UNCLASSIFIED Paper No. 2-3

Transcription

1 Paper No. -3 An Opimal -Dv Guidance Law for Inerceping a Boosing Targe Absrac Lawrence C. Ng*, Eric Breifeller, and Arno G. Ledebuhr Lawrence Livermore Naional Laboraory P.O. Box 808, L-78, Livermore, CA We a Lawrence Livermore Naional Laboraory (LLNL) have developed a new missile guidance law for inerceping a missile during boos phase. Unlike oher known missile guidance laws being used oday, he new - v guidance law opimally rades an inercepor s onboard fuel capaciy agains ime-o-go before impac. In paricular, his guidance law allows a missile designer o program he inercepor o maximally impac a boosing missile before burnou or burn erminaion and hus negaing is abiliy o achieve he maximum kineic velociy. For an inerconinenal range ballisic missile (ICBM), i can be shown ha for every second of earlier inercep prior o burnou, he ICBM ground range is reduced by 350 km. Therefore, inerceping a mere 15 seconds earlier would resul in a miss of 5,50 km from he inended arge or approximaely a disance across he coninenal Unied Saes. This paper also shows how he - v guidance law can incorporae uncerainies in arge burnou ime, prediced inercep poin (PIP) error, ime-o-go error, and oher rack esimaion errors. We believe ha he - v guidance law is a sep oward he developmen of a new and smar missile guidance law ha would enhance he probabiliy of achieving a boos phase inercep Acronyms APNAV Augmened Proporional Navigaion ACS Aiude Conrol Sysem ADACS Axial/Diver and Aiude Conrol Sysem ATKV Advanced Technology Kill Vehicle BP Brillian Pebble BPI Boos Phase Inercep ICBM Iner-Coninenal Ballisic Missile IFTU In-Fligh-Targe-Updae Isp Propellan specific impulse KV Kill Vehicle LOS Line-of-Sigh NFOV Narrow-Field-of-View Pdf Probabiliy densiy funcion PIP Prediced Inercep Poin PNAV Proporional Navigaion T Time before (arge) burnou Tgo Time o go Vbo Burnou velociy WFOV Wide-Field -of-view ZEM Zero-Effor-Miss Inroducion Disribuion Saemen A: Approved for public release; disribuion is unlimied. * Chief Scienis, Senior Member. larry.ng@llnl.gov Elecronics Engineer, Member. breifeller1@llnl.gov Advanced Inercepor Technology Program Leader, Member. ledebuhr1@llnl.gov This paper describes a new missile guidance law designed specifically for a boos phase inercep mission. I akes maximum advanage of a kineic kill vehicle (KV) capable of hrus-on-demand, axial/laeral diver, propulsion sysem such as he Advanced Technology Kill Vehicle (ATKV) currenly under exploraory developmen a LLNL. For reasons o be explained laer, his new guidance law is called he opimal - v guidance law. The key aribues of his guidance law are: (1) he KV would aemp o inercep a boosing arge as early as possible in is boos phase, and () he KV would also aemp o minimize he oal v (propellan) consumpion hroughou he engagemen. In shor, he - v guidance law is designed o maximize he ime before arge burnou and minimize he overall propellan usage. The key advanage of his new guidance law is o increase he probabiliy and effeciveness of a successful boos phase inercep. The - v guidance law, when applied o he boos phase inercep mission, accomplishes his by consanly choosing a vehicle acceleraion command o achieve a compromise beween earlies inercep and minimum v expendiure. The - v guidance is significanly differen from he radiionally well known guidance laws for inerceping a maneuvering (or acceleraing) arge such as Augmened Proporional Navigaion (APNAV) and Zero-effor-miss (ZEM) [1]. The key difference, of course, is ha neiher APNAV nor ZEM has explicily aken he need o inercep he arge before burnou ino accoun. The significance of inerceping early in boos phase can no be overemphasized. For example, inerceping a boosing arge jus a momen before burnou does very lile o aler he hrow weigh

2 Repor Documenaion Page Repor Dae 9JUL00 Repor Type N/A Daes Covered (from... o) - Tile and Subile An Opimal -Dv Guidance Law for Inerceping a Boosing Targe Conrac Number Gran Number Program Elemen Number Auhor(s) Ng, Lawrence C.; Breifeller, Eric; Ledebuhr, Arno G. Projec Number Task Number Work Uni Number Performing Organizaion Name(s) and Address(es) Lawrence Livermore Naional Laboraory P.O. Box 808, L-78 Livermore, CA Sponsoring/Monioring Agency Name(s) and Address(es) Performing Organizaion Repor Number Sponsor/Monior s Acronym(s) Sponsor/Monior s Repor Number(s) Disribuion/Availabiliy Saemen Approved for public release, disribuion unlimied Supplemenary Noes See Also ADM Papers from Unclassified Proceedings from he 11h Annual AIAA/MDA Technology Conference held 9 July - Augus 00 in Monerey, CA., The original documen conains color images. Absrac Subjec Terms Repor Classificaion unclassified Classificaion of Absrac unclassified Classificaion of his page unclassified Limiaion of Absrac UU Number of Pages 9

3 Paper No. -3 velociy and herefore is impac poin. On he oher hand, an early inercep (10-15s before burnou) will significanly shoren he impac poin (by km) from is inended arge locaion. Saemen of he Problem Assuming he availabiliy of a lighweigh, high mass fracion kill vehicle, such as he ATKV wih is flexible, hrus-on-demand, axial/diver and ACS (ADACS) propulsion sysem, we wan o explore he relaive advanages of such a sysem and in paricularly how a missile guidance law migh ake advanage of his new capabiliy o improve he overall sysem performance such as longer sandoff range and greaer inercep bale space. Fig. 1 illusraes a possible boos/ascen phase inercep (BPI) scenario and he poenial advanage of ADACS. Using he Navy Sandard Missile as an example, he kill vehicle is siing on op of a hree sage booser sack. Each sage uses a solid propellan engine wih he hird sage capable of firing wo separae pulses. In Fig. 1 we assumed ha each pulse is preceded by an IFTU for appropriae course correcion. Afer he 3 rd sage burn, he kill vehicle s axial velociy is fixed. For our example, we assumed a burnou velociy of 4.5 km/s, a burnou ime of 80s, and a burnou aliude of abou 100 km. The kill vehicle hen coass unil arge acquisiion. A arge is successfully acquired if i appears wihin he narrow field of view of he KV seeker which has been poining oward he PIP. The endgame, lasing approximaely 5 o 10 seconds, allows he KV o home o a arge using i s diver engine. Noe in he figure he KV reachabiliy envelope (in aliude versus ground range) is described by a se of flyou curves marked by a consan ime profile (in minues) and a every pich over angle. The ICBM arge, launched a 100 km downrange, is also shown wih sage burnou ime marked in minues in he rajecory profile. We assumed inercep occurs a he 4 minue mark, jus prior o deploymen of he re-enry vehicle and decoys. Now comparing he he flyou ime for he inercepor (3 minues) and he arge (4 minues), one can deduce ha he inercepor missile mus launch in less han one minue of delay from he arge. The inercep baske is defined by he blue fan. For a 10 second diver a 1 km/s of v, he maximum span of he fan is less han 0 km. On he oher hand, a KV wih an ADACS such as he ATKV, he inercep baske is significanly larger. Wih a longer range and wider field of view acquisiion sensor, he ATKV can burn axially o effecively increase he burnou velociy, resuling in a significanly larger reachabiliy baske (red fan). Thus he ATKV can reach he arge before burnou a he.5 minue mark wih abou 30s of launch delay. We assumed ha he ATKV can add more han km/s of axial velociy or for an equivalen inercepor burnou velociy of 6.5 km/s. Fig. 1 A kill vehicle wih flexible axial/diver propulsion sysem expands he inercep bale space. Increasing Vbo for Inercep Deph For a successful BPI mission, i is imporan o inercep prior o arge burnou. In fac i is advanageous o do so, as menioned previously, since for every second of cu off before burnou, he arge range reduces by approximaely 350 km for an ICBM class (~10,000km range) missile []. We are ineresed in exploring he acceleraion and burnou velociy (Vbo) requiremen for inerceping he arge a earlier imes in fligh. Using a simple kinemaic model and ignoring he amospheric drag, Fig. shows poenial inercep poins agains a hypoheical hrea launched 1000 km downrange ha has approximaely a 00s burnou ime a an aliude of 50 km. We assumed an ideal inercepor missile has a 60s launch delay, a burnou ime of 60s bu wih variable acceleraion capabiliy. I can be seen ha he Vbo increases rapidly wih increasing inercep deph (earlier boos phase). The increasing Vbo is a resul of wo facors: increasing inercep range and decreasing fligh ime. Since a ypical booser provides a fixed Vbo, he ADACS as envisioned by he ATKV design can provide he desired variable axial v capabiliy. Increasing v for Targe Maneuvers One of he well known and effecive counermeasures agains a BPI inercepor is arge maneuvering. A maneuvering arge degrades he rack esimae resuling in a significan increase in PIP error. This ranslaes ino a larger diver v and greaer 11 h AIAA/MDA Technology Conference and Exhibi, Monerey, CA. 9 July - Augus 00

4 Paper No. -3 acceleraion requiremens for he KV for a given miss disance specificaion. Since increasing inercep deph (more axial v) and overcoming poenial arge maneuvers (more diver v) are boh compeing for greaer fuel usage and ha he v can no be pre-deermined a priori (i.e., we do no know wheher and when he arge would maneuver), a proper balance beween hese wo compeing facors is needed. A KV wih an ADACS is capable of achieving his balance. Wha is needed is he developmen of a guidance law which opimally deermines he proper fuel expendiure beween axial and diver guidance modes in real ime for a robus BPI mission scenario. and 4 diver hrusers capable of hrusing respecively. The ATKV also has an Inegraed Muli-specral NFOV Seeker and wo WFOV sensors for long range plume acquisiion and racking. Fig. 4 summarizes he key aribues of he ATKV. I achieves high v (.5 km/s) and high vehicle acceleraion (10 gs dry) by ma ximizing propellan specific impulse, Isp, and mass fracion variables of he rocke equaion. To achieve high acceleraion, high propellan mass flow rae is needed. Tradiional approach using a pressure-fed sysem requires he use of high pressure heavy fuel anks. As par of he Brillian Pebble Space Based Inercepor echnology innovaion, LLNL developed and paened a lighweigh pump which no only delivers he high propellan flow rae needed bu using low pressure lighweigh anks. I resuls in a ne ank mass reducion equivalen o 40% of propellan weigh [5]. The pumped propulsion approach was experimenally demonsraed in he 1994 ASTRID fligh es. Anoher Brillian Pebble innovaion is he developmen of lighweigh passive/acive sensor suie which was flown in he Clemenine Moon Mapping experimen [6]. As shown in Fig. 4, ATKV can achieve a mass fracion of 0.6 which is more han double he radiional, pressurefed propulsion based KV designs. Fig. Increasing D v requiremen for earlier inercep ime (model neglecs aerodynamic drag resuling in a conservaive esimae of he D v requiremens). Formulaion of he -Dv Guidance Law To help visualize how a KV can have flexible axial and diver capabiliy, Fig. 3 shows he ATKV concep vehicle currenly under exploraory engineering developmen a LLNL. Uilizing a lighweigh pumped propulsion approach [3], he ATKV has a mass budge of 30kg, a oal v of.5 km/s disribuable flexibly beween axial and diver mode via a swivel hruser design. Noe a fixed axial hruser approach can also be considered. The opimum choice will depend on in process performance rades wih vehicle mass, size, volume and mechanical reliabiliy. For he swivel hruser approach here are hree operaional modes: 4A, AD, and 4D ha denoes 4 axial hrusers operaing, axial and diver hrusers operaing, ATKV Guidance, Navigaion and Conrol The ATKV employs an inegraed guidance and conrol sraegy in which he KV guides he missile from launch o inercep, uilizing as many (or as few) IFTUs as available o fuse informaion colleced from he onboard sensor suie. Using a muli-specral, muliaperure approach, he WFOV sensors allow he ATKV o operae auonomously wih early arge acquisiion and KV guidance. The key sraegies, as summarized in Fig. 5, are : early deec and rack; guide wih flexible axial and diver DACS; and lock ono he arge a all imes wih a muli-aperure, muli-specral seeker. Fig. 3 LLNL s ATKV concep vehicle. 11 h AIAA/MDA Technology Conference and Exhibi, Monerey, CA. 9 July - Augus 00 3

5 Paper No. -3 Derivaion of he -Dv Guidance Law Defining as ime before arge burnou (assuming we have perfec knowledge of i for now) o a desired PIP, and v is he corresponding fuel usage o reach i, hen one can form a weighed cos funcion as shown in Eq. (1) and seek is minimum. The firs erm is minimized a zero effor and he second erm is minimized wih increasing inercep deph as shown in Fig. 6. The choice of he weighed coefficiens affecs he opimal soluion. J β ( aaxial, adiver ) = α v + (1) Fig. 4 LLNL s ATKV is a high mass fracion vehicle uilizing pumped propulsion, lighweigh sensors, advanced packaging, and non-oxic propellan for rapid ground esing. Now suppose he KV is heading oward a PIP corresponding o he arge burnou locaion (as shown in Fig. 5 and we are ineresed in swiching he PIP o earlier imes, say a poins A, B, or C. Poin A may be oo close o booser burnou and herefore has minimal impac on arge burnou velociy. Poin C has maximum inercep deph bu may be in danger of running ou of fuel. Then here exiss a desirable poin B, locaed beween poins A and C, which simulaneously minimizes he v consumpion and maximizes he ime before booser burnou (). Since he proposed guidance approach opimizes over boh ime and v space, we have accordingly named i he - v guidance law. Fig. 5 Deerminisic mahemaical formulaion of -D v guidance law showing opimal choices for differen se of coefficiens. Le v be he opimal soluion, and le go be he imeo-go compued using Eq. (5), he acceleraion vecor command o he inercepor is hen given by: ZEM a = () go where ZEM, he zero effor miss vecor, is relaed o v in Eq. (1) as: ZEM v = (3) go Fig. 5 Basic -D v guidance and conrol sraegy is designed o maximize he probabiliy of inercep before arge boos phase burnou 6DoF Simulaion of a Sea-based BPI Mission using he -Dv Guidance Law In order o demonsrae he applicabiliy of he - v guidance law, we conduced 6DoF BPI simulaion sudies. Example of a successful inercep scenario is 11 h AIAA/MDA Technology Conference and Exhibi, Monerey, CA. 9 July - Augus 00 4

6 Paper No. -3 shown in Fig. 7. The arge is an ICBM class missile launched a 950km down range wih a burnou ime of 195s and a burnou aliude of 70 km. An ATKV was launched 45s laer. The booser burned ou a 48 km wih a burnou velociy of 5 km/s. The KV unshrouded a 80 km aliude or a 70s of fligh. The KV aligned is hrusers in 4A mode owards he PIP wihin s, burned for 6s, and produced approximaely 1. km/s of addiional v since aerodynamic drag is negligible. The KV hen acquired he arge wihin s and rolled o he diver plane, auonomously hrusing in AD mode using - v guidance for 10s. Finally he KV homed ono he boosing arge in 4D mode using 50s of ZEM guidance. Inercep occurred in 140s fligh ime or 10s before arge burnou. Fig. 7 Example of 6 DoF simulaion of inercep ime hisory and ATKV flyou engagemen sraegy. Fig. 8 In-plane axial and diver acions showing zero effor miss disance being driven o near zero. Fig. 8 shows he ou of plane ZEM and acceleraion ime hisory. Noe ha he axial acceleraions, shown in red, are used o exend he inercep range or equivallenly earlier inercep ime. Also noe he simulaneous operaion of hrusing in he axial (red) and diver (blue) mode. Performance Comparison of ZEM and -Dv Guidance For he same BPI scenario, we compare hree differen guidance sraegies afer KV has been unshrouded: (1) guide wih ZEM only (no axial hrusing), () guide wih 6s in 4A mode, 30s in AD ZEM mode, and 30s in 4D ZEM mode; and (3) 6s of 4A mode, 30s in AD - v mode, follow wih 30s in 4D ZEM mode. Fig. 9 shows he simulaion resuls assuming he inercepor was launched wihin 30s of he arge launch. The PIP was chosen o coincide wih he arge burnou posiion. We observed ha he ZEM guidance inerceped he arge a 1.5s afer arge burnou bu used only 1.4 km/s of v. Since he KV has a oal v of.5 km/s, 1.1 km/s of v are unspen. This brings ou one of he drawbacks of ZEM, i achieves inercep by nulling he ZEM disance wihou aking ino accoun he KV fuel reserve and he desire o inercep before arge burnou. Since i inerceps a a laer ime, he v requiremen is less as shown in Fig.. Nex le s examine case. Since he axial v is increased by 1. km/s, he ZEM guidance inerceped a 7.5s before arge burnou and spen 1.5 km/s. Thus a inercep he KV sill has 1.0 km/s in reserve. We can draw wo conclusions: (1) increasing axial v will increase he inercep deph, and () ZEM guidance does no ake ino accoun KV fuel reserve and he deph of inercep. I jus happens in his case ha he inercep occurred before arge burnou. Finally le s examine case 3, which differs from case only in he 30s AD mode, where - v guidance was used. The - v guidance law coninuously adding axial acceleraion o increase he deph of inercep by aking ino accoun of he reserve v available and he earlies inercep or minimum ime -o-go. I inerceped a 13s before arge burnou and spen.4 km/s of v wih a reserve of jus 0.6 km/s a impac. One can no overesimae he advanages for an earlier inercep. No only i can reduce he impac range a a rae of abou 350 km per each second of inercep before burnou, i also makes he inercep problem easier because he closing velociy is smaller. Noe a ypical ICBM arge gains 15% of is final burnou velociy in he las 10 seconds. To furher gain a beer undersanding of he - v guidance law, le s compare several well known missile 11 h AIAA/MDA Technology Conference and Exhibi, Monerey, CA. 9 July - Augus 00 5

7 Paper No. -3 guidance laws and examine heir design crieria. Referring o Fig. 10, we see ha proporional navigaion (PNAV) achieves inercep by nulling he line-of-sigh (LOS) rae as illusraed in he figure. Augmened proporional navigaion (APNAV), on he oher hand, nulls he combined LOS rae and he esimaed arge acceleraion across he LOS angle. ZEM reduces he prediced miss disance o zero a he esimaed go. Lamber guidance deermines he velociy ha solves he hi equaion wih go as a free parameer. Finally he - v guidance law opimizes over ime before arge burnou and he onboard reserve v, i maximizes he probabiliy of a boos phase inercep. Dealing wih Uncerainy in Targe Parameers Thus far we have assumed perfec knowledge of he arge rajecory and is burnou ime o demonsrae he feasibiliy of he - v guidance law. In his secion we firs show ha he - v guidance law can be gracefully degraded o ZEM guidance when no apriori knowledge of he arge is assumed. Second we will demonsrae how he guidance law can be reformulaed aking ino accoun of he imprecise knowledge of he arge parameers. In Eq. (1), if we choose α = N/ze m, β=0, compue go using range divided by closing velociy and use he relaion in Eq. (3), hen Eq. (1) reduces o Eq. (), which defines he ZEM guidance law wih N as he guidance gain. Now for he uncerainy parameer case, le s assume he arge burnou ime can be described by a probabiliy densiy funcion (pdf), say Guassian wih prescribed mean and sandard deviaion. Therefore for a given (a deerminisic parameer), he locaion of he arge is simply given by he same pdf bu shifed down by seconds as shown in Fig. 11. Now suppose a ime, he inercepor and he arge are locaed a posiions shown in Fig. 11. For a given go, one can compue he prediced posiion of boh he inercepor and he arge wih he appropriae uncerainy ellipses. The prediced miss disance vecor (or zero effor miss) Pi(go)-P(go) is also random wih known saisics. Therefore we can rewrie Eq. (1) as: Fig. 9 Simulaion resuls showing how -D v guidance law is able o inercep 13 s prior o booser burnou, while ZEM inerceped laer han he burnou. J( a) = Where go bo Pi ( go) P ( go) β α + go = bo = Gauss( bo, σ bo ) (4) (5) and we seek he opimal soluion ha derives from a * op = min( v) max( ) { Ε[ J( a) ] } (6) Fig. 10 Comparisons of differen guidance laws and heir opimizaion crieria. where he operaor E[ ] represens he expeced value. We are seeking a soluion for he acceleraion command ha yields he minimum value of v usage for a maximum or inercep deph. Since he cos funcion involves he square of he raio of wo random variables, he resuling probabiliy densiy funcion can be shown o be relaed o he 11 h AIAA/MDA Technology Conference and Exhibi, Monerey, CA. 9 July - Augus 00 6

8 Paper No. -3 Cauchy disribuion [4]. Once he pdf of J(a) is found, one can proceed o carry ou he minimizaion as shown in Eq. (6). The resuling pdf is quie complex. A much simpler and useful approximaion can be found as follows: increases for increasing inercep deph or greaer, he increased weigh causes he minimum o shif o he lef or o inercep a a laer ime. This is inuiively correc since uncerainy in arge parameers and he PIP error should favor a sraegy o inercep a a laer ime in order o conserve v. The validiy of his observaion is borne ou in Fig. 1. For a given value of α and β, he deerminisic soluion yields a minimum a =16s. Now adding he uncerainy in bo, or ime of burnou, wih a sandard deviaion of 40s, he analyical soluion and he ensemble average from 50 Mone-Carlo simulaion runs yields he same opimal value. Using Eq. (8) insead of (4) significanly reduces he compuaional load for he implemenaion of he - v guidance law. Fig. 11 Probabilisic formulaion of he -D v guidance law. Le random variables X and Y represen he prediced miss disance and go respecively, we can hen rewrie Eq. (4) as: J ( a) where X, Y are he means and x,y are he (7) corresponding zero mean random variables. Noe ha boh x and y are very much less han 1 since uncerainy in he miss or go is significanly less han he mean prior o inercep. Assuming he random variables are saisically independen, we can ake he expecaion of Eq. (7) and obain he desired resul in Eq. (8). s 3s 3s s b = X Y X Y D (8) x y x y [ ( a) ] a V + E J = a = a X Y a DV X Y b + 1+ x 1 y + ( 1+ x) ( 1 y + 3y...) + Comparing Eq. (8) o (4), we see ha uncerainy in he prediced miss disance and go resuls in an effecive increased weigh on he v erm. Since v b + b Fig. 1 Minimum of analyical soluion maches almos exacly wih he Mone -Carlo ensemble average calculaion. In deriving he sochasic - v guidance law, we only assume a probabilisic model of he arge burnou ime. Wihou loss of generaliy, he arge burnou ime could be replaced by he desired arge inercep ime. For example, one could specify ha he desired arge inercep ime is say 100s afer missile launch wih a sandard deviaion of 0s. Thus he - v guidance law does no require apriori knowledge of arge burnou ime or he rajecory for is implemenaion. Finally we invesigaed he feasibiliy of applying he - v guidance law from inercepor missile launch insead of jus guiding he KV afer 3 rd sage burnou. Fig. 1 shows he resuls from a 6DoF simulaion run incorporaing arge uncerainy and rack esimaion error. Earlier guidance resuled in an addiional gain in inercep ime a only a modes increase in v expendiure. 11 h AIAA/MDA Technology Conference and Exhibi, Monerey, CA. 9 July - Augus 00 7

9 Paper No. -3 as shown in Eq. (1). A reasonable choice for α is o make i inversely proporional o he square of he v available. Thus wih a large v reserve or equivalenly mass fracion, he KV will more likely o spend addiional v o chase down he hrea and vice versa. On he oher hand, a reasonable choice for β is o make i proporional o he square of go. Wih a large go, he KV is mo re likely o selec a larger or seek an earlier inercep. Fig. 1 Exending he -D v guidance all he way o inercepor missile launch gains addiional inercepor deph wih lile addiional cos in D v. Summary, Conclusions, and Recommendaions We have derived and examined in deail a new missile guidance law called - v ha minimizes he oal fuel usage (oal v) agains he desire o achieve earlier inercep ime for he boos phase inercep mission. We demonsraed ha he - v guidance law can be degraded gracefully ino he convenional ZEM guidance when no a priori knowledge of he arge is assumed. However when saisics of he PIP (prediced Inercep poin) and oher arge parameers are uilized, we demonsraed via 6 DoF simulaions ha he - v guidance law can opimally rade earlier inercep ime for minimum v consumpion. Wih flexible axial and diver hrusing, he - v guidance law can opimally disribue he propellan usage beween achieving maximum inercep deph and overcoming arge maneuvers. We have also developed an analyical soluion o he complex minimizaion of a sochasic cos funcion, as required for he derivaion of he guidance law, resuling in a significan reducion in he compuaional requiremens. To make maximum uilizaion of he - v guidance law, he kill vehicle mus have a flexible axial/diver (ADACS) burn capabiliy such as he ATKV currenly being explored a LLNL. Finally we found ha i is advanageous o apply he - v guidance law as soon as possible and preferably a as early as inercepor missile launch. We have no ye finalized he sraegy o selec he coefficiens α and β in he weighed cos funcion Acknowledgmens The auhors wish o acknowledge he echnical inpus from Dr. Donn McMahon of Lawrence Livermore Naional Laboraory and he suppor from Drs. Waler Dyer and James Mulroy of he Missile Defense Agency. The auhors were also benefied from echnical discussions wih Dr. Paul Zarchan of MIT Lincoln Laboraory. References [1] Zarchan, P., Tacical and Sraegic Missile Guidance, nd Ediion, AIAA Press, [] R. Bae, D. Mueller and J. Whie, Fundamenals of Asrodynamics, pp , Dover publicaion, [3] Whiehead, J., Hydrogen Peroxide Gas Generaor Cycle wih a Reciprocaing Pump, 38 h AIAA/ASME/SAE/ASEE Join Propulsion Conference and Exhibi, 7-10 July 00. Paper AIAA [4] Papoulis, A., Probabiliy, Random Process, and Sochasic Processes, McGraw-Hill, [5] Brillian Pebbles (BP) - BP was funded by he Sraegic Defense Iniiaive Organizaion (SDIO) in he lae 1980s. Since BP was a space-based inercepor, i needed o saisfy wo criical requiremens: lighweigh (~10 kg) and high v (> 1.5 km/s). Some varian of LEAP KKVs have approached his low mass value, bu no he larger v specificaion. To achieve he high v requiremen, LLNL invened and paened a lighweigh pumped propulsion concep allowing he use of very lighweigh propellan anks. For a ypical pressure-fed sysem, he ank weigh is abou 50% of he propellan weigh. For a pumped-fed sysem, he ank weigh needs only be 10% of he propellan weigh, resuling in a ne mass budge saving equivalen o 40% of he propellan weigh. The saving however needs o be offse by he addiional mass budge of he pump, gas generaor, and oher fluidic conrol hardware. To be more specific, for a 30 kg we,.5 km/s v, 0.6 mass fracion ATKV design, a pressure-fed sysem will 11 h AIAA/MDA Technology Conference and Exhibi, Monerey, CA. 9 July - Augus 00 8

10 Paper No. -3 require a ank weigh as much as 9 kg, whereas only ~ kg is needed for pumped-fed anks plus 1 kg of pump propulsion relaed hardware for a ne saving of as much as 6 kg. [6] The Clemenine Mission o he Moon: Scienific Overview, Science, December 16, BIOGRAPHY Dr. Lawrence C. Ng received his B.S. and M.S. degrees in Aeronauics and Asronauics from he Massachuses Insiue of Technology in early 1970s, and a Ph.D. degree in Elecrical Engineering and Compuer Sciences from he Universiy of Connecicu in 1983 under a Naval Undersea Warfare Cener (NUWC) Fellowship. In addiion, Dr. Ng received his commission as an Air Force officer in 1973 and served a he Hanscom Air Force Base in Bedford, MA. His work experience includes: four years wih General Dynamics Elecric Boa Divis ion in Groon, CT, responsible for he developmen of he TRIDENT submarine digial conrol sysems; seven years a he NUWC where he led he developmen of he advanced sonar signal processing for he Seawolf submarine. Since 1986, he joined he Lawrence Livermore Naional Laboraory where he was he group leader of he signal/image processing and conrol group and is currenly he Chief Scienis for he Advanced Inercepor Technology Program. Dr. Ng is focusing his research in micro-spacecraf guidance and conrol, inegraed ground esing, and ballisic missile defense sysems analysis. In addiion Dr. Ng is a member of several professional socieies, including honorary memberships in Sigma Xi, Tau Bea Pi, and he Naional Research Council. He has published numerous papers in signal esimaion and precision vehicle guidance and conrol. amospheric Kill Vehicle (EKV). Upon reurning o LLNL in 1997 he assumed he lead GNC engineering posiion on he former Clemenine-II program (currenly he MicroSa Technology program). Precision conrol and esimaion algorihms were designed in a 6DOF environmen, and hen applied o he fully-funcional 5DOF (3DOF ACS + DOF ranslaion) ho-gas micro-saellie. While no working on missile inercep problems, he has been involved in roboic applicaions relaed o he alignmen of opical fibers o wave guides, and o beam seering of singlebeam linear paricle acceleraors. Dr. Arno G. Ledebuhr earned an undergraduae degree in Physics and Mah in 1976 from he Universiy of Wisconsin and masers and docorae degrees in Physics from Michigan Sae Universiy in 198. Dr. Ledebuhr spen he following four years a he Hughes Aircraf Company and earned 15 paens in projecion display echnology. He has been a Lawrence Livermore Naional Laboraory since 1986 and led he developmen of advanced sensors for he Brillian Pebbles inercepor program and he design of he Clemenine sensor payload. In 1996 he was he Clemenine II Program Leader and is currenly he Program Leader for he Advanced Inercepor Technology Program. His ineress include microspacecraf and kineic kill vehicle echnologies, including sensors and propulsion sysems. Eric F. Breifeller has been an elecrical engineer a Lawrence Livermore Naional Laboraory (LLNL) from and 1997-presen. From he was a Hughes Missile Sysems Company. He received his M.S.E.E. in 1988, from Ohio Sae Universiy, wih emphasis on conrol sysems. From he worked on guidance, navigaion, and conrol (GNC) 6DOF simulaions relaed o he Brillian Pebbles program. Subsequenly, he suppored BMDO hrough he POET, where he developed a 6DOF simulaion ha was used in rade sudies as hey relaed o missile inercep scenarios. While a Hughes (Rayheon) he developed he aiude conrol sysem (ACS) for he Exo - 11 h AIAA/MDA Technology Conference and Exhibi, Monerey, CA. 9 July - Augus 00 9