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# 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 = o t k k k k k k y H x ; y H x f k System (state) equation (model) = + η k k 1 k 1 k x M x 1 (y y ) State update x x = Κ a f o k k k k k Error Update Ρ = − Κ Η Ρ a k k k (1 ) f k Ρ Η Η Ρ Η + f T f T 1 k k k k k k k ( R ) Kalman gain update Κ = State time extrapolation = Μ f a k k 1 k x x 1 Error time extrapolation Ρ = Μ Ρ Μ + f a T k k 1 k 1 k 1 k Q 1 System random forcing covariance = Ε η η T k k Q ( k ) Measurement error covariance = Ε ε ε T k k k R ( ) Estimation error covariance Ρ = Ε ν ν T k k k ( ) Input measurement matrix = Η = ∂ k k y / x k Input system random forcing covariance = Q k Input state extrapolation = Μ k Input measurement o k y Input measurement error covariance = R k Filter iteration − − − f (k 1) , estimate a (k 1) , 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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• Spring '03
• RogerD.Kamm
• Estimation theory, Methane, Kalman filter, Ensemble Kalman filter, Geophysical Research, global chemical transport

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

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