fig.6.It is a local approximation of the spherical wave.This approximation is reasonable in the local region around the radar line of sight.θis the squint angle.λis the wavelength in the plane wave propagation direction.λxandλyis the wavelength in thexandydirection.φis the angle betweenλandλy.And the projection ofλin the squint direction isλθ.

Fig.6Plane wave geometric diagram in squint case

Equation(14)is the wave number in the squint direction that contains the coupling term of the range frequency and the azimuth frequency as well as the squint modulation term.It determines the first term in(10).

The complete expression of the signal in the two dimensional(2D)wave number domain is

whereW(ka,kr)is the amplitude in the 2D wave number domain.The imaging process is further discussed below.From(10),(13)and(14),we can get

Sincercis a known term,we compensate the first order of wave numberkrat first.

The second phase term in(17)is the first order of wave numberkathat determines the target position.The first phase term is mainly derived from the squint effect,which can be compensated by

After the compensation,the squint modulation in the phase is eliminated.Note that(i)φchanges withkaandkr,so this item should be compensated in the point wise way.(ii)SS2(ka,kr;θ)implies the squint angleθ.For example,the actual data in our system contains multiple angles,such as theMangles shown in Fig.3.Therefore,each angle data should be compensated according to its squint angle.Moreover,the squint causes the Doppler center frequency offset.The azimuth wave number center is

The first phase term in(18)is the first order of the azimuth wave numberka,which determines the azimuth position of the target in the image,and does not affect the focusing.The second phase term is the coupling term of the wave numberkaand the wave numberkrin the propagation direction.Equation(18)can be further transformed into

Since the system has multiple angle data,we keep the squint angleθin the left-hand variable as a marker of different angles.We perform the Stolt interpolation ofto(20),and it becomes

Note that we perform Stolt interpolation to all multiangle data simultaneously,and finally the data are coherently accumulated into a data matrix,which is denoted as

And in actual engineering,it can be implemented by the parallel algorithm.After the above processing,the wave numbers corresponding to the squint anglesθ1,θ2,...,θMare substantially projected to two mutually orthogonal wave numbers ofandka,which have the wavelength ofλxandλy,respectively,as shown in Fig.7.

Fig.7Multi-angle wave numbers geometry

In the end,the inverse FT is performed on the signal of(22)to obtain a focused image,

whereF?1represents the inverse FT.Wx(·)andWy(·)are the envelope functions in the azimuth and the range,respectively.They are determined by the system ambiguity function.The entire algorithm flow is shown in Fig.8.

Fig.8Flow chart of high squint multi-angle imaging algorithm

4.Simulation and real data experiments

The system parameters are shown in Table 1.The antenna pattern used in this paper is shown in Fig.9,and the corresponding angle of the E plane response at–3 dB is 18?which is the azimuth beam angle.Section 4.1 analyzes the performance of the algorithm through simulation.Section 4.2 shows the deformation measurement experiment in the laboratory.Section 4.3 shows the actual test scenario and the results of the actual data processing.

Table 1System parameters

Fig.9Antenna gain diagram

4.1Performance analysis by simulation

Firstly,the RCMC analysis is performed on the scene center point according to different squint angles.Fig.10(a)shows the linear component of RCMC.It can be seen that as the squint increases,the contribution of this item to RCMC increases significantly.Within the suboptimal aperture time,the linear component can exceed the range resolution.

Fig.10 RCMC analysis on the scene center

Fig.10(b)shows the quadratic component of RCMC.It can be seen that as the squint state increases,this term decreases.In most squint cases,the quadratic components are basically smaller than the range resolution.However,when approaching the side-looking,the quadratic component must be considered for compensation.The algorithm in this paper does not perform any approximation on the slant-range,and can fully compensate for the linear and quadratic components at any squint angle.

Next,we verify the performance of this method through single squint angle experiments.We set the 3×3 lattices arranged equidistantly in the scene.The distance of the scene center is 200 m.The imaging results with squint angles of 90?,105?and 120?are simulated respectively,and the corresponding imaging results are shown in Fig.11(a),Fig.12(a)and Fig.13(a),respectively.The back projection(BP)algorithm is a time-domain high-precision imaging method[29].Although the algorithm is very timeconsuming,it is often used as a comparison method.Therefore,we use BP for comparison imaging.BP imaging results are shown in Fig.11(b),Fig.12(b)and Fig.13(b),respectively.Due to symmetry,results atθ=60?,θ=75?are omitted.

Fig.11Imaging results at θ=90?

Fig.12Imaging results at θ=105?

Fig.13Imaging results at θ=120?

From the comparison between Fig.11(a)and Fig.11(b),Fig.12(a)and Fig.12(b),Fig.13(a)and Fig.13(b),it can be seen that the imaging position of this method is consistent with the BP method under different squint angles,and no obvious geometric deformation occurs.Table 2 gives an analysis comparison of these imaging results.We select the azimuth resolutionρaand the azimuth peak sidelobe ratio(PSLR)of the center point in each image as comparison parameters.Because the range processing of the two methods is consistent,only the azimuth parameters are compared.In general,it can be seen that the method in this paper is close to the BP imaging results.

Table 2Analysis comparison of imaging results

Usually in the airborne SAR system,since the system has a limited pulse repetition frequency(PRF)and the platform moves at a high speed,high squint can cause Doppler ambiguity.However,in our GB-SAR system,due to the slow motion of the radar,e.g.,0.03 m/s in this paper,the Doppler frequency center does not exceed the PRF,so this paper does not consider the Doppler ambiguity problem.

The simulation experiment of a large-scale scene is done below,and the point targets are arranged at intervals of 20 m in a range of 200 m×200 m with a center distance of 200 m,as shown in Fig.14.

Fig.14 Scene layout for large scene simulation

First,we simulate the data acquisition process of a conventional system and use the BP imaging algorithm.The imaging results are shown in Fig.15(a).Since the conventional system has bounded the beam angle,there are blind areas in the field of view.Only a part of point targets in the scene is displayed.Then,we simulate the data acquisition process of the improved system and perform imaging by this algorithm.The result is shown in Fig.15(b).Compared with the conventional system,for the same observation scene,the field of view imaged by the improved system is larger.

Fig.15 Large scene simulation imaging results

The simulated point targets in the whole scene are all displayed.We select one of the point targets for focus quality analysis as shown in Fig.16.The measured azimuth and range resolutions are 0.70 m and 0.30 m,respectively.

Fig.16 Point target response analysis after imaging by the proposed method

4.2Deformation measurement of indoor experiment

The indoor experimental scene is shown in Fig.17.A corner reflector is placed in the scene with 2.5 m from the radar.

Fig.17Indoor deformation test scene

The multi-angle scanning is performed at 75?,90?and 105?for an observation time of 2 h.During the interval of scanning,we artificially moved the corner reflector about 3 mm.Fig.18(a)is the SAR image of the corner reflector.The deformation is represented by Fig.18(b).And 16:50 indicates the point in time when the deformation occurs.Before and after this time,the deformation is close to 0 mm.Moreover,the two pictures below the deformation figure are the speed and acceleration of deformation change with time,respectively.It can be seen from the experimental results in Fig.18 that the displacement around 16:50 suddenly reaches 3 mm,and then quickly drops to around 0 mm,which coincides with the fact.

Fig.18Indoor deformation test results

4.3High squint multi-angle imaging experiment for large-scale infrastructure construction

The Yongding River Bridge is currently under construction in Beijing.The design sketch is shown in Fig.19,which shows the full view of the bridge after it is completed.The bridge length is about 600 m,which belongs to the double tower diagonal-pull type.The heights of the two towers are 120 m and 73 m,respectively.

Fig.19Design sketch of Yongding River Bridge

In Fig.19,the bridge pier corresponds to the observation object in Fig.20 that is the current status of the bridge during on-site observation.The radar placement position can also be seen in Fig.20.

Fig.20Field experiment scene

The system after installing the turntable is shown in Fig.21.The angle of the turntable can be controlled by the computer and set to a new angle during the return of radar on the platform after scanning.We use the conventional side-looking mode and propose the multi-angle mode to monitor the Yongding River Bridge,seperatlely.In the multi-angle imaging mode,each group of squint angles includesθ=60?,75?,90?,105?and 120?.After imaging by this method,the overall outline of the bridge is clearly visible.

Fig.21Improved GB-SAR with radar turntable

Fig.22 is the amplitude image of the large field of view of the bridge obtained by the method in this paper.This does not represent the deformation of the bridge.Deformation inversion needs to be obtained by differential interferometry on the basis of time-series complex images.However,in practice,the method in this paper can be further applied to large field differential interferometry processing.

Fig.22 Imaging result of bridge by the proposed method

Fig.23 shows the comparison of the imaging results in the traditional mode and the proposed model.

Fig.23Imaging results comparison

The outline of the bridge is more complete after the multi-angle imaging proposed in this paper.As it can be seen from Fig.23(b),the target information around the bridge is significantly increased.

5.Conclusions

In this paper,the hardware of the existing linear rail GB-SAR system is slightly modified,that is,the turntable is installed on the radar base to realize the acquisition of multi-angle echoes.The large field of view monitoring is realized by joint imaging of multi-angle data in the wave number domain.By deriving the high squint twodimensional frequency domain expression of echo data,we eliminate the influence of high squint,and then decouple the coupling of azimuth and range frequencies by Stolt interpolation in the wave number domain.Finally,multiangle data are accumulated to accomplish the large field of view imaging.It is applied to the imaging of the Yongding River Bridge in Beijing that demonstrates the ability of wide- field imaging.