Hybrid High-Fidelity Modeling of Radar Scenariosusing Atemporal, Discrete Event, and Time-Step

SimulationYuanPin Cheng, Don Brutzman, Phillip E. Pace, and Arnold H. Buss

Abstract—Many simulation scenarios attempt to seek abalance between model fidelity and computational efficiency.Unfortunately, scenario realism and model level of detail areoften reduced due to the complexity of experimental designand corresponding limitations of computational power. Suchsimplifications can produce misleading results. For example ifthe Radar Cross Section (RCS) effects in response to time-varying target aspect angle are ignored.

A hybrid, high-fidelity sensor model can be achieved byusing a Time-Step (TS) approach with precomputed atemporalresponse factors (such as RCS) each situated on active entitiesthat interact within an overall Discrete Event Simulation (DES)framework. This paper further applies regression analysis tothe cumulative results of 100 replications times 255 scenariosto provide additional insight. This new methodology adapts thebest aspects of each simulation paradigm to integrate multiplehigh-fidelity physically based models in a variety of tacticalscenarios with tractable computational complexity.

Index Terms—Discrete Even Simulation (DES), regressionmodel, Nearly Orthogonal Latin Hyper Cube (NOLH), RadarRange Equation, Hybrid sensor model.

I. INTRODUCTION

THERE is always a dilemma for simulation developersand users. On the one hand, modelers want the simu-

lation to contain as many details as possible, so the resultscould be closer to the real world, and on the other hand, asimulation needs to be executed efficiently and smoothly. Inthis dilemma, “better is the enemy of good enough.” As themodels get more complicated, the computational complexityand cumbersome system are the price paid, especially whendealing with a high complexity physical model, like a radarsystem, in simulation. Better levels of detail create high com-putational complexity which negatively impacts efficiency.

A search radar-targets simulation scenario, seeking forradar’s time-to-detect targets, contains numerous factors thatcontribute to model performance, such as target’s distance,antenna sweeping period, aspect angle of targets and targetspeed etc. Some parameters are sensitive to the performanceof the whole system and the computation is nearly toocomplex to accomplish in a real time simulation, such as

Manuscript received June 30, 2016; revised July 30, 2016. This work wassupported in part by the Office of Naval Research, ONR Code 31.

Y. Cheng is the Army Major of the Republic of China, Taiwan withthe Modeling, Virtual Environments, and Simulation Institute (MOVES),Naval Postgraduate School (NPS), Monterey, CA, 93943 USA e-mail:(ycheng@nps.edu).

D. Brutzman and A. H. Buss. are with MOVES, Naval PostgraduateSchool, Monterey, CA, 93943 USA e-mail: (brutzman, abuss@nps.edu)

P. E. Pace is with the Center for Joint Services Electronic Warfare and theDept. of Electrical and Computer Engineering, Naval Postgraduate School,Monterey, CA, 93943 USA e-mail: (pepace@nps.edu)

Radar Cross Sections (RCS) of targets from different aspectangles.

Wang et al., in their study of constructing radar systemsimulations, propose a universal program framework thatconsiders the radar-target scenario using an object templateThe template divides the simulation into three subsystemsclassified by functions. These functions include: 1) Scenetarget echo generation system, 2) Radar information processsystem, 3) Radar control, display and estimation system [1].

A reoccurring problem in approaches to dynamic target-sensor scenarios, when a sensor’s detection algorithm isbased on the range between sensor and target [2], or sensordetectable perimeters [3] this neglects the factor of aspectangle of targets. The change of aspect angle can lead to dras-tic variation in RCS response. So the maximum detectablerange of sensor derived from radar range equation [Eq. (1)]also fluctuates along with aspect angle. RCS can have ahuge influence on received signal power at the receiver, andhas been recommended as a topic of future work in RadarModeling and Simulation (M&S) research by Inggs et al. [4].

Wang et al.’s study has incorporated RCS values intomodeling by a ground clusters numerical Weibull model ina Radar M&S focusing on Terrain Environment effects [5].The cluster backscatter RCS is the function of terrain rangeand aspect angle relative to the sensor in the Weibull modelthat has been previously measured and built in prior research.

However, when integrating a non-parameterized RCSmodel generated from an arbitrary target, a simulation ap-plication might produce incoherent responses due to consid-erable computational latency from generating target RCS.

To fill in these gaps in target-sensor scenarios at runtime, this research integrates modeling structure from threecategories with a multi-stage approach as shown in Figure.1.The three catagories are: 1) Atemperal construction, 2) Dis-crete event simulation construction, 3) Time step costruction.There are two major contributions of this structure approach:

1) Integrating a high-fidelity physical radar range equa-tion, which considers dynamic position between sen-sors and targets through simulation, into a comprehen-sive detection algorithm. This work constructs a hybridmodel with three modeling constructs that mitigatethe disparate simulation time mechanisms of eachparadigm.

• Atemporal models, i.e. models that cannot beinteractive in real time simulation scenario dueto its tremendous computational latency, such astarget’s RCS response .

• Discrete Event Simulation (DES) structure forprecise and efficient event execution.

Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA

ISBN: 978-988-14048-2-4 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2016

Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA

ISBN: 978-988-14048-2-4 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2016

Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA

ISBN: 978-988-14048-2-4 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2016

Enter

Range

(m,s)

A Ping

(m,s)

Exit

Range

(m,s)

(!s.getContact.Contain(m))

{Angle =findIntersectionAngles(m, s)

RangeMax =s.getRmaxByAngle(Angle)

MSDistance =

Math2DAngle.findCurrentDistance(m, s) }

DetectUnDetect

(m,s)

m

m

(!s.getContact.Contain(m) && Rmax > MSDistance))

(s.getContact.Contain(m) && Rmax < MSDistance)

(s.getContact.Contain(m))

RCSMediator

Fig. 4. Hybrid Mediator Event Graph Ensures Fair Adjudication of WhetherDetection Occurs.

Fig. 5. Radar Range Equation Parameters only Configured by Sensors

follow:

Ru =C

2 · prf(2)

The detectable range of targets from the sensor has tosatisfy both equations (1) and (2) i.e. the threshold rangeRdetect in which the sensor will detect targets needs to meetthese two criteria: Rdetect < Ru and Rdetect < Rmax.

The parameters, applied in radar range equation, havebeen classified into two categories in this study: 1) theparameters that can only be configured by the radar system.The parameters are listed in Figure.5 and they can be set upas modeler’s attempt. 2) the rest of the parameters that haveinteractive relationship with other factors in the scenarios areset up accordingly.

A. Radar Cross Section σT

RCS is the property of a scattering object that representthe magnitude of the echo signal returned to the radar by thetarget [7]. RCS fluctuates as a function of radar aspect angleand frequency. When the signal operational wavelength ismuch smaller than the target extent, this condition is referredto as the optics region. The optics region is applied in thescenario in this research. A further question, does targetphysical size indicate RCS size? Comparing an illustrativeRCS example of two different geometry objects:

• The RCS of a flat plate at broadside, A2 is the area ofplate

σPlate =4πA2

λ

∣∣∣∣λ=0.1m,f=3GHz,A=1m2

= 1000(m2)

Fig. 6. F-16 Falcon Fighter Model RCS Measure in [0◦, 360◦)

• The RCS of a Cone-Sphere, a is the radius of the spherewith 30◦ cone angle

σCone =2πa

λ

∣∣∣∣λ=0.1m,f=3GHz,a=0.564m

= 0.001(m2)

There is a million-to-one difference in the RCS of two targetseven if each of them has the same projected area. RCS isdeadly, a critical factor.

The RCS of complex targets such as aircraft, missiles,vessels and terrain can also be vary considerably dependingon the view aspect and radio frequency. In this paper, theRCS values are computed [0◦ ∼ 360◦) from a F-16 falconfighter 3D model in full-scaled size using signal frequency10 (GHz) by a high-fidelity electron magnetic simulationsoftware, CST Studio [8]. Computing one angle of RCS fromthe target takes about 3 minutes. A whole 360◦ range of RCSvalues of the target with 0.5◦ resolution may take days orweeks to accomplish by a PC. This computation delay cancause huge computational latency in simulation if we do notisolate this atemporal factor from others.

B. Pulse Integration Improvement Factor NIntThe pulse integration improvement factor is determined

by the number of pulses returned from a point target [7]during a scan of radar with a pulse repetition rate prf(Hz),an antenna 3dB beamwidth θ3dB (we only consider azimuthangle effect in this study), and antenna revolutions per minute(rpm).First, the effective radar signal illumination time on target(ToT) per revolution is calculated as follow:

ToT =60s

rpm× 360◦× θ3dB AZ (second)

then the number of effective pulses provided to the integra-tion improvement factor is

NInt = ToT × prf

A mono-static radar is assumed in this scenario, whichmeans the transmitting and receiving signal are from thesame source at the same station. A coherent integrationimprovement factor can be applied in this system.

Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA

ISBN: 978-988-14048-2-4 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2016

C. Target Fluctuation: Swerling III model χ2df=4

Target detection algorithm utilizing the square law detectorassumes a constant RCS. This work was extended by PeterSwerling to four distinct cases of target RCS fluctuation[9]. We apply Swerling III, a chi-square probability densityfunction with four degree of freedom, in this study. Thisfactor models the fluctuation loss from targets betweeneach antenna scan. The RCS is assumed to be constantwithin a scan and independent from scan to scan [10]; theseconditions are the same as those in this simulation scenario.The sensor model generates stochastic time-to-detect resultsdue to this fluctuation loss model which is represented by aChi-Squared random variable with degree of freedom = 4.

IV. DESIGN OF EXPERIMENTS AND DATA ANALYSIS

Regression analysis is a statistical method that investigatesthe relationship between two or more variables related in anon-deterministic manner [11]. The relationship is expressedin the form of an equation or more explanatory predictor vari-ables. To learn the system behavior or predict the outcome,associated with the input parameters of the system, requiressufficient experiment data that cover as many detail levels inparameters as possible. Tallavajhula [12] applies data-drivenmethods to learn the relationship between input parametersand system state and construct a high fidelity model for aplanar range sensor.There are two crucial considerations for design of experiment(DoE):

• The number of available experiments must be statisti-cally significant for designer and analyzer. Nevertheless,because of realistic constraints such as budget, timeor available exercise space to conduct experiments,experimenters are usually unable to get unlimited ex-perimental results for analysis. Efficiently designingexperiments is important.

• How well the space is filled reflecting the systemparameters from the DoE is also important. The moredetailed levels are included in the DoE, the more therelationship between system and parameters will becaptured by the analysis. This need for detail must bebalanced with the need for efficiency. A well-coveredand succinct DoE is necessary.

A. Design of Experiment (DoE) by Nearly Orthogonal LatinHypercube (NOLH)

To analyze the interactive relationship between all inputparameters in the model, a DoE that efficiently fills space inthe range of parameters is crucial to reveal the relationshipbetween parameters and system state. In full factorial design,if applying five factors with 250 levels of each factor, thenumber of design points = 2505 ' 9.7 × 1011. For eachdesign point executing 100 repetitions, the total simulationexecution amount will be up to ' 9.7×1013. Even though inthis computer based simulation, the number of experimentsthat can be conducted is not restricted, this execution amountis still unbearable.

The Nearly Orthogonal Latin Hypercube presented byCioppa at. el [6] provides an efficient space filling DoE thatallows view of 255 levels of up to 29 factors in 255 designpoints. With 100 repetitions, the total number of simulation to

Fig. 7. DoE for simulation by Nearly Orthogonal Latin Hypercube (NOLH)

TABLE IVFACTORS LEVEL RANGE AND DECIMALS SETTING BY NOLH DOE

factorname

Waypoint(km)

Speed(km/hr)

Sweepinginteger(sec)

prf(Hz) θ3dB(degree)

low level -57.7 200 1 375 3high level 57.7 1200 8 1500 6decimals 2 2 1 1 1

process is 25, 500. This makes three billion-to-one differenceon simulation executing. In Figure.7 shows that the designpoints of each factors fill in the DoE space quite evenly withonly minor overlapping correlation to each other.

Even though the parameters listed above are set up inconventional units of radar applications, it is important tohave all parameter units consistently applied in the simu-lation to avoid misrepresenting quantity of parameters. Inthe simulation, the unit of the antenna “Sweeping Integer”parameter is converted from seconds to hours in order tomatch the length unit within the “Target Speed” parameterin TABLE IV.

B. Linear Regression Estimation of time-to-detect (TTD)

Executing the DoEs through the hybrid sensor modelsimulation, yields time-to-detect-target data, which is asso-ciated with 255 design points. Next, a meta-model is formedby linear regression analysis for predicting the responsevariable “time-to-detect” the target by the sensor. For a goodmeta-model, the goal is to make the difference betweenmeta-model and baseline hybrid simulation model small.An simple linear regression model that describes the rela-tionship between response variable Y and predictor variablesX1, X2, · · · , Xp is defined as follow [13]:

Y = β0 + β1X1 + β2X2 + · · ·+ βpXp + ε

where β0, β1 · · · , βp, called the regression coefficients andε is assumed to be a normal random error to represent the

Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA

ISBN: 978-988-14048-2-4 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2016

Fig. 8. Residual Plot by Predicted Time to Detect of Fit Model

failure of the model to fit the data exactly. It is representedas follow:

ε ∼ N(0, σ2)

These values are unknown constants to be determined fromthe simulation-output data. Backward elimination of Least-Squares estimation is applied to form the regression meta-model. It is a commonly used technique to fit the modelwith minimum sum of squared errors between meta-modeland sample data. Mean squared error (MSE) is defined as theerror between fit model and sample data. It is represented asfollow:

σ2 =SSE

n− I=MSE = 0.00001

where sum of squared errors is SSE, the total number of datasamples is n=6878 and the number of data sample groups isI = 39 in this meta-model. Applying the predictor parametersup to four degrees of factorial and polynomial terms in fitmodel should allow for capture of some curvatures in thesample data distribution. The meta-model has R-Square =0.9947. R-Square is a statistical measure of how close thedata are fitted to the regression line. R-Square is [0, 1]. Ahigher R-Square value indicates more response data aroundthe baseline model mean.Figure.8 shows the residual of fit model by predicted “time-to-detect.” Certain heteroscedasticity can be observed inresidual distribution, which means unequal variance acrosstreatments that is not the ideal assumption for forming ameta-model by linear regression. However, “all models arewrong, but some are useful,” as observed by George Box.Thus the fidelity of this fit model is evaluated further.

C. Logistic Regression of Probability of Detection (Pd)

For a dichotomous dependent variable, such as if thetarget is detected, the numerical value of the variable is notintrinsically interesting. The key point to focus on is whetherthe classification of cases into one or another categories ofthe dependent variable can be predicted by the independentpredictor variables [14]. The probability of an event happen-ing is denoted as P (Y = 1). If the probability of an eventhappening is known, then the probability of an event not

and the range of parameters set up is listed in Table IV

Fig. 9. TTD t-test between Meta and Hybrid Sensor Model

happening is also known: P (Y = 0) = 1−P (Y = 1). Logis-tic regression analysis models the ratio between P (Y = 1)and P (Y = 0) with a natural logarithm of the ratio. Thisexpression is called logit of Y:

ln

{P (Y = 1)

[1− P (Y = 1)]

}= logit(Y )

= α+ β1X1 + β2X2 + · · ·+ βpXp

then we can convert the logit(Y ) back to the probability that(Y=1) with predictor variables in such equation:

Probability(Y = 1) = P (Y = 1)

=1

1 + e−(α+β1X1+β2X2+···+βpXp)

A logistic regression analysis is run of the probability ofdetection (Pd) by a sensor of targets, using predictor param-eters of up to a degree of two polynomial and factorial terms.This logistic regression analysis has an RSquare = 0.843. Thelogistic meta-model determines if the target is detected by thesensor in this DoE with a predicted probability. If the targetdetection is determined true by comparing the Pd with auniform random variable [0,1], then time-to-detect the targetcon be estimated by the linear regression model described inSection IV-B.

D. Meta-Model Validation

The validation of the meta-model was verified by examin-ing the mean (first moment) and variance (second moment)of predicted results. Testing the first moment and secondmoment between predicted results and baseline data canindicate how well the meta-model represents the hybridmodel.

• Two-sample t-test.Processing a two sample t-test on TTD from both metaand hybrid models with 100 repetitions in one designpoint [Figure.9]. Because the t-Ratio = -0.7687 it retainsthe null hypothesis of equal mean assumption at a 95%confidenc inteval. In other words, the mean of predictedTTDs are statistically the same as the hybrid sensormodel.

• O’Brien unequal variance test.The p-value of this unequal variance test was less then0.0001. It rejects the null hypothesis of equal varianceassumption. The test indicates the variance of predictedTTDs is different from the hybrid model in Figure.10.

Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA

ISBN: 978-988-14048-2-4 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2016

Fig. 10. TTD Variance test between Meta and Hybrid Sensor Model

V. CONCLUSIONS

This work demonstrates a hybrid structure sensor modelthat successfully integrates high fidelity radar range equationswith dynamic RCS response from targets. Based on computa-tionally efficient DES structure with isolated atemporal RCSmodel, the hybrid model not only introduced angle varyingRCS factor into the dynamic sensor-target scenario, but alsokeep the computational complexity of whole scenario downto reasonable level. A typical desktop PC is capable ofexecuting 250,500 DoE scenario repetitions in a matter ofminutes.

Even with these benefits of a DES-based structure for thehybrid model, the embedded TS mechanism for emulatingantenna sweeping period is still a key latency for a compre-hensive model. Additionally, the model also needs to includemaximum detectable range table for the target. These factorsstill make the model bulky in some sense. This research alsoutilizes efficient NOLH DoEs which provides a well-filledspace of parameters with significantly fewer design pointscompared with full factorial design.

Finally, a meta-model is fit from the experimental dataexecuted by the DoEs with Least-Squares estimation. Themeta-model does present the hybrid model characteristicsin certain sense with much more concise structure, even ifthe fit model showed some heteroscedasticity in predictionresults. This difference in variance might result from highorder factorial and polynomial terms that had been includedin the meta-model. Further data analysis and regressionmethodologies can also be applied in future work to forma better meta-models of interest.

ACKNOWLEDGMENT

The authors gratefully acknowledge Dr. David C. Jennin ECE department of NPS for RCS computation on CSTStudio insight and support and Dr. Thomas W. Lucas and theSimulation Experiments Efficient Designs (SEED) Center ofNPS for providing guidance on DoE and data analysis.

REFERENCES

[1] Z. W. L. X.-l. Wang Lei, Chen Ming-yan, “A universal program frame-work for radar system simulation,” Computer Science and AutomationEngineering (CSAE), IEEE International Conference, vol. 1, pp. 595– 599, May 2012.

[2] S. V. Migel and I. G. Prokopenko, “Radar simulation system managedby script language,” 15th International Radar Symposium (IRS), IEEE,pp. 1–5, June 2014.

[3] A. H. B. Buss and P. J. Sanchez, “Simple movement and detection indiscrete event simulation,” IEEE, Dec 2005.

[4] A. K. M.-F. D. V. M. M. R. Inggs, C. A. Tong, “Modelling andsimulation in commensal radar system design,” Radar Systems (Radar2012), IET International Conference on, pp. 1–5, October 2012.

[5] G. G. H. K. Wang Quanmin, Wang Chuncai, “Rf effect algorithms ofterrain environment in signal-level radar system simulation,” ComputerModeling and Simulation, ICCMS ’10. Second International Confer-ence, IEEE, vol. 4, pp. 178 – 181, January 2010.

[6] T. Cioppa and T. Lucas, “Efficient nearly orthogonal and space-fillinglatin hypercubes,” Technometrics, p. 45, February 2007.

[7] M. Skolnik, Introduction to Radar Systems (Third Edition). Mc-GrawHill, 2002, ch. 2, pp. 45–49.

[8] [Online]. Available: https://www.cst.com/Products/CSTMWS[9] B. R. Mahafza, Radar Systems Analysis and Design using Matlab

(Third Edition). CRC Press, 2012, ch. 13, p. 438.[10] M. Skolnik, Introduction to Radar System (Third Edition). Mc-

GrawHill, 2002, ch. 2, pp. 66–73.[11] J. L. Devore, Probability and Statistics for Engineering and The

Sciences (Sixth Edition). Thomson Learning Academic ResourceCenter, 2004, ch. 12, pp. 496–516.

[12] A. Tallavajhula and A. Kelly, “Construction and validation of a highfidelity simulator for a planar range sensor,” International Conferenceon Robotics and Automation (ICRA), IEEE, pp. 6261 – 6266, may2015.

[13] B. P. Samprit Chatterjee, Ali S. Hadi, Regression Analysis by Example(Third Edition). Wiley-Interscience, 2000, ch. 1, pp. 1–18.

[14] S. W. Menard, Logistic Regression From Introductory to AdvancedConcepts and Applications. SAGE Publication, 2010, ch. 1, pp. 12–18.

Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA

ISBN: 978-988-14048-2-4 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2016