Chaînes de Markov cachées e flrage parculare 2-22 anver 2002 Flrage parculare e suv mul-pses Carne Hue Jean-Perre Le Cadre and Parck Pérez
Conex Applcaons: Sgnal processng: arge rackng bearngs-onl rackng fuson of acve and passve measuremens Image analss: people rackng n oher work arge bearng observer
Generc rackng ssues renalzaon Mssng measuremens Cluer false alarms Non-lnear Non observabl Challenges Specfc mulple-arges ssues Complex Assocaon and esmaon smulaneouls Varng number of arges
Basc ngredens Sae varables poson veloc of he arges Daa bearngs ranges Esmaon of poseror Dnamcs: Lkelhood:
Sae varables and dnamcs Sngle-obec sae varable: Mulple-obec sae varable: Sngle-obec dnamcs pror: Markovan process where Mul-obec dnamcs: ndependen sngle-obec dnamcs V I I X I I I X + + 2 2 2 2 2 2 2 0 x V N σ σ 0 0 0
Daa Bearngs-onl rackng: hghl non-lnear wr he sae varable How o assgn he daa o he saes?
Daa assocaon Noaon: assocaon vecor: f s ssued from arge Assocaon assumpons: Hone measuremen can orgnae from one obec or from he cluer false alarms H2 one obec can produce zero or one measuremen H3one obec can produce zero or several measuremens a one me Algorhms based on exened Kalman fler: H + H2 -> pdaf H + H3 ->pmh Our proposon: parcle fler usng probablsc assocaon MOPF: Anoher proposed algorhm: parcle fler based on pda Sr-pda
Curren cloud a me Parcle flerng
Parcle flerng Propagaon b samplng from he dnamc pror or from an mporance funcon based on he daa
Parcle flerng Weghng accordng o daa lkelhood
Parcle flerng Resamplng from he weghed parcle se
Parcle flerng Predcon agan...
Example: bearngs-onl rackng Smulaed bearngs: One parcular run and confdence ellpses N000 parcles
Example: bearngs-onl rackng Parcle cloud for one obec N 0000 parcles
Example: bearngs-onl rackng Parcle cloud for one obec
Example: bearngs-onl rackng Parcle cloud for one obec
Example: bearngs-onl rackng Parcle cloud for one obec
Example: bearngs-onl rackng Parcle cloud for one obec
Example: bearngs-onl rackng Parcle cloud for one obec
Example: bearngs-onl rackng Averaged esmae over 00 runs and 2 σ confdence ellpses N000 parcles
Mul-obec daa lkelhood M m x x X Y p m M x x X p H 3 + m M x X p V 0 π π assocaons all u u m K p K X Y p H 2 assocaons all m u u K p K X p MOPF SIR-JPDA M π π 0 à esmer
MOPF: use of a Gbbs sampler Esmaon of he assocaon probables vecor wh a Gbbs sampler: For τ τ end : Sample K τ + from p K X τ Π τ Y0 : Sample Π τ + from p Π X τ K τ + Y0 : Sample X τ + from p X K τ + Π τ + Y0 : Compue τ τ end ˆ π π τ τ end τ beg τ τ beg
One eraon of he Gbbs sampler + + 0 f / f from Sample 0 V M x p K p K π π τ τ τ τ } : { where ; from Sample : K Card K n K n Mulnoma l M M Π + + τ τ π law based on he predced cloud from a Sample X + τ X Y K Π - X Y K Π me
Sr-pda Énuméraon exhausve des assocaons avec M m x x X Y p assocaons all m u u K p K X p Φ Φ M D d M D d u F u u u u P P p m K p!! Φ u nombre de fausses alarmes dans u K
Example: bearngs-onl rackng Measuremen equaon Smulaed bearngs for he hree obecs Occluson perod for arge
Example: bearngs-onl rackng MOPF- esmaed assocaon probables Esmaed raecores: MOPF Sr-pda
Example: rackng wh hgh cluer deecon probabl for each arge P d 0.9 cluer ~ Posson law of parameer λ V 0 2 3
Example: rackng wh hgh cluer λ V ; N 000 parcles MOPF Sr-pda
Acve and passve measuremens: Too dffcul scenaro:onl ver close bearngs -> bad esmaon
MOPF usng mulple recevers measuremen s receved b recever known bearng or range bearngs-lkelhood or range lkelhood......... n m r n m r r x x X p x x X Y p m r + m n r x X p V 0 π π
Example:range and bearngs Range measuremens added a ceran mes: ρ obs 2 x x + obs 2 R ρ + Z ; Z N 0σ ρ z σ z 0 6 20 percen of acve measuremens; 50 percen
Concluson and furher work MOPF: Generc mul-obec racker based on a mx of parcle flerng and Gbbs samplng suable for varous applcaons Sr-pdaf: parcle flerng and pda Drawbacks Fxed number of obecs Cosl Perspecves Tes wh varng number of obecs Compare he resuls wh a poseror Cramer-Rao bounds
The End Quesons?