MANEUVERING TARGET TRACK PREDICTION MODEL

Size: px

Start display at page:

Download "MANEUVERING TARGET TRACK PREDICTION MODEL"

Gary Palmer
5 years ago
Views:

1 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 MANEUVERING ARGE RACK PREDICION MODEL igpig Yu Xiaomig You ad Sheg Liu 3 College of Electroic ad Electrical Egieerig Shaghai Uiversity of Egieerig Sciece Shaghai 060 Chia School of Maagemet Shaghai Uiversity of Egieerig Sciece Shaghai 060 Chia ABSRAC he issues about maeuverig target track predictio were discussed i this paper. Firstly usig Kalma filter which based o curret statistical model describes the state of maeuverig target motio thereby aalyzig time rage of the target maeuverig occurred. he predict the target trajectory i real time by the improved gray predictio model. Fially residual test ad posterior variace test model accuracy model accuracy is accurate. KEYWORDS Curret Statistical Model Maeuverig arget Kalma Filter Gray heory.he SAE DESCRIPION OF MANEUVERING ARGE o build model of maeuverig target motio by curret statistical model to use Kalma filter process trackig.. o build curret statistical model for maeuverig target Curret statistical model is a ozero mea time-depedet model. Curret acceleratio probability desity is described by the modified Rayleigh distributio. It is assumed that the target acceleratio a(t) satisfies the followig relatioship: a(t) a(t) a (t) = + () ' a (t) = αa (t) + ω(t) () I the above formula: a is the mea acceleratio ad it is a estimate (a costat i each samplig period) about previous time acceleratio; a (t) is a first order Markov process of zero mea α is the reciprocal of the maeuverig time costat; ω (t) is zero mea Gaussia white oise. he discrete state equatio of curret statistical model is: DOI: 0.5/ijci

2 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 X (k+ ) = F(k) X(k) + U(k) a(k+ ) + W(k) (3) X ( k) is state vector F( k) is state trasitio matrix U( k) is Disturbace trasfer matrix W( k) is zero mea white oise with variace ( k )radar sca for s so the samplig period =takeα = the followig expressio: ' '' X (k) = x(k) x (k) x (k) (4) α ( + α + e ) / α α F( k) ( e ) / α α 0 0 e (5) α ( + α / + (e ) / α ) / α α U( k) = ( e ) / α α e (6) I the above formula is the samplig period. Variace adaptive algorithm based o curret statistical model that is the followig equatio adaptive variace: q q q3 (k) = E[W(k) W (k)] = ασ a q q q 3 q3 q3 q 33 (7) he variables are as follows: q = [ e + α + α / 3 α 4 αe ] / α α 3 3 α 5 q = [ + e e + α e α + α ] / α α α α 4 q3 = [ e α e ] / α α α 3 q = [4e α 3 e α + α ] / α 3 q3 = [ e α + e α ] / α q α 33 = [ e ] / α (8) (9) () () (3) 4

3 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 4 π [a max a(k)] a (k) > 0 π σ a = 4 π [a max a(k)] a(k) < 0 π (4) a max is the maximum positive acceleratio Measuremet equatio: Z (k) = H(k) X(k) + V(k) a max is the maximum egative acceleratio. (5) I the above formula H(k) is measuremet matrix V(k) is white oise that it's zero mea ad variace is R (k).. Kalma filter based o curret statistical model Kalma filter based o curret statistical model smooth the state of the target o the past ad preset time while predictig the target movemet i the future time icludig the locatio of the target velocity ad acceleratio parameters. State variable method is a valuable method to describe a dyamic system usig this methods the system iput-output relatioship is described i the time domai by the state trasitio model ad output observatio model. Iput ca be determied by dyamic model cosisted of a fuctio of time ad upredictable variables or radom oise process to describe. Output is a fuctio of the state which ofte disturbed by radom observatio errors ca be described by measuremet equatio. Dyamic equatios of discrete-time systems (state equatios) ca be expressed as: X (k) = F(K) X(k ) + a(k) U (k) + W(k) he measuremet equatio of discrete-time systems: Z(k) = H (k) X(k) + V (k) (6) (7) H (k) is the measuremet matrix V (k) is zero mea Gaussia white oise sequece. Differet time measuremet oise is idepedet. he formulas of Kalma filter algorithm based o the curret statistical model are: X (k k ) = F(k) X(k k ) + a(k) B(k) P(k k ) = F(k) P(k k ) F (k) + (8) (9) 43

4 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 K g X(k k) = X (k k ) + K (k)[z(k) H (k) X(k k )] g (k) = P(k k ) H (k)[(h(k) P(k k ) H (k) + R(k)] P(k k) = [I K g (k) H(k)]P(k k ) () () Wherei W (k) ~ N(0 ) V(k) ~ N(0R). Kalma filter does ot require savig measuremet data i the past whe ew data measured accordig to ew data ad various valuatio i previous time by meas of state trasitio equatio of the system accordig to the above recurrece formula thereby calculatig the amout of all the ew valuatio.. RACK PREDICION BASED ON HE GRAY HEORY o solve track forecast problem of aerial target a aerial targets track predictio method based o gray theory is proposed i this paper. Grey system theory is based o ew uderstadig about objective system. Although isufficiet iformatio o some systems but as a system must have specific fuctios ad order but its iheret laws are ot fully exposed. Some radom amout o rules iterferece compoet ad chaotic data colums from gray system poit of view is ot cosidered to be elusive. Coversely i gray system theory a radom amout is regard as a gray amout withi a certai rage accordig to the proper way to deal with the raw data grey umber is coverted to geeratio umber ad the get strog regularity geeratio fuctios from geeratio umber. o achieve a real-time olie track predictio ad improve the predictio accuracy a improved GM forecastig model is established. I the case of limited data the model is used to predict the track effectively. he basic steps of aerial target track grey predictio: ) the raw data accumulated geeratig ; ) the establishmet of GM ( ) predictio model; 3) to test the model; 4) establishmet of a residual model; 5) target track forecast... arget track predictio he curret track graphics coordiate iformatio is kow. Figure. he curret track data 44

5 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 Provided the origial data sequece: X = (x () x ()... x ()) Y = (y () y ()... y ()) Z = (z ()z ()...z ()) (x (i) y (i)z (i)) is the coordiates of the target (Figure data) i rectagular coordiate system with the ceter of earth. x (i) > 0i =...m y (i) > 0i =...m z (i) > 0i =...m usig the data sequece geeral procedures to establish GM () model is: he first step: to do the first order accumulated geeratig of the origial data series AGO) get accumulated geeratig sequece: () () () () X = (x () x ()... x ()) () () x () = x () x (k) = x (i)(k = 3...) Wherei i= he secod step: the first order accumulated geeratig sequece model gettig related albio differetial equatios: () dx (t) dt ax k () + (t) = b (3) X (i.e. - () X established GM ( l) (4) Where a is the developmet factor reflectig the developmet tred betwee x $ () ad x $. B is gray actiothe gray actio of GM () model is mied from the backgroud data it reflects the relatioship to data chages so the exact meaig is gray. he related gray differetial equatio form as: x (k) + ad (k) = b k = 3... (5) () () d () () d (3) B = M M () d () he third step: Solvig the parameters a b. Parameter sequece determied by the least squares method: Φ = [B B] B A ca be 45

6 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 () d () () d (3) B = M M () d () d (k) = [x (k) + x (k )] () () () A = (x () x (3)... x ()) he fourth step: I the iitial coditios $ () () x () = x () = x () Geerate data series models are available: () $ $ b a(k ) b x (k) = (x () $ ) e + $ (k = 3...) a$ a$ (6) he fifth step: I the iitial coditios $ () () x () = x () = x () Geerate data series models are available: $ $ $ $ a b$ a(k ) x () = x () x (k) = ( e )(x () )e k = 3... a$ (7) Namely $ x () = x () $ a$ b a$ (k ) x (k) = ( e )(x () $ )e a$ k = 3... So k = 3... is substituted ito the formula gettig the fitted values of the iitial data; whe k > to get the gray model predictive value for the future. he sixth step: Y = (y () y ()... y ()) Z = (z ()z ()...z ()) steps oe to step five repeat.. Model accuracy test Gray model predictio test are geerally residual test ad posterior variace test. First the relative size of the error test method it is a straightforward arithmetic test methods comparig poit by poit. I this method predictio data is compared with the actual data observig the relative error whether satisfies the practical requiremets. he actual data set is used for modelig: X = (x () x () x (3)... x ())accordig to GM () modelig method to obtai () () () () () X = (x $ () x $ () x $ (3)... x $ ()) X () do a regressive geerate trasformed ito X Model value of actual data: $ $ $ $ X = (x () x () x (3)... x ()) Computig residuals residual sequece is: 46

7 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 ( e()e()...e()) X X E = = (8) $ where e (i) = x (i) x (i) i =... Calculate the relative error the relative error is: e(i) x(i) x$ (i) ε (i) = 00% = 00% x (i) x (i) (9) m e(i) ε (i) = 00% ε (i) = ε (i) x (i) is the origi of the error m i= is the average relative error of GM()model; o p = ( ε (k) ε ) 00% is the model accuracy of GM()modeli.e. o o miimum error probability ad it geerally requires p > 80% best p > 90%. Secod posterior deviatio test belogs to the statistical cocept it is accordig to the probability distributio of residual test. If the actual model data used was: X = (x () x ()... x ())gettig model value of actual data with the GM (l l) modelig method: () $ () $ () $ () $ () X = (x () x () x (3)... x ()) Assumig variaces of the actual data sequece S are ad S S = (x (i) x ) x = (i) i = x ad i = S = (e(i) e) e = (i) i = e ad i = calculatig Posterior variace ratio: X ad residuals sequece E separately C = S S (30) Determie the model level idicators such as able : able. Model accuracy class Model accuracy class Small Error probability P Posterior iferior C I >0.95 <0.35 II >0.8 <0.5 III > IV

8 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 S Level Descriptio: C values as small as possible i.e. S is much smaller tha the 0.raw date discrete is large predictio error discrete is small ad predictio accuracy is high; P bigger the better equally error probability is small fittig accuracy high. If the residual test posterior variace test ca be passed it ca be predicted by their model otherwise corrected residuals. able. arget predictio locatio arget predictio Small error probability Posterior variace ratio Model accuracy X 0.88 I Y 0.07 I Z 0.5 I.3. rack forecast results ad aalysis he radius velocity ad rage agle β of observatio poit D are kow the plae parallel to the directio of velocity ad passed poit D ca be approximated as missile flight plae plae that through geocetric Opoit D ad perpedicular to the directio of the bullet speed plae 3 that through geocetric O placemet B ad perpedicular to the directio of the bullet speed. Agle betwee plae ad plae 3 is the rage agle β. Release impact coordiate show i FIG. v 3 D β B O Figure. Solvig placemet schematic If plae is A x + B y + Cz ormal vector is = Ai + B j + Ck ad i j k = rod v = x0 y0 z0 v v v the equatio. x y z i j k are uit vector for each axis the flat ca be solved by 48

9 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 If plae is A x + B y + Cz ormal vector is = Ai + B j + Ck ad i j k = rod = x0 y0 z 0 A B C the flat ca be solved by the equatio. If plae 3 A is 3x + B3 y + C3z ormal vector is 3 = A3i + B3 j + C3k ad 3 = 3 cos β 3 3 = the flat 3 ca be solved by the equatio itersectio of the plae the plae 3 A x + B y + Cz A3 x + B3 y + C3z x + y + z = R = ad B ad the earth's surface is the placemet of B ( x y z) Placemet coordiates ca be obtaied by solve formulas after forecast Placemet coordiates is 0( ) ( )error radius 000malgorithm complexity. Figure 3. Forecastig model predicted target track REFERENCES [] Li Feg Ji Hogbi Ma Jiachao. A New Method of Coordiate rasformatio Uder Multi- Radar Data Processig System [J].Cotrol & Measuremet 0073(4): [] Su Fumig. Research o State Estimatio ad Data Associatio of Motio argets [D]. Uiversity of Sciece ad echology of Chia

Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 [3] Sog Yigchu. Research o Kalma Filter i Kiematic Positioig [D].Cetral South Uiversity 006. [4] Liu Na.

he Research o Data Associatio i Multi-target rackig [D].XiDia Uiversity008. [6] Zhou Hogre. Maeuverig target "curret" statistical model ad adaptive trackig algorithm [J].

10 Iteratioal Joural o Cyberetics & Iformatics (IJCI) Vol. 4 No. February 05 [3] Sog Yigchu. Research o Kalma Filter i Kiematic Positioig [D].Cetral South Uiversity 006. [4] Liu Na. Study o Data Associatio Method i Multitarget rackig of Ballistic Missile Defese Radar [D]. Natioal Uiversity of Defese echology 007. [5] Feg Yag.he Research o Data Associatio i Multi-target rackig [D].XiDia Uiversity008. [6] Zhou Hogre. Maeuverig target "curret" statistical model ad adaptive trackig algorithm [J]. Joural of Aeroautics9830:73-86 [7] Yao Jijie. Research o echiques of arget Localizatio based Statios[D].North Uiversity of Chia0. [8] Liu Gag. Multi target trackig algorithm research ad Realizatio [D]. Northwester Polytechical Uiversity003. Authors ig-pig Yu is curretly studyig i Mechaical ad Electroic Egieerig from Shaghai Uiversity of Egieerig Sciece Chia where she is workig toward the Master degree. Her curret research iterests iclude at coloy algorithm their desig ad develop i Embedded system. Xiao-Mig You received her M.S. degree i computer sciece from Wuha Uiversity i 993 ad her Ph.D. degree i computer sciece from East Chia Uiversity of Sciece ad echology i 007. Her research iterests iclude swarm itelliget systems distributed parallel processig ad evolutioary computig. She ow works i Shagha i Uiversity of Egieerig Sciece as a professor. 50

Study on Coal Consumption Curve Fitting of the Thermal Power Based on Genetic Algorithm

Study on Coal Consumption Curve Fitting of the Thermal Power Based on Genetic Algorithm Joural of ad Eergy Egieerig, 05, 3, 43-437 Published Olie April 05 i SciRes. http://www.scirp.org/joural/jpee http://dx.doi.org/0.436/jpee.05.34058 Study o Coal Cosumptio Curve Fittig of the Thermal Based