Detection of UAV Target Based on Continuous Radon Transform and Matched Filtering Process for Passive Bistatic Radar

Luo Zuo, Yuefei Yan, Jun Wang, Xin Sang, Yan Wang, Dongming Ge,Lihao Ping, Zhihai Wang, Congsi Wang

Abstract: Long-time integration technique is an effective way of improving target detection performance for unmanned aerial vehicle (UAV) in the passive bistatic radar (PBR), while range migration (RM) and Doppler frequency migration (DFM) may have a major effect due to the target maneuverability.This paper proposed an innovative long-time coherent integration approach,regarded as Continuous Radon-matched filtering process (CRMFP), for low-observable UAV target in passive bistatic radar.It not only mitigates the RM by collaborative research in range and velocity dimensions but also compensates the DFM and ensures the coherent integration through the matched filtering process (MFP).Numerical and real-life data following detailed analysis verify that the proposed method can overcome the Doppler mismatch influence and acquire comparable detection performance.

Keywords: passive bistatic radar; unmanned aerial vehicle; long-time coherent integration; Radonmatched filtering process

1 Introduction

In recent years, the massive emergency of unmanned aerial vehicle (UAV) has posed a serious threat to air route safety and urban security [1].The identification of the UAV target is increasingly necessary for the surveillance field.However, robust and efficient detection of UAV is a more challenging problem due to its typical feature of the low-observable target, i.e., low or ultra-low flight altitude, slow-moving velocity,and micro-size [2].With tremendous advances in the radar system and signal processing, passive bistatic radar (PBR) systems have drawn substantial attention in UAV target detections.As there is no need for the deployment of expensive transmitting hardware, the PBR can operate in covert mode [3, 4].Further, PBR system has other features such as the superior low-altitude coverage capability, and it is harmless to the electromagnetic environment [5].All these features show that PBRs have the natural advantage to detect the low-observable target.

In general, target detection is committed by calculating of cross-correlation of the surveillance and reference signal in PBR system [6].Integration results are distributed in range Doppler (RD) units and the unit size is defined by the signal bandwidth and the coherent processing interval (CPI).However, the target maneuverability and low radar cross-section(RCS) of low-observable target pose considerable challenges in target detection, which causes the weak radar return and thus seriously reduces the target’s integration energy [7, 8].Increasing the integration time can enhance the target detection ability by means of coherent integration technique, i.e., RD processing [9].However,range migration (RM) and Doppler frequency migration (DFM) effects will occur because of the complex motion characteristics of velocity and acceleration of maneuvering UAV target within one long CPI, which severely limit the integration performance of the conventional RD processing [10, 11].

There are three popular long-time coherent detection methods for RM and DFM effect elimination.The first method exploits keystone transform (KT) to realize coherent accumulation [12].The second method achieves target energy focusing by dividing continuous time to conduct crosscorrelation and performing two-step Doppler processing (CC-TDP) [13].The premise of these two methods is the construction of intra- and interpulse time dimensions, i.e., the continuous wave(CW) signals which should first be divided into multiple time slots to imitate pulse radar.Nevertheless, when the illuminator of PBR emits a phase modulation signal, the Doppler mismatch effect will result in the performance loss of pulse compression (PC), which limits the target integration energy.The third method utilizes timedomain stretch processing (SPT) for target energy accumulation [14].Although the method provides RM and DFM correction, it has a significant computing overhead when the compensating scope of Doppler frequency is broad.

In order to solve the above problems, a novel method based on continuous Radon-Matched filtering process (CRMFP) is presented to achieve fast long-time coherent accumulation for maneuvering UAV target.More specifically, the presented method may not only eliminate RM impact via collaborative research in range and velocity dimensions, but also compensate the DFM resulting from the radial acceleration and obtain the coherent integration through the matched filtering process (MFP).The simulated and real-life data are supplied to demonstrate the efficiency of the proposed method, which shows superior performance compared with existed methods.

2 Signal Model and Problem Formulation

Assume that the PBR signal uses the technique of orthogonal frequency division multiplexing(OFDM).After the reconstruction operation, the complex envelope of the baseband reference signal may be modeled as follows

wherefcis the carrier frequency;τris an illumination signal propagation delay from the station to the receiver;x(t) is the complex signal envelope, i.e., the OFDM baseband signal, as

whereTsdenotes the OFDM signal length;Kis the carrier number;ckis information-bearing constellation symbol; Δfdenotes the subcarrier spacing to ensure orthogonality.

For the purpose of simplicity, a single moving target echo with initial rangerIatt=0 is considered in the surveillance channel.Ignoring the high-order components and assuming the target moves with uniform acceleration, the instantaneous slant distance between PBR and the target can be written as

wherevIandaIdenote the radial velocity and acceleration, respectively.Therefore, the baseband surveillance signal complex envelope can be represented as

wherecis the speed of radio wave in air;ρ=[c-(2vI+aIt)]/cis defined, and denotes the time companding factor (scaling factor).Further,ρcan be rewritten as (c-2vI)/cfor the acceleration andaIis very small in real UAV detection system.

By (4), it is obvious that the scaling factorρwill cause scale-effect of the signal envelopex(t)(time stretching or shrinking) because of the UAV’s maneuvering feature.The scale-effect of the signal complex envelope will be aggravated as time and velocity increase, causing signal deformation.When the offset caused byρexceeds the range resolution ΔR, i.e., ΔR=c/[2Bcos(β/2)],whereBandβare signal bandwidth and the bistatic angle, respectively, the RM effect will occur in RD processing results.Moreover, the third exponential term in (4) is the Doppler modulation phase induced by the target maneuverability (the target’s radial acceleration),which results in DFM effect and causes target’s energy to be defocused.The coherent integration of target energy in typical RD processing would be severely affected due to the RM and DFM effects.As a result, a suitable long-time coherent integration technique is highly desirable.

3 Coherent Integration via CRMFP

The detailed procedures of the proposed approach, CRMFP, are described in this section based on the standard Radon-Fourier transform(RFT) and MFP.Furthermore, we compare the computational complexity of the proposed method with SPT.

3.1 Definition of RFT

For the sake of improving radar detection performance, RFT method is proposed with its definition as shown below.Suppose a two-dimensional(2-D) complex functionf(t,rs)∈C is defined in(t,rs) plane and a line equationrs=r+vtis utilized for the search of arbitrary lines in the plane[15].The RFT is represented as

whereεis a known constant aboutf(t,rs).

In the range versus time plane (t,rs), RFT can obtain the desired results by traversing for motion parameters.As a result, the RFT is not affected by the RM effect, and the signal to interference plus noise ratio (SNR) may be increased over a longer dwell time.However, the RFT will be invalid because of the target’s maneuvering features (DFM effect) in many actual circumstances.

3.2 Definition of Matched Filtering Process

For the maneuvering UAV target, the DFM effect is caused by the radial acceleration of the target.From (4), the phase in the azimuth dimension can be treated as a chirp signal with its definition given below.Suppose a linear frequency modulated (LFM) signal represented as

whereA,f0andγ0denote the complex amplitude,the centroid Doppler frequency and the chirp constant (chirp rate) of the LFM signal, respectively.

For estimation of the chirp phase with low calculation, the matched filtering function can be defined as

whereγis the searching rate.

The desired chirp rate can be obtained by passing through the matched filter, whenγ=γ0is satisfied, as

whereF(·) is Fourier transform operator;fdis the center frequency of Doppler-filtering;Tis the CPI.

By (8), it is noted that the MFP is able to concentrate the LFM signal energy on the same Doppler cell and the estimated function ofγ, i.e.γ0which can be achieved as

3.3 Description of CRMFP

In pulse radar field, the operation of RFT is based on the fast-slow time property.On the contrary, the PBR signal is transmitted in the form of CW.Therefore, we have introduced a novel method called CRMFP that creatively combines the fundamental principles of standard RFT and MFP.This innovative approach enables long-time coherent integration of maneuvering UAV targets, providing enhanced detecting and tracking capabilities.

Without loss of generality, the definition of CRMFP is given as follows.Consider a 2-D complex functionf(t,r)∈C is defined in (t,r) plane and a line equationr(t) =r0+vtrepresenting the motion trail of UAV is implemented for searching lines in the range versus time plane.Note that since the acceleration of UAV target is relatively small, i.e.the RM effect caused by the acceleration less than the range resolution ΔR, its influence on the searching line equation can be ignored.Then the CRMFP is descripted as follows:

1) Range-Dimension Coherent Processing(RCP)

RCP is performed by calculating the conjugate dot product between the time-delayed reference signal and surveillance signal and is shown as

whereτis the target propagation delay.

From (10), it is noted that the RCP result is a 2-D matrix.When the target moving distance exceeds the range resolutionvIT＞ΔR, the range informationτof the target is no longer a fixed value, which will change over time.That is,the range informationτis determined byrIandvI.

2) Matched Filtering Process

Since the target propagation delayτis timevarying, the subsequent matched filtering process should be performed along an oblique line defined byr(t) =r0+vt, which can be expressed as

From (11), it is obvious that for the UAV target moving at a uniform acceleration, when the searching ranger0, velocityvand accelerationγare equal to the realrI,vI, andaIrespectively, the proposed CRMFP method can obtain its peak value.The target energy distributed along multiple RD cells could be accumulated during the long CPI.In the case that the peak value of (10) is greater than the specified threshold, the target motion parameters could be obtained.In addition, the searching scopes ofvandγare defined as [vmin,vmax] and [γmin,γmax], where the searching intervals are Δv=c/(2Tfc) (Tis CPI) and Δγ=c/(2T2fc) respectively.

4 Performance Analysis

4.1 Properties of CRMFP

It is obvious that CRMFP satisfies several important properties based on the above analysis as follows:

1) Inear Additivity

Firstly, the CRMFP is linear as

wherea1anda2are the constant coefficients.The linear additivity indicates that the CRMFP meets the superposition rule, which is an advantage for detecting multiple maneuvering target.Further, (12) can be extended as

2) Similarity

Consider thatg(t,r)=h(a3t,r), in whicha3is a nonzero real number, and the CRMFP will satisfy the following rule

4.2 Computational Complexity

In this section, the computational complexity of the proposed method is investigated.For simplicity, complex multiplication (CM) is only considered.Without loss of generality, multi-rate conversion is performed on the RD processing result.We assume that the coherent time, sampling frequency, the observation range cells, the observation Doppler frequency cells and the searching acceleration number areT,fs,Mr,MdandMarespectively.Note that the signal sampling length isN, whereN=Tfsand the signal sampling length after multi-rate conversion isNm.For the proposed method, the range processing is firstly applied to reference and surveillance signals,which requiresMr(N+Nm) CMs.Then, the implementation of algorithm CRMFP can be divided into two steps: 1) the matched filtering process based on target motion modelr(t) requiresNmMdMrMaCMs; 2) the coherent integration via FT costs (Nm/2log2Nm)MdMrMaCMs.For comparison,MdNlog2N+MrMd(N+Nm)+MrMdMa(Nm+Nm/2log2Nm) CMs are required for the SPT method.Assume that the digital television terrestrial multimedia broadcasting (DTMB) is exploited as the illuminator, and the relevant system parameters are set as follow:T= 1 s,fs= 8 MHz,Nm= 8 000,Mr= 300,Md= 600,Ma= 50.We introduce theηas the computational complexity ratio between the CRMFP and the SPT method, and therefore the computational complexity ratio is calculated asη≈ 25%, which suggests that the CRMFP is more efficient.

4.3 Some Remarks

According to the above analysis, some advantages and differences of CRMFP compared with existing methods are given as follows:

1) The CRMFP is a linear transform which means it wouldn’t be affected by the cross-term interference based on its definition in (10).Further, CRMFP combines the ideas of RFT and MFP.Thus it not only has the distinct accumulation ability but also works well as a useful tool for non-stationary and time-varying target echo detecting.

2) Compared with the popular integration algorithm, such as RD processing and KT, the proposed CRMFP method takes into account the influence of acceleration and has a more accurate representation of the maneuvering movement of the UAV.The PBR detection performance is reduced by the DFM effect because of the UAV acceleration.As CRMFP can correct RM and DFM well, it outperforms the RD processing and KT methods over a reasonably long integration time.

3) The CRMFP realizes the long-time coherent integration via traversing the motion parameters, which can make maximum use of the target energy.Therefore, CRMFP can be viewed as a special Doppler filter bank, which can simultaneously represent and compensate the target’s velocity and acceleration.Compared with CCTDP method, CRMFP doesn’t require the support of intra- and inter-pluse time, so it is a continuous transform.It will not be subject to the Doppler mismatch and can obtain better integration performance.

5 Results

To evaluate the long-time coherent integration performance of the CRMFP method in the presence of maneuvering UAV target, numerical and measured data are presented in this section.

5.1 Numerical Results and Analysis

In this simulation, the DTMB is considered as the PBR signal, and the simulation parameters are shown in Tab.1.A weak target return with DFM effect is synthesized in the surveillance channel to emulate the maneuvering UAV.The UAV target is at the vicinity of bistatic ranger0= 1.2 km, radial velocityv= 50 m/s and accelerationa= 3 m/s2with SNR = -40 dB.

The coherent integration results of UAV target via RD processing, KT, CC-TDP, SPT and the proposed CRMFP method are presented in Fig.1.Fig.1(a) gives the integration result of conventional RD processing in which the target energy is discretized into different RD cells dueto RM and DFM influence.The integration results for CRMFP and SPT are shown in Fig.1(b)and Fig.1(c) respectively, which indicate that the target energy is well integrated and forms an obvious peak.However, the computational burden of CRMFP is much lower than SPT.Fig.1(d)and Fig.1 (e) provide the integration result of KT and RFT, respectively, and because of the DFM effect, it cannot fully accumulate the target energy.Moreover, the integration result of CC-TDP is also given in Fig.1 (f).Although the target’s energy is focused, the integration gain is reduced due to the Doppler mismatch in PC.In order to better illustrate the long-term accumulation performance of the above methods, Tab.2 shows the SNR corresponding to the respective algorithms.Observing Tab.2, it can be seen that compared with traditional RD, the signal-to-noise ratio of the target processed by the proposed method is increased by 11.43 dB, which will greatly improve the detection performance of the system.

Tab.1 Parameters of PBR system

Fig.1 Coherent integration results of RD processing, CRMFP, SPT, KT, and CC-TDP: (a) RD processing method; (b) CRMFP;(c) SPT; (d) KT; (e) RFT; (f) CC-TDP

Tab.2 The SNR of different methods

5.2 Detection Performance Analysis

In this section, the detection performance of the abovementioned methods with different SNRs is further investigated via Monte Carlo trials.The simulation parameters are consistent with the previous subsection.Subsequently, we add 10 dB of complex Gaussian white noise to the echo and set the constant false alarm ratio (CFAR) asPfa=10-5.The detection probabilities of the different methods in various input SNRs are shown in Fig.2.The input SNR changes with the interval 1 dB from -50 dB to -30 dB.Obviously, the detection ability of the proposed CRMFP method is better than RD processing, KT and CC-TDP methods because it can correct the RM and DFM effect as well as obtain superior performance on signal accumulation.Moreover, it achieves performance comparable to SPT with a lower computing overhead.

5.3 Measured Results and Analysis

The practical feasibility of the presented method was validated in this part using field experimental data gathered from a DTMB-based PBR system.The experiment was conducted on August 10, 2020, near an open space at Xidian University.Fig.3 shows the PBR system and experimental situation.The PBR system utilizes the Xi’an television tower as the illuminator.The reference and surveillance channels are formed by an eight-element line array and the system operating parameters are shown in Tab.1.This experiment is to assess the capability in detecting the maneuvering UAV target by the proposed CRMFP method.The UAV target is specifical DJI INSPIRE 1 with 20 m/s and the flight altitude less than 100 m.

Fig.4 shows the measured data results of the typical RD processing method.The integration results in the range and Doppler dimension are shown in Fig.4(a) and Fig.4(b), respectively.It is clear that the RM and DFM effect occurs and the target energy disperses in multiple RD cells.The integration results of RFT are given in Fig.5, since the presence of DFM effect cannot fully accumulate the target energy.Fig.6 gives the experimental results of the proposed CRMFP method.In particular, the target accumulation results in range and Doppler domain are given in Fig.6(a) and Fig.6(b) respectively,in which the target formed a noticeable peak in one RD cell, which means the RM and DFM effects have been corrected.Further, the target’s SNR increased by about 4.6 dB by means of the proposed method, which will significantly enhance the target detection probability.

Fig.4 Coherent integration via RD processing: (a) range dimension; (b) Doppler dimension

Fig.5 Coherent integration via RFT: (a) range dimension;(b) Doppler dimension

6 Conclusion

This letter presented a novel long-time coherent integration method, i.e., CRMFP, for low-observable UAV target in PBR system.Both the RM and DFM effects can be eliminated and the PBR detection capability can thus be enhanced by performing the CRMFP coherent method.More specifically, CRMFP realizes the signal extraction on the integration results of range dimension with a 2-D traversing along the directions of range and radial velocity.After that, MFP is performed to compensate the DFM and achieve coherent accumulation of the UAV target echo.Finally, the effectiveness of the proposed method is verified by simulated and real-life data.In general, the CRMFP is superior to the RD processing, KT, and CC-TDP methods in detection ability and requires a lower computation cost than SPT.