Data fusion of target characteristic in multistatic passive radar

CAO Xiaomao ,YI Jianxin,* ,GONG Ziping ,RAO Yunhua,2 ,and WAN Xianrong,*

1.School of Electronic Information,Wuhan University,Wuhan 430072,China;2.Shenzhen Research Institute,Wuhan University,Shenzhen 518057,China

Abstract:Radar cross section (RCS) is an important attribute of radar targets and has been widely used in automatic target recognition (ATR).In a passive radar,only the RCS multiplied by a coefficient is available due to the unknown transmitting parameters.For different transmitter-receiver (bistatic) pairs,the coefficients are different.Thus,the recovered RCS in different transmitter-receiver (bistatic) pairs cannot be fused for further use.In this paper,we propose a quantity named quasi-echo-power(QEP) as well as a method for eliminating differences of this quantity among different transmitter-receiver (bistatic) pairs.The QEP is defined as the target echo power after being compensated for distance and pattern propagation factor.The proposed method estimates the station difference coefficients(SDCs) of transmitter-receiver (bistatic) pairs relative to the reference transmitter-receiver (bistatic) pair first.Then,it compensates the QEP and gets the compensated QEP.The compensated QEP possesses a linear relationship with the target RCS.Statistical analyses on the simulated and real-life QEP data show that the proposed method can effectively estimate the SDC between different stations,and the compensated QEP from different receiving stations has the same distribution characteristics for the same target.

Keywords:data fusion,multistatic passive radar,radar cross section (RCS),target characteristic.

1.Introduction

Automatic target recognition (ATR) is an important part of modern radars.And radar cross section (RCS),which contains abundant target information,is a fundamental and important attribute of targets and is widely studied in the field of ATR [1−5].Generally,measuring target RCS in an anechoic chamber [6,7] or in a standard testing field [8] with dedicated equipment is the most accurate way.However,if the anechoic chamber or targets are unavailable,those accurate measurement methods will fail to work.

In practice,for active radars,target RCS can be derived from the radar equation [9−11].On the contrast,it is almost impossible to obtain target RCS from the radar equation in a passive radar due to the unknown transmitting parameters.Aiming at this problem,a method using signals from the reference channel to help extract RCS from target echo power was proposed in [12].It introduces direct path signals to help cancel out transmitting parameters and obtains a recovered RCS which is the true RCS with an unknown parameter.For a single transmitterreceiver (bistatic) pair,the parameter is almost constant for all detected targets and would not affect the target characteristics.

However,in a real situation,it is hard to collect enough and comprehensive data by a passive radar with only one transmitter-receiver (bistatic) pair for analyzing target characteristics and training a good classifier for ATR.For one thing,for such a fixed passive radar,it is time-consuming to collect enough target data by only one receiving station due to its limited observation area.For another,for civil aviation aircraft,the flight paths of the aircraft change very little within a certain airspace,thus the radar’s observation angle to the target is limited and target information collected by the radar is incomplete.Thus,we hope to use multiple receiving stations to simultaneously observe the target at different angles so as to improve the efficiency of data collection as well as obtain comprehensive target information.Each receiving station can form a transmitter-receiver (bistatic) pair with the transmitting station.However,as the parameter settings of different transmitter-receiver (bistatic) pairs are not exactly the same,the unknown coefficient in the recovered RCS varies with different receiving stations.Thus,the recovered RCS from different receiving stations is incomparable and cannot be fused.To the best of our knowledge,there have been no literature reporting on data fusion for target characteristics analysis in multistatic passive radars yet.

To tackle the aforementioned problem,in this paper we propose a quantity named the quasi-echo-power (QEP) as well as a method for eliminating differences of this quantity among different transmitter-receiver (bistatic) pairs.The relationship between the QEP compensated for station difference and RCS is a simple linear relationship.Thus,it is the same to analyze target characteristics using the compensated QEP as using RCS.The compensated QEP overcomes the problem that the recovered RCS in different transmitter-receiver (bistatic) pairs is not comparable,which makes it possible to fuse data from different receiving stations for target characteristics analysis and further use in ATR.

The remainder of this paper is organized as follows.Section 2 presents the formulation of station difference coefficient (SDC) and QEP.Section 3 shows the simulation results of SDC estimation and statistical analysis of distribution characteristics of QEP.Section 4 uses experimental data to validate the effectiveness of the proposed QEP as well as the method of eliminating station difference in a real situation.Conclusionsare drawn in Section 5.

2.Formulation of SDC and QEP

For a single transmitter-receiver (bistatic) pair,the classical bistatic radar equation is defined as follows [13]:

wherePris the received echo power of the target;Ptis the transmitting power of the signal;Gtis the gain of the transmitting end;Ft(θt,φt) is the pattern propagation factor for the transmitter-to-target path; θtand φtare the two components of the angle between the transmitter-totarget line and the normal direction of the transmitting antenna;Gris the gain of the receiving end;Fr(θr,φr) is the pattern propagation factor for the receiver-to-target path;θrand φrare the two components of the angle between t he receiver-to-target line and the normal direction of the receiving antenna; λ is the wavelength; σ is the bistatic RCS (BRCS);Rtis the transmitter-to-target range;andRris the receiver-to-target range.

In a real situation,the transmitting antenna is often omnidirectional in the azimuth plane and the antenna beam in the vertical plane is able to cover targets in low altitudes.Thus,the pattern propagation factor for the transmitter-to-target path can be taken as an angle-independent variable,i.e.,Ft(θt,φt)=1.Meanwhile,the pattern propagation factor for the receiver-to-target path is known to us.Thus,Fr(θr,φr) can be compensated.Under this assumption,(1) can be rewritten as follows:

For a certain transmitter-receiver (bistatic) pair,thiskparameter is a constant and we call it the constant of the transmitter-receiver (bistatic) pair.With this constant,we can find out the difference of parameter settings between different transmitter-receiver (bistatic) pairs so as to compensate target echo power in different receiving stations to the same power level.

Assume there is a multistatic passive radar with one transmitter,which is denoted asTx,and two receivers,which are denoted asRxiandRx j.The two receivers operate on the same frequency and polarization state.Denote the transmitter-receiver (bistatic) pair composed ofRxiandTxas transmitter-receiver (bistatic) pairi,whose constant of the transmitter-receiver (bistatic) pair iski,the transmitter-receiver (bistatic) pair composed ofRx jandTxas transmitter-receiver (bistatic) pairj,whose constant of the transmitter-receiver (bistatic) pair iskj,and chooseRx jas the reference receiving station.And assume there is a target whose BRCS under incident angle of (θi,φi) and observation angle of (θs,φs) is σ.This target is moving in the detection area of the radar.At two different moments oftiandtj,the two receiving stations receive two target echo powers,i.e.,PriandPr j,under the same incident angle (θi,φi) and observation angle(θs,φs),as shown inFig.1.The incident angle (θi,φi) and observation angle (θs,φs) are defined in the target coordinate system,and the coordinates of the two positions,i.e.,(xti,yti,zti) and (xt j,yt j,zt j),corresponding totiandtjare defined in the radar coordinate system.It should be noted that (xti,yti,zti) and (xt j,yt j,zt j) are not necessarily two points in a same track,but the (θi,φi) and (θs,φs) at these two positions are the same.And since the BRCS of a target is only related to its own characteristics as well as the frequency,wave form,and polarization state of the incident electromagnetic wave but has nothing to do with other factors such as the observation time,the target BRCSs observed by the two receiving stations attiandtjare equal,i.e.,σi=σj=σ.ForRxi,the target comes from angle of (θri,φri) in the radar coordinate system withRxias the origin.ForRx j,the target comes from angle ofin the radar coordinate system withRxjas the origin.

Fig.1 Sketch map of the relationship between the multistatic radar and the target

Then we have two relationships of the target echo power and the BRCS according to (2),i.e.,

As mentioned before,we have σi=σj=σ.Thus,we can obtain the following relationship betweenkiandkjaccording to (4) as

where αijis defined as the SDC ofkirelative tokj.Meanwhile,we also have αijfrom (3) as follows:

Equation (6) is the definition formula whereas (5) is for calculation. Then,dividein (4) by αijand compensate bothandfor distance and denote the compensated target echo power asand,respectively.We callQEP andthe compensated QEP.In other words,the QEP is the target echo power only compensated for the pattern propagation factor and distance,whereas the compensated QEP is the one also compensated for station difference.Then we have

Since σi=σj,as mentioned before,we haveMoreover,if σi≠σj,then.In this case,the differ ence betweenandonly comes from target RCS but not from the parameter setting of the two transmitterreceiver (bistatic) pairs,which makes the compensated QEP inRxiequivalent to be in the same station as the QEP inRx j.Since the SDC of the reference receiving station relative to itself is 1,the QEP in the reference receiving station can also be seen as the compensated QEP.Thus,data in the two stations become comparable and can be fused for the analysis of target characteristics.Moreover,the compensated QEP has a linear relationship with BRCS,which means the compensated QEP is also equivalent to a quasi-BRCS.Thus,we are able to know the characteristics of a target’s BRCS by analyzing the compensated QEP.

3.Simulation results

3.1 Estimation of SDC

There are three targets used in the simulation,namely Cessna 172,Airbus 320,and Boeing 747,as shown inFig.2(a),Fig.2(b),andFig.2(c).For each target,we randomly generate 1000 tracks and pick 953 tracks that are in the area of interest.The length of each track is 20 points.The start points of these tracks are uniformly distributed in the area of interest while their orientations conform to the uniform distribution in [0,2π].We set the target speed to 200 m/s for all three targets.The simulation scenario is shown inFig.2(d),where the black parallelogram whose size is 8 km ×8 km denotes the given area for target moving;the red triangle marked withTxis the simulated transmitting station;the three blue triangles marked withRx1,Rx2andRx3are the three simulated receiving stations.Their receiving gain are set to be 10 dB,15 dB,and 20 dB,respectively.Thus,the true values of SDCs ofRx2andRx3relative toRx1can be obtained according to (6),which are 3.16 and 10.The array antenna used in the three receiving stations are all set to be uniform linear array but with 5 elements,7 elements,and 11 elements respectively.It should be noted that the location coordinates of the three receiving stations and the height of the given area are not shown in true proportions in order to show their relationship clearly.At the meantime,the BRCS database of the three targets is calculated by the commercial software High Frequency Structure Simulator (HFSS) at a frequency of 546 MHz.Then,the incident angle and the scattering angle of the electromagnetic wave in the target coordinate system corresponding to each point on the track are estimated according to the target position,the station layout of transmitting station,and the receiving station and the target attitude which is estimated according to the method proposed in [14].Using the estimated angles,we extract BRCS for each point on the track from the aforementioned BRCS database.Then,we generate the simulated target echo power for each track.Without loss of generality,assume all echo power data are received with an array pattern formed at the azimuth angle of 45°.The array patterns for the three receiving stations are shown inFig.2(e).

Fig.2 Configuration for simulation

We chooseRx1as the reference receiving station and then estimate SDCs ofRx2andRx3relative toRx1according to (5).It should be noted that when matching the incident angles and observation angles of two sets of data,we do not require the corresponding angles to be exactly equal in value,but when their difference is less than a threshold,they are considered to be equal.In this paper,the threshold of angle difference is set to 1° in consideration of the limited angle measurement accuracy of reallife radars.In a real situation,influences from noise and fluctuation of BRCS on the target echo power are inevitable,which would lead to estimation error of SDC.Two simple and intuitive ways to reduce the estimation error are to average multiple measurements and to increase the signal-to-noise ratio (SNR).Due to the angle matching strategy used,it is required that the target echo power should be slowly fluctuating with the attitude angle,in order to employ the method of averaging multiple measurements to reduce the estimation error of SDC.Thus,in the SDC estimation,it is required to use targets of Swerling I and Swerling III.We generate multiple sets of target echo power with different SNRs.The SNR ranges from 5 dB to 50 dB with a step of 5 dB.The estimated SDCs forRx2andRx3are shown inFig.3andFig.4,respectively.

Fig.3 SDC estimation of Rx2

Fig.4 SDC estimation of Rx3

InFig.3,the true value is 3.16;the black part inFig.3(c)denotes that there are many curves gathering around the same value,which means the estimation converges to that value.

InFig.4,the true value is 10,and the black part inFig.4(c)denotes that there are many curves gathering around the same value,which means the estimation converges to that value.

It can be seen fromFig.3(d)that when SNR>30 dB and the number of repeated measurements is greater than 35,the estimated value of the SDC becomes stable.This result indicates that the SDC converges to the true value when SNR and the number of repeated measurements increase.In particular,SDC ofRx2converges to 3−3.5 with the number of repeated measurements increasing,as shown inFig.3(b).At the meantime,when the number of repeated measurements for average reaches a certain amount,the SDC ofRx2would also converge to 3−3.5 with the SNR increasing.As shown inFig.3(c),the estimation curves concentrate on around the value of 3,which indicates that most of the estimations are close to 3.The same variation trend and conclusion are also applied to the SDC estimation ofRx3,as shown inFig.4.What is different is that the SDC estimate ofRx3converges to about 10.

3.2 Analysis of distribution characteristics of QEP

In this section,we choose simulated target data whose SNR=30 dB to estimate the SDC for the reason that this SNR is in accordance with the real situation in our passive radar system.Fig.5shows the SDC estimates ofRx2andRx3between different SNRs when the number of repeated measurements is 100.It can be seen fromFig.5that when SNR=30 dB,SDC estimates forRx2andRx3are 3.16 and 10.55,respectively.Compared to the values we set in the simulation,which are 3.16 and 10,the percentage errors are 0.00% and 5.50%,respectively.Using these two SDCs,we compensate the simulated QEP and get the compensated QEP data.For each track,we have a time sequence of the QEP.For each sequence,we calculate three features,i.e.,the minimum value,the median value,and the maximum value.The following statistical analysis is made based on the tracks corresponding to angle ranges of 90◦≤θi≤120◦,0◦≤φi≤30◦,90◦≤θs≤120◦,90◦≤φs≤120◦in the target coordinate system.

Fig.5 SDC estimates of Rx2 and Rx3 between different SNRs when the number of repeated measurements is 100

(i) Comparison of characteristics of QEP among different stations

We take Cessna 172 as an example to investigate the distribution characteristics of each QEP feature of the target in different receiving stations,as shown inFig.6.It should be noticed that to conveniently make comparisons,we take the amplitude of the histogram,connect it into a broken line,and express the histogram into a broken line graph.The upper figures inFig.6are results with compensation only for distance and the pattern propagation factor for the receiver-to-target path whereas the lower figures are results with compensation also for the station difference.It can be seen from figures on the upper row inFig.6that the distributions of the features in different receiving stations are quite different from each other before compensation for station difference.Not only do the peak locations of the distribution curves from different receiving stations differ from each other,but also their abscissa ranges differ.However,after compensation for the station difference,distribution curves for the same feature almost coincide with each other,as shown inFig.6(d),Fig.6(e),andFig.6(f).These results indicate that the compensated QEP from different receiving stations are comparable and can be fused.We can also see fromFig.6(d),Fig.6(e),andFig.6(f)that distribution curves of the same feature from different receiving stations are not exactly the same,even if they are compensated for the station difference.The reason about this is that the amount of tracks used to make statistical analysis in each receiving station is not equal.Since the distribution of occurrence rate is an approximation of the probability distribution,the unequal amount of data used to make statistical analysis will lead to differences in the distribution of the occurrence rate.

Fig.6 Occurrence rate distribution histogram of Cessna 172’s three features from three simulated receiving stations

(ii) Comparison of characteristics of QEP among different targets

In this section,we discuss the influence of the station difference on target characteristics and show the necessity to compensate for the station difference in order to obtain correct characteristics of the targets from the fused data.We fuse target data from different receiving stations by packing them according to the target type.Both the data with and without compensation for the station difference are fused in order to make comparison.Results of statistical analysis are shown inFig.7.It can be seen fromFig.7(d)that the right end of the distribution curve of Cessna 172 after compensation is only about 25 dB,whereas the right end of the one before compensation is extended to about 40 dB,as shown inFig.7(a).The main reason for this is that the value range of the QEP before compensation is extended by the SDC.The extension of the QEP value range could cause the values not belonging to Cessna 172 to be mistakenly classified as Cessna 172’s.And just because of the extension of the value range,the distribution histogram of the occurrence rate is changed and deviates from the true target characteristics.As shown inFig.7(a)andFig.7(d),the distribution before compensation differs a lot from the one after compensation.The aforementioned phenomenon and analysis coming from the distribution characteristics of the minimum value are also applied to the other two features.These results demonstrate that compensation for the station difference is necessary to obtain the correct target characteristics.

Fig.7 Occurrence rate distribution histogram of three features from three different simulated targets

4.Experiment results

Experimental data are collected in Luoyang Beijiao Airport with multistatic passive radar developed in Wuhan University,whose configuration is shown inFig.8(a).The multistatic passive radar consists of one transmitter and two receivers,namelyRx1andRx2.Two receiving antenna arrays directing to different directions are used to collect abundant information of airplanes.Information of cooperative targets,which are SR20 and MA600,are obtained and confirmed by the automatic dependent surveillance broadcast (ADS-B),as shown inFig. 8(b)andFig.8(c).It should be noted that SR20 is a small plane whose size is smaller than that of MA600.High-precision tracks with target echo power are obtained by using methods proposed in [15].

Fig.8 Configuration of the multistatic passive radar and the cooperative targets

Before conducting ATR with the output data,preprocessing including eliminating the station difference of data from different receiving stations is required so as to obtain correct target distribution characteristics from statistical analysis.We chooseRx1as the reference station and estimate the SDC ofRx2relative toRx1.Result of the SDC estimation is shown inFig.9.

Fig.9 Estimated SDC of Rx2

The horizontal axis inFig.9denotes the number of repeated measurements of SDC. As can be seen fromFig.9,with the number of repeated measurements increasing,the value of the estimated SDC tends to be stable,which means the estimation is convergent and validates the use of averaging on repeated measurements in SDC estimation.Thus,we choose the value after an average of 100 times as the final estimation ofRx2’s SDC,which is 0.34.

We compensate target echo power fromRx2for station difference using the aforementioned SDC estimate.Meanwhile,target echo power fromRx2andRx1are both compensated for distance and pattern propagation factor for the target-to-receiver path.In this way,we obtain the corresponding compensated QEP.To validate the SDC estimate ofRx2,a comparison between the target distribution characteristics of SR20 obtained from the data before compensation for SDC and those obtained from the data after compensation for SDC is made inFig.10.It should be noted that the following statistical analysis is made based on tracks corresponding to the angle range of 90◦≤θi≤120◦,0◦≤φi≤30◦,1 20◦≤θs≤150◦,2 10◦≤φs≤240◦in the target coordinate system.

It can be seen fromFig.10that distribution curves of the same target in different receiving stations differ from each other.Difference of the curve shape comes from different amounts of data.Since these curves are approximations of the probability distribution function and the amount of data used in analysis would affect the curve shape,the difference in the curve shape is reasonable and acceptable in consideration of the similar change trend of these curves.However,difference in abscissa ranges of the curve should be eliminated since it comes from the station difference.This difference will lead to obtaining wrong distribution characteristics of the fused data.As shown in the upper row ofFig.10,there is a deviation for the green curve from the red curve which is the reference curve.After compensation for station difference using SDC,this deviation is offset,as shown in the lower row ofFig.10.Results shown inFig.10validate the correctness of the estimated SDC.

Fig.10 Occurrence rate distribution histogram of SR20’s three features from two receiving stations

A further comparison between target distribution characteristics obtained from fused target data before compensating the station difference and those obtained from fused target data after compensating the station difference is also made inFig.11.For one thing,the curve span is reduced after compensation for station difference.Reason for this is that the station difference reflecting on the SDC makes the QEP level inRx2lower than that inRx1.Thus,the value range of QEP is extended on the lower boundary after data fusion,making the curve span before compensation wider than that after compensation.For another,an obvious change in the curve shape is observed from the comparison.As shown inFig.11(c)andFig.11(f),position of the curve peak of MA600 changes from around 180 dB to larger than 200 dB.If we consider this peak location as an identifying feature,the difference resulted by station difference could lead to very different recognition results.Comparison shown inFig.11demonstrates the necessity to compensate station difference of QEP in target characteristics analysis for multistatic passive radars.

Fig.11 Occurrence rate distribution histogram of three features from different measured targets

5.Conclusions

In this paper we propose a method to eliminate the station difference in target echo power for multistatic passive radars.We estimate the SDCs of all receiving stations relative to the reference receiving station and compensate the QEP data with them.Statistical analysis on the simulated and real-life QEP data show that the station difference can be effectively compensated by the estimated SDC,which validates the effectiveness of the proposed method. Moreover,statistical results also demonstrate that the features defined on the time sequence of the compensated QEP possess obvious difference for different targets,which indicates that they are beneficial features to be used in ATR.