On the convergence of the unscented Kalman filter
Assia Daid, Éric Busvelle, Mohamed Aidène
Abstract
A convergence analysis of the modified unscented Kalman filter (UKF), used as an observer for a class of nonlinear deterministic continuous time systems, is presented. Under certain conditions, the extended Kalman filter (EKF) is an exponential observer for non-linear systems, i.e., the dynamics of the estimation error is exponentially stable. It is shown that unlike the EKF, the UKF is not an exponentially converging observer. A modification of the UKF – the unscented Kalman observer – is proposed, which is a better candidate for an observer. This paper is a first step towards a proof of the global convergence of the high-gain version of the UKO.
Topics & Concepts
Extended Kalman filterControl theory (sociology)Alpha beta filterObserver (physics)Unscented transformKalman filterInvariant extended Kalman filterConvergence (economics)Fast Kalman filterEnsemble Kalman filterNonlinear systemComputer scienceMathematicsMoving horizon estimationArtificial intelligencePhysicsControl (management)Economic growthEconomicsQuantum mechanicsAdaptive Control of Nonlinear SystemsTarget Tracking and Data Fusion in Sensor NetworksDistributed Control Multi-Agent Systems