Transcription of The Unscented Kalman Filter for Nonlinear Estimation
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The Unscented Kalman Filter for Nonlinear Estimation
Second-order ,therelationshipbetweentheKalmanFilter(K F)andRecursiveLeastSquares(RLS)isgivenin [3].TheuseoftheEKFfortrainingneuralnetwo rkshasbeendevelopedbySinghalandWu[9]andP uskoriousandFeldkamp[8].DualEstimationAs pecialcaseofmachinelearningariseswhenthe inputisunobserved, ,weagainconsideradiscrete-timenonlineard ynamicsystem,(6)(7) ,weintroducetheUnscentedKalmanFilter(UKF ) ,inSection4, ,are-cursiveestimationforcanbeexpressedi ntheform(see[6]),predictionofpredictiono f(8)Thisrecursionprovidestheoptimalminim ummean-squarederror(MMSE)estimateforassu mingthepriorestimateandcurrentobservatio nareGaussianRandomVari-ables(GRV).
agation of a Gaussian random variable (GRV) through the system dynamics. In the EKF, the state distribution is ap-proximated by a GRV, which is then propagated analyti-cally through the first-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may
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