Constrained Extended Kalman Filer

7/24/2019 Constrained Extended Kalman Filer

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CONSTRAINED EXTENDED

KALMAN FILER

Presented by

NISHA.R.L

14MO06


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Constraints on state variables are commonlyencountere in ynamic state estimation in t!e "ormo" al#ebraic e$uality an%or ine$uality constraints.

&or 'ea(ly nonlinear systems) t!e e*tene +alman,lter -+&/ !as "oun numerous uses as a subotimalstate estimator.

n"ortunately t!e structure o" t!e ,lter oes not

inclue constraints on t!e states. It is comutationally e""icient but o"ten "ails to

ac!ieve esire accuracy an is (no'n to iver#e "oreven simle nonlinear systems.

IN2RO3C2ION


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2!e +& estimates are not constraine in any 'ay)

'!ic! is o"ten a cause "or t!e "ilters instability. 2!e MH class o" estimators !ave become t!e natural

c!oice '!enever t!ere are e$uality an%or ine$uality

constraints an nonlinear system ynamics. 2!e C+& analytical solution can be e""iciently

imlemente comare to e*ensive otimi5ation inMH.

2o imose strict ine$uality constraints or constraintson inuts) t!e MH is t!e re"erre "ormulation anstate constraints) t!e C+& is s!o'n to be su""icient.

Cont..


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CONS2RAIN3 LINAR S2IMA2ION

Consier t!e "ollo'in# measurement e$uation

7!ile it is esire to estimate t!e rocess states "romt!e measurements) t!e states may be sub8ect toaitional linear constraints o" t!e "orm)

State estimation is ose as)

It minimi5es t!e errors in a least s$uares sense.


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2HORM 1

9iven y : C* ;


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2HORM ?

&or C o" any ran() t!e least s$uares estimate is


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@ALI2 CONS2RAIN2S

Consier t!e "ollo'in# nonlinear rocessmoel an measurement e$uations)

Consier strict e$uality constraints on t!estates)


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2!e available in"ormation is no' 'ritten as

'!ere B N-0) >/ to #ive t!e "ollo'in# "orm

'!ere C is o" "ull column ran( an v is 5ero meannoise 'it! a bloc( ia#onal covariance matri* R

: ia#-R) >/. 7!en 2!eorem 1 is alie toe$uation it yiels t!e constraine ma*imum aosteriori -MA>/ state estimates.


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Al#orit!m 1D C+& "or e$uality constraints


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IN@ALI2 CONS2RAIN2S

7e consier ine$uality constraints on t!e states tobe o" t!e "orm)

2!e ine$uality constraints are re'ritten usin# nonEne#ative slac( variables as "ollo's)


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Al#orit!m ?D C+& "or Ine$uality Constraints


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CONS2RAIN3 F2N33 +ALMAN&IL2R


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2HAN+ O

Constrained Extended Kalman Filer

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