lec24 (1) - KALMAN FILTER: A REVIEW Table 1: Kalman Filter...

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Table 1: Kalman Filter Equations * Definition Equation Measurement equation (model) =+ ε = ot kk kk kk yH x ;yH x f k System (state) equation (model) −− = 1 k 1 k xM x 1 ( yy ) S t a t e u p d a t e xx −= Κ − af o kk k Error Update Ρ =− Κ Η Ρ a k (1 ) f k ΡΗΗΡΗ+ fT 1 k k k (R ) Kalman gain update Κ= State time extrapolation fa 1 k 1 Error time extrapolation Ρ=Μ Ρ Μ + T 1 k 1 k 1 k Q 1 System random forcing covariance =Εηη T Q( k ) Measurement error covariance =Εεε T k R() Estimation error covariance Ρ=Ενν T k () Input measurement matrix = Η =∂ y/x k Input system random forcing covariance =Q k Input state extrap o l a t i o n = Μ k Input measurement o k y Input measurement error covariance =R k Filter iteration −−− f (k 1) , estimate →− a extrapolate →−−− f (k) , ___________________________________________________________________ *A superscript a or superscript f denotes respectively the value before (f) or after (a) an update of an estimate using measurements, and k denotes the measurement number. In general, errors are assumed random with zero mean and measurement and estimation errors are uncorrelated.
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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lec24 (1) - KALMAN FILTER: A REVIEW Table 1: Kalman Filter...

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