Thermal weapon sights with integrated fire control computers: algorithms and experiences

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by  Rothe Hendrik, Graswald Markus, Breiter Rainer.

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Thermal weapon sights with integrated fire
control computers: algorithms and experiences
ARTICLE in PROCEEDINGS OF SPIE - THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING · JANUARY 2008
Impact Factor: 0.2 · DOI: 10.1117/12.776175
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Thermal weapon sights with integrated fire control
computers: algorithms and experiences
a a b
Hendrik Rothe , Markus Graswald , and Rainer Breiter
a
Helmut-Schmidt-University, Holstenhofweg 85, 22043 Hamburg, Germany
bAIM Infrarot-Module GmbH, Theresienstr. 2, 74072 Heilbronn, Germany
ABSTRACT
The HuntIR long range thermal weapon sight of AIM is deployed in various out of area missions since 2004
as a part of the German Future Infantryman system (IdZ). In 2007 AIM fielded RangIR as upgrade with
integratedlaserRange finder (LRF), digital magnetic compass (DMC) andfire controlunit (FCU). RangIRfills
the capability gaps of day/night fire control for grenade machine guns (GMG) and the enhanced system of the
IdZ.Duetoprovenexpertiseandproprietarymethodsinfirecontrol,fastaccesstomilitarytrialsforoptimisation
loops and similar hardware platforms, AIM and the University of the Federal Armed Forces Hamburg (HSU)
decided to team for the development of suitable fire control algorithms. The pronounced ballistic trajectory
of the 40mm GMG requires most accurate FCU-solutions specifically for air burst ammunition (ABM) and
is most sensitive to faint effects like levelling or firing up/downhill. This weapon was therefore selected to
validate the qualityofthe FCUhard-andsoftwareunder relevantmilitary conditions. For exteriorballistics the
modified pointmass model accordingto STANAG 4355is used. The differentialequations ofmotions aresolved
numerically,the twopointboundaryvalue problemissolvediteratively. Computingtime variesaccordingto the
precision needed and is typical in the range from 0.1 - 0.5 seconds. RangIR provided outstanding hit accuracy
including ABM fuze timing in various trials of the German Army and allied partners in 2007 and is now ready
for series production. This paper deals mainly with the fundamentals of the fire control algorithms and shows
how to implement them in combination with any DSP-equipped thermal weapon sights (TWS) in a variety of
light supporting weapon systems.
Keywords: thermalweaponsight,firecontrolunit,automaticgrenadelauncher,firsthitprobability,firecontrol
algorithms
1. INTRODUCTION
Onthebasisofpresenttechnologiesitwasonlypossibletoequiplargeweaponsystems,e.g. tanks,planes,rockets
or ships with fire control computers. However, the asymmetric threats which arose in the last ten years make
fire control computers also desirable for light supporting weapons, like the Grenade Machine Gun 40 x 53 mm
(GMG, Heckler & Koch) or the Barrett light fifty 12.7 x 99 mm (Barrett Rifles). A high first hit probability is
necessarytoprotectthelivesofoursoldiers,tofulfilthetasksofthemissionsandtominimizecollateraldamage.
The same is true for image intensifier based or thermal weapon sights (TWS), where we - in contradiction to
firecontrolcomputers-canseeconsiderableprogressforlightweapons,evenassaultrifles,submachinegunsand
service pistols.
Ananalysisofcombatscenariosclearlyshowedthatthe highestfirsthit probabilitiesforlightweaponscould
be achieved by a combination of thermal weapon sights with integrated fire control computers, particularly if
the ammunition has a pronounced ballistic curve, i.e. for indirect fire. The GMG is such a weapon, and is
also equipped with a thermal weapon sight, namely the cooled thermal weapon sight RangIR of AIM GmbH
(cf. Fig. 1) which ensures a identification range of 1500 m also under adverse weather conditions. The RangIR
weapon sight features a digital signal processor (DSP) for image processing. Obviously, this DSP could be also
used as fire control computer, if an efficient fire control algorithm was available. Fire control means basically
the real-time solution of a two-point boundary value problem for a system of ordinary differential equations.
Formerly, this was a task for highly specialized hard-wired electronics. By using the most recent generation of
DSPs it should now be possible to solve the fire control problem with this COTS hardware - provided that a
appropriate real-time algorithm could be developed.
Infrared Technology and Applications XXXIV, edited by Bjørn F. Andresen, Gabor F. Fulop, Paul R. Norton,
Proc. of SPIE Vol. 6940, 69401K, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.776175
Proc. of SPIE Vol. 6940 69401K-1
2008 SPIE Digital Library -- Subscriber Archive Copy
Dual FOV lens
NFOV 2.3◦ x 3.0◦
WFOV 6.8◦ x 9.1◦
ID Range 1500 m
LRF eye-safe 1.5 µm
DMC
Mass < 3 kg
Operation time > 4 h
Picatinny rail weapon adaptation
Figure 1. Thermal weapon sight RangIR.
Afirecontrolcomputeronthebasisofathermalweaponsightshouldcontainalsothe followingcomponents:
• laser range finder (LRF)
• digital magnetic compass (DMC) with inclinometer
• sensors for air pressure, temperature, and wind strength/direction
• GPS
Thegunmanusesonlythethermalweaponsightforfirecontrol. HelooksatthescreenoftheTWSandaims
at a target with the electronic crosshair. Then he activates the LRF, the distance is measured and by using all
theinformationoftheintegratedsensorsthefirecontroldataiscomputedinlessthen0.5seconds. Thecrosshair
is moved to a new position on the screen. The gunman now has to move the weapon in such a way that the
crosshair is again on the target. If he now pulls the trigger he will hit the target with the first round, or salvo.
A TWS with integrated fire control computer is especially useful for indirect firing weapons with a rather
low first hit probability, like a GMG. This low first hit probability is due to the low muzzle velocity of the
grenades, which is in the range from 175 m/s to 250 m/s, and can not be enlarged because of recoil/weapon
weight restrictions.
2. HIT PROBABILITY
The effectivity of automatic fire controlfor a GMG 40 x 53 mm can be shown by a demonstrative example. We
use a Cartesian coordinate-system (x,y,z). We shoot in the direction of the x-Axis. All random variables are
normally distributed (Gaussian). The range of fire is Wx, besides Wx (cid:1)Wy >Wz.
Thenthehitprobabilityforapointtargetpisequaltoastripwithwidth2R,whereRistheradiusofaction
of the grenade. If the variances are symmetric we can write:
(cid:1) (cid:2)
2R
P =Φ , (1)
Ex
where Ex being the averageerror in range. Using the two-error-schemeof exterior ballistics we get:
(cid:3)
Ex = Ex20+Wx2, (2)
where Ex0 is the group (or salvo) error. The most important influential factor on Ex0 is the error in target
distance measurement, which always prevails. We can write:
Ex0 =kX, (3)
Proc. of SPIE Vol. 6940 69401K-2
Table 1. Hit probability for several distances X.
Measurement k µ X, m
method 500 1000 1500
Estimation 0.1 0.99 0.21 0.11 0.07
Walking 0.04 0.94 0.53 0.33 0.24
Map 0.05 0.96 0.43 0.26 0.19
LRF 0.005 0.20 1.00 0.98 0.92
where k is a constant which depends on the method for target distance X measurement. Wx itself grows with
distance X, from experience follows: Wx ∼ 0.01X. The hit probability of a salvo with N dependent rounds is
given by: (cid:4)
pN =p1+(puN −p1) 1−µ2, (4)
where µ is the correlation coefficient of the rounds, puN =1−(1−p1)N is the hit probability of N independent
rounds. The values of the first hit probability for different methods for target distance measurements are given
in Table 1. Parametersare R=7m and N =5 rounds. It can be seen that a fire controlcomputer is extremely
useful for a GMG 40 x 53 mm.
3. MATHEMATICAL MODEL OF EXTERIOR BALLISTICS
The mathematical model of exterior ballistics is based on the laws of classical Newtonian mechanics. The
movement of a point mass (point mass model (PMM)) is described under the influence of gravity and air drag:
Mv˙ =q+R, (5)
where M is the mass of projectile, q is the force of gravity Mg, R is the air drag. Gravity is a function of the
geographicalcoordinates and is computed according to WGS-84. The absolute value of the air drag R is:
ρ
2
R=cw Av . (6)
2
TheairdragcoefficientisafunctionoftheMachnumberandcanbeapproximatedbythefollowingequation:
cw =C1Ma−C2. (7)
where C1 and C2 are constants which characterize the aerodynamic properties of the projectile. A is the cross
section of the projectile, ρ the density of air. In our case the properties of the air are measured, but it is also
permissible to use data of the ICAO atmosphere, or national standards (e.g. DIN 5450). The influence of the
temperature on the propellant and hence the muzzle velocity can be covered by the empirical IKOPZ formula:
V0 =V0∗[1+0.0011(T −T∗)] , (8)
where V∗ and T∗ are the reference values.
0
Thevectordifferentialequationofexteriorballistics canbe transformedto a systemoftwoscalardifferential
equations:
Mx¨=−RcosΘ, (9a)
My¨=−Mg−RsinΘ, (9b)
where Θ is the angle between velocity of the projectile and x-axis. Since time of flight t is unknown, it makes
sense to transform the t-dependent differential equations into as system which is distance(x)-dependent. The
Proc. of SPIE Vol. 6940 69401K-3
new system of four first order differential equations becomes:
du R 1
=− , (10a)
dx M v
dp g
=− , (10b)
dx u2
dy
=p, (10c)
dx
dt 1
= . (10d)
dx u
In so doing u= vcosΘ is the horizontal projection of the velocity and p= tanΘ. The value u is connected
with the projectiles velocity v in the following way:
v
u= (cid:4) (11)
1+p2
The initial conditions for x=0 can be written as:
u(x=0)=v0cosΘ0,p(x=0)=tanΘ0,y(x=0)=0,t(x=0)=0. (12)
This system of ordinary differential equations (ODE) describes the motion of the projectile without the
influencesofCoriolis force,windandspin. Itisdifficulttomodelthisinfluencesanalytically. Thereforeempirical
formulaeareusedtoconsiderwindofeverystrengthanddirection. E.g.,forwindperpendiculartothemotionof
the projectile Didions formula can be used. The deflection Z due to the spin of the projectile can be computed
as Z =Kt2 where K =0.1...0.15 is the constant spin coefficient.
McCoy provides the following equation for the deflection due to Coriolis force:1
Ωx2sinΨ
Zc = (13)
[u]
where Ψ is the latitude, [u]is the meanof the horizontalspeedof the projectile,Ω is the angularspeed of earth.
The ODEs of the ballistic model are nonlinear. Therefore,they have to be solved numerically. In this case a
standard method can be applied: the Runge-Kutta method of order 4. To minimize the number of integration
steps Richardson extrapolation is implemented for stepsize control.
Hittingatargetinacertaindistanceinacertainazimuthundertheinfluenceofspin,Coriolis forceandwind
requires the solution of a rather complicated two-point boundary value problem. This can be done iteratively
only: elevation and azimuth of the weapon have to be changed in such a manner that the target is finally hit:
this is the requiredfire controlsolution. We use a regula falsi for these iterations,and, of course the ODEs have
to be integrated several times in the iteration loop.
4. STRUCTURE OF A DSP FIRE CONTROL COMPUTER
The automated optronic fire control computer has to work in real time, i.e. 0.1...0.5 seconds. The following
influential factors have to be taken into consideration:
• target distance
• air temperature and pressure, wind strength, and direction
• attitude and height over sea level (Coriolis force and g-dependence)
• terrain angle and azimuth of the target (see above)
Proc. of SPIE Vol. 6940 69401K-4
Atmospheric
data
g g
n n
essi als essi nals
Podsaittaion proc sign DSP proc tsig EAlezvimatuiotn
t u
e u e p
ul p ul t
d n d u
o i o o
M M
Target
coordinates
Computational
modules
Figure 2. Principle design of a GMW fire control computer.
The sensors required for a small fire control computer are available since the mid-nineties, the computing
power, however was not available until now. Two to three years ago (i.e. two Moore cycles) a hardened PC
would have been required to perform the computations in real time. To carry such a computer with his power
generators in the field would have been totally unrealistic because of the manpower and infrastructure needed.
Specific needs for the hardware of a miniaturized fire control computer are:
• high operation speed for computing and sensor signal processing
• high speed serial data interfaces (analog/digital)
• absolutely no moving parts
• low power consumption
• low cost, robustness, compactness
• high reliability, and last but not least
• conformity with military standards (e.g. MIL STD 810C)
TheserequirementsaremetbythenewestgenerationofDSPs,e.g. theTMS320C6713ofTexasInstruments.
Figure 2 shows the structure of general fire control computers with DSPs. Figure 3 shows the actual RangIR
system.
Proc. of SPIE Vol. 6940 69401K-5
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Figure 3. Block diagram of RangIR.
Table 2. Comparison of thefirecontrol algorithm with shooting tables.
Parameter Average deviation, %
Elevation 1.13
Time of flight 0.52
Wind, Coriolis force, spin 16.05
Height of crest 0.66
Target velocity 0.44
Angle of fall 2.38
5. RESULTS AND EXPERIENCES
For real-time fire control systems a short computing time is essential, for the gunman possibly life-saving. The
code has to be tuned intensively. A coarse glue could be the fact that the algorithm comprises about 350 lines
of source code. For the floating point DSP TMS 320 C 6713 (clock 200 MHz, initial integration stepsize 50m)
runtime is 30...60 ms, for the fixed point DSP TMS 320 C 5415 (400 MHz, initial integration stepsize 50m)
runtime varies between 15...100 ms. This DSP is used in the TWS HuntIR for image processing and as it can
be seen is also suited perfectly for fire control. (Computing time increases with distance, since more integration
steps are needed for a longer distance.) Consequently, the requirements for real-time fire control computers can
be met with such DSPs and the introduced fire control algorithm.
Table 2 shows a comparison between the results obtained by the numerical real-time fire control algorithm
and the German service shooting tables for the GMG 40 x 53 mm ammunition. The precision is fully sufficient
for practical purposes and can of course be adjusted by variation of the initial integration stepsize.
Figure 4 (left) shows RangIR mounted on the GMG 40 x 53 mm during test firings at the infantry school
in Hammelburg. The gunmen adopted the TWS with FCU instantly and were able to use it for high precision
fire. A competing electro-mechanicalFCU was rejected by common consent of the soldiers. Moreover,the army
applied pressure to the German procurement agency to accelerate fielding of RangIR, since it was considered a
life insurance for the soldiers in Afghanistan. Figure 4 (right) shows a view on the display of RangIR. In the
middle of the picture the standard crosshairs can be seen. There are two targets in a distance of 550 meters.
The FCU crosshair is on the right target. Deflection is either due to wind, spin, or Coriolis force. The right
Proc. of SPIE Vol. 6940 69401K-6
Figure 4. RangIR used as Fire Control Unit for the40 mm GMG.
target will be hit with the first salvo. By using the standard fixed crosshair for this distance the target would
have been missed. Since the display shows the scene upright (aspect ratio 3:4), the trajectory of the projectile
can be seen during the flight.
6. RANGIR APPLICATIONS
6.1 WBZG for the German IdZ - Extended System
Thefollow-onprogramGermanInfantrymanofthefutureprogramIdZextendedsystemwillincreasecapabilities
based on the lessons learned and technological progress. A further integration level and link of sub components
will be realized. The concept and design phase ended in the realization of prototypes delivered end of 2007
followed by field trials and an expected series production in 2009. The different optronics equipment was
introduced in.2–4
The WBZG is developed by AIM and based on the new sight RangIR which is an upgrade of the HuntIR
with a LRF, DMC and wireless data link to the kernel system of the soldier. Due to the modular architecture
adaptation or integration of new components for specific program requirements are possible without changing
the complete design. Functionality can be configured by the firmware of the electronics. The electro/optical
performance still satisfies the IdZ ES requirements since weapon engagement ranges did not change. For better
first hit probability an automatic fire control is implemented making use of the 1.5 µm eye-safe LRF and the
3-axis DMC. An ergonomic control of the new features is realized by an additional keypad located directly at
the weapon. Communication with the C4I equipment of the soldier is realized for the trial phase with a WLAN
interface and an additional LAN interface as backup in case of wireless transmission problems. The data link
is used to transmit e.g. target location data to the kernel system of the soldier as well as live video data. For
video transmissionoverthe LAN and WLAN interface JPEG2000video compressionis used. A battery charger
electronics is implemented to serve the logistical supply concept of the WBZG.
6.2 Fire Control for the Grenade Machine Gun
The RangIR device also perfectly matches the requirements of a fire control unit for the 40 mm high velocity
Grenade Machine Gun (GMG). To cover the typical engagement ranges from 250 m to 1200 m the device is
mounted in a 90◦ rotated orientation on the GMG (see Fig. 4). The implementation of the rotated menu and
electronic reticule is possible due to the fully electronic architecture of the signal path from sensor to display.
Switching operation to GMG fire control is achieved only by selection of the weapon in the setup menu. While
target identification is done in the NFOV firing is executed in the WFOV of the imager. Operating in the
WFOV the device offers a vertical FOV of 9.1◦ for direct targeting within an engagement range of 250 m
and 1200 m required due to the ballistic trajectories of the 40 mm ammunition. The range can be extended by
indirecttargetingusingtheevaluationinformationoftheintegratedDMCandtwoelectronicmarkers. Sincethis
solution avoids any mechanical movement between gun and fire control unit high precision and reproducibility
areachievedandnoagingandweartakeplace. The lowtotalheightofthe setupresultsina safeandergonomic
low exposition of the gunner.
Proc. of SPIE Vol. 6940 69401K-7
TherightsideofFig.4showsanimagetakenduringatrialinJune2006. Thecontinuouslyvisibletrajectory
allows manual correction of the set point in case of wind as well as fast reaction to suddenly appearing targets.
In case of automatic fire control the LRF is used to measure target distance. For an ergonomic handling
an additional interface allows to connect a control key directly placed near the handle of the gun. With this
buttonLRFmeasurementisinitiatedaswellasDMCmeasurementfollowingcalculationoftheinternalballistics
computer. The resulting set point is shown by a colored marker in the display. If the LRF shows no reasonable
resultsduetootherobjectsthanthetargettherangecanbemodifiedmanually. Theballisticscomputerconsiders
nextto ammunitionparametersalsovariationsofthe muzzle velocityv0 due to temperatureor differentcharges
as well as evaluation to the target for fighting in mountain scenarios and atmospheric conditions. Also bank is
considered given by the DMC to avoid a precise leveling of the GMG. The ballistics computer also calculates
the resulting time of flight to serve air burst ammunition (ABM). With an additional external data interface of
the RangIRdevice the ABM controllercanbe programmedwith the desiredtime of explosiongivenby distance
information.
7. CONCLUSION
DSPbasedfirecontrolcomputersinconnectionwithTWSimprovetheeffectivenessoflightsupportingweapons
considerably. Thefirecontrolalgorithmsusedarethesameasinheavyweaponryandenableaveryhighfirsthit
probability. Thisisimportantunderasymmetricthreatsandespeciallyimportantfortheprotectionofthelifeof
thesoldiers. Duringtestfiringsitturnedoutthatthegunmenwereabletooperatethe RangIRsysteminstantly
with very good firing results. The system will become a part of the German procurement project Infantryman
of the Future (IdZ). The described TWS based fire control system was tested successfully in 2007 and 2008 at
Meppen proving ground and the infantry school Hammelburg. Series production and general fielding will start
in 2009.
ACKNOWLEDGMENTS
ThisdevelopmentwaspartiallysupportedbytheGermanMODunderdifferentBWBcontracts. Goodergonomic
design and the qualification of devices on various small arms were only achievable in this short time due to the
help of the German Infantry School. This support is gratefully acknowledged.
REFERENCES
[1] McCoy, R. L., [Modern Exterior Ballistics], Schiffer Military History, Atglen (1999).
[2] Breiter,R.,Ihle, T., Mauk,K.-H.,Mu¨nzberg,M., andRode,W., “Longrangethermalweaponsightsfor the
German Future Infantryman program IdZ,” Proceedings SPIE Defense&Security 6542 (2007).
[3] Fritze, J. and Lenz, H., “Video visor for German army soldier-of-the-future program,” Proceedings SPIE
Defense&Security 6542 (2007).
[4] Heinrich, J., “The handheld multifunctional thermal imager and surveillance instrument of Jena-Optronik
withinthe GermanProject: IDZ-InfanteristderZukunft,” Proceedings SPIE Defense&Security6542(2007).
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